A111D3 QSb3SS

NATL INST OF STANDARDS & TECH RI.C.

A1 11 03056385

_ Conference o/Basic optical prope

100 U57 N0.574, 1980 C.1 NBS-PUB-C 19

V„U Of * NBS SPECIAL PUBLICATION 574

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

Basic Optical Properties of Materials

Summaries of Papers
NATIONAL BUREAU OF STANDARDS

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Basic Optical Properties of Materials

Summaries of Papers

NATIONAL BUREAU

OF STANDARDS

LIBRARY

APR 2 1 1980

nt> t- 0-CC- -Ct4<

Presented at the Topical Conference

on Basic Optical Properties of Materials

Held at the National Bureau of Standards

Gaithersburg, Maryland, May 5-7, 1980

&C/60

. as?

J9Po

Edited by:

Albert Feldman

Center for Materials Science

National Measurement Laboratory

National Bureau of Standards

Washington, D.C. 20234

In cooperation with:

The Optical Society of America

1816 Jefferson Place, NW

Washington, DC 20036

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Luther H. Hodges, Jr., Deputy Secretary

Jordan J. Baruch, Assistant Secretary for Productivity, Technology, and Innovation

3. NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued May 1980
Library of Congress Catalog Card Number: 80-600038

National Bureau of Standards Special Publication 574

Nat. Bur. Stand. (U.S.), Spec. Publ. 574, 252 pages (May 1980) CODEN: XNBSAV

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Foreword

This Special Publication contains summaries of papers to be presented at the Topical Conference on Basic Optical Properties of Materials to be held at the National Bureau of Standards in Gai thersburg

,

Maryland on May 5-7, 1980. The conference is sponsored by the National

Bureau of Standards in cooperation with the Optical Society of America.

This publication contains summaries of 62 papers which include 14

invited papers. The principal topical areas are:

Nonl inear Optical Properties

Ultraviolet Properties

Infrared Properties

Graded Index Materials

Inhomogeneous Materials

Properties of Thin Films

Optical Fibers

Planar Optical Waveguides

External Influences: Piezo-optics , Thermo-opti cs

,

Magneto-optics

The purpose of the conference is to discuss the state of the art

in the measurement of the optical properties of optical materials. The

emphasis is primarily on materials properties rather than on optical

devices. The primary focus of the conference is on the measurement and

theory of basic optical properties of materials in bulk, thin film, and

fiber form.

The manuscripts for the conference have been prepared by the

authors in camera-ready form, and any questions pertaining to their

content should be addressed to those authors.

Albert Feldman

Chai rperson

Acknowl edgements

We wish to thank the following individuals for their invaluable

assistance in preparing for the conference and this summary:

Jeanmarie Bartlett, Marilyn Dodge, Barbara Hyde, Jo Ann Lorden, and

Kathy Stang. Special thanks are due to Kimberly Morgan for organizing

the mailings for the conference, and for editing and assembling the

completed Summary of Papers. Thanks are due to the Word Processing

Center of the National Measurement Laboratory for retyping several of

the manuscripts.

i i i
Program and Editorial Committee

Albert Feldman - Chairperson

National Bureau of Standards

Edward Pal i k - Co-Chairman

Naval Research Laboratory

Michael I. Bell

National Bureau of Standards

Arthur H. Guenther

Air Force Weapons Laboratory

Ivan P. Kami now

Bell Telephone Laboratories

Bernard Bendow

Rome Air Development Center

Harold E. Bennett

Michel son Laboratory

Naval Weapons Center

Robert V. Mohr

Catholic University

Alfred J. Thelen

Optical Coating Laboratory

Disclaimer

Certain commercial equipment, instruments, or materials may be

identified in this publication in order to adequately specify the

experimental procedure. In no case does such identification imply

recommendation or endorsement by the National Bureau of Standards,

nor does it imply that the material or equipment identified is

necessarily the best available for the purpose.

iv
CONTENTS

Page

Foreword iii

Keynote Address — Important Areas of Optical Materials

Research 1 *H. V. Winsor

NONLINEAR OPTICAL PROPERTIES

Properties of Low-Index Laser Materials 3

*M. J. Weber

Nonlinear Optical Susceptibilities of Semiconductors

and Optical Bi stability 9

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan,

A. Passner, A. C. Gossard, and W. Wiegmann

Band Structure Calculations of the Two-Photon Absorption

Coefficients of InP and CdTe 13

A. Vaidyanathan, A. H. Guenther, and S. S. Mitra

ULTRAVIOLET PROPERTIES

Measurement and Interpretation of Ultraviolet Properties

of Solids 16

*D. W. Lynch

The Optical Properties of Kapton: Measurement and

Applications 20

L. R. Painter, E. T. Arakawa, M. W. Williams

and J. C. Ashley

Optical Properties of TiC x ( 0 . 64<x<0 . 90 ) From 0.1 To 30eV ... 24

D. W. Lynch, C. G. Olson, D. J. Peterman, and

J. H. Weaver

Superconvergence Relations and the Analysis of Optical Data . . 28

*D. Y. Smith

INFRARED PROPERTIES

Measurement of the Far Infrared Optical Constants of

Disordered Solids 32

*U. Strom and P. C. Taylor

*Invited Speaker

v
Infrared Impurity Absorption Spectra of Premium - Q Quartz. . . 36

H. G. Lipson

Far Infrared Study of the Reflection Spectra of SnS 40

D. G. Mead and H. R. Chandrasekhar

Infrared Absorption in Highly Transparent Cubic Zirconia. ... 44

B. Bendow, H. G. Lipson, R. C. Marshall, and D. Billard

The Temperature Dependence of the Optical Absorption of

Metals 48

M. Bass, D. Gallant, and S. D. Allen

GENERAL OPTICAL PROPERTIES

The Statistical Description of Optical Inhomogenieties 51

E. L. Church

Photoconductivity at 77K In Undoped Tellurium 55

N. G. Shyamprasad, C. H. Champness, and I. Shi

h

Extrinsic States in Cinnabar (a-HgS) Grown by Chemical Vapor

Transport 59

C. T. Simpson, W. Imaino, and W. M. Becker

Differential Ref lectometry - An Optical Technique for

Investigating Band Structure Changes Associated with

Alloying, Dealloying, Corrosion and Ordering 63

R. J. Nastasi-Andrews, J. B. Andrews, C. W. Shanley,

J. Finnegan, and R. E. Hummel

Free Carrier Absorption in Semiconductors in Quantizing

Magnetic Fields 67

H. N. Spector

NONLINEAR OPTICAL PROPERTIES

Multiphoton Absorption in Direct Gap Solids 71 *S. S. Mitra

Measurements of Two Photon Absorption 77

A. F. Stewart and M. Bass

Three-Photon Absorption in Nd:YAG . 81

R. W. Boyd and M. A. Kramer

vi
POSTER PAPERS

Refractive Index and Thermo-Optic Coefficients of CD*A 85

L. G. DeShazer and K. E. Wilson

On the Use of a Calorimeter to Investigate Loss Mechanisms

in Optical Fibers 87

F. T. Stone

Computerized Refractive Index Measurement for Fiber Optic

Glasses 91

D. L. Wood and J. W. Fleming

Stress Optic Coefficient of Optical Fibers 92

N. Lagakos

Chromatic Measurements of Gradient Index Materials By

Multiple Wavelength Interferometry 96

D. P. Ryan

Optical Coupling Coefficients for Pulsed C0

2 Laser Radiation

on Bare and Painted Aluminum Surfaces 100

S. C. Seitel, J. 0. Porteus, and W. N. Faith

Thermomodulation Spectra of High-Energy Interband Transitions

in Cu, Pd, Ag, Pt, and Au 104

C. G. Olson, D. W. Lynch, and R. Rosei

El lipsometric Observations on Thermally Grown Oxide Films

on Titanium 108

A. H. Musa and W. E. J. Neal

Optical Properties of A-15 Thin Films and Single Crystals . . .114

R. C. McKee, D. W. Lynch, C. G. Olson, J. W. Osmun,

and J. H. Weaver

IR Absorption Bands in Multilayer Thin Films of Some II/VI,

V/VI Materials 118

J. S. Seeley, R. Hunneman, and A. Whatley

Multiwavelength Laser Rate Calorimetry on Various Infrared

Window Materials 122

G. S. Coble, D. V. Dempsey, J. A. Detrio, N. C. Fernelius,

J. A. Fox, P. R. Greason, G. T. Johnson, and D. B. O'Quinn

Optical Constants of Boron Carbide in the Infrared 126

J. L. Lauer and H. Adari

vi i
Critical Point Analysis of Multiphonon Infrared

Absorption in Zinc Selenide 131

C. A. Klein and R. N.Donadio

Multiphoton Absorption in Infrared Glasses Based on Zirconium and Hafnium Fluorides 135

H. G. Lipson, B. Bendow, and M. G. Drexhage

GRADED INDEX AND INHOMOGENEOUS MATERIALS

Optical Characterization of Bulk Graded Index Materials .... 139

*D. T. Moore

Measurement of Axial, Gaussian Index Distribution 143

G. W. Johnson

Graded-Index AR Surfaces for Improved Laser-Damage

Resistance 147

W. H. Lowdermilk and D. Milam

Reflectance Properties of Pressed Tetraf luoroethylene

Powder 149

J. J. Hsia and V. R. Weidner

Measurements of Large Optical Absorption Coefficients By

Diffuse Reflectance 152

R. K. Waring

El 1 ipsometric Measurements of the Optical Properties of

Compacted Powders 156

F. C. Zumsteg

PROPERTIES OF THIN FILMS I

Material Properties By Spectroscopic Ellipsometry 160

*D. E. Aspnes

Dielectric Function of Superlattice Materials 164

P. J. Price

Determination of Thin Film Optical Dispersion From

Spectrophotometer Data 167

A. L. Bloom and D. Fischer

vi i i
Page

OPTICAL FIBERS

Optical Properties of Doped-Sil ica Waveguide Glasses in the

0.8-1.8 ym Region 171

*R. Olshansky

The Use of a Scattering Cube to Characterize the Spectral

Loss of Optical Fibers 178

D. L. Phi len and F. T. Stone

Transition Element Absorption in Moleculary-Doped Optical

Fiber Glasses 182

A. Barkatt, D. C. Tran, and J. H. Simmons

Measured Pockels Coefficients and Predicted Static Pressure

Sensitivity for Interferometric Fiber Optic Hydrophones .... 185

R. Hughes, N. Lagakos, H. Dardy, and J. Bucaro

PROPERTIES OF THIN FILMS II

Absorption and Scattering Phenomena in Thin-Fi lm-and

Bulk-Materials 188

*M. S. Sparks

The Measurement of Interface and Bulk Absorption in Thin

Films and Bare Substrates 194

*P. A. Temple

Infrared Optical Properties of Silicon Monoxide Films:

Application to Radiative Cooling 201

A. Hjortsberg and C. G. Granqvist

EXTERNAL INFLUENCES

The Photoelastic Effect in Optical Materials 204

*A. Feldman and R. M. Waxier

The Relation of Elastooptic and Electrostricti ve Tensors. . . . 209

D. F. Nelson

Photoelastic Properties of Magnesium Fluoride 213

S. Chung and H. R. Carleton

A Microscopic Approach To Predict Refractive Indices and

Electro- or Strain-Optic Coefficients 217

M. D. Ewbank, P. R. Newman, and W. A. Harrison

ix
Page

Dispersion of Thermo-optic Coefficients of Nd Laser

Materials 221

K. E. Wilson and L. G. DeShazer

Temperature Dependence of the Optical Properties of Some

Metals at Visible and Infrared Wavelengths 223

D. L. Decker and V. A. Hodgkin

PLANAR OPTICAL WAVEGUIDES

Optical Properties of Ti Diffused LiNbO^ Waveguides 225

*W. K. Burns

J

Optical Properties of Thin Films By Guided Waves and

Surface Pol ari tons 226

*J. D. Swalen

Properties of Low Loss Diffused Optical Waveguides in Glass . . 230

T. Findakly and E. Garmire

Thickness Measurement of Very Thin-Films By Observing

Anomalous Light Absorption 234

H. Kitajima, K. Hieda, and Y. Suematsu

Interferometric Wavelength Measurement of Infrared Surface

Waves 238

Z. Schlesinger and A. J. Sievers

Author Index 240

x
IMPORTANT AREAS OF OPTICAL MATERIALS RESEARCH

Harry V. Winsor

Maj., USAF

Defense Advanced Research Projects Agency

Arlington, VA 22209

This paper discusses the many areas of optical properties measurement

improvement needed to develop the optical properties needed by advanced

applications in energy, defense, communication, resources, surveillance, lasers, industrial processing, and optical system design and

fabrication

.

There are two central points to the talk:

Optical systems are very special purpose, so each

application may require information that is not

apparent from the outset.

The interaction of light with matter is very

complex, leading to literally millions of measurable properties for each material.

In support of these two central points, several examples of critical

optical properties will be discussed including, perhaps, topics from

the following areas:

Solar energy systems properties

Thermal control coatings performance

High power laser windows and mirrors parametrics

Optical detector characterization

Fiber optics measurement

Non-linear conversion materials properties

Light emitting diodes and solid state lasers

Laser host materials behavior

Laser materials efficiency

Saturable absorber characterization

Photochemical reaction vessels design

Space environmental degradation

Radiation damage to optical materials

Temperature dependent optical properties

Acousto-optic coefficient

Electro-optic constants

Magneto-optic effects measurement

Stress-optic effects

Optical activity and its measurement

Chemical spectroscopy

1
Luminescence and fluorescence

Polarizers and polarization dependent phenomena

The examples (and others not discussed in detail) reveal an extraordinarily large optical measurements task which co-exists with a corre- spondingly large effort to optimize the relevant optical properties of

optical materials. The talk will end with consideration of how these

large problems can be systematically addressed by the optical research

community.

2
PROPERTIES OF LOW-INDEX LASER MATERIALS

M. J. Weber

Lawrence Livermore Laboratory

University of California

Livermore, California 94550

The use of large, high-power lasers for inertial confinement fusion

experiments has prompted the search for improved optical material sJ

These include glasses and crystals for both passive components (lenses,

windows, substrates) and active components (amplifiers, Faraday rotators). Neodymium-doped glass lasers, which operate at * lym, have been

the most widely used fusion lasers. Of major concern for these lasers

are (1) the nonlinear optical properties, including intensity-dependent

changes in the refractive index, multiphoton absorption, and damage

processes, and (2) the spectroscopic properties of the active laser ion

which affect energy storage and extraction and the overall lasing

efficiency. To reduce self-focusing and beam breakup, materials for

the amplifying medium and transmitting optics must have a small non- linear refractive index r\2- This is characteristic of low-refractiveindex materials. In the past few years, the optical properties and

preparation of many low-index materials have been investigated. From

this search, fluoride crystals and glasses have emerged as superior

optical materials for short-pulse high-power lasers. Of these,

fluorophosphate2 5 3 ancj fl uoroberyllate^'^ glasses have received particular attention.

The large variety of inorganic glass forming systems^ provides many

opportunities to tailor materials for specific applications. Optical

properties are generally most affected by the glass network former,

however within a given glass type, further variations are possible by

the selection of the network modifier cations. The optical properties

of Nd3+ in hundreds of oxide, fluoride, and oxyfluoride glasses have

been investigated to determine the range of variations possible by

altering the host glass composition. Examples of the ranges of optical

and spectroscopic properties observed for some common oxide and

fluoride glasses are summarized in Table I. These represent values

observed to date at the Lawrence Livermore Laboratory, but are not

necessarily the extreme values possible. Depending upon the mode of

operation and the environment of the laser, other physical and chemical

properties may also be important. All of these properties are dependent, in varying degrees, on the chemical composition of the host.

Measurements of n£ for a large class of oxide and fluoride crystals and

glasses have been made using 100-ps, 1.06-ym laser pulses and timeresolved interferometry

.

~l Values of for various glasses are sum- marized in Table I. These results established that low-index,

3
TABLE I. Observed variations of Nd laser glass properties.

4 4 Spectroscopic properties are for the F~ /9 -> transition.

NL Index Cross Section Linewidth Lifetime

Glass n

? (10~13 esu) a(pm2

) AX ff (nm) x R (ys)

Si 1 icate > 1

.

2 1 .0-3,,6 34-43 170--950

Phosphate > 1

.

0 1 .8-= 4,,7 23-•34 320--560

Tellurite > 10 3 .0--5. 1 26--31 140-•240

Fluorophosphate > 0. 5 2 .2-4, 3 27--34 350-•600

Fluoroberyl late > 0. 3 1 .7-4.,0 19--28 550-•1000

low-dispersion materials have small n2 values. These are materials

having low atomic number anions and cations and small optical polarizabilities. Boling, Glass, and OwyoungS have discussed various

empirical relationships that can be used to predict the nonlinear index

based upon simple measurements of the linear index and dispersion.

These relationships provide valuable guidance for screening materials.

For short pulse durations and large beam diameters, the principal

refractive index nonlinearity arises from the optical Kerr effect. For

longer pulses (> Ins), electrostrictive effects may become important.

These contributions have been found to be smaller for low-index materials. 9

Most n2 measurements in solids have been made at wavelengths far

removed from the fundamental absorption edge. At shorter wavelengths,

r\2 will increase due to resonant and nonresonant contributions to the

wavelength dispersion of noJG This consideration is germane for

fusion lasers such as KrF (248 nm) or the use of higher harmonics of

Nd lasers (532, 355, 266 nm). At present, however, there is no data

on the magnitude and functional dependence of the wavelength dependence

of n2-

Low-index materials are generally wide band gap materials. 11 Therefore

materials selected to reduce self-focusing will probably also have

small linear and nonlinear absorption. At ultraviolet wavelengths,

most materials are subject to two-photon absorption (TPA). TPA coefficients at short wavelengths are known for only a few optical

materials J 2 Measurements of TPA spectra of a variety of materials are needed to select laser materials with minimum losses at short wavelengths.

4
iABLE II. Comparison of Ndifluoroberyllate laser glasses.

Composition

(mol. %)

98 BeF

2 + 2 NdF^

58 BeF

2 + 32 KF + 6 CdF

2 + 2NdF

3

47 BeF

2 + 27 KF +

14 CaF

2 + 10 A1F

3 + 2NdF

3

4

F 4 T Spectroscopic

Properties

x (nm)

P 1046 1048 1047

a(pm2

) 2.0 3.8 3.2

AX

eff

(nm) 27.7 20.1 23.2

x R(ys) 920 600 610

Re 1 ati ve bma 1 1 - Signal Gain

Coefficient. ^

g (m

_1

) 7.8 17 (estimate) 14.8

Laser-induced damage thresholds of materials have also been found to

vary with refractive index. Bettis, Guenther, and House^ have

measured damage thresholds for surfaces and thin films of many materials at 10.6 ym. They find a systematic increase in damage fluence

with decreasing refractive index. Low-index fluoride materials have

the highest damage thresholds. This behavior continued to hold at

shorter wavelengths.^

Whereas low-index materials are clearly superior based on their non- linear optical properties and laser-induced damage thresholds, for the

amplifying medium, the effects of compositional changes on the spectroscopic properties must also be considered. From Table I we see that

the Nd^+ stimulated emission cross section a can be varied by more than

a factor of 5. There are corresponding large changes in the radiative

lifetime tr. For xenon flashlamp pumping, the population inversion

obtainable in various glasses in a standard rest setup are comparable,

but the small-signal gain coefficient varies because of the different

a values. Therefore glasses having large cross sections, such as phosphates, have large gain coefficients. By varying the composition,

5
f 1 uoroberyl late glasses having either small or large cross sections and

gain coefficients are possible. Several examples are given in

Table II and in Ref. 4. The spectroscopic variations achieved for

Nd3+ should also be obtained for other rare-earth laser ions.

The absorption and emission spectra and gain profile of rare earths in

glass are inhomogeneously broadened because of site-to-site differences

in the local environment of the laser ion. This structural disorder is

not evident in amplifiers operating under small-signal conditions, but

under large-signal or saturated gain conditions, spectral hole burning

may occur. 16 in addition, the energy extracted from an inhomogeneous

system is always less than that obtainable from a homogeneous system

having the same initial small -signal gain.

To minimize these effects, one seeks materials in which the ratio of

the homogeneous to inhomogeneous linewidths is as large as possible.

The effective fluorescence linewidth in Table I is a measure of a combination of the extent of the crystalline Stark splitting of the

initial and final J manifolds and the inhomogeneous broadening. Of the

glasses studied to date, fl uoroberyl late glasses have the narrowest

effective linewidths. Our knowledge of the effects of glass composition on the homogeneous linewidth, on the other hand, is still very

limited. Laser-induced fluoroscence line narrowing techniques are used

to measure tne homogeneity of the spectroscopic properties in glass.

The homogeneous linewidths of oxide and fluoride glasses measured thus

far do not differ greatly. 18 Therefore fl uoroberyl late glasses should

have good saturation properties. Additional studies of the homogeneous

linewidths for a wider range of glasses are underway. 19

Of the various low-index materials, fl uoroberyl late glasses have the

smallest refractive index nonli nearly and a large range of transparency.

Inclusion-free materials have high damage thresholds. 20 Fl uoroberyl

late glasses have now been prepared by the Corning Glass Works^l in

sizes up to 20-cm diameter by 5-cm thick. The toxicity of beryllium

necessitates special handling requirements for the melting and finishing of these glasses. The hygroscopicity of BeF2 is well known, but

by the addition of suitable modifier cations, the chemical durability

can be greatly improved. Although the water solubility is still

greater than for most commercial optical glasses, it is less than for

many alkali halide optical crystals. 22

Acknowl edgements

Many colleagues at LLL have contributed to the results summarized in

this paper. It is a pleasure to thank S. Brawer, C. Cline, D. Kingman,

G. Linford, J. Lynch, D. Milam, R. Saroyan, W. L. Smith, and

S. Stokowski for their contributions.

This work was performed under the auspices of the U.S. Dept. of Energy

Office of Basic Energy Sciences and the Lawrence Livermore Laboratory

under Contract No. W-7405-Eng-48.

6
References

X M. J. Weber, "Optical Materials for Neodymium Fusion Lasers," in

Critical Materials Problems in Energy Production, ed. C. Stein

(Academic Press, New York, 1976), p. 261.

2 0. Deutschbein, M. Faulstich, W. Jahn, G. Krolla, and N. Neuroth,

"Glass with a Large Laser Effect: Nd-Phosphate and Nd-Fl uorophosphate," Appl. Optics 17_, 2228 (1978).

3 J. T. Wenzel, D. H. Blackburn, W. K. Haller, S. E. Stokowski, and

M. J. Weber, "Development of Fl uorophosphate Optical Glasses,"

SPIE Vol. 204, Physical Properties of Optical Materials (in press).

h C. F. Cline and M. J. Weber, "Beryllium Fluoride Optical Glasses:

Preparation and Properties," Wiss. Ztschr. Friedrich-Schiller-Univ.

Jena, Math. -Nat. R. , 28_, Jg. H. 2/3, 351 (1979); also available as Lawrence Livermore Laboratory Rpt. UCRL-81168.

5 K. H. Sun, "Fluoride Glasses," Glass Technology 20, 36 (1979).

5 H. Rawson, Inorganic Glass-Forming Systems (Academic Press, London and

New York, 1967).

7 M. J. Weber, D. Milam, and W. L. Smith, "Nonlinear Refractive Index of

Glasses and Crystals," Opt. Engin. V7, 463 (1978).

8 N. L. Boling, A. J. Glass, and A. Owyoung, "Empirical Relationships

Predicting Nonlinear Refractive Index Changes in Optical Solids,"

IEEE J. Quantum Electron. QE-14 , 601 (1978).

9 D. Heiman, R. W. Hellwarth, and D. S. Hamilton, "Raman Scattering and

Nonlinear Refractive Index Measurements of Optical Glasses," j. NonCry st. Solids 34, 63 (1979). m R. W. Hellwarth, "Third-Order Optical Susceptibilities of Liquids and

Solids," in Progress in Quantum Electronics, Vol. 5 (Pergamon Press,

London, 1977).

n S. H. Wemple, "Optical Oscillator Strengths and Excitation Energies in

Solids, Liquids, and Molecules," J. Chem. Phys. 67, 2151 (1977).

^W. L. Smith, "Laser-Induced Breakdown in Optical Materials," Opt.

Engin. ]]_, 489 (1978).

B J. R. Bettis, A. H. Guenther, and R. A. House II, "Refractive-Index

Dependence of Pul sed-Laser- Induced Damage," Optics Lett. 4_, 256

(1979).

7
1I+ B. E. Newman and D. H. Gill, "Ultraviolet Damage Resistance of Laser

Coatings," NBS Spec. Publ . 541, Laser Induced Damage in Optical

Materials: 1978, p. 190.

15 J. Linford, R. A. Saroyan, J. B. Trenholme, and M. J. Weber,

"Measurements and Modeling of Gain Coefficients for Neodymium

Laser Glasses," IEEE J. Quantum Electron. QE-15 , 510-523 (1979).

i6 See, for example, V. I. Niki tin, M. S. Soskin, and A. I. Khizhnyak,

"Influence of uncorrelated inhomogeneous broadening of the 1.06 y

band of the Nd^+ ions on laser properties of neodymium glasses,"

Sov. J. Quantum Electron. 8, 788 (1978).

17 S. A. Brawer and M. J. Weber, "Observation of Fluorescence Line

Narrowing, Hole Burning, and Ion-Ion Energy Transfer in Neodymium

Laser Glass," Appl. Phys. Lett. 35, 31-33 (1979).

3+ 18 J. Hegarty and W. M. Yen, "Optical Homogeneous Lindewidths of Pr in

BeF

2 and Ge0

2 Glasses," Phys. Rev. Lett. 43 1126 (1979).

19 J. M. Pellegrino, J. Hegarty, W. M. Yen, and M. J. Weber, "Composition

Dependence of Nd3+ Homogeneous Linewidth in Glasses," Bull. Amer.

Phys. Soc. (March, 1980) and to be published.

20 W. H. Dumbaugh and D. W. Morgan (private communication).

21 S. E. Stokowski, D. Milam, and M. J. Weber, "Laser Induced Damage in

Fluoride Glasses: A Status Report," in NBS Spec. Publ. 541, Laser

Induced Damage in Optical Materials: 197

8

3 p. 99.

22 C. F. Cline, D. D. Kingman, and M. J. Weber, "Durability of Beryllium

Fluoride Glasses in Water: Comparison with other Glasses and

Crystals, J. Non-Cryst. Solids 33, 417 (1979).

8
NONLINEAR OPTICAL SUSCEPTIBILITIES OF SEMICONDUCTORS

AND OPTICAL TESTABILITY

H.M. Gibbs, S.L. McCall, T.N.C. Venkatesan,

A. Passner, A.C. Gossard, and W. Wiegmann

Bell Laboratories

Murray Hill, New Jersey 07974

The transmission of 500 ns pulses through GaAs-AlGaAs

heterostructures has been studied as a function of light

intensity and wavelength; see Fig. I

1

. The intrinsic exciton

absorption can be modeled by the sum of a small unsaturable

background and a dominant term which saturates as a Bloch

resonance; see Fig. 2. Corrections for the Gaussian transverse spatial profile and finite optical thickness lead to

150 W/cm2 for the uniform-plane -wave saturation intensity

for an optically thin GaAs exciton transition. The nearly

Bloch-like saturation curve does not imply that the free

exciton transition is a simple saturable two-level system,

but does suggest that it saturates as a homogeneously

broadened line.

A signal beam transmitted by a Fabry-Perot cavity can be

modulated by a control beam which changes the refractive

index of the intracavity medium. High finesse at the signal

wavelength and strong absorption at the control wavelengths

result in efficient optical gating and modulation. Such

modulation has been observed using GaAs with detectorlimited switch-on times of 1 ns and switch-off times of 2-20

ns and a physical length of only 5 ym; see Fig. 3. 2 In a succeeding paragraph, the refractive index extracted from

these data is compared with that calculated from the nonlinear absorption measurements above.

Using these free exciton optical nonl inearities in GaAs,

optical bistability has been observed in a semiconductor for

the first time 1

' 3

; see Figs. 4 and 5. The bistability is

primarily dispersive with the nonlinear refractive index

arising from light- induced changes in exciton absorption.

Using light of frequency just below the exciton peak,

bistability was observed from 5 to 120°K with 40-ns turn-off

and subnanosecond turn-on times with 1 mW/um 2 holding

intensity.

For many optical bistability applications, the larger the

nonlinearity the better. If one calculates the change in

refractive index An^lO" 2 for the intensity changes Al-100

kW/cm 2 used in the GaAs optical modulation . and bistability

experiments, one calculates An/AI«10" lt cm 2 /kW. This, of

9
course, is not 112 • Those experiments were performed at

intensities far above the I s =0.6 kW/cm 2 from Fig. 2. Presumably, this was necessary because the sample was ten times

thicker and because the laser wavelength was 20 to 40 A away

from the exciton peak to reduce the unsaturable background

absorption

.

One may represent the contribution of the exciton resonance

to the refractive index as

nEX (A) = (aEXA/47T) AA/6A

(1)

the wavelength A exceeds the wavelength of peak exciton

absorption by AA, and 6A is the width (HWHM) of the exciton

resonance with peak absorption a£xL.

The nonlinear index n£ can be calculated as dngx/dl for 1 = 0:

Aa-p Y( AA/ 6 A)

n

2 =

" TT ' W

4ttI s (1+(AA/6A) 2

) 2

This has extreme values for AA = ±6A: |

| (max) =Aagv-/16TrI s ; the value is 0.4 cm 2 /kW for GaAs with aEx= 4/ym and I s = 150 kW/cm 2 from Ref. 1. Values of aEX as high as 6/ym have

been seen. 1 There is considerable hope that thinner GaAs

etalons can be constructed with sharper exciton features and

less background absorption permitting bistable operation

much closer to the exciton resonance and with much lower

input intensities.

A subsequent observation of optical bistability in a semiconductor was reported recently by Miller, Smith, and Johnston using an uncoated 560-ym long etalon of InSb at 5°K. 4 They find ni is 10" 2 to 10" 1 cm 2 /kW.

A large n2 is desirable if one wants to reduce the holding

intensity, but the time response of n2 is crucial for fast

devices. In GaAs, the saturation which turns on the bistability can be subpicosecond 5

, but the recovery once the light

is removed seems to be governed by the carrier lifetime

which can be nanoseconds unless shortened by impurities or

defects. 2 Switching times for the InSb bistability have not

been reported.

1 H. M. Gibbs, A. C. Gossard, S. L. McCall, A. Passner,

W. Wiegmann, and T.N.C. Venkatesan, Solid State Commun.

30, 271 (1979).

10
H.M. Gibbs, T.N.C. Venkatesan, S.L. McCall, A. Passner,

A.C. Gossard, and W. Wiegmann, Appl . Phys. Lett. 34 , 511 (1979)

.

H.M. Gibbs, S.L. McCall, T.N.C. Venkatesan, A.C. Gossard,

A. Passner, and W. Wiegmann, CLEA:IEEE J. Quantum.

Electron. QE-15 , 108D (1979) and Appl. Phys. Lett. 3_5,

451 (1979) . D.A.B. Miller, S.D. Smith, and A. Johnston, Appl. Phys.

Lett. 3_5, 658 (1979). D.A.B. Miller and S.D. Smith,

Opt. Commun. 31, 101 (1979).

C.V. Shank, R.L. Fork, R.F. Leheny, J. Shah, Phys. Rev.

Lett. 42 , 112 (1979) .

Imax ( x 0 7 ), no sample

10°K 840 830 820

WAVELENGTH (nm)

810

Fig. 1 Nonlinear transmission of 500 ns pulses through an

antiref lection-coated AIq 24^ a

0 76^s ~^ a^s 24^ a

0 76^s heteros tructure with layer thicknesses in ym o£ 2.38-0.42-

3.33, respectively. I max-43 kW/cm 2

.

L = O 26 +

1 + 1/06

0 01 0 1 1 10 INTENSITY (kW/cm2

)

100

Fig. 2 Saturation of the free exciton resonance in GaAs

with 500 ns pulses of wavelength equal to the wavelength of

peak exciton absorption. The solid curve is a least squares

fit of aL=A[l+B/ (1+I/Is) ]

, which yielded A=0 . 257±0 . 033

,

B=6.65±0.99, and I s = 0 . 605±0 . 064 kW/cm 2.

11
FP PEAK

Fig. 3 Control of a 10-mW cw dye laser beam I s (A s =821.3nm)

by 2.5-W 200-ps modelocked Ar pulses I c (A c =514.5 nm) . The

device consists of a molecular-beam, epitaxially- grown sandwich of 4.1 ym of GaAs between 0.21 ym thick A1 A .»Ga n ro As

U . 4 L U.jo

windows with reflectivities of 0.9 and 0.25 at A s and A c , respectively

.

Fig. 4 Excitonic optical bistability in GaAs at 15°K and

819.9 nm laser wavelength. Bistability as seen in (a) x-y

display and (b) time display. The 45° line in (a) shows

etalon transmission at the next etalon peak (^830 nm)

.

Fig. 5 Approximate GaAs absorption

aL(a) , roundtrip phase shift cj)(b),

and Fabry-Perot transmission under

conditions of optical bistability

(c) and Fig. 4. The solid curves

are for zero input intensity where

the exciton absorption is fully

effective. The dashed curves are

for intensities which are high

enough to saturate the exciton

feature, but low enough to leave

the band-to-band contributions to

a and $ unaffected. The peak

absorption ag^L at the exciton

resonance was 10 in our sample.

WAVE LENGTH

12
BAND STRUCTURE CALCULATIONS OF THE TWO-PHOTON ABSORPTION

COEFFICIENTS OF InP AND CdTe

A. Vaidyanathan and A. H. Guenther

Air Force Weapons Laboratory

Kirtland AFB , NM 87117

and

S. S. Mitra

Department of Electrical Engineering

University of Rhode Island

Kingston, R. I. 02881

In the last two decades there have been numerous theoretical and

experimental studies of two-photon absorption coefficients in crystalline solids. In spite of these extensive investigations, a generally

accepted quantitative description of two-photon absorption has not

been achieved even for the case of the simplest semiconductors, as is

evidenced by the unacceptably large disparity between theoretical

estimates and available experimental measurements. These differences

stem in part from the simplifying models employed to describe the

electronic band structures and oscillator strengths. In an attempt to

improve this situation we have calculated the two-photon absorption

coefficients of crystalline InP and CdTe by first computing their

electronic band structures by means of the empirical pseudopotential

method (EPM), followed by a numerical evaluation of the two-photon

transition probability employing second-order perturbation theory.

We start with the following expression for the transition probability rate of an electron in a solid, with direct energy gap

Eg, from an initial valence band state f/l<> to a final conduction

band |bk> by the simultaneous absorption of two photons whose

frequency is such that 2 Aw > E > "hco

, H H 2 / \ Ji*. V vn nc s(E

vc (£)-2tJ

(2tt 3 \/mj + V vc J

n

E vn

(k) "^

13
In eq. (1) E yi

(i = c,n) is the energy separation between bands v and

i at wave vector £, the summation n is over all intermediate states, and

the t integral extends over the entire first Brillouin zone. The H-.'s

occurring in eq. (1) are the Hamiltonian matrix elements given by 1J

2TTTi e

m

2 w

» 2 (2)

where N is the photon number density and the P .

.

1 s are appropriate

momentum matrix elements.

It is obvious from eqs.O) and (2) that to evaluate the two-photon

transition probability, knowledge of the electronic energies and wave

functions throughout the first Brillouin zone is needed. We obtain

these by carrying out EPM calculations of the energy bands, using available pseudopotential form factors. In order to numerically integrate

eq. (1) we convert the delta function in energy to a delta function in wave vector by use of the following relation:

"vc (£)-2n»j = ^2 (3)

where represents all values of k for which E vc

(k) = Zfjoo momentum matrix elements are obtained from the relation:

The

-> 2 _

i ,£ >

2 p.

.

1J

<j h (4)

are the Bloch functions of the states i and j

at wave vector k. We then calculate the two-photon transition probabilities of InP and CdTe by including the transitions originating from

the three highest valence bands (which are degenerate at k = 0 in the

absence of spin-orbit splitting), and ending in the lowest conduction

band. The intermediate states in the highest 4 valence bands and

lowest 31 conduction bands were included in the summation in equation

(1), resulting in a convergency better than 0.01%. Finally, the twophoton absorption coefficient (3) is obtained from the two-photon transition probability rate by use of the following expression.

14
I

where I is the intensity of the radiation.

The resulting values of 3 for InP and CdTe are reported in Table I,

together with available experimental data and the results of earlier

theoretical calculations.

Table I. Two-Photon Absorption Coefficients of CdTe and InP

in units of (cm/MW)

Crystal Wavelength THEORETICAL EXPERI-

( ym ) Keldysh 9 Braunstein 5

Basov

c Lee and d

Present MENTAL

Fan

InP 1.064 0.026 0.008 0.0003 0.096 0.722 0.18-

0.26

d

CdTe 1.064 0.023 0.007 0.0005 —- 0.201 0.02-

0.3

e

a. L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

b. R. Braunstein and N. Ockman, Phys. Rev. 134 , A499 (1964); see also

S. S. Mitra, L. M. Narducci , R. A. Shatas, Y. F. Tsay, and A.

Vaidyanathan, Appl . Opt. 1_4, 3038 (1975).

c. N. G. Basov, A. Z. Grasyuk, I. G. Zubarev, V. A. Katulin, and 0. N. Krokhin, Sov. Phys. JETP 23, 366 (1966). Also, A. Vaidyanathan,

T. W. Walker, A. H . Guenther, S. S. Mitra, and L. M. Narducci,

Phys. Rev. B (in press)

.

d. C. C. Lee and H. Y Fan, Phys. Rev. B 9_, 3502 (1974).

e. J. M. Ralston and R. K. Chang, Opto-electronics T, 182 (1969);

J. H. Bechtel and W. L. Smith, Phys. Rev. B13, 3515 (1976);

S. J. Bepko, Phys. Rev. Bl_2, 669 (1 975); and M. Bass, E. W. Van

Stryland, and A. F. Stewart, Appl. Phys. Lett. 34, 142 (1979).

Acknowledgement

This research was supported in part by an Air Force Systems

Command-National Research Council Postdoctoral Resident Research

Associateship (A.V.).

15
MEASUREMENT AND INTERPRETATION OF

ULTRAVIOLET OPTICAL PROPERTIES OF SOLIDS

David W. Lynch

Ames Laboratory-USDOE and Department of Physics

Iowa State University, Ames, Iowa 50011

This paper reviews methods of measuring the optical properties of solids

in the energy range above 6eV and some of the experimental problems en- countered. General interpretations are discussed with some examples.

References prior to 1978 may be found in references 1 and 2.

Above 6eV, measurement techniques become somewhat limited compared with

those used in the visible region because of the limited number of transparent materials. Special problems arise in making polarizers which

are highly efficient over a large wavelength range, and transparent

materials, other than unsupported thin films, are not available for use above lleV as substrates for thin films. The advent of synchrotron

radiation has ameliorated problems associated with sources above 6eV.

It usually provides a known state of polarization as well. The problems

associated with the samples themselves often become more severe above

6eV. Thin film samples may incorporate oxygen during their preparation,

and the 2p electrons of oxygen absorb strongly from 6eV to very high

energies, 75eV or more. Both thin film and bulk samples may have surface oxides as well, and the correction for such an overlayer is far

less reliable when it is an absorbing oxide instead of a transparent

one. Finally, surface roughness often has a more deleterious effect on reflectance data at shorter wavelengths. The ideal measurement has not

yet been made, one in which the sample surface was shown to be clean,

e.g., by Auger spectroscopy, unstrained, e.g., by LEED, and flat, e.g.,

by measuring scattered light, during the measurement of the optical

properties

.

Measurements of optical properties fall into three general classes,

1. Ellipsometry . Such methods appear to have been used only once

in the vacuum ultraviolet . [3] Although synchrotron radiation is

polarized, the need to analyze refelected radiation with a polarizer

of low efficiency and limited spectral range makes ellipsometric methods

unattractive

.

2. Photometric reflectance. One either measures the reflectance at one angle over a wide energy range and Kramers-Kronig analyzes the

reflectance (by far the most popular method) or fits it to a series of

oscillators, or one measures the reflectance at several angles of incidence and uses the Fresnel equations to obtain the optical constants.

One then must know the state of polarization of the incident radiation

or treat it as a third unknown. In at least one case it has not been

very constant during the course of the measurements . [4 ] In addition

16
to the effects of surface roughness and oxides mentioned above, additional errors can arise for insulators from luminescence. A detector

which scans continuously over angle can detect luminescence and surface scattering. It can be eliminated in some cases by suitable choice

of detectors, and in some cases by gating the detectors and using the

pulsed nature of synchrotron radiation. At energies above about 30eV

the reflectance of most materials falls to very low levels. To maintain

accuracy the measurements must be made at large angles of incidence,

necessitating larger samples.

3. Photometric transmission. Above 30eV the reflectance is usually

so low that corrections for multiple reflections are negligible.

Transmission measurements on samples of different thicknesses then give

absorption coefficients which can be KK analyzed to get the refractive

index.

There are other methods. Characteristic electron energy losses can be

analyzed to get optical constants and this method is an excellent one

for anisotropic materials, especially highly anisotropic layered

materials [51 for which most of the above-mentioned methods give poor

results for E c. The total yield of photoelectrons gives a spectrum

generally proportional to the absorption coefficient spectrum, but in

arbitrary units, above an energy of about 20eV. Finally, modulation

spectroscopic methods can be used to at least 200eV to measure the

dependence of optical properties on applied uniaxial stress, and electric and magnetic fields, and on temperature.

The accuracy of the resultant optical constants is difficult to determine, being so strongly dependent on the degree to which the actual

sample approaches the ideal. Kramers-Kronig integrals and resultant

sum rules and "super" sum rules can be very useful in determining consistency, but only when data believed to be reliable extend over a very

wide energy range. Such consistency tests work rather well for Al, but

not for Au, and they have been carried out for very few other materials.

Above 6 to lOeV the reflectance of most solids falls with increasing

photon energy, and the anisotropy of the optical constants diminishes,

then disappears. If there are core levels deep enough so that they do

not exhibit band effects, deeper than about lOeV, the reflectance and

absorption will increase at the threshold for the core level. The core

levels are usually spin-orbit split so the measured spectra must be

separated into two components before interpretation. The core levels

have definite angular momenta and are localized on one atomic site.

The selection rules for the excitation at their simplest make the

spectrum resemble one component of the angular-momentum-and site-decomposition of the density of empty states. The strong localization also

causes the oscillator strength to be spread over a very wide energy

range. The localization of the transitions makes such core level studies promising for the stody of alloys, but the lack of satisfactory

interpretation in the cases in which it has been employed makes future

utility doubtful.

17
The core edges do however, offer some novel features. For both semiconductors and insulators, core excitons can form and the binding energy

may be quite high because of the extreme localization of the exciton.

In the case of semiconductors the binding energies are higher than can

be understood at present [6] . Also for semiconductors the core excitons

can be used to study the conduction band by itself, something not possible with conventional uv spectroscopy which uses the highly dispersed

valence band for initial states. In metals many-body effects cause additional structure at the soft x-ray core edges in simple metals,

while Coulomb- induced coupling of quasi-discrete and continuum transitions causes unusual line shapes for core edges of metals with incomplete d-shells. All these phenomena may be studied by modulation

spectroscopy. [7,8]

Many soft x-ray core transitions exhibit extended x-ray absorption fine

structure (EXAFS) similar to that seen above deep core x-ray edges, but

the structure is usually overlapped by other nearby soft x-ray core

edges

.

If there are no core levels in the 5-30eV range the reflectance may

still rise at some threshold. This is the case with most transition

metals and with noble metals. Here there are bands lying 5-15eV above

the Fermi level, bands which are not free-electron like. These bands

are relatively flat and transitions to them cause an increase in the

absorption. They begin at an energy which depends, to first order,

primarily on the crystal structure. As far as is known, such flat

bands do not form in a number of transition metal compounds, e.g., TiC,

A-15-structured superconductors, and NaxW03, ^ut tne reason is not

always the greater spacing between the transition metal ions.

The falloff in reflectance often signifies a plasma edge as in the case

of a free-electron gas. One can plot the loss function for the

excitation of volume longitudinal excitations, Im(-l/g), which is the zero wave-vector limit of a more general function best measured by the

inelastic scattering of fast electrons. We have found that most transition metals have two distinct peaks in both the volume and the surface

loss functions. The larger is always near the free electron plasmon

energy, counting the d and the s-p electrons. The other is always

lower in energy, lying in the absorption minimum just below the threshold energy for the excitation of electrons into the high-density bands

mentioned above. This peak represents some sort of screened plasmon,

the collective motion of a group of electrons whose mutual Coulomb

interaction is screened by other electrons. For transition metals one cannot identify the groups of electrons from only data. They may be

just the d- electrons, just the s,p- electrons or neither. In layered

semiconductors a similar phenomenon occurs, but the groups of electrons

there are better defined, being bonding and non-bonding valence electron-. The occurrence of two volume plasmons is easily seen from a macroscopic dielectric model, but a microscopic interpretation is still

lacking. The optical data are of considerable aid in understanding the

18
electron energy loss data, for in reactive materials the energy loss

measurements are usually made with reflected electrons . [9] The volume

and surface losses cannot be separated easily, and their spectral

features are known to overlap severely.

This work was supported by the U.S. Department of Energy, contract No.

W-7405-Eng-82, Division of Materials Science budget code AK-01-02-02-2

References

1. D. W. Lynch, J. de Physique 39, C4-125 (1978).

2. D. W. Lynch in C. Kunz, ed . , Topics in Current Physics, Vol. 10,

"Synchrotron Radiation, Techniques and Applications" (SpringerVerlag, Berlin, 1979), Chapter 7.

3. M. Schlederman and M. Skibowski, Appl . Opt. 10, 321 (1971).

4. D.Beaglehole, M. De Crecenzi, M. L. Theye, and G. Vuye, Phys.

Rev. B19, 6303 (1979).

5. C. H . Chen and J

.

Silcox, Phys. Rev. B20, 3605 (1979).

6. A. Quattropani, F. Bassani, G . Mar^aritondo , and G. Tinivella,

11 Nuovo Cim. 51B, 335 (1979).

7. C. G. Olson and D. W. Lynch, Solid State Comm. 31, 601 (1979).

8. C. G. Olson and D. W. Lynch, to appear in Solid State Comm.

9. w. K. Schubert and E. L. Wolf, Phys. Rev. B20, 1855 (1979).

19
THE OPTICAL PROPERTIES OF KAPTON: MEASUREMENT AND APPLICATIONS*

L. R. Painter, 1" E. T. Arakawa, M. W. Williams, and J. C. Ashley

Health and Safety Research Division

Oak Ridge National Laboratory

Oak Ridge, Tennessee 37830

Kapton Type H polyimide film 1 is used extensively in situations

demanding good electrical insulation, radiation resistance, and/or

chemical resistance, particularly at high operating temperatures. At

room temperature the physical properties of Kapton are similar to those

of Mylar polyester film 1

, but Kapton is less affected by temperature

changes and is also =50 times more resistant to radiation damage than

Mylar. In fact, Kapton has been found to retain its useful properties

over the wide temperature range from -269°C to +400°C. In view of its

extensive use, measurements of the optical properties of Kapton and

calculations of the transport parameters for ionizing radiations,

particularly low energy electrons, in Kapton are of interest.

We have found over the past decade that the most satisfactory way to

obtain the absorption spectrum of an organic material over an extended

wavelength region that includes essentially all of the oscillator

strength of the valence electrons is by transmission measurements.

Unfortunately methods developed for obtaining samples of organic

materials suitable for transmission measurements at wavelengths below

*Research sponsored jointly by the Deputy for Electronic Technology, Air Force Systems Command, under Interagency Agreement DOE

No. 40-226-70 and the Office of Health and Environmental Research,

U.S. Department of Energy, under contract W-7405-eng-26 with the Union

Carbide Corporation.

+Also Department of Physics and Astronomy, University of Tennessee,

Knoxville, Tennessee 37916.

Manufactured by E. I. du Pont de Nemours and Company.

20
the UV absorption edge (1-4), in which uniform thin films of an organic

material have been obtained by vacuum evaporation or from a solution of

the material in a suitable solvent, cannot easily be applied to Kapton.

Kapton is available 1 as Type H film with nominal thicknesses from

7.6*10~ 6 m to 1.27xl0_lt m. Such films are too thick for transmission

measurements in the vacuum UV region. The optical properties of Kapton were thus obtained for wavelengths in the range of 16.3 nm to 2500 nm from reflectance measurements on Kapton films stretched over a sample

holder. At each wavelength the measured reflectance as a function of

the angle of incidence was least-squares fit to Fresnel's equations to

yield the real and imaginary parts of the complex refractive index,

n = n + ik, and of the complex dielectric function, e = e : + ie 2

. At

photon wavelengths where the extinction coefficient k is zero, normal

incidence reflectance and transmittance were measured and a direct

calculation made of the refractive index n. Transmission measurements

on the thinnest Kapton films in the wavelength region of the ultraviolet

absorption edge were also used to calculate k values in the region of

the edge. Measurements were made with a spectrophotometer (Cary Model

14) in the 2500 nm to 300 nm range, a Seya-Namioka monochromator

(McPherson Model 235) in the 620 nm to 82.7 nm range and with a grazingincidence monochromator (McPherson Model 247) in the 95.4 nm to 16.3 nm

range. Below 165 nm, measurements were made using line sources (hydrogen discharge and a condensed air spark) while above 165 nm continuum

sources were employed. The estimated uncertainties on the values

obtained for n and k were everywhere < ±6%.

As a test of the general validity of the data obtained, the measured k

values for Kapton, which has a monomeric unit of -\C 2 2^i o^z^^t, were

combined with estimated values of k at shorter wavelengths to form a spectrum extending over the oscillator strength of both valence and core

electrons. The values of k due to valence electrons were extrapolated

to lower wavelengths and estimations (4) made of superimposed structure

in k due to the C, N, and 0 K-shell electrons. A Kramers-Kronig

analysis of this k-spectrum (3,4) yields n-values in the experimental

21
region which agree with the measured values within the estimated

uncertainties associated with the measurements. As a further overall

check on the values of k over the entire wavelength range, the "k sumrule" (3,4) was performed on these data and yields a total number of

electrons consistent with the known number of valence plus core electrons per monomeric unit of 188. Thus the optical constants over the

whole wavelength range, arrived at by a combination of measurements and

estimations, are internally self-consistent. These data were then used,

as previously demonstrated for polystyrene (5,6) and polyethylene (4),

to calculate values of the mean excitation energy of Kapton, electron

mean free paths in Kapton, and the stopping power of Kapton for

electrons.

Values of the mean free paths in Kapton for electrons of energies from

=1.6xl0-17

J to x 1.6xl0 -15

J were calculated from the variation with

photon wavelength of the energy loss function, Im[-l/e], obtained from

the measurements of e. The values agreed with those predicted by a recently proposed (7) simple expression for calculating electron mean

free paths, A, in solid organic insulators, i.e.,

A np_ = f(E),

M

where n is the number of valence electrons per monomeric unit, p the

density of the material, M the molecular weight of the monomeric unit,

and E the energy of the incident electron. This expression was based on

a theoretical formula for mean free path with input parameters derived

from the experimental optical properties of six organic insulators -- the only data then available which extended over a sufficiently wide

wavelength range. The agreement of the values of A obtained by calculations based on the optical properties, e, of Kapton and from the

simple expression for A given in Ref. 7 assuming a density of 1.42xl0 3

kg/m 3 for Kapton 2

, increases our confidence both in the measured values

2 Electrical Insulation Products Division Du Pont Film Department,

Bulletin H-1D.

22
of the optical properties of Kapton which were difficult to obtain

accurately and in the simple expression for electron mean free paths in

solid organic insulators which was based on only six materials.

REFERENCES

1. T, Inagaki, R. N. Hamm, E. T. Arakawa, and L. R. Painter, Optical

and dielectric properties of DNA in the extreme ultraviolet.

J. Chem. Phys. 61_, 4246-4250 (1974).

2. T. Inagaki, R. N. Hamm, E. T. Arakawa, and R. D. Birkhoff, Optical

properties of bovine plasma albumin between 2 and 82 eV.

Bio-polymers 1_4, 839-847 (1975).

3. T. Inagaki, E. T. Arakawa, R. N. Hamm, and M. W. Williams, Optical

properties of polystyrene from the near-infrared to the x-ray

region and convergence of optical sum rules. Phys. Rev. B 15 , 3243-3253 (1977).

4. L. R. Painter, E. T. Arakawa, M. W. Williams, and J. C. Ashley,

Optical properties of polyethylene: measurement and applications.

Accepted for publication by Radiation Research.

5. J. C. Ashley, Mean excitation energy of polystyrene. Phys. Rev. B

19, 5429-5430 (1979).

6. J. C. Ashley, C. J. Tung, and R. H. Ritchie, Inelastic interactions

of electrons with polystyrene: calculations of mean free paths,

stopping powers, and csda ranges. IEEE Trans. Nuol. Sei. NS-25 , 1566-1570 (1978).

7. J. C. Ashley and M. W. Williams, Electron mean free paths in

solid organic insulators. Accepted for publication by Radiation

Research.

23
OPTICAL PROPERTIES OF TiC (0 . 64<x<0 . 90) FROM 0.1 TO 30eV

x

D. W. Lynch, C. G. Olson and D. J. Peterman

Ames Laboratory-USDOE and Department of Physics

Iowa State University, Ames, Iowa 50011

and

J. H. Weaver

Synchrotron Radiation Center, University of Wisconsin-Madison,

Stoughton, Wisconsin 53589

The absorptance of four bulk samples of TiC were measured in the 0.1-

4.6eV energy range and the reflectances measured between 4 and 30eV.

For x=0.64 the sample was polycrystalline, previously fused, while

single crystals were used for x=0.833, 0. 90, and 0.97. All samples were

electropolished before measurements. The samples for x=0.64 and 0.90 were large enough so that absolute data could be obtained for Kramers

Kronig analysis. The reflectances and absorptances of the other two

samples are in arbitrary units.

Our data are in poor agreement with earlier data on sintered samples [1]

and with infrared and visible data on single crystals, [2] but in general agreement with vuv data on single crystals. [2] Figure 1 shows the

reflectances of our samples while the optical conductivity obtained by

KK analysis for two samples is shown in Fig. 2. From these figures

one can see that there is a one-for-one correspondence of the structures

in the reflectance and the conductivity so the trends with stoichiometry

can be followed meaningfully in the reflectance spectra. The partial

sum rule on shows that about 4.3 electrons per molecule contribute

to optical absorption between 0.4 and 30eV for x=0.90 vs 4.1 for x=0.64.

Interband absorption occurs at very low energies, down to O.leV, so meaningful Drude parameters cannot be extracted.

Discussions of bonding in TiC and related compounds have a long history.

We attempted to explain our data on the basis of two recent band calculations [3,4] and had more success with the latter of the two, which

was self-consistent. The lowest curve in Fig. 2 shows the calculated

joint density of states for TiC (x=l) calculated from parameterization

of the bands of Ref . 4, which are shown in Fig. 3. The agreement is

surprisingly good. The strong absorption in the 1-10. 7eV region arises

from transitions between bands based on Ti 3d and C 2p levels. Their

exhaustion occurs at the minimum in the conductivity at 10.7eV. The

rise at higher energy is due to transitions from the C 2s band, the

lowest band in Fig. 3. The calculated structures appear too sharp, no lifetime broadening having been included. A detailed assignment to

particular regions of reciprocal space is premature.

24
Most of the stoichiometry dependence occurs above 5eV. Above 10.7eV

the transitions primarily originate on the C 2s levels and their con- ductivity should then fall as x decreases. This occurs, but the final

states, which involve hydridized Ti 3d and C 2p levels should change

as well. (Also the Fermi level should move, but there is no evidence

in our data for the validity of the simple rigid band model.) The

low energy peak at 1.3eV does not change as x changes. It appears to

be a transition between parallel bands cut by the Fermi level, e.g.,

along A in Fig. 3.

Figure 4 shows the electron energy loss functions for volume and sur- face longitudinal excitations. (No electron energy loss spectra

have been reported for TiC.) The high energy peak in the volume loss

function is near the free electron plasmon energy, calculated with the

2s and 2p electrons of C as well as three electrons per Ti. The lower

energy "plasmon" occurs at the minimum in the conductivity. The surface loss function peaks are at lower energies than those in the

volume loss function, but are not related by a factor of 1/v^as for

a free electron gas. The low energy peaks in the volume and surface

loss functions overlap and would not be resolved in electron energy

loss spectra measured in reflection.

This work was supported in part by the U.S. Department of Energy,

contract No. W-7405-Eng-82 , Division of Materials Sciences, budget code

AK-01-02-02-2 and in part by the National Science Foundation under

contract DMR 7821080.

The single crystals of TiCx were kindly supplied by Wendell S. Williams

of the University of Illinois. The polycrystalline sample was produced

by F. A. Schmidt of the Ames Laboratory. The storage ring is operated

by the Synchrotron Radiation Center, University of Wisconsin-Madison,

under contract DMR 7721888 from the National Science Foundation. We

thank K. H. Schwarz and A. C. Switendick for supplying us with a table

of energy eigenvalues.

References

1. J. F. Alward, C. Y. Fong, M. El-Batanouny , and F. Woo ten, Phys. Rev.

B 12, 1105 (1975); Solid State Comm. 17, 1063 (1975).

2. R. G. Lye and E. M. Logothetis, Phys. Rev. 147 , 622 (1966).

3. V. Ern and A. C. Switendick, Phys. Rev. 137 , A1927 (1965).

4. A. Neckel, P. Rastle, R. Eibler, P. Weinberger, and K. Schwarz,

J. Phys. C. 9, 579 (1976).

25
Figure 1.

Reflectance spectra

of TiC for several

stoichiometrics

.

Reflectance scales

for x=0.83 and 0.97

have been adjusted and are essentially arbitrary.

15 ENERGY (eV)

15 ENERGY feV)

Fig. 2. Optical conductivity of TiC . Solid: x=0.90, dashed, x=0.64,

Obtained from the date of Fig. 1 by Kramers-Kronig analysis.

The lowest curve is the conductivity for x=l calculated without dipole matrix elements from the bands of Ref. 4 (Fig. 3).

26
Ti C

in

'X) o

VOLUME

SURFACE /

10 15 ENERGY (eV) 20 25 30

Figure 4. Electron energy loss functions, Im(-l/g) (volume) and

Im(-l/(g+l)) (surface) for TiC . Solids, x=0.90;

dashed, x=0.64. x

27
SUPERCONVERGENCE RELATIONS AND THE ANALYSIS OF OPTICAL DATA"'

D. Y. Smith§ Physikalisches Institut der Universitat Stuttgart

7 Stuttgart 80, Germany

and

Argonne National Laboratory

Argonne, Illinois 60439, U. S. A.

and

E. Shiles

Virginia Commonwealth University

Richmond, Virginia 23284, U,S,A,

Recent studies have shown that the optical constants satisfy a large

number of sum rules in addition to the well-known f sum rules. These

provide tests of agreement with both theoretical constraints and independently measured quantities. They are particularly valuable in com- bining optical measurements obtained by different techniques to form

composites of data covering a wide spectral range. In conjunction with

an iterative self-consistent Kramers-Kronig procedure, optical sum rules

have been used to analyze the optical properties of Al , Si and GaAs.

This approach has made it possible to select the most probable values

from the available optical measurements and has pinpointed a number of

systematic experimental errors.

1 . Sum Rules for the Optical Constants . It has been known for many years

that the imaginary part of the complex dielectric function,

e(oo) = £i (oo) +i£2 (w) , the imaginary part of the complex refractive index,

N(oo) = n(oo)+iK(co) , and the energy-loss function, Im£(co)

-1

, satisfy f sum

rules. For example

oo -J]- 2 f 00£2 (Gi)) dGO = tt<jO , ( 1 )

0 ^ p

2 1 12 where go^ is the plasma frequency, U)p=(4n>Ve /m) , with-/!' the electron

density.

By applying methods originally developed for dispersion analysis of

scattering data m high-energy physics, it has recently been shown ' that similar superconvergence relations or sum rules hold for the real

parts of the optical functions. Some simple examples are

-OO - / {n(Go) - 1 } dGO = 0 (2)

0 and

OO - , 9 / {e.(go) - 1} dGO = -2tt a(0), (3)

0 1

28
where cr(0) is the d.c. conductivity. There are, infact, an infinite

number of such relations 3 involving higher powers and products of £1

,

£2, n and k. Generalizations'* of all these rules exist for circularlyand elliptically-polarized light, and a number of finite-energy f sum

rules 5 hold under special circumstances.

Mathematically the rules are a consequence of the analyticity of the

optical functions and their asymptotic behavior at high frequencies.

Physically they are a consequence of causality and the equations of

motion 3. For example, in classical linear response theory Eqs. 2 and

3 are just a restatement of the law of inertia while Eq. 1 is equivalent to Newton's equation of motion.

In addition to these superconvergence relations for the optical functions, the mean energy loss of a fast charged particle penetrating

through matter, i.e. the stopping power, is related to the dielectric

function through a sum rule 6

. This provides a useful test of the

dielectric function particularly at higher energies.

2. Self-Consistent Kramers-Kronig Analysis . The Kramers-Kronig relations are widely used in the analysis of optical data. However, they

require the knowledge of one optical function over the entire spectral

range. Experimentally this requirement is never fulfilled, rather,

optical measurements consist of a mixture of reflection, absorption,

refractive index, and ellipsometric measurements in different, generally non-overlapping spectral regions.

Commonly the Kramers-Kronig relations are applied to a single optical

quantity by using plausable extrapolations into the ranges for which

measurements of this property are not available. However, superior results can be obtained by treating the mixture of all optical measurements by an iterative, self-consistent solution to the Kramers-Kronig

relations. In practice this involves choosing one optical property, preferably available over a wide range of energies, as a starting function.

To augment the measured values, provisional estimates of the function

outside the range of measurements must be made from other data. The

provisional solution is then improved iteratively using all available

data until satisfactory convergence is achieved. Application of the

constraints given by the various optical sum rules provides a systematic procedure for selecting the most probable values from the

available optical measurements during the iterative process.

3. Application: The Bulk Optical Properties of Al, 0.04 to 10,000 eV . The self-consistent Kramers-Kronig procedure has been applied to

elemental Al and Si, and to GaAs. The most detailed results 7 have been

obtained for aluminium and these will be outlined here. Reflectance

measurements on samples of aluminum prepared in ultrahigh vacuum are available from the far infrared to the near ultraviolet and formed the

basis for the initial trial function. These data are probably the best

available at present and are free from surface contamination and

29
surf ace-plasmon effects. At wavelengths shorter than the plasma edge

the normal reflectance was calculated from a combination of measured

absorption data and refractive index estimates from a preliminary

calculation of Sasaki and Inokuti 8 based on model fits to reflectance

and transmission measurements. On iteration it was found that the region

near the plasma edge (15eV) was the most uncertain because of difficulties associated with both reflectance and transmission measurements in

this transition region. Electron energy-loss measurements were therefore used as a guide by requiring that the dielectric function reproduce the energy-loss function.

The optical functions were tested at various stages in the iterative

calculation with the optical sum rules. The d.c. conductivity sum rule

provided a useful control on the conduction-electron portion of spectrum since it is insensitive to band-to-band transitions. Agreement of

a(0) with direct measurement was always well within experimental

error. From the beginning application of the f sum rule disclosed a significant systematic error: the electron density corresponding to the

experimental spectrum was over 14 electrons/atom (e/a) rather than the

known value of 13 e/a.

The spectral region responsible for this inconsistency could be

located because the valence, K-shell and L-shell absorptions are well

separated and finite-energy f sum rules 5 could be applied. It was found

that the absorption measurements for several hundred volts above the

L-edge (72eV) were systematically some 14 % too high. All reliable measurements in this region have been made in transmission on thin film

samples. However, these samples have a high surface oxide-layer to

bulk ratio and appear to be subject to spurious effects. A combination

of ad hoc reduction of the extinction coefficient in this region and

new data from Frascati yielded agreement with both the partial f sum rules and the total f sum as well as the average excitation energy for

charged particle energy loss.

In addition to providing a more reliable composite of the optical

constants, this analysis has disclosed two interesting physical processes: (a) the "shielding" of valence-electron processes by the

polarizable core electrons and (b) the exchange of oscillator strength

between core and valence electrons.

The first of these appears as a difference between the partial f sums

for £2,K and the energy-loss function for the conduction electron

spectrum. Each quantity measures a somewhat different physical process

and the "effective" number of electrons contributing to each process

differs because of the polarizable ion cores. Denoting the dielectric

constant of the fictitious medium made up of the ion cores alone by e^,

the effective number of conduction electrons calculated from the sum rules for £2>k and the energy-loss function are in the ratio 5

:

30
I I , "J/2 "2 /n

eff'£2 eff'x eff'e b b

I

• * 7 In the case of aluminum £, is found to have a value of 1.03s.

b The second effect, the exchange of oscillator strength, appears as a departure of the oscillator strength for a given shell of electrons

from the occupation number (i.e. from the assumption of unit oscillator

strength per electron) . This is well known in atomic physics but does

not appear to have been as generally demonstrated for solids heretofore. It is easily understood in the one-electron approximation as a result of the Pauli-principle prohibition of transitions to occupied

states. Thus, electrons in the K-shell cannot make transitions to

occupied states at higher energies and lose oscillator strength.

Similarly, valence electrons cannot make downward transitions (which

have negative oscillator strength) and hence have oscillator strengths

greater than one. In the case of Al the three valence electrons contribute an oscillator strength of 3 . 1 i

, the eight L-shell electrons have

a strength of 8.27, while the two K-shell electrons have a strength

of only 1 . 6 1 . The oscillator strength lost by one shell is gained by

the others so that the total remains 13.

FOOTNOTES AND REFERENCES

Work supported by the Deutsche Forschungsgemeinschaf t and the U.S.

Department of Energy.

§ Permanent address: Solid State Science Division, Argonne National

Laboratory, Argonne, Illinois 60439, U.S.A.

1. M. Altarelli, D.L. Dexter, H.M. Nussenzweig, and D.Y. Smith,

Phys. Rev. B6, 4502 (1972).

2. W. M. Saslow, Phys. Lett. 33A, 157 (1970); A. Villani and A. H.

Zimerman, Phys. Rev. B _8 , 3914 (1973) and Phys. Lett. 44A, 295

(1973); K. Furuya, A. H. Zimerman and A. Villani, Phys. Rev. B L3>

1357 (1975); and F. W. King, J. Math. Phys. _T7, 1509 (1976).

3. M. Altarelli and D.Y. Smith, Phys. Rev. B _9, 1290 (1974).

4. D.Y. Smith, Phys. Rev. B J_3, 5303 (1976).

5. D.Y. Smith and E. Shiles, Phys. Rev. B L7> 4689 (1978).

6. U. Fano, Phys. Rev. K)3, 1202 (1956).

7. E. Shiles, T. Sasaki, M. Inokuti, and D.Y. Smith (submitted for

publication)

.

8. T. Sasaki and M. Inokuti, Conference Digest of the Third Internat.

Conference on Vacuum Ultraviolet Radiation Physics, Y. Nakai, editor

(The Physical Society of Japan, Tokyo 1971) page 2aC2-2.

31
MEASUREMENT OF THE FAR INFRARED OPTICAL

CONSTANTS OF DISORDERED SOLIDS

U. Strom and P. C. Taylor

Naval Research Laboratory

Washington, D. C. 20375

The study of optical properties in the region from 0.1 to 100 cm requires diverse experimental techniques depending on the specific

material and frequency of interest. Traditionally, Fourier transform

spectroscopy (FTS) has been the primary spectroscopic tool in the far

infrared (FIR). This technique is fast and reliable, but suffers from

wea| radiation sources at the long wavelength end of the spectrum (< 10 cm ). Furthermore, FTS is poorly suited to the measurement of the

broad spectral features expected for disordered materials.

We briefly outline here recent developments in the far infrared

spectroscopic study of disordered solids over a large range of discrete

frequencies. The sources of radiation are optically pumped molecular

gas lasers (5-150 cm ) and Klystrons (< 5 cm ). The primary optical

constants obtained are the imaginary (s") and real (£') parts of the

dielectric constant and their dependences on temperature and frequency.

These in turn are related to the index of

_ jef raction n and tl^e con- ductivity a by a = U)£", n = V^' and na(cm ) = 120 7ta(Q cm ).

The simplest experiment which can be performed is direct optical

transmission. For a free-standing thin parallel-faced slab of material

of thickness d and complex refractive index N = n-ik the transmission

at normal incidence (for^ k = 0) is found to vary with a period of

(2nd) in wavenumbers. The transmission will be reduced for k > 0

(where Of = 2iok/c). In Fig. 1 we show the measured far-infrared transmission of a freestanding 10.4 pm thick film of amorphous Ge. The

solid line represents the expected transmission for an absorption-free

film with n = 4.25. The difference between the ^o curves yields an absorption coefficient Of which peaks near 105 cm . This absorption is

forbidden by selection rules in crystalline Ge but occurs in a-Ge

because of the lack of long-range periodicity.

In Fig. 2 the absorption curve for Ge is extended below 50 cm by microwave cavity measurements. Measurements of such small values of

absorptions are made possible by the sensitivity increase over direct^

transmission by a factor which is comparable to cavity Q values (~ 10

to 10 ). Generally, a perturbative technique is used, in which small

changes in cavity Q and resonance frequency f can be directly related to

e" and &' , respectively. As seen in Fig. 2, the absorption falls off

nearly quadratically with decreasing frequency (of « u) ) . This quadratic

dependence of the FIR absorption coefficient is characteristic of many

disordered solids, such as Se in Fig. 2, other chalcogenide and oxide

glasses, as well as polymers. * It is attributed to the disorder32
100 io80 100 120 140

WAVENUMBER (CM~')

Fig. 1. Transmission at 300K of

a 10.4 [jm thick film of amorphous

Ge evaporated at 2$/sec. Dashed

curve through measurement. Solid

curve represents absorption free

(k=0) transmission with n=4.25.

_ 10

o

9

C

to

4

—1 1 T /A

-

Ge-/ /-Se /-At

_i 1

0.1 1.0 10 100 wave number (cm"1 ) Fig. 2. Absorption of

bulk (As, Se) and evaporated film (Ge) elemental amorphous semiconductors at 300K.

induced optical coupling to Debye-l^ke lattice excitations which have a density of states proportional to U) . For a one-phonon process this

absorption is predicted to be temperature independent, as is indeed

observed above 10 cm

In a few amorphous and disordered solids the frequency dependence

of a in the FIR is faster than quadratic; i.e., a a u) with n > 2.

Examples are amorphous As in Fig. 2 and the ionic conductor Na {3-Alumina

in Fig. 3. In the case of As the 3-fold coordination of the As-atom

introduces structural rigidity^which inhibits optical coupling to

long-wavelength lattice modes. Such reduced optical activity would

also be expected for amorphous Ge (a-Ge) which is four-fold coordinated. However, the a-Ge structure is over-constrained to such an extent that sizeable voids, which are free of Ge, form within the

evaporated film. There is evidence, from changes in the FIR absorption

with evaporation conditions , that the FIR absorption is dominated by

the presence of charged defects on the interior surfaces of the voids.

Thus, the "intrinsic" absorption in "void-free" a-Ge is possibly lower

than even that of As.

We contrast these results with Na 0-Alumina, a crystalline _ material which exhibits certain properties of a disordered solid. Na

P-Alumina consists of spinel-like blocks of kS,^0^ which are separated

by highly disordered planes occupied by Na and 0 ions. At T > 300K the

Na cations diffuse rapidly within a conducting plane, resulting in an ionic conductivity which is typical of liquids. With cooling the

33
WAVENUMBER (cm-' )

I0" 3 IO"2 10"' I 10 I0 2

FREQUENCY ( Hz)

Fig. 3. Conductivity a (where

na=120na) of Na p-Alumina with

electric field parallel to con- ducting planes.

o

crB

_!

LjJ Q u/

s

a:2

CRYSTAL(Si02)

"SUPER"

\IONIC CONDUCTOR

•. (Na^QALUMINA)

GLASS*. .• (Si02) \

"

—I 1 1— 0.5 I 2 5 10 20

TEMPERATURE (K)

Fig. 4. Change in dielectric

constant versus temperature

at 10 GHz (0.33 cm ) for

crystalline and glassy SiO^

and the ionic conductor

Na (3-Alumina. ~ Vertical

full scale 10 .

cation layers remain disordered and exhibit dielectric, thermal and

resonancg properties similar to those of glasses. The low T dielectric

response is shown in Fig. 4, which illustrates the "glass-like" behavior of the ionic conductor. The local vibrational motion leads to

a strong FIR absorption peak near 65 cm , as seen in Fig. 3. This

motion is essentially decoupled from the considerably higher frequency

vibrational modes of the AiLO^ structure. In addition, the coupling to

long wavelength acoustic modes is also inhibited as evidenced by the

rapid fall-off of the absorption at long wavelengths (measured at 4K to

remove^the effect of^a temperature dependent vibrational peak near

12 cm ), i.e. a ~ w with n < 4.

The above examples are illustrative of the potential for careful

measurements of the optical constants at discrete frequencies in the

far infrared region. For disordered solids such measurements are particularly sensitive to the degree and nature of the disorder.

Although the sensitivities of the_measurements below 5 cm are high

(A£'/£' ~ 1 part in 10 at 0.3 cm ) because of high Q cavities, the

measurement accuracy above 5 cm is much less precise. HoweverA ^ carefully designed confocal resonators for the region above 5 cm can provide considerably improved sensitivity. Such improvements, coupled

with the great number of far infrared lines available from optically

pumped FIR lasers, promise an increasing wealth of optical information

in a relatively unexplored spectral region.

34
References

1. O.S. Heavens, Optical Properties of Thin Films (Dover, New

York, 1935), p. 20.

2. P.C. Taylor, U. Strom, J.R. Hendrickson and S.K. Bahl, Phys.

Rev. B 13, 1711 (1976).

3. U. Strom and P.C. Taylor, Phys. Rev. B 16, 5512 (1977).

4. C.R. Pidgeon, CD. Holah, F. Al-Bakdar, P.C. Taylor and

U. Strom, Proc. 3rd International Conf. on Submillimeter Waves,

Univ. of Surrey, England (1978).

5. U. Strom, P.C. Taylor, S.G. Bishop, T.L. Reinecke and

K.L. Ngai, Phys. Rev. B 13, 3329 (1976).

6. U. Strom, M. von Schickfus and S. Hunklinger, Phys. Rev.

Lett. 41, 910 (1978).

35
INFRARED IMPURITY ABSORPTION

SPECTRA OF PREMIUM-0 QUARTZ

Herbert G. Lipson

Rome Air Development Center

Deputy for Electronic Technology

Hanscom AFB , MA 01731

Applications such as precision quartz oscillators and surface acoustic

wave devices place stringent requirements on the purity and consistency

of high grade synthetic quartz. The frequency stability of satelliteborne oscillators, particularly when operated in a ionizing radiation

environment, may be affected through changes in impurity-related defects present in the quartz. In practice, it has been found that

sweeping, or electrodiffusion , where an electric field is applied

parallel to the z-axis while the material is heated to temperatures between 400 and 550C, markedly reduces frequency changes induced by

ionizing radiation.

Characteristic impurity bands found in the low temperature infrared

spectra provide more information for early evaluation of oscillator

quartz than the usual quality control methods which rely on room temperature absorbance measurements at one specific wavenumber. In this

paper the impurity bands found in state-of-the-art Premium-Q and

optical grade quartz are classified and changes in these bands introduced by sweeping and ionizing radiation, as well as their polarization

dependence are discussed.

A comparison of absorption spectra of unswept and swept quartz measured

at 300, 85 and 15K is shown in Figure 1 .

_-|

At 300°K, only one impurity band at 3585cm can be resolved above the

broad peaks characteristic of ^he Si-0 lattice mode overtone absorption at 3200, 3300 and 3400c m~ . Since the frequency value 3500cm"1 widely used for quartz characterization at room temperature is on the

side of the 3400cm

-'' Si-0 vibration and does not coincide with any

specific band, this method is not sensitive enough to evaluate Premium-Q

material. The impurity bands, which are well-resolved at 15K, can be

distinguished above the Si-0 background at 85K . Four principal bands

designated_.S

1

, S , S and S

4

with peak positions at 3349, 3396, 3438,

and 3581cm , respectively, at 85K are found in nearly all synthetic

quartz. While the band positions do not shift appreciably between 85

and15K, and vary only slightly (+ 1cm _1

) from sample to sample, wide

variations have been observed in the intensities of these bands

measured for different bars of the same autoclave run or even for

adjacent regions of a bar. Thus the s-bands are sensitive indicators

36
SARP PREMIUM-Q QUARTZ

D14-45

1. Absorption spectra taken at 300, 85 and 15K with E J_ Y for

unswept and swept Premium-Q quartz from Sawyer Research Products

autoclave run D14-45.

Note the labeled impurity bands appearing at low temperature

S-| - S4 , characteristic for synthetic quartz and e-| and e2

produced by electrodiffusion (sweeping).

37
of inhomogeneities resulting from the crystal growth process.

Sweeping ( electrodiffusion ) changes the s-band intensities very little,

but introduces two additional bands with peaks at 3306 and 3366cm - '' which have been^cjesignated e^ and . These bands are also produced

by electron or Co irradiation^'^ of unswept quartz.

The same impurity bands characteristically present in swept Premium-Q

quartz are also found in selected material classified as optical grade

as shown in Figure 2.

SWEPT PREMIUM Q QUARTZ

85- K

2. Absorption spectra for Premium-Q

optical grade quartz taken at 85K

indicating the effect of orientation

of the sample with respect to the

E-vector on the and s^ bands.

WAVENUMBER (CM- 1

)

As with other Premium-Q quartz, most of the band intensities depend on polarization. With E X Z , the So, s4 , ei and e2 bands are stronger

and S-j is weaker than with ElY, while S2 is nearly unaffected. The

S4 and bands designated in the figure which have half-widths equal

to or less than 1cm

- (instrument resolution), respectively, show the

strongest polarization. When the absorption of the same sample is

measured with infrared radiation propagating in the Y-direction and a wire grid polarizer set for E It C (E||Z), the ep band can hardly be

resolved above the background and the S4 band is very weak. With EXC,

strong absorption is observed for both bands.

The impurity absorption bands arise from interstitial H

T ions which

can assoc^a^e with a non-bonding oxygen orbital in the form of OH

molecules '

. During the sweeping process charge-compensating alkali

38
ions such as Na on Li , pnesent on purposely intnoduced into the melt,

are moved away fnom substitutional aluminum impurities by the electnic

field and are replaced by hydrogen present in the ambient gas. A

similar movement of the alkali ions can also be produced by ionizing

radiation at sufficiently high temperatures^'^.

Widely different e2 band intensities resulting for samples swept com- mercially by the same process^ has led to the conclusion that the

strength of this band is principally determined by the initial substitutional aluminum concentration in the quartz. The results of an investigation in progress on samples with identical initial infrared

spectra and more uniform aluminum concentration to determine whether

changes in e-band strength are sufficiently sensitive to monitor the

sweeping process will be presented. Also the use of e-band intensity

as a possible indicator of the extent of radiation hardening of

oscillator quartz will be discussed.

References

1. D.B. Fraser, Physical Acoustics , Vol 5, W.P. Mason, Editor, Academic Press, New York, pp. 59-110; J.C. King, U.S. Patent 3,932,777

(1976)

2. B. Sawyer, IEEE Trans. Sonics and Ultrasonics SU-19 , 41 (1972).

3. H.G. Lipson , F. Euler, and A. Armington, Proc . 32nd Annual

Symposium on Frequency Control, 11(1978).

4. R.N. Brown and A. Kahan , J. Phys . Chem. Solids, 36, 467(1975).

5. H.G. Lipson, F. Euler and P. A. Ligor, to be published in Proc.

33rd Annual Symposium on Frequency Control (1979).

6. A. Kats, Phillips Research Reports, 17, 133(1962).

7. D .M . . Dodd and D.B. Fraser, J. Phys. Chem. Solids, 26, 673(1965).

8. J. J. .Martin, L.E. Halliburton, M. Markes, N. Koumuakalis, W.A.

Sibley, R.N. Brown and A. Armington, to be published in Proc. 33rd

Annual Symposium on Frequency Control ( 1979)

.

The author would like to thank Mr. F. Euler fo( r helpful discussions.

39
FAR INFRARED STUDY OF THE REFLECTION SPECTRA OF SnS

D. G. Mead*

Nicolet Instrument Corporation, Madison, WI 53711

H. R. Chandrasekhar+ Dept. of Physics, University of Missouri -Columbia, Columbia, MO 65211

Tin sulphide SnS is a IV-VI semiconductor possessing an orthorhombic

structure with eight atoms per unit cell forming double-layer planes

normal to the c(longest) axis.l Thus, SnS cleaves very easily in a plane perpendicular to the c-axis, suggesting a weak inter-layer bonding. Unpglarized infrared transmission and power reflectivity spectra

of SnS, ' polarized infrared and Raman^ have been reported and lattice

dynamical calculations 5 investigated.

The reported polarized infrared power reflection spectra^ were analysed

by means of a Kramers-Kronig (KK) relation and the infrared active

transverse-optic (TO), associated longitudinal phonon frequencies and

the dielectric constants determined for all three principal directions.

A similar analysis was also carried out for isomorphs SnSe^, GeS^ and

GeSe^. For GeS^ the widely used formula of the damped classical oscillator (see eq. 1, ref. 6) was fitted to the reflectivity data to yield

the position, strength and damping constant of each oscillator. No

such analysis was reported for SnS and SnSe^ or GeSe 5 . It is evident

from the oscillator fits to GeS^ that only poor agreement between the

calculated and experimentally observed spectra were obtained. The fit

presented for the electric vector Ej |c_ was found to be substantially

worse than for E_||a_and Ej |b directions .

6

As part of an investigation to accurately determine the far infrared

optical constants of GeS and its isomorphs. we have re-examined the

polarized power reflection spectra of SnS.

In view of the failure of the classical oscillator fit to GeS, we have

attempted to fit the reflectivity data of SnS with the aid of a four

parameter dispersive model based on the factorized form of the complex

dielectric function. 9 ,10

N Q

2

. • - a) 2 - iy, „ -co £ (u))= £

, (aJ )+ie"(a))=e00 n —^

(1)

j = l Q

2 - ej 2

- l'y w Toj Toj

Here ^Toj> fi l_oj> YToj > Y|_ch are tne frequencies and dampings of the TO

and LO modes of the jth oscillator. Eq. 1 has been shown to have se- veral advantages ,8,9 including the fact that the model equation allows

the damping constants yjio anc' YjLO ^° nave se P ara te identities so that

40
fits may be made to reflection features having wide bands, as found in

SnS. A non-linear least-squares minimization algorithm to fit the ex- perimental data was used.H Table 1 lists the resulting fit parameters.

The value of the static dielectric constant is given by:

N w

2 Loj

.

3=1

w Toj

and are shown in Table 1, including the corresponding mode frequencies

and dielectric constants obtained from a KK analysis. ^ Table I indicates that the mode frequencies and dielectric parameters are in overall

good agreement with those obtained from the KK analysis. However, for

the Ej |c_ polarization there is a discrepancy outside the range of experi

mental error. The LO fit frequency situated at 215.9 cm

- l lies well

outside the estimated frequency obtained from the KK results. Fig. 1 shows the oscillator fit (solid line) to the observed data for E_[ |c_ obtained with the relevant parameters of Table 1 inserted in eq. 1. Discrepancies outside the range of experimental error are particularly no- ticeable in certain regions surrounding the two prominent reststrahl

bands. Hence, model eq. 1 cannot adequately describe the power reflection for this particular orientation and so allow the dielectric function to be obtained.

It was decided to obtain directly the experimental 300K complex reflection (amplitude and phase) coefficient for the same orientation using a dispersive Fourier Michelson interferometer, 1^ to enable the complex

dielectric function to be experimentally obtained without the need for

any theoretical models or devices. Sample preparation and polishing

techniques have been given elsewhere^ except that the b face used (surface area -0.16 cm2) was polished flat to less than 0.3ym to avoid distortions of the phase coefficient 0 occurring. The amplitude coefficient (the square root of the power reflection coefficient) revealed

essentially the same features as in Fig. 1 and is not given here. The

measured phase reflection coefficient is shown over the 80-400 cm

- l re- gion in Fig. 2. The phase rises slowly, then descends very quickly at

-280 cirri where the amplitude coefficient fal 1 s to a small value (-0.1).

The resulting complex (real e

1 and imaginary e" part) dielectric function using standard formulae are shown in Fig. 3. The TO and L0 frequencies were derived from peaks in the associated energy loss functions

and are given in Table 1. The results support the KK calculated mode

frequencies. ^ The imaginary part e" spectrum reveals an asymmetric line

shape particularly on the high frequency side of TO3. Model eq. 1 implies a constant damping factor while an asymmetric line shape suggests

a more sophisticated model is necessary which includes a frequency dependent damping function.

Finally, with typical carrier concentrations ofp-10^/cc. expected for

SnS compounds, it has been speculated that coupled pi asmon-phonons modes

are present. 13 Hughes et al 13 have suggested that SnS exhibits a plasma

edge at about 280 cm-l, since the reflectivity data do not conform to

41
pure phonon behaviour. (Our attempt to account for the reflection spectrum by imposing a secondary oscillator positioned at -280 cm~l in eq. 1 resulted in much poorer agreement with the experimental data). However,

eq. 1 allows for a system of coupled plasmon-phonon modes by setting one

of the 9,jQ frequencies to zero. This procedure has been recently used

to explain the reflectivity data of GaAs,l 4 >15 CdTe 15 and Ti02i_ x

* Modified eq. 1 included the plasma frequency ftp, the plasmon damping yn

and the damping Yo at zero frequency. The parameters of the coupled LO

modes are given in Table 1, and resulted in an overdamped plasmon present at 164 cm-1. Identical TO modes were found to those obtained from

eq. 1. Agreement between the fit and experimental data was excellent

up to -220 cm-1, but the phonon-plasmon model could not account for the

high frequency side of the spectrum, and shows the disadvantage of model

fitting for obtaining the optical properties.

References

1. OKAZAKI , A., J. Phys. Soc. Japan 13_, 1151 (1958).

2. NIKOLIC, P. M. et al., Proceed. XII Int. Conf. on Phys. of Semiconductors, Stuttgart, 1974, Ed. PILKUHN, M. H., p. 331 (unpublished).

3. HAAS, C. & CORBEY, M. M. G., J. Phys. Chem. Solids 20, 197 (1961).

4. CHANDRASEKHAR, H. R. , HUMPHREYS, R. G., ZWICK, U. & CARDONA, M.

,

Phys. Rev. B15, 2177 (1977).

5. FREY, A., Thesis, University of Stuttgart (1977), unpublished.

6. WILEY, J. D., BUCKEL, W. J. & SCHMIDT, R. L. , Phys. Rev. B13, 2489

(1976).

7. CHANDRASEKHAR, H. R. & ZWICK, U., Solid State Commun. 18, 1509

(1976).

8. The original experimental data from ref. 4 was used for this investigation.

9. BERREMAN, D. W. & UNTERWALD, F. C, Phys. Rev. 174, 791 (1968).

10. GERVAIS, F. & PIRI0U, B., J. Phys. C7, 2374 (19747.

11. BROWN, K.L. & DENNIS, J. E., Numerische Mathematik 18, 289 (1972).

12. MEAD, D. G. & GENZEL, L., Infrared Phys. 18, 555 (1978).

13. HUGHES, 0. H. et al . , Phonon Scattering in Solids, p. 312, Plenum

Press (1976).

14. KUKHARSKI I , A. A., Solid State Commun. 13, 1761 (1973).

15. PERK0WITZ, S. & THORLAND, R. H., Solid State Commun. 16, 1093

(1975).

16. BAUMARD, J. F. & GERVAIS F., Phys. Rev. B15, 2316 (1977).

*Work performed in part at Max Planck Institute fur Festkorperforschung,

Stuttgart, West Germany.

+A. P. Sloan Fellow

Acknowl edgement

We are grateful to Prof. L. Genzel for use of the facilities at M.P.I.

42
Fig. 1

200 FREQUENCY (cm-1

)

200 300 FREQUENCY (cm-1

)

E a

TO

Table 1

LO YTO Y

LO

1. 99-0 105.9

(99) (10T)

8.2

2. 177. 8 213.3 9-6 6.1 29.0 11.2

(178) (215)

3. 220.2 276. 15 1* 7.8 29.2

(222) (277)

(32+1+) (1U+2)

E| |b 1. 1U5.1 265.3 7.8 30.5 UU.5 13.3

(1U5) (265) (U8+5) (16+2)

Fig. 2

200 300 400 FREQUENCY (cm-')

1. 67.5 68.0 3.2 U.U

(69) (71)

2. 189.I* 215.9 6.2 19.0 29.6 12.7

(188) (193) (32+U) (16+2)

*189.0 *193.0

3. 216.8 288.2 15.7 23.3

E| |c_ (220) (289)

*219.0 *288

COUPLED LO MODES

219.3 8.3

286.1 8.1

PURE PLASMON PARAMETERS

% = 16U Y

p

= 828 yq = 832

Fig. 3

43
INFRARED ABSORPTION IN HIGHLY TRANSPARENT

CUBIC ZIRCONIA

Bernard Bendow, Herbert G. Lipson and Robert C. Marshall

Solid State Sciences Division, Rome Air Development Center

Hanscom AFB, MA 01731 USA

Didier Billard

Centre de Recherche sur la Physique des Hautes Temperatures

CNRS, 45045 Orleans Cedex, FRANCE

Cubic zirconia possesses an unusual combination of properties which

make it attractive as an optical material for a variety of applications tit is very hard, has a very high melting temperature, resists

chemical attack and is an excellent insulator. It is readily doped

with various rare-earth and transition-metal ions to provide a wide

range of potential laser-host materials. The purpose of the present

work is to investigate the absorption characteristics of yttriastabilized cubic zirconia in the highly transparent regime from approximately 1500 to 2300 cm~l, at temperatures ranging from 85 to 1000°K.

The present measurements constitute the first detailed analysis of

absorption in the highly transparent (three to four phonon) regime of

zirconia

.

The crystals utilized for this study were produced at RADC employing a relatively new process called "skull melting", in which the melt is

contained within a solid "skull" of identical composition-'-. This procedure minimizes difficulties with reaction and contamination encountered in conventional crucible-type growth. Heating is accomplished by

coupling RF energy to zirconium metal placed into the charge. Crystals

are finally obtained by preferential freezing of the melt when the crucible is slowly lowered through the coil. The yttria-stabilized crystals obtained in this way possess hardness ~ 1370 Knoop, density

5.9 gm/cm^, thermal conductivity ~ .018 W/cm/°C and visible refractive index ~ 2.15-2.18. The yttria concentration varied from around

twelve to twenty-five weight percent. The detailed frequency (co) and

temperature (T) measurements described below were performed on samples

containing fifteen weight-percent yttria, with thickness ranging from

approximately .2 to 1.3 cm.

The absorption coefficient ( a ) was deduced from transmission spectra

obtained utilizing a Digilab FTS-14 Fourier spectrophotometer operated

in the double-beam mode using a dry nitrogen gas atmosphere. For the

low temperature measurements, the sample was clamped against an indium

ring in contact with the coolant reservoir of a dewar positioned close

to the focal point of the spectrophotometer sample compartment. Elevated temperature measurements were made in a small furnace placed in

the same position. Temperatures were measured with a Cu-constantan

44
thermocouple in contact with the polished face of the sample. Absorption values were determined in the usual fashion2 from measured values

of transmittance and reflectivity.

Typical results for the absorption coefficient as a function of w and

T are indicated in Figs. 1 and 2. The spectra in Fig. 1 display a near

exponential decrease with increasing frequency, behavior characteristic

of intrinsic multiphonon absorption 3

. Only weak structure (shoulders

in the 1900-2100 cm~l region) is evident, consistent with the multiphonon

spectra of other ionic materials 3 . Raman and Reststrahlen spectra4 indicate fundamental optical vibrations spanning the 350-700 cm

-1 regime,

which suggests that the shoulders arise from three to four phonon combination processes involving these strong vibrations. To gain more insight regarding the average number of phonons involved, and to corroborate that the absorption is due to intrinsic multiphonon processes, it

is useful to analyze the T-dependence of a over a range of frequencies

(see Fig. 2). In regimes where the absorption is nearly exponential,

a may be represented by the approximate formula^

a(x,y) = a

oe~^[N(y)+l] X/[N(xy)+l]

x = w/oo , y = -ha) A„T o

1 o B

where N is the Bose-Einstein function, and co0 is an appropriate average

optical frequency. The solid lines in Fig. 2 indicate a fit to the

measured data obtained with w = 480 cm-1 ,^A = 7.4xl0-3

, ot Q=2.2 x 10 5

. The agreement between theory and experiment is quite good, with expected

departures due to deviations from exponential frequency dependence. The

value utilized for ojq

is consistent with IR data for the fundamental

regime, which reveal a broad peak in the range 400-550 cm~l. We conclude, then, that the present data span a range of approximately 3 to

4^ phonons (on the average) , with the shoulder occurring in the 4-4 1/3

phonon regime. We have also performed preliminary measurements at

higher temperatures 600-1000°K, which indicate similar trends to those

displayed in Fig. 2. Detailed analysis of measurements in this temperature range are currently in progress.

In order to assess the effect of yttria concentrations on the absorption

in the highly transparent regime, we have measured the room temperature

spectrum for a series of samples with different yttria concentrations

varying from twelve to twenty-five weight-percent. The data display

relatively small shifts (typically 10-30 cm""l) of the absorption edge

in the 1600 to 2000 cm~l range. It therefore appears that the dominant

contribution to the absorption in this regime stems from zirconia, with

only a minor contribution from the yttria.

The authors thank P.D. Gianino for assistance with the numerical

computations

45
1. See, for example, D. Michel et al, Jour. Crystal Growth 43 , 546

(1978) and references therein.

2. See, for example, H. Lipson et al, Phys. Rev. B 13, 2614 (1976).

3. B. Bendow, in "Solid State Physics", H. Ehrenreich et al, eds

(Academic, NY, 1978), Vol. 33.

4. C. Perry et al, in Proc. of Sixth Intrnl Conf. on Raman

Spectroscopy, Vol 2.

5. B. Bendow, Appl. Phys. Lett. 23, 133 (1973).

46
1

0

\\ w

v\\

Fig. 1. L °g|Q °^ the absorption

coefficient oC measured in cm \ vs frequency U) for cubic zirconia at

various temperatures indicated

\\ \ 585 in the figure.

- CUBIC ZIRCONIA

i i i

\\ 490

\ 300

80

i 1.4 1.6 1.8 2.0 2.2 2.4 00 (103 cm~1

)

Fig. 2. Absorption coefficient Ql vs temperature T for cubic zirconia.

The discrete points are measured

values and the solid curves theoretical predictions.
THE TEMPERATURE DEPENDENCE OF THE OPTICAL ABSORPTION OF METALS*

Michael Bass, David Gallant and Susan D. Allen

Center for Laser Studies

University of Southern California

University Park, Los Angeles, California 90007

The temperature dependence of the optical absorption of metals must be

determined in order to throughly understand the optical properties of

metals and the interaction between intense laser light and metallic

surfaces (1,2). In this paper results are presented for three metals

(Mo, Al and 1018 steel), at two wavelengths (10.6 and 1.06 ym) , and over the temperature range from room temperature to 600 C. These

experimental parameters were selected because: 1, laser metal working

most often employs either 10.6 and 1.06 ym lasers for these and similar

materials, and 2, these combinations of metals and wavelengths might

aid in testing the applicability of the Drude-Lorentz model for the

optical properties of metals (1) . The model predicts nearly equal

room temperature absorptions at 10.6 and 1.06 ym while the experimental results show that at 1.06 ym the absorption is ^10X larger

than it is at 10.6 ym. A linear fit can be used to approximate the

Drude-Lorentz prediction for the increase of absorption with temperature based on measurements of the dc conductivity. This behavior is

experimentally observed for Fe and Mo at both wavelengths and Al at

10.6 ym. However at 1.06 ym the absorption of Al decreases with increasing temperature.

Laser calorimetry was used to measure the absorption as a function of

temperature (3) . The samples were polished conventionally with the

final finish obtained using Linde A polishing compound. Polished

samples were placed in a thermally isolated mount in an evacuable

quartz chamber with an NaCl window. This window permitted both 10.6

and 1.06 ym laser energy to irradiate the sample. The chamber was evacuated to pressures of <2 x 10-

^ T using an oil free pumping system

consisting of LN2 sorption pump and an ion pump. With this system,

the sample could be heated to 600 C in a radiant heating oven with no significant surface contamination or decomposition.

Thermocouples (0.8 mm diameter chrome 1-alumel) were attached to the

sample to measure its absolute temperature when irradiated relative to

a reference sample. The heating and cooling curves obtained with the

differential thermocouple pair were analyzed by the "three slope"

method (3) to obtain the fractional power absorbed at each temperature.

Figure 1 shows the results of such an experiment for Mo at 10.6 ym.

The experimental and theoretical results are summarized in Table I.

48
The Drude-Lorentz calculations were performed using the formlism of

Ref. 1 and the dc conductivity versus temperature data found in Refs.

4 and 5. On the basis of the Drude-Lorentz model the room temperature

absorption at 1.06 ym of these metals should be approximately equal

and the absorption should increase linearly with increasing temperature .

The experimental results show that the absorption at 1.06 ym is, in

general, £10X that at 10.6 ym. In part, these differences may be

attributed to the role of interband transitions in these metals near

1 ym. In any case, it is evident that the Drude-Lorentz formalism is

not applicable to these materials at 1.06 ym. For Fe and Mo, the

predicted linear increase in absorption with temperature is observed

at both wavelengths. For Al , however-, the 1.06 ym absorption de- creases as the temperature is increased. This type of deviation in

the sign of da/dT from the Drude-Lorentz result was observed by

Decker in measurements of the temperature dependence of the reflecttivity of vacuum deposited Ag films at 1 and 4 ym(6) . At 10 ym,

the Ag films behaved as the calculations predicted. However, both

Decker (6) and Wieting(7) found Al films have positive da/dT for

wavelengths from 1-20 ym. Further studies will be conducted using

laser calorimetry and more ideally finished samples in order to re- solve the disagreement between the properties of bulk surfaces and

films of Al . In addition measurements of a and da/dT for Ag will be

carried out.

0.06r100 200 300 400 500 600 700

TEMPERATURE (°C)

Fig. 1. The 10.6 ym absorption of Mo versus temperature. The X's are data points obtained during heating and the 0's are points obtained as

the sample cooled down to room temperature. The straight line is a least squares fit of the data.

49
TABLE I

Metal

1018 Steel at:

10.6 ym

1.06 ym

Molybdenum at:

10.6 ym

1 . 06 ym

Aluminum at

:

10.6 ym

1.06 ym

Drude-Lorentz Model

anm (%) da/dT (%) RT

3.4

4.6

1.3

1.4

1.0

1.0

9.2

3.8

x 10

x 10

-3

-2

3.6 x 10

5.5 x 10

= 3 = 3

3.1 x 10

5.2 x 10

-3

= 3

Experimental Results

aRT (%) da/dT (%) ( C)

2.3

22.6

2.0

19.7

.1.4 20.0

5.5 x 10

1.1 x 10

-3

-3

4.5 x 10

1.4 x 10

-3

-2

1.9 x 10

-9.2 x 10

-3

-3

Temperature Dependent Absorption of 1018 Steel, Mo and Al

The Drude-Lorentz Model gives results that have been approximated by

at least squares fit straight line. For each metal, the experimental

data has been fit with a straight line, as shown in Fig. 1 for Mo.

REFERENCES

1. T.J„ Wieting and J.T. Schriempf, "Free Electron Theory and Laser

Interactions with Metals", Report of NRL Progress, June 1972,

Naval Research Laboratory, Washington, D.C.

2. M. Sparks and E. Loh, Jr., J. of Optical Soc. Am. 69, 847 (1979)

M. Sparks and E. Loh, Jr., J. of Optical Soc. Am. 69, 859 (1979).

3. M. Hass, J.W. Davidson, P.H. Klein and L.L. Boyer, J. Appl . Phys.

45 , 3959 (1974)

.

4. "Handbook of Thermo-Physical Properties of Solid Materials" Vol. I,

A. Goldsmith, T. Waterman and H. Hirschorn, eds. (McMillan Co.,

New York, NY, 1961)

.

5. P.R. Pallister, J. of the Iron and Steel Institute (1957).

6. D.L. Decker and J.M. Bennett, SPIE Proceedings 140 , 32 (1978),

and D.L. Decker "High Energy Laser Mirrors and Windows", Semi—

Annual Report No. 4, Sept. 1973 - Mar. 1974, D-ARPA Order No. 2175

pp. 66-83.

7. T.J. Wieting, Bull. Am. Phys. Soc. 19, #1, 92 (1974)

T.J. Wieting, Bull. Am. Phys. Soc. 19, #3, 339 (1974).

^Research supported by Office of Naval Research through Selected

Research Opportunities Program, Contract No. N000 14-79-C-0896.

50
THE STATISTICAL DESCRIPTION OF OPTICAL INHOMOGENIETIES

E. L. Church

US ARRADCQM

Dover NJ 07801

Index horaogeniety is an iaportant attribute of optical materials, which

is usually tested by interferometry ; that is, by measuring the wavefront distortion, £>tp

p induced into a plane wave traversing a slab of

material. Results are described in terms of an average index fluctuation per unit thickness, = S^/kT (i)

mapped over the interferometer field Here T is the slab thickness and k = 2T("/A«

A representative value is $n = 10"^, which, for T = 2.5 cm, corresponds

to a wavefront distortion of A/25 at HeNe wavelengths. Distortions of

this magnitude decrement the Strehl intensity factor by ~ 6%. Effects

of this magnitude are important for high-performance optics, especially

in multi-element systems.

In principle, it is possible to reconstruct the distribution of the inhomogenieties in a volume of material by multiscan interferometry , similar to CAT scanning ^2^. Both the single- and multi-scan methods lead

to a deterministic output which provides the basis for judgement of the

quality of the sample under test.

This paper explores the description of the optical inhomogenieties in

statistical terms, which may provide a more general basis for quality

control and specification. Interest is also prompted by the increasing

availability of "digital" interferometers capable of performing on-line

analysis, and recent advances in the analogous area of surface-finish

specification [3^ .

The optical properties of an element involving random fluctuations generally depend on the second-order statistics of those fluctuations.

Here the natural second-order statistic is the index covariance function, which describes the spatial distribution of the index fluctuations within the sample. ^To define this quantity, write the index of

refraction at any point 71 within the three-dimensional sample volume

as the sum of an average "n" and a local fluctuation Sn:

mix) = 7a +- sm(7o • (2)

For the present discussion we take the medium to be statistically isotropic, homogeneous, and stationary. The index covariance function is

then the scalar quantity: _^

Cna(t) = <S/tiU+t)-SffW/0> (3)

51
where denotes the ensemble average and t is the lag parameter.

The gross features of Cn are characterized by "height" and "width" parameters, <J" n and tn ; the rms magnitude of the index fluctuations and

their correlation length, respectively. Specifically, (T~ n

^ - Cn (0)

and t n is the first root of C n

(t n) = Cn(0)/e.

The phase of the transmitted wavefront, If , can also be written as the sum of two terms; the first corresponding to the average medium and the

second to the fluctuations arising from the index fluctuations. The

relevant statistic is the phase covariance function:

C,p(t) -S4>(t)> > (4)

where s is the position vector in the two-dimensional interferometer

field and t is again a lag parameter. This covariance function may be

calculated directly from the measured wavefront distortion, although in

practice it is only possible to measure over a limited range of t.

The phase covariance is related to the index covariance via the wave

equation applied to a particular model. In the usual geometricaloptics limit, the result for a slab geometry is easily seen to be:

The problem is now this: Given a measurement of C ^ (t), which obviously depends on the slab thickness T, how do we deduce Cn? The point of

determining C nis that it is an intrinsic property of the medium, and once obtained, can be plugged back into Eq. (5) or its equivalent for

another geometry to determine the optical properties of an element made

of the same, or statistically equivalent, material.

Equation (5) is an integral equation for the unknown function Cn , which

can be solved in closed form. Here, however, we indicate the physics

involved by examining two natural limiting cases: the thin- and thicksample limits.

In the thin limit, T«tn , where the slab thickness is much less than

the index correlation length, Eq. (5) reduces to

CyLt) = (kT fc^(t) ' (6)

That is, the index and phase covariances are proportional. At the zerolag point, t = 0, this leads to a simple relationship between the rms phase and index fluctuations:

cr^ = kT<rm > (7)

which is a precise version of Eq. (1).

In other words, in the thin-sample limit, the rms phase fluctuations

scale as the first power of the sample thickness.

52
In the opposite, or thick-sample limit, T»tn , where the slab thickness

is greater than the index correlation length, Eq. (5) reduces to

C(f (t)=2fe

IT^^^Cm

(X) • <s)

This states that the phase covariance is the Abel transform or half integral of the index covariance. The inverse is the ha If-derivative relationship:

00 dLx dL

(9)

In general, there is little resemblance between the analytic expressions for Cn and C^in this limit.

For example, the exponential index covariance:

Cm (t) =G^* EXP(-t/tm )

•> (10)

corresponds to the thick-sample phase covariance

(t) = £k*TG^t„ [w.K,<U>] > (ID

where u = t/tn and is a modified Bessel function £4].

When Eq. (5) and its inverse are evaluated at zero lag, they relate the rms fluctuations in one domain to the covariance function in the other.

In the thin-sample limit the measured phase variance is proportional to

C n (0). In the thick-sample limit it is proportional to the area of Cn : (T^ = (o) = Z^Ct ^dX Cm

CX) • (12)

Note though, that the area of any simple form of Cn is proportional to

the product <Tn

2tn» so tnat , ay = # kcrm vUT • (13)

Here ff is a number of the order of unity, the precise value of which

depends on the form of Cn . Examples are easily generated.

In other words, in the thick-sample limit the rms phase fluctuations are expected to scale as the square root of the sample thickness.

What happens when the sample is neither thin nor thick? That is, when

the thickness parameter Z = T/tn falls between the limits of 0 and 00

considered above. This region can be explored using the general solution of Eq. (5), a Gaussian form for Cn (for which Eq. (5) can be

evaluated in closed form) , or by perturbation expansions.

Here we examine the Z dependence of Eq. (5) at the particular point

t = 0, where it becomes an expression for the measured phase variance:

53
o>

z = C ¥ (°) -£kl T^d.x (i-x/T)Cm

(x) • oi,)

The transition of this expression between the thin- and thick-sample

limits has been explored using different forms for Cn : a Gaussian, an

exponential, and a Lorentzian. The ratio of the phase variance for arbitrary thickness to that for infinite thickness is found to increase

rapidly as Z*- for Z = 0 to 1, but to approach unity only slowly, as Z"*-,

Values of Z = 6 - 20 are required to reach a ratio of 0.9.

Another important relationship is that between t^and tn

. In the thinsample limit tq>/tn

= 1 for any form of Cn , as shown by Eq. (6). In

the thick-sample limit, however, the relationship depends on the form

of Cn , as shown by Eqs. (8) and (9). For the three cases considered

above, direct evaluation gives ty/tn

= 1.0, 1.7 and 1.9, respectively.

Taken together, these results suggest that T^ t q> /2 and T > 20t^ are required to ensure the practical applicability of the thin- and thicksample results, Eqs. (6)-(7) and Eqs. (8)-(13), respectively.

SUMMARY

This paper discusses the relationship between interferometric measurements of an inhomogeneous optical medium and the statistics of its index fluctuations. It is hoped that these results will focus interest on experimental studies of this method of materials characterization.

Subjects not covered in this Summary are the validity of the underlying

physical and statistical assumptions, the practicality of obtaining

sufficient and sufficiently accurate data for analysis, and bandwidthlimit effects such as those which appear in the related analysis of

random surface-height fluctuations L^l.

ACKNOW LEDGEMENTS

I thank Dr. H. E. Bennett at the Naval Weapons Center for drawing attention to the importance of index inhomogenieties on system performance,

Dr. J. A. Cochran at Washington State University for his inversion of

Eq. (5), and Dr. J. M. Zavada at ARRADCOM for helpful discussions.

REFERENCES

1. F. W. Rosberry, App. Opt. £ 961 (1966); F. E. Roberts and

P. Langenbeck, ibid. 8 23lT (1969).

2. R. D. Matulka and D. J. Collins, J. Appl. Phys. 42 1109 (1971);

D. W. Sweeney and C. M. Vest, App. Opt. 12 2649 (1973).

3. E. L. Church, H. A. Jenkinson and J. M. Zavada, Opt. Engineering

18 125 (1979); E. L. Church, J. Opt. Soc. Am. 69 1404A (1979).

4. Tables of Integral Transforms , Vol. 2 (McGraw Hill Book Company,

1954). A. Erdelyi Ed.

54
PHOTOCONDUCTIVITY AT 77K IN UNDOPED TELLURIUM

N.G. Shyamprasad, C.H. Champness and I. Shin

Electrical Engineering Dept. , McGill University,

3480 University Street, Montreal, Canada H3A 2A7.

1. Introduction Apart from the potential of tellurium as an infrared

detector material [1] between 3 and 4 ym wavelength, there is a need for

better characterization of photoconductivity in this substance. This is

especially so in crystals with a minimum of imperfections, since tellurium is known to be very sensitive to lattice damage. Arising from the

high quality crystals grown in our laboratory [2] by the Czochralski

method, the present work was carried out. It consisted of a study of

the wavelength and thickness dependence of the photoconductivity in

monocrystalline undoped tellurium samples at 77K. Some preliminary

results on polycrystalline thin film samples are also reported.

2

.

Samples The bulk samples were cut using a solvent saw [3] from

single crystal ingots, pulled in the c-direction from melts of high

purity undoped tellurium. The dimensions of the samples are given in

Table I and the orientations are illustrated in Fig. 1. Transport measurements showed such samples to be intrinsic at room temperature but ex- trinsically p-type at 77K. Three thin film polycrystalline samples were

also prepared by evaporating tellurium on Pyrex slides on which gold end

and side electrodes had been previously sputtered.

3. Method of Photoconductivity Measurements The samples were mounted in

a dewar with an IRTRAN 2 window. Monochromatic polarized light at wavelengths between 1 and 4.5 microns and chopped at 13 hertz from a Perkin

Elmer model 13 spectrophotometer was focused on to the sample, maintained at 77K. The voltage change across the sample was measured using

a lock-in amplifier. The intensity level at each wavelength was determined from the vacuum thermopile detector within the monochromator

.

4. Experimental Results Plots of photoconductive sensitivity against

wavelength (A) are shown in Figs. 2 and 3 for a set of samples cut with

the longest dimension (i.e. the direction of bias current) parallel to

the c-axis, see inset. The ordinate is Aahv/(a J), representing the

relative conductivity change per incident photon. Here, Aa is the photoinduced change of conductivity, a is the dark conductivity, J is the

incident energy flux at a frequency v and h is Planck's constant.

The difference between having the E-vector of the incident polarized

radiation parallel or perpendicular to the c-axis is contrasted in Fig.

4 for two samples with the same thickness. It is evident that on the

short wavelength side of the maxima the photoconductivity falls off

faster with decreasing X for Ej.c than E//c. This was observed previously by Grosse and Winzer [4]. Similar results were obtained on samples

55
Bulk Samples used in Photoconductivity HeaeureaentB

Saaple no. Dimensions (mm) Orientation

Length Width Thick. Bias curr.

to c- a x 1 s Plane of lllua.

CZ-77-1 Ik 9 1 .8 parallel ( i olo

)

CZ-77-1/B 8 2.0 0.25 perpend. ( i oTo

)

CZ-77-1/C 8 1.9 perpend. (0001

)

CZ-76-10/A 8 2.1 parallel (1010) CZ-76-10/B 7 2.5 U.BO perpend. ( i oTo

)

CZ-76-10/C 8 2.0 perpend. (0001

)

CZ-76-20/A2 9 1 .8 parallel (1010) CZ-76-20/B2 8.5 1.9 1 .20 perpend. ( l oTo

)

CZ-76-20/C2 9 1.7 perpend. (0001

)

CZ-76-20/A1 9 2.0 parallel (ioTo) CZ-76-20/B1 10 1 .8 2 .20 perpend. ( l olo

)

CZ-76-20/C1 10 1.7 pe r pend

.

(0001

)

A

-nxis

B

n-nxis

Fig.l Orientation of samples chemically cut from Te crystals.

WAVELENGTH ( u ) Fig. 2 Photoconductive photon

sensitivity, La/ (a J ) , for

E-vector parallel ?oP

c-axis of

4 bulk Te samples cut with

orientation shown in the inset.

r

O CI-77-l/fl * CI-76-10/S C7-76-20/B2 0 CZ-76-20/BI

WAVELENGTH ( m 1 Fig. 3 Photoconductive photon

sensitivity, Aa/( a0

J

Dh )' for

E-vector perpendicular to c-axis

of 4 bulk Te samples cut with

orientation shown in the inset.

56
cut in the other orientations shown in Fig. 1 but, within the reproducibility of the data, no dependence of photoconductivity on current

orientation was observed.

The effect of sample thickness (d) is brought out more clearly in Fig. 5,

which shows photoconductive sensitivity Aa/ (a J) at X = 2ym plotted

against d. For the bulk samples (Ej_c) , the photoconductivity increases

with decreasing thickness, at least down to 0.25 mm. On the other hand,

results for the thin film polycrystalline samples indicate a slight

decrease with decreasing thickness.

5 . Theory The relative change of conductivity under a photon flux

J = J/hv can be shown, with certain assumptions, to be given by:

y + y J x Ag _ n p ph

°o

=

yPP

od 1"K

2 L

2 i

- exp(-Kd) + KL

(KL-a) exp(-Kd)- (KL+a)

1 + coth(d/2L)

(1)

where a = sL/D, s is the surface recombination velocity, L the diffusion length, D the diffusivity, x the lifetime, K the absorption co- efficient, yn the electron mobility, the hole mobility and pQ the

extrinsic equilibrium hole concentration.

y + y J

(i) Thick Sample If d»l/K&L, eq. (1) gives: = — 2- -ES.

, (2) a y p d

o p o

so that the photoconductivity varies inversely as sample thickness.

Aa y + y

(ii) Thin Sample If d «1/K & L, eq. (1) gives: = — ^- KJ x , (3)

if s = a=0, so that photoconductivity is thickness independent,

/ever, if s > 0 , consideration of i increases weakly with increase of d.

However, if s > 0 , consideration of equation (1) shows that Aa/aQ

6. Discussion and Conclusions The variation of photoconductivity with

sample thickness, shown in Fig. 5, is qualitatively in accordance with

the theory presented above. The decrease with increasing d for the bulk

samples evidently corresponds to the "thick" regime, while the slight

increase for the evaporated film samples corresponds to the "thin"

regime. The maximum response appears to lie at a thickness between 10

and 100 ym. Analysis of the spectral variations, such as those shown

in Fig. 4, indicates s-values between 1000 and 5000 cm/sec. These calculations were done using eq. (1) and taking x to be lOOy sec. A

smaller value of s for the (1010) surfaces compared with that for (0001)

surfaces, as reported by Grosse and Winzer [4], was not observed in the

present work. Absorption coefficients were calculated from the results

using eq. (1) with an assumed L-value of 3.6x10"^ cm. These results, as shown in Fig. 6, extend to lower wavelength than those of Blakemore and

Nomura [5] . The larger K-values for Ej.c than E//c are consistent with

direct photoelectron transitions across the gap for the former orientation. It is apparent from the present work that photoconductivity does

offer a convenient method of determining absorption coefficient in a

57
A-region where the large values make transmission measurements difficult.

[1] D.F. Edwards and M. Mercado, Infrared Phys. , 1, 17, 1961.

[2] I. Shih and C.H. Champness, J. Cryst. Growth, 44, 492, 1978.

[3] M.El-Azab, C. McLaughlin , C.H. Champness , J. Cryst . Growth , 28,1, 1975.

[4] P. Grosse and K. Winzer, Phys. Stat. Solidi, 13_, 269, 1966.

[5] J.S. Blakemore and K.C. Nomura, Phys. Rev. 127 , 1024, 1962.

C2-76-20/A2 1.2 HH r

£ 10'

- -

1 1 \ \\ \ \ \\i

1

W \ \\\ W w

\\ \ \V w v\ V

-

1

c

I 1 1 >

URVCLtNCTH C m I UAVELENGTH ( M 1 Fig. 4 Photoconductive photon sensi- Fig. 6 Absorption coefficient calc.

tivity, Aa/(a

Q

J ) , for two samples from photoconductive data.

of same thickness 1.2 mm, with the Curves 1,2: sample CZ-76-20/A2;

orientations E//c and Ej.c. curves 3,4: sample CZ-76-20/B2

;

curves 5,6: data of reference [53.

2h

THIN FILM POLTCRTSTBL

10"* THICKNESS (cr

10«

Fig. 5 Photoconductive sensitivity, Aa/(a J) at X=2ym plotted against

sample thickness, d. The solid line for the bulk samples (Exc)

corresponds to a 1/d variation.

58
EXTRINSIC STATES IN CINNABAR (df-HgS) GROWN

BY CHEMICAL VAPOR TRANSPORT

C. T. Simpson, W. Imaino, and W. M. Becker

Department of Physics, Purdue University

West Lafayette, Indiana 47907

INTRODUCTION

Cinnabar, the trigonal form of mercury sulfide, is a wide band-gap semiconductor whose crystal structure belongs to the space group P3i21 (D^)

[l]. Some of the interesting properties exhibited by cinnabar are a pronounced band-edge dichroism [2], a large birefringence [3], remarkable optical activity [4], and one of the strongest acousto-optic effects

observed [5], Because of the potential applications of cinnabar, it is

important to establish the nature of extrinsic states due to native defects or chemical impurities introduced during the growth process. A

further stimulus for this study is the recent observation of new Raman

modes in cinnabar grown by chemical vapor transport (CVT) [6] ; these

modes exhibit striking resonant enhancement for exciting photon energies

near the electronic transitions discussed in this paper. We have used

photoluminescence (PL), optical absorption and excitation spectroscopy

to study CVT-grown cinnabar. An understanding of the observed spectra

presents new opportunities for the characterization of this material.

EXPERIMENTAL

Both dendritic and tabular habit (TH) crystals occur in a single growth

run. As we reported previously [7], narrow spectral features were observed only in the TH crystals; we confine our discussion to these samples. The volume of TH samples ranged up to ~5 mm^ with a typical sample having dimensions 0.3 X 1 X 2 mm. The largest crystal face was bounded by the_basal plane , _c{ 0001} . Other prominent forms present were

rflOll], -r{011l], and m{ 1010} . Impurity analysis revealed that iodine,

the transport agent, was the major impurity 10^ cm~3) [7]. The photoluminescence and excitation spectra were measured on a Raman scattering spectrometer system employing various cw laser excitation sources, a double monochromator , a cooled photomultiplier detector and photon

counting electronics.

Figure 1 shows a typical PL spectrum for a TH sample when ftu^, the ex- citing laser energy, is in the range, E(X^) ^ hoi-^ < E . Three peaks,

labeled X]_ , X2 and B2 , are observed; at 22 K the peak energies are

E(Xi) = 1.872 eV, E(X2) = 1.854 eV and E(B 2 ) = 1.78 eV, with half-widths

of 3.7, 6.6 and 113 meV, respectively. In the temperature range,

20 ^ T ^ 80 K, the half-widths of X]_ and X2 increase linearly with

59
temperature at rates of 0.25 meV/K and 0.46 meV/K, respectively. At low

temperatures, T < 10 K, the half-widths appear to be temperature independent and are typically a few meV at super fluid helium temperatures.

The peak intensity of the B2 band decreases by over two orders of magnitude from 20 to 60 K. The and X2 peak intensities vary only by a factor of 3 for this same temperature range.

Figure 2 exhibits the excitation spectrum of the B2 luminescence. For

ftcjjT < E(X^) the excitation is weak. A dramatic peak in the excitation

occurs for ftu)^ — E(X^). The excitation decreases but persists for

ftuj^ > E(X^). Because the B2 excitation remains strong for ftuJL well

above E(X-^) , we conclude that a continuum of states is involved in the

excitation process. The excitation spectrum of the X2 luminescence is

very similar to that of the B2 luminescence. We conclude from this

similarity that the same excitation process is involved in the excitation of both X2 and B2.

DISCUSSION

The results exhibited in Figs. 1 and 2, together with the observation of

a sharp, asymmetric absorption at E(X^) , suggest that the X^ transition

involves a discrete state and a continuum. Resistance and Seebeck co- efficient measurements indicate that the TH CVT-grown cinnabar samples

are n-type with gp , the Fermi energy, lyings 0.5 eV below the conduction band edge. To account for the Xi PL and absorption, we postulate a donor state at ~ 1.873 eV, which we label 2 in Fig. 3. Excitation

spectra lead us to propose that the X^ , X2 and B2 PL features result

from the excitation of a valence band electron into level 2. The recom- bination of photoexcited electrons in level 2 with free holes yields the

X^ luminescence. No absorption or PL excitation can be detected for

photon energies near E(X2). For this reason, we conclude that in the TH

CVT-grown samples studied, e F lies above a state at «=- 1.855 eV, which we label 3 in Fig. 3. The recombination of electrons already occupying

level 3 with free holes generated by the photoexcitation of electrons

into level 2 yields the X2 luminescence. The mechanism we propose for

the broad B2 band is a donor-acceptor pair transition broadened by

strong coupling to lattice vibrations. As indicated in Fig. 3, the zero phonon transitions are between level 2 and level 5, or level 3 and

level 5, or both. We cannot distinguish between these two processes be- cause of the lack of structure in the B2 emission. Levels 1 and 4 shown

in Fig. 3 are used to explain PL features not shown in Fig. 1; these

features are discussed elsewhere [7,8],

The dramatic decrease in the peak intensity of the B2 band with increasint temperature can be discussed in terms of a configuration-coordinate

model. Further details of this model will be presented elsewhere [8],

The thermal broadening of the X-^ and X2 PL can be interpreted in terms

of a lifetime effect. Due to the electron-phonon interaction the ex- cited state lifetime is reduced, yielding a broadened lineshape [9,10j.

60
In order to account for the peak in the optical absorption and the excitation spectra at ftU) ~ E(X, ) , we performed a simple model calculation of

band-to-impurity absorption in cinnabar [11]. The details of this calculation will also be presented elsewhere [8], however the result which

is of importance here is that the peak is a consequence of the matrix

element between the initial and final electronic state wave functions

.

ACKNOWLEDGMENTS

This work was supported by the NSF-MRL Program No. DMR 77-23798 and the

National Science Foundation Grant No. DMR 77-27248.

REFERENCES

r m 4

[1] K. L. Aurivillius, Acta Chem. Scand. 4, 1413 (1950). P3 1 21 (D 3) is

the space group for the right-handed form; the enantiomorphic

left-handed form belongs to P3

2 21 (D^)

.

[2] R. Zallen, in II-VI Semiconducting Compounds , edited by D. G.

Thomas (Benjamin, New York, 1967), p. 877.

[3] W. L. Bond, G. D. Boyd, and H. L. Carter, Jr., J. Appl. Phys. 38,

4090 (1967).

[4] B. Ayrault, F. Lefin, H. Langlois, Y. Toudic , and J. F. Palmier,

Opt. Commun. _5, 239 (1972).

[5] J. Sapriel, Appl. Phys. Lett. 19, 533 (1971).

[6] W. Imaino, C. T. Simpson, W. M. Becker, and A. K. Ramdas, Phys.

Rev. B. (to be published).

[7] C. T. Simpson, W. I. Imaino, W. M. Becker, and S. P. Faile, Solid

State Commun. 28, 39 (1978).

[8] C. T. Simpson, W. Imaino, and W. M. Becker (to be published).

[9] K. Colbow, Can. J. Phys. 41, 1801 (1963).

[10] R. Barrie and K. Nishikawa, Can. J. Phys. 41, 1823 (1963).

[11] We follow the approach of D. M. Eagles, J. Phys. Chem. Solids 16 , 76 (1960) and W. P. Dumke, Phys. Rev. 132* !998 (1963).

61
1.90 1.85 1.80 ENERGY (eV)

1.75 1.70

1.86 1.88 1.90 1.92

-fiw L (eV)

Figure 2 Excitation spectrum (ES) of

the B2 photoluminescence peak

in the vicinity of E(X^) the

X

-L emission energy.

Figure 1 Photoluminescence spectrum of

CVT-grown cinnabar excited by

1.959 eV (6328 A) radiation.

, E(eV)

n ///A

2.275--

2.270--

.873--

.855-

0.250-

0.050

0

©

©

CB

VB

Figure 3

An energy level scheme for tabular

habit CVT-grown cinnabar. States

labeled 1-5 lie within the forbidden gap. The band continua are re- presented by cross-hatching.

62
DIFFERENTIAL REFLECTOMETRY - AN OPTICAL TECHNIQUE FOR

INVESTIGATING BAND STRUCTURE CHANGES ASSOCIATED WITH

ALLOYING, DEALLOYING, CORROSION AND ORDERING

R. J. Nastasi-Andrewst , J. B. Andrews t, C. W. Shanley*,

J. Finnegant and R. E. Hummel

Department of Materials Science and Engineering

University of Florida, Gainesville, FL 32611 U.S.A.

The differential ref lectometer measures the normalized difference

in the spectral reflectivity between two specimens mounted side by side.

The instrument is capable of determining within a hundredth of an

electron volt the energy for interband transitions of electrons.

Light coming from a monochromator is alternately scanned by a vibrating mirror across the two samples (Figure 1) . The signal from

X-Y

recorder

Figure 1. Schematic diagram of the differential ref lectometer

.

a photomultiplyer tube which picks up the reflected light from the

specimens is electronically processed to obtain the normalized_

difference in reflectivity (AR/R) . An x-y recorder plots AR/R

automatically as a function of wavelength. A scan between 200 and

800 nm requires between one and three minutes.

For studying changes in the band structure due to alloying, the

two specimens which are scanned by the light beam have a small difference

in composition (compositional modulation). Applying a line shape

analysis to the resulting differential ref lectogram, three different

63
8000 6000 £

4000 2000 2

' 3 4

' 6 E, eV

Figure 2. Differential ref lectogram of a Cu/Cu - 0.1% Al sample

pair.

transitions can be identified (Figure 2): a) A threshold energy for

interband transitions around 2.2 eV (peak A) which involves the upper

d-bands and the Fermi energy. This transition energy does not change

for solute concentrations up to approximately 1 at. %, confirming the

theory by Friedel concerning screening of solute charges at low solute

concentrations. Experimental evidence is given which suggests that

both the d-bands and the Fermi energy are raised by alloying,

b) Lower d-band to Fermi energy transitions around 5 eV (peak D)

behave in many respects similar to the upper d-band to Fermi energy

transitions, except that the lower d-bands appear to be raised much

less due to alloying. c) A conduction-band to conduction-band

transition around 4 eV (peaks B and C) was observed to decrease in

energy with alloying.

In corrosion experiments, one-half of a specimen is protected by

an insulating lacquer, while the other half is allowed to form a thin

film corrosion product . The use of a transparent lacquer permits

monitoring the film in situ. Owing to the differential nature of

the technique, the effect of the metal substrate is essentially

subtracted out, so that the resulting differential reflectogram is

related to the absorption spectrum of the corrosion product. Unique

spectra for cuprous oxide, Cu20 (Figure 3) and cupric oxide, CuO

(Figure 4), were obtained and their identities verified either by using

conventional optical techniques or by using calculated electronic band

structures. The intensity of the structure in the differential

reflectogram is related to the thickness of the corrosion film.

64
5k

Figure 4. Differential ref lectogram of CuO on copper substrate.

Differential ref lectometry studies were performed on short-range

ordering in a Cu-17 at.% Al alloy. The differential reflectogram of

a short-range ordered, versus a disordered specimen, shows a pronounced

peak at 2.64 eV which is attributed to new structure in the ordered

state. The new structure can be explained using the folding band

concept, which yields additional interband transitions. Short-range

ordering decreases the energy of peak "C" in the differential

ref lectograms by 0.04 eV. This shift is equivalent to an increase in

solute concentration amounting to one-half of a percent.

Dealloying studies of copper - 5 at. % Zn alloys (red brass)

showed that, contrary to literature reports, these alloys dezincify

similarly as yellow brass.

65
Present address:

^Present address

:

^Present address:

University of Alabama in Birmingham

Motorola, Inc., Plantation, Florida

Bell Labs, Murry Hill, NJ

Bibliography

R. E. Hummel, D. B. Dove and J. A. Holbrook, Phys. Rev. Letters, 25

(1970), 290.

J. A. Holbrook and R. E. Hummel, Rev. of Scientific Instruments, 44 , (1973), 463.

R. E. Hummel and J. B. Andrews, Phys. Rev., B8, (1973), 2449.

R. J. Nastasi-Andrews and R. E. Hummel, Phys. Rev. B, 16, (1977), 4314

C. W. Shanley, R. E. Hummel and E. D. Verink, Jr., Corrosion Science,

in press.

J. Finnegan and R. E. Hummel, Corrosion Science, submitted for

publication

.

J. B. Andrews, R. J. Nastasi-Andrews and R. E. Hummel, Phys. Rev.,

submitted for publication.

66
FREE CARRIER ABSORPTION IN SEMICONDUCTORS IN QUANTIZING

MAGNETIC FIELDS

Harold N. Spector*

Department of Physics

Illinois Institute of Technology

Chicago, Illinois 60616

Free carrier absorption in semiconductors is of interest both because

it is the dominant mechanism for the absorption of electromagnetic

radiation of frequencies lower than those which give rise to interband

transitions (i.e.,-fift<E ) and because the dependence of the free

Q

carrier absorption coefficient on photon frequency and temperature

depends critically on the dominant scattering mechanism for the free

carriers in a particular semiconductor. We have extended the theory

of free carrier absorption in nondegenerate semiconductors to take

into account the presence of quantizing magnetic fields for the case where acoustic phonon scattering is the dominant mechanism for the

scattering of the free carrier. 1 Previous work only considered the case where the electromagnetic radiation was polarized parallel to the

d.c. magnetic field and neglected the possibility of stimulated emission of photons in the semiconductor. The latter assumption is correct

if the energy of the photon is much greater than the thermal energy of

the free carriers, i.e. lift » k^T, but is not true in the reverse case. Here the theory is extended to take into account the stimulated emission of photons and to treat the situation where the radiation can either be polarized parallel (longitudinal case) or perpendicular

(transverse case) to the d.c. magnetic field. For the transverse case,

photons can be absorbed in intraband transitions between adjacent

Landau levels even in the absence of collisions of the free carriers

with phonons or impurities in the semiconductors when the cyclotron

resonance condition is satisfied, i.e., ft = u> . For the longitudinal

case, and also for the transverse case when we are on the low field

side of the cyclotron resonance frequency, absorption of the radiation

can only occur via phonon or impurity assisted transitions between

the various Laundau levels.

In a quantum theory, the free carrier absorption coefficient is calculated by relating it to the transition probability for an electron

to make an intraband transition from a given initial state by absorbing or emitting a photon while simultaneously emitting or absorbing

the phonon which is involved in the scattering process. This transition probability W.

a,e

is given by the Born, second order golden rule

approximation, 1

W.

a ' e = j£ Z|< f|M|i >|

2

6(E

f

- E. ±-fift) (1)

67
where <f|M|i> is the transition matrix element for the electron-photonphonon interaction and we have neglected the energy of the acoustic

phonons in the argument of the energy conserving delta function. This

latter approximation is valid at all except the very lowest temperatures since the electrons only interact with the very long wave length

acoustic phonons in nondegenerate semiconductors. Here E. and E f are

the initial and final energies of the carrier and -HQ is the energy of

the photon which is emitted (+sign) or absorbed (-sign). In terms of

the transition probabilities for the absorption or emission of the

photon, the free carrier absorption coefficient is given by

h

K =

f- 2 (W.

a

- W.

e

) f . (2)

where e is the dielectric constant of the material, f. is the free

carrier distribution and the sum goes over all the initial states of

the free carriers. The above expressions have to be evaluated using

the energy eigenvalues and eigenfunctions of the free carriers. For

electrons in a parabolic energy band, these eigenvalues and eigenfunctions are

E M

= (n^)fk

c + (3)

|k,n> = ax

Ly

)

_!5 exp[i(ly + k

z z)] <J> n (x-A

2

k

y

), (4)

respectively. Here ty^ are the harmonic oscillator wave functions, k

y

and k

z are the components of the free carriers wave vector in the y and

z directions, m* is the free carriers effective mass, and k = (-fic/eB)^.

Using the Landau gauge for the vector potential, we can use the eigenvalues and the eigenfunctions for the free carrier in quantizing magnetic fields to evaluate the matrix element for the electron-photonphonon interaction. Once this matrix element is obtained, it can be

used in equations (1) and (2) to evaluate the free carrier absorption

coefficient K. It is particularly simple to express the magnetic field

dependence of the free carrier absorption by expressing our results in

terms of the dimensionless ratio of the free carrier absorption co- efficient in the presence of the magnetic field to that in the absence

of the magnetic field. The reason for presenting our results in terms

of this dimensionless ratio is that all fundamental constants and ma- terial parameters, except those that come into the cyclotron resonance frequency od , cancel and therefore, this dimensionless ratio yields a universal relation for the magnetic field dependence of the free car- rier absorption which only depends on the photon frequency Q, the absolute temperature T, and the cyclotron frequency w = eB/m*c. For

the longitudinal case, this dimensionless ratio is

68
Kn

(B) 3w

K(oT~

=

1 +

nu)Q exp

exp K i^V L

" ~J/ (5)

HQ

12K

BT

while for the transverse case, this dimensionless ratio is

Kj_(B)

KToT

_3

16 x uj HI

L v c w -Q

c

nu».

coth

si nh

l2K

BT

> (6)

Q exp

V

2KB7 0 ^2K

B T

1+-

Q

In equations (5) and (6), K (x) is the modified Bessel function of

order n and argument x. The results for the longitudinal polarization

reduce to those previously obtained when the photon energy is much

greater than the thermal energy of the free carriers. In this case,

the contribution of stimulated photon emission to the free carrier absorption coefficient can be neglected as all initial states from which

stimulated emission of photons could occur have negligible population.

The absorption coefficient for this case is an oscillatory function of

the magnetic field which increases in magnitude as the magnetic field

increases. 1 The results for the transverse case are similar in that

the absorption coefficient is an oscillatory function of the magnetic

field on the low field side of the cyclotron resonance frequency. However, instead of reaching a peak value at certain values of the ratio

of the cyclotron frequency to the photon frequency as in the longitudinal case, the absorption coefficient diverges logarithmically at

these values of the ratio. The reason for this logarithmic divergence

in the transverse case is the same as for the logarithmic divergence

of the transverse magnetoresi stance in nondegenerate semiconductors 2

, namely that the collision time for the electron-phonon interaction

diverges for carriers traveling with low velocities along the magnetic

field for this configuration and the Born approximation can no longer

be used to calculate the absorption coefficient. In fact, one would

69
expect that the correct approach would be to follow a procedure similar

to that used by Arora and Peterson3 to extend the theory of the magnetoresi stance of nondegenerate semi-conductors beyond the simple Born

approximation. Such an approach has proved to be successful in calculating the cyclotron resonance linewidth in nondegenerate semiconductors. 4

* Research supported by a grant from the NSF Material Research Laboratory Program, Grant No. DMR 76-24466.

REFERENCES

1. E. R. Generazio and H. N. Spector, Phys. Rev. B (in press).

2. E. N. Adams and T. D. Holstein, J. Phys. Chem. Solids 10, 254

(1959).

3. V. K. Arora and R. L. Peterson, Phys. Rev. B 12, 2285 (1975).

4. V. K. Arora and H. N. Spector, Phys. Stat. Sol idi (b) 94, 701

(1979).

70
MULTIPHOTON ABSORPTION IN

DIRECT GAP SOLIDS

S.S. Mitra

Department of Electrical Engineering

University of Rhode Island

Kingston, R.I. 02881

Introduction

Because of the availability of high power laser sources, non-linear

absorption processes in gases and solids have been the subject of extensive investigations in recent years. This interest has been stimulated

in part by the role of non-linear absorption in laser-induced damage of

optical components, as well as by its many fundamental applications

such as determination of non-linear susceptibility, band perturbation

under strong illumination (dynamic Franz-Keldysh effect), parity and

selection rule assignments, band structure analysis in semiconductors,

etc. In this review, we shall limit our discussion to multiphoton

absorption processes in non-metallic solids.

Phenomenological Description

The multiphoton absorption can be described in a phenomenological manner

by the generalized Beer-Lambert's law:

= -I a I n (1) dx n n [?n— 3

(length)

- /

(power) n

f , I the light flux (Wm ) and x the propagation direction.

If for a given field strength and frequency the nth order process

dominates, the attenuation rate of the light flux is

- £ a I n (2) dt /e

n

oo

where c is the speed of light in vacuum and the high frequency

dielectric constant of the material . _^The relation between I and the

peak electric f^eld amplitude E

q

(Vm ), as well as the photon number

density N ^ (m ) is given by

E (e )

'2

I = u

0 / 2Z = -S -ficoN , ( 3 ) o ve ph

71
where ZQ is the vacuum impedance. Accordingly, the rate of photon

absorption per unit volume is expressed as

dN , a

ph _n jn

dt >hoj - n dN

i e dt (4)

where Ne is the density of conduction electrons created by the n-photon

absorption process. In terms of the transition rate W(= dNe ) f a i s given by dt

2nfia) (21 ) n W (E

2n

) a n/2 c 2n

oo o

(5)

Theory

The general theory of multiphoton absorption in atoms was outlined by

M. Goppert-Mayer A There are essentially two approaches to calculate

a for solids, viz., the second2,3 ancj higher-order time dependent perturbation theories, and the "dressed-state" model of Keldysh.4

By assuming that the transitions take place between Stark-shifted energy

bands, and that the wave functions are described by Houston functions,

Keldysh obtained the following expression for W

W = ( 9\) (

3/2, e

2 A

Eo 16 m* oo 2 E vc g

i

<x+l>

x (|) (2<x+l> - 2 x)'

2 P

2 e E

x exp 2<x+l> (1 =; ) 4m* oj E vc g

(6)

where x r^- and the effective band gap

e 2 E 2

E

^

= E

^ +

4m*

^go vc

(7)

72
subject to the condition

2 P

2 e co 4m* oj 2 E vc g

« 1 (8)

The photon multiplicity is given by

n = <x+l>

where < > denotes the integer part of the argument, m*^ the reduced

mass of the valence (v) and the conduction band (c) electrons. The

Dawson integral (p (z) is defined by

(?)

U) = exp (-z

2

) / e

y dy

o The transition rate for a two-photon process from the second order

perturbation theory2/3 i s given by

(10)

w d

3 1 1

H H vn nc

E (k) -/Cue vn v

6{ E (k) - 2Ku) } vc (ID

where h\.'s are the interaction matrix elements. The k integral extends

over the entire first Brillouin zone, the index n extends over all

possible intermediate states, and the delta function expresses the

energy conservation required. Braunstein and Ockman^ assumed only one intermediate state situated above the conduction band, and all three

bands were parabolic and isotropic. Depending on the symmetries of

the bands, three types of two-photon transitions were possible:

allowed-allowed, allowed-forbidden and forbidden-forbidden. Basov et

al. assumed that the intermediate states were in the valence and the

conduction bands themselves. They also used isotropic and parabolic

energy bands.

Recent Work

Mitra, Vaidyanathan and co-workers have recently critically examined the

three models. They have used both the parabolic and a non-parabolic^

energy bands, given, respectively by

vc

at) +

*

2 k

2

2m^vc

(12)

73
and E (£) = E (1 + « -| ) vc g m* E vc g

2.2 ^ (13)

Keldysh's model uses only the non-parabolic band structure (13). We

have shown that the Keldysh formula is closely related to Braunstein's

for allowed-allowed transitions, while Basov's proposed formula more closely corresponds to Braunstein's for allowed-forbidden transitions.

A number of improvements and corrections to both Braunstein and Basov

formulas will be indicated. The two-photon absorption coefficients for

several direct-gap seminconductors and alkali halides are calculated

from these formulas and compared with the available experimental data.

The formulas of Keldysh and Braunstein for describing allowed-allowed

transitions, where one considers excitonic intermediate states and

nonparabolic energy bands, are found to give results in fair agreement

with published experimental results. Basov's and Braunstein's absorption coefficients for allowed-forbidden transitions are smaller than

available experimental data by orders of magnitude.

Vaidyanathan, Guenther, and Mitra^ have recently proposed a new model that combines the elements of second order perturbation theory and

electronic energy band structure calculations. This procedure is found || j to represent a significant improvement over currently available theoretical models reviewed above. Results for CdTe, GaAs, InP and ZnSe are ; in good agreement with available experimental data.

)! 8, Keldysh model is capable of predicting the n-photon absorption coefficient for any value of n. For example, Fig. 1 shows such a calculation for PbTe for up to 4-photon transitions. In the passing, it may

be remarked that we have previously shown^ that the one-photon absorption edge in direct-gap crystals predicted by the Keldysh formula agrees

with the results of conventional perturbation theory to within a factor

of order unity. This is in contrast to the frequently stated opinion

that the Keldysh formula is incorrect or invalid when the photon multiplicity is small.

9 Kovarskii and Perlin have treated the three-photon absorption in

direct gap solids by an improved but similar model to that of Keldysh.

Bassani and Hassanl^ have presented a perturbation calculation for the

third order coefficient. Judell, Mitra, and Vaidyanathanll have used

the third-order time dependent perturbation theory to determine the

three-photon absorption coefficient for several direct-gap semiconductors using both parabolic and non-parabolic band structures.

Intermediate levels needed in these calculations are the higher energy

bands obtained from band structure calculations. The dispersion of a-j

closely follows that of Keldysh's result in shape but not in magnitude

as shown in Fig. 2. Our result for CdS agrees closely with the

experimental valued.

74
Acknowledgment

The author is very grateful to Dr. A. Vaidyanathan for many helpful

discussions

.

References

1. M. Gioppert-Mayer, Ann. Phys. (Leipzig) 9_, 273 (1931).

2. R. Braunstein, Phys. Rev. 125 , 475 (1962); R. Braunstein and N.

Ockman, Phys. Rev. 134, A499 (1964).

3. N.G. Basov, A.Z. Grasyuk, I.G. Zubarev, V.A. Katulin and O.N.

Krokhin, Sov. Phys. JETP 23, 366 (1966).

4. L.V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

5. S.S. Mitra, L.M. Narducci, R.A. Shatas, Y.F. Tsay and A. Vaidyanathan,

Appl. Opt. 14, 3038 (1975); A. Vaidyanathan, T. Walker, A.H. Guenther,

S.S. Mitra, and L.M. Narducci, Phys. Rev. B (in press).

6. E.O. Kane, J. Phys. Chem. Solids 1, 249 (1957).

7. A. Vaidyanathan, A.H. Guenther and S.S. Mitra, to be published.

8. L.M. Narducci, S.S. Mitra, R.A. Shatas, P. A. Pfeiffer and A.

Vaidyanathan, Phys. Rev. B14, 250 (1976); A. Vaidyanathan, T. w. Walker, A.H. Guenther, S.S. Mitra and L.M. Narducci, Phys. Rev. B2Q,

3526 (1979).

9. V.A. Kovarskii and E. Yu Perlin, Phys. Status Solidi 45, 47 (1971).

10. F. Bassani and A.R. Hassan, Nuovo Cimento B7 313 (1972).

11. N. Jodell, S.S. Mitra and A. Vaidyanathan, to be published.

12. A. Penzkofer and W. Falkenstein, Opt. Commun. 16, 247 (1976); I.M.

Catalano and A. Cingolani, J. Appl. Plys. 50, 5638 (1979).

75

MEASUREMENTS OF TWO PHOTON ABSORPTION*

Alan F. Stewart and Michael Bass

Center for Laser Studies

University of Southern California

Los Angeles, CA 90007

Since the first observation of a two photon absorption (TPA) process by

Kaiser and Garrett in 1961(1), there have been many conflicting experimental results and theoretical predictions (2,3). An absolute measurement of the TPA coefficient, 3 , for any given material has proven

to be experimentally difficult and reported values differ by an order

of magnitude or more. New measurements of TPA are reported here for

several zincblende and wurtzite materials employing the technique of

nonlinear laser calorimetry (4) . Internal reflections in our samples

were eliminated by appropriate antireflection coatings and an accurate

determination of the TPA coefficient was possible. The results are in

agreement with previous state-of-the-art measurements using the transmission technique (5)

.

The propagation of light in a medium which exhibits both linear and

TPA is described by

dl(x,y,z,t ) = _ (ct+ BI(x Z/t) ) i (x , y , z ,t) (1) dz

2 where I(x,y,z,t) is the light intensity in MW/cm , z is the direction

of propagation, a is the linear absorption coefficient in cm

- -'- and 3 is

the TPA coefficient in cm/MW. Internal reflection at the exit surface

creates a counterpropagating field which may interfere with the incident

radiation inside the crystal. In a semiconductor with a large refractive index the reflectivity may reach 30% per surface. Thus constructive interference between incident and reflected beams can increase the

intensity inside the crystal by a factor of 2.4. An unmeasurable en- hancement of this magnitude would distort the results of any experiment

designed to measure an intensity squared dependent process such as TPA.

How much enhancement occurs in the crystal will depend on the reflectivity, surface figure and the angle between incident and reflected

beams

.

In order to account for internal reflections we consider only that

occurring at the exit surface of the sample. The following equations

for the incident and reflected intensities were obtained from the con- tributing terms of the nonlinear polarization assuming perfect spatial

overlap and constructive interference:

* This work was supported by National Science Foundation

Grant No. ENG-7820470

77
dl

dz

-a I - 31 (I + 21 ) R

(2)

5

dz

"R aI

R

+ BI

R

(I

R

+ 2I) (3)

where I is the incident intensity and Ir is the reflected intensity.

In reference (4) the coefficient of the cross terms was set equal to

unity because it was felt that the lack of parallelism and the imperfect surface quality of the sample faces resulted in imperfect con- structive interference of the two beams. Intuitively, one would expect

the coupling between the two beams to be greatest near the exit surface.

The coupling should decrease to zero as the two beams physically separate and lose their phase coherence nearer the entrance surface. The

surface parellelism required in order to observe interference effects

in transmission from a low reflectivity etalon is typically less than

one arc minute for 1 ym light (5) . However, field enhancement in a 1mm

thick slab of material would occur over most of the thickness with a required parallelism of slightly less than one degree. Thus, field

enhancement must be present in a typical TPA experiment but the magnitude of the effect has not been determined until now.

The experimental procedure used in this study follows that outlined in

reference (4). A passively Q-switched NdrYAG laser which operates in

the TEMqq mode at low repetition rate (4Hz) was the source for this

work. The beam intensity reaching the sample was adjusted using a two

polarizer attenuator. The total absorption of the sample was measured

as a function of the incident intensity using standard procedures for

laser calorimetry (6) . The Gaussian intensity distribution reaching

the sample was measured by scanning the beam with a narrow slit in

front of a pyroelectric detector. The temporal profile was measured

with a fast photodiode (risetime of 0.1 nsec) and was completely smooth

and nearly Gaussian when observed on a R7912 Transient Digitizer. Any

temporal structure in the laser pulse represented intensity fluctuations

which precluded accurate measurement of 3 and hence that condition was carefully avoided.

The crystals used in this study were selected from three lattice families: sphalerite or zincblende structure, wurtzite structure and

simple cubic. The orientation of these crystals was chosen to preclude

second harmonic generation which if followed by linear absorption would

also appear as an intensity squared dependent process. For zincblende

materials the incident light propagated along the (110) direction and was polarized in the (001) direction. For wurtzite materials the incident light propagated along the optic axis. The linear absorption was measured using conventional calorimetric techniques and a CW Nd:YAG

laser. All crystals were high resistivity (>10° fi-cm) except for the

Cd Sq 25 S e 0.75 which was accidentally uncompensated and showed a re- sistivity of <1q3 fl-cm.

73
The role of internal reflections was determined by applying multilayer

antireflection coatings to one surface each of samples of CdTe, CdSe

and GaAs. In this way, the total absorption as a function of intensity could be measured with no internal reflection or exactly one internal reflection simply by turning the sample around. The TPA co- efficient, 3, was obtained from data taken with the antireflection

coating on the exit surface using Eq. (1) . Once the value of 3 was known the data obtained with the antireflection coating on the en- trance surface was analyzed using Eqs. (2) and (3) with the coefficient of the cross terms as the fitting parameter. As a final check,

uncoated but otherwise identical samples of these materials were measured and again the best fit coefficient for the cross terms in Eqs.

(2) and (3) was determined. In order to use Eqs. (1) , (2) and (3) to

analyze the experimental results numerical integrations were carried

out over the temporal and spatial profiles of the incident pulses.

The results of these experiments appear in Table I. In all cases a cross term coefficient in Eqs. (2) and (3) of unity resulted in the

best fit to the data. Also we have observed no spot size dependence

in our measurements indicating that diffusion of free carriers is not

important on a nanosecond time scale for beams with 1/e radii

greater than 100 urn. Table I Measured Absorption and TPA Coefficients

GaAs CdTe CdSe

a(cm

_1

) 1.50 +0.15 0.049 + Q.005 0.026 +0.003

B(cm/MW) 0.030 +0.009 0.041 +0.012 0.043 +0>013

CdS0 ^ c Se n CdS n e Se„ _ KRS-V

0.25 0.75 0.5 0.5

a (cm"

1

) 0.028 +0.003 0.254 +0.03 0.0047 +0,0005

B(cm/MW) 0.075 +0.023 0.031 +0.009 0.0016 +0.0005

A good example of the sensitivity of this technique is demonstrated

in our measurement of KRS-V. Since nonlinear calorimetry compares

the magnitudes of linear and TPA processes the minimum detectable

TPA coefficient is limited by the maximum intensity that does not

damage the sample and linear absorption coefficient. In KRS-V,

which has a linear absorption of only 4.7 x 10-3 cm

-1

, a 400% in- crease in the total absorption was detected with only 20 MW/cm2 of

incident intensity. This same intensity would result in only a one percent change in transmission. Nonlinear laser calorimetry shows

its greatest promise in measuring TPA in highly transparent materials.

The experimental errors indicated in Table I were primarily caused by

uncertainty in the absolute determination of the incident intensity

of each pulse. The uncertainty comes from calibrations of both the

79
pyroelectric detector and the average power meter used. Additional

contributions arise from laser intensity fluctuations and uncertainties in the measurements of the laser spot size and temporal

profile. As with any calorimetry experiment there is some additional

uncertainties resulting from analysis of the heating and cooling

curves

.

In conclusion, we have measured the TPA coefficient in six materials

and have obtained results in good agreement with those obtained in

a very different type of experiment. This suggests that the experimental results are asymptotically approaching the true value of $•

It is clearly impractical to apply antireflection coating to all materials to be tested for nonlinear absorption. In this research it

has been demonstrated that a cross term coefficient of unity in Eqs.

(2) and (3) allows proper analysis of data obtained from uncoated

samples. It should be noted that if the true coupling coefficient had some other value between 0 and 2, assuming a value of unity leads to an estimated uncertainty in 3 which is at most 20%.

REFERENCES

1) W. Kaiser and O.G.B. Garrett, Phys. Rev. Lett. 7_, 229 (1961)

2) C.C. Lee and H.Y. Fan, Phys. Rev. B 9_, 3502 (1974)

3) J.H. Bechtel and W.L. Smith, Phys. Rev. B 13_, 3515 (1976)

4) Michael Bass, Eric W. Van Stryland, and A.F. Stewart, Appl. Phys.

Lett. 34, 142 (1979)

5) Raoul Weil and Dalia Neshmit, Appl. Opt. 16, 2847 (1977)

6) A. Hordvik, Appl. Opt. 16, 2827 (1977).

80
THREE-PHOTON ABSORPTION IN Nd : YAG

Robert W. Boyd and Mark A. Kramer

Institute of Optics

University of Rochester

Rochester, New York 14627

The narrow spectral linewidths characteristic of transitions of rare-earth ions (Fig. 1) make rare-earth-doped

crystals interesting systems in which to study resonant

and near-resonant optical nonlinearities . While population

inversion and consequent laser action is a common example

of a nonlinear effect involving the rare earths, other

types of optical nonlinearity also exist. The generation

of sum and difference frequencies of applied laser fields

through a second-order "%u^ nonlinearity is such an example.

For a laser frequency close to a resonance frequency of

the rare-earth ion, these nonlinearities are by theoretical

arguments expected to become very large.

Another type of optical nonlinearity involving the rare

earths, and the subject of this article, is three-photon

absorption in Nd:YAG. In the schematic setup of Fig. 2,

a 6 nsec pulse of 30 kW peak power at 5933 £ is focussed

to an 18 um spot size in a 5-mm-long sample of 1 wt percent

Nd : YAG . Blue fluorescence light is found to be emitted

from the focal volume, and it is of sufficient intensity

to be easily observed by eye. A spectrum of the fluorescence is shown in Fig. 3. No fluorescence is observed at

wavelengths shorter than that of the intense doublet at

4000 In addition, a number of longer wavelength lines

appear throughout the visible. The fluorescence spectrum

for wavelengths greater than the excitation wavelength

closely mimics the normal, low intensity, one-photoninduced fuorescence spectra, such as those shown in Fig. 4,

which were also taken with the apparatus of Fig. 2 but with

the laser defocussed.

The intensity of the 4000 A* fluorescence is found to vary

as the third power of the laser intensity over a range of

30 in laser intensity. The process giving rise to this

fluorescence is thus interpreted as three-photon absorption

followed by a partly radiative and partly nonradiative

de-excitation, and is illustrated in Fig. 5. Following

81
excitation to level 2 by three-photon absorption, the atom

decays nonradiatively to level 3, radiatively to level 4,

and nonradiatively back to level 1. In principle, levels

2 and 3 or levels 1 and 4 could be coincident, but the

observed fluorescence spectrum suggests that the dominant

decay route is as illustrated in Fig. 5.

Nd:YAG is known to essentially opaque for wavelengths

shorter than 2400 S. Three-photon absorption thus permits

the probing of levels such as level 2 which are more than

42,000 cm above the ground state and are thus inaccessible by conventional spectroscopic techniques.

The intensity of the 4000 8 fluorescence is plotted as a function of laser wavelength in Fig. 6a; below it the product of the laser power (shown in 6b) and the crystal transmission is plotted in 6c. It should be noted that each

peak in 6a matches a dip in 6c, thus indicating that an

enhancement of the three-photon-absorption process occurs

whenever the laser is tuned to a one-photon resonance.

Similarly, theory predicts an enhanced three-photon absorption rate if the energy of two photons is equal to the

energy of a two-photon-allowed transition. Since threephoton absorption necessitates the existence of level 2 of

Fig. 5 at an energy equal to that of three incident photons

it can be concluded from the data of Fig. 6 that a broad

energy level or several overlapping levels exist some

51,000 cm

- "'" above the ground state of Nd:YAG.

In conclusion, a method is presented for studying the energy-level structure of Nd:YAG and similar rare-earth-doped

crystals in an energy region where one-photon techniques

are not possible. This three-photon-absorption process is

presently being studied over a much broader range of laser

wavelengths, and the results of this investigation will be

reported in the future.

This work was partially supported by NSF grants SER77-06914

and ENG79-08038.

Reference

1 W. F. Krupke, IEEE J. Quantum Electron., QE-7 , 153, 1971

82
3000 4000 5000 6000

\(A)

1^ 1^ 1^ I I 7000 8000 9000

Figure 1. Absorption spectrum of Nd : YAG at 300 K.

SAMPLE

I LASER p

STRIP CHART (~2 [pmtI

M0N0CHR0MAT0R

Fig. 2. Experimental setup,

4000

Fig. 3

5000 6000 7000

X(A)

8000 9000

Emission spectrum for three-photon

excitation at 5933 8.

83
Fig. 6. a) Intensity of

4000$ fluorescence, b) Laser

power vs. wavelength. c)

Power transmitted by 5mm

sample.

84
REFRACTIVE INDEX AND THERMO-OPTIC

COEFFICIENTS OF CD*A

L. G. DeShazer and K. E. Wilson

Hughes Research Laboratories

3011 Malibu Canyon Road

Malibu, CA 90625

The refractive indices of CD*A were measured at 29 wavelengths by the

method of minimum deviation. The crystal was cut into a prism with

the optic axis parallel to the prism apex edge enabling both the

ordinary and extraordinary refractive indices to be measured without

altering the position of the prism in its mount. The index measurements were made in a dry environment to prevent deterioration of the

CD*A polished surfaces by moisture. The level of deuteration of the

measured crystal was about 90%.

A two- resonance Sellmeier formula was fit by the method of least

squares to the measured index values. The formula used was

n

2 = 1 + AA 2 /(A2 -B) + CX7(A2 -D).

The determined Sellmeier constants are listed in Table 1 for both the

ordinary and extraordinary indices. For example, the indices at

1.0642um are Ne = 1.5366 and n Q = 1.5531.

Table 1. Sellmeier Constants for CD*A

A' B(ym') C D(umz

) Ordinary 1 .402934 0.0132 0.14654 24.0117

Extraordinary 1 .34951 0.012227 0.062868 25.0

The thermo-optic coefficients ct n ( = n _1 dn/dT) of CD*A were measured as

a function of wavelength from 325 to 632.8 nm using a double interferometric technique involving both Twyman-Green and Fizeau configurations. The thermal coefficient of linear expansion of CD*A

perpendicular to the optical axis was also measured by this technique

and was determined to be 8. 7+0.2xlO" 6 /°C At 632. 8nm, dn/dT = 25.78xlO' 6 /°C for ordinary polarization and -20.19xlO" 6 /°C for extraordinary polarization. Using this data, Type I phasematch solutions

were calculated for CD*A as a function of temperature. Figure 1 shows

the phasematch plots for three frequency mixing in CD*A at room temperature which can be used to design sum frequency generators(SFG)

,

difference frequency generators, and optical parametric oscillators.

For example, in SFG the wavelength on the abscissa represents the sum

frequency and the wavelengths on the ordinate axis represents the input

frequencies

85

ON THE USE OF A CALORIMETER TO INVESTIGATE

LOSS MECHANISMS IN OPTICAL FIBERS

F. T. Stone

Bell Laboratories

Norcross, Georgia 30071

Loss mechanisms in optical fibers are classed as intrinsic , i.e., caused by the inherent limits of the materials and

structure, and extrinsic, i.e., added on during processing.

To attain low loss in fibers, the fundamental limits must

be understood; then any additional contributions to fiber

loss must be identified and reduced to negligible levels.

In our lab we have used a calorimeter to aid in meeting

these objectives. Calorimetry has the capability to:

(1) directly measure absorption and total loss, (2) measure

the loss of short (~lm) samples to determine uniformity over

the fiber length, (3) measure extremely low fiber losses

(-0.01 dB/km) , (4) measure mode-dependent loss for multimode

fibers (to determine the variation of loss over the core

region) or measure the loss accurately in small-core-diameter

fibers by exciting only a single mode even when these fibers

support more than one mode (thus avoiding mode-cut off complications) , and (5) measure the loss of the same segment of

the fiber coated (or even completely packaged) and bare to

quantify coating (or packaging) loss. We present here

examples illustrating a variety of uses of calorimetry in

fiber loss measurements.

MODE DEPENDENT LOSS

Since short lengths of fiber can be measured, the mode

distribution set up at the input face of the fiber is

essentially the distribution in the fiber length being

measured. (Extremely lossy cladding, leaky, and marginal

bound modes are eliminated immediately after launch with a

mode stripper.)

Different mode groups are excited in the graded-index multimode fibers studied by scanning a focused laser beam across

the fiber core. Lowest order modes are excited with the

beam focused at the center of the core, highest order modes

with beam focused on the core-cladding boundary. Figure 1

presents the mode-dependent loss of two fibers: for fiber

399, which exhibits a large amount of higher-order mode

attenuation, other measurements indicate core-cladding

boundary problems; fiber 4 34, on the other hand, is a

87
TOTAL LOSS

(dB/km)

14

12 FIBER 399

/

FIBER 434

Ge-B-S,0 2 CORE FIBERS X = 647nm

CORE DIA. = 55H m

Fig. 1. Modedependent loss

characteristics

of two fibers

0 5 10 IS 20 BEAM POSITION ( r| reasonably good fiber of the same type inserted for comparison. These plots illustrate how mode-dependent loss

data aids in localizing the region of excess fiber loss.

UNIFORMITY OF THE LOSS OF VARIOUS SEGMENTS OF A LONG FIBER

_i i 25 27.5

The title of this section presents one aspect of a fundamental problem in fiber manufacture - how uniform are the fiber

parameters with position down the fiber. This question is

also pertinent in evaluating a technique such as calorimetry

that provides information on limited regions of the fiber.

We have examined the loss-uniformity of many fibers using

an optical time-domain ref lectometer , a scattering cube, and

a calorimeter. Figure 2 is a presentation of absorption

ABSORPTION

LOSS

(dB/km)

3 0

2 0

1 0

° MEAN OF 5 MEASUREMENTS TAKEN AT

Z = 0, 1000, 1500, 2000 AND 2300m

I TOTAL RANGE OF RESULTS

FIBER LL

Fig. 2. Absorption loss measured on segments

taken from different regions

of a 2300m long

fiber.

647 n m

0 5 10 15 20 25 27.5 BEAM POSITION <pm)

88
data of fiber segments taken from various places along a

2 . 3-km fiber. As can be seen, the absorption appears uniform throughout the fiber; hence, measurements on any one

segment are typical of the whole fiber.

Using calorimetry, the loss versus length of a fiber can

also be measured for situations where loss differences are

caused by changes in the mode distributions in the fiber,

not by changes in the fiber itself. By doing this, one can,

for example, study the effectiveness of different excitation conditions in launching an approximation to the steadystate mode distribution.

EFFECT OF COATING

Figure 3 demonstrates the way a coating can increase the

IS

TOTAL LOSS

(dB/km)

5

- « HARD POLYMER COATING

° UNCOATED FIBER

Fig. 3. Coated

vs . uncoated

fiber loss

illustrating the

measurement of

packaging loss

0 I 1 1 I I J 0 5 10 15 20 25 BEAM POSITION | H

m)

higher-order mode loss, probably by causing microbending.

Such results can be used to compare different packaging

materials, for instance, in an environmental study, and to

settle questions such as whether or not a given coating is

responsible for excess loss measured in a fiber by other

techniques

.

SPECTRAL LOSS

Figure 4 is the absorption loss of an experimental singlemode fiber that was examined to determine the cause of the

excess loss. The results show absorption far greater than

that of a good fiber (see 64 7-nm data point in Figure 4)

.

By using various lines of a Krypton laser, the absorption

can be obtained at a number of wavelengths in the visible

and near IR, giving a good outline of the spectral characteristics of the absorber. In this case the outline matches

that of nickel in sodium borosilicate glass as reported by

Beales et al.l This has not been directly verified, however.

Another aspect of the usefulness of calorimetry is illus39
ABSORPTION

LOSS

(dB/km)

SINGLE MODE FIBER

LOW LOSS SINGLE MODE FIBER ABSORPTION AT 647 ]nm —

600 X („m|

TOTAL LOSS

SORPTION J*' LOSS

752 Snm

-J

Fig. 4. Spectral

absorption loss

of a single mode

fiber with large

extrinsic

absorption

trated by this example, namely the capability to measure

separately the fiber absorption and the total fiber loss

FUNDAMENTAL LOSS MEASUREMENTS

Since only short lengths of fibers are needed for calorimetry, the lack of mode mixing enables the power distribution to be determined rather exactly, for example, by

measuring the near-field radiation pattern. Thus, power

distributions can be excited that probe only the regions

of the fiber that one wishes to study. If one wished to

examine the loss of the glass itself, one could avoid

launching energy in the vicinity of the core-cladding

boundary, thereby avoiding complications caused by the

unknown nature of this boundary. Furthermore, the loss

history of the glass could be examined as a function of

various environmental conditions - heat, humidity, radiation, etc. - and this glass effect could be separated out

from any effects due to packaging changes.

Because calorimetry can detect very low losses, these various measurements mentioned can be made with great sensitivity and repeatability (~0.01 dB/km for ~1 watt through

the fiber) . By optimizing the calorimeter structure and

the measurement electronics, appreciably lower losses could

be measured. For these reasons calorimetry is a useful

measurement technique to examine the intrinsic and extrinsic loss characteristics of optical fibers.

K. J. Beales, C. R. Day, W. J. Duncan, J. E. Midwinter, and

G. R. Newns, Proc. IEE 123, 591 (1976).

90
COMPUTERIZED REFRACTIVE INDEX

MEASUREMENT FOR FIBER OPTIC GLASSES

D. L. Wood and J. W. Fleming

Bell Laboratories

Murray Hill, New Jersey 07974

In screening glass compositions for possible waveguide

applications it is necessary to evaluate the refractive

index and its first and second derivatives with respect

to wavelength. We have constructed an apparatus to perform

this task with a minimum of operator time required but with

accuracy in the fifth decimal place of the index routinely

achieved.

The apparatus is built around a 20-bit digital angle sensor

which measures the deviation of monochromatic radiation

through a prism of the composition to be investigated. A

minicomputer controls the experiment, records the data and

calculates the index values from the measured angles. We

chose an optical system involving an off -ax is parabolic

collimating mirror and a reflecting rear face on the prism

so that measurements at other than room temperature can

also be conveniently made, and a broad wavelength range can

be covered.

Index values for germanium silicate glasses of various compositions have been measured, and these results together

with temperature coefficients near room temperature will be

reported

.

91
STRESS OPTIC COEFFICIENT OF OPTICAL FIBERS

N. Lagakos

The Catholic University of America

(Present Address: Naval Research Laboratory

Code 8133, Washington, D.C. 20375)

Introduction : The introduction of a mechanical clad under compression

as a possible solution to the static fatigue problem of optical

fibers-^ has necessitated the develovpment of a polariscope for measuring the stress optic coefficient and the stress profile of optical

fibers. Such a polariscope has been developed. This polariscope

could be used for evaluating the acoustic response of the optical

fiber acoustic sensors^.

Experimental set-up : The stress optic coefficient of fibers, f, was determined by the experimental set-up shown schematically in Fig. 1, which

is based on the Friedel's method of compensation^ . The light from an

Argon ion laser after becoming partly incoherent by passing through a scrambler (a rotating semitransparent plastic disc) was incident perpendicularly on the fiber. The observed part of the fiber was immersed in

a refractive index matching liquid and it was placed between a polarizer

and an analyzer with their vibration axes perpendicular to each other

and at 45° with the fiber axis. A quarter-wave plate was placed before

the analyzer to ensure linear light polarization. A 20x microscope objective and a projection lens focused the fiber cross section on the

plane of a 0.7mm diameter pinhole in front of a photomultiplier . By

slight translation of the projection lens the transmitted light from

different parts of the fiber could be detected. The fiber was held

horizontally with one end fixed and the other clamped by a mount which

could freely slide horizontally in a slot. A weight suspended at the

end of a string, which was attached to the moveable mount around a pulley, was applied along the fiber axis introducing some stress a z

. This stress would rotate the light polarization (retardation) by an

angle 9 , which is given by the rotation angle of the analyzer axis

for minimum transmitted light. It can be shown that 0

z= Nf/L,

where N( = 9/180) is the relative retardation and L is the

light path length in the fiber. It can be shown that f can be obtained from the slope, S, of the plot of weight, W, vs resultant light

retardation 9 as follows:

The retardation profile of the clad was obtained by translating the

projection lens in small steps. This would translate the fiber image

f=

180LS (1)

92
on the pinhole plane allowing different parts to be detected. The

retardation was then obtained directly from the rotation angle of the

analyzer for minimum transmitted light power. From the retardation

profile and the stress optic coefficient the stress profile was obtained and the average clad compression was calculated.

Experimental Results ; The stress optic coefficient, f, was first determined for a suprasil fiber without clad. (In this case the light

path was a diameter). The results of this experiment are shown in

fig. 2, where the applied weight is plotted against the resultant re- tardation. From the best linear fit of these data the slope S was determined, and from eq (1), f was found to be 3.19 ±4% brewsters,

in agreement with the literature^. In addition, f was also determined

for a phasil fiber^ (a 96% silica type glass made by sintering a puri

fied leached porous glass), without clad. The value was found to be

3. 16 ±4%, which is almost identical to that for suprasil. Finally, f was determined in the clad of four different fibers with phasil clad

and silica core doped with CS2O for the first three fibers and

Cs20-K.20-B£20 3 for the fourth (table I, column I). For these four

fibers as well as for four more fibers with core dopant Cs20-K.20~Bi20

the stress profile was determined from the clad retardation and the

stress optic coefficient and the average clad stress was calculated

(table I, column III). (For the last four fibers f was taken to be

equal to the one found for the fourth fiber). These results were

compared with the stress determined on the fiber preforms (table I,

column II) using an optical polarizing microscope equipped with a tilting compensator. (The values for f found for the fibers were

used). It seems that the stress found in the preforms is slightly

but consistently higher than the fiber clad compression. Finally,

the compression strengthening of these fibers was obtained directly

from tensile tests^ using an Instron testing machine (table I, column

IV) and it was found to be in good agreement with the results of the

above described technique.

References

1. D.A. Krohn and A.R. Cooper, J. Amer. Ceram. Soc. 5_2 (12) 661-64

(1969).

2. FOSS Workshop at NRL, Washington, D.C., December 12-14, 1979.

3. A.J. Durelli and W.F. Riley, Introduction to Photomechanics,

Prentice Hall, Englewood Cliffs, N.J. (1965).

4. M.J. Saunders, Rev. Sci. Instrum. 47, 496 (1976).

5. P.B. Macedo, et. al., U.S.A. patent 3, 938,974, Feb. 17 (1976).

6. O.H. El-Bayoumi, R.K. Mohr, N. Lagakos, and P.B. Macedo,

"Residual Stress Measurements of Optical Fibers with Surface

Compression," to be submitted for publication to the J. of the

Am. Ceram. Soc.

93
TABLE I

Strees

Optic Preform Fiber Fiber

Coefficient Stress Average Strength

Stress results

brewsters kpsi kpsi kpsi

3.16 ± 7% 19 i 15% 24 ± 7%

2.80 ± 5/o 14 - 5 /o 10 ± 12% 11 ±4%

2.69 ± 7% 12 10 ± 12% 10 ±5%

2.78 ± 7% 26 21 ± 12% 22 ± 5%

33 33 ± 10% 32 ±6%

34 31 ± 8% 36 ± 5%

31 26 ± 9% 24 ± 5%

25 20 ± 13% 22 ± 4%

LASER

mirror

mirror.

i wave

k Plate

fiber

polarizer scrambler

analyzer

mmM.O 1—I o Q

1 /

projection

lens

phototube

mirror

recorder

Fig. 1 Experimental set-up for measuring stress optic coefficient

and stress profile in fibers.

94
0 1 I I I i_

0 10 20 30 40

RETARDATION »• degree

Fig. 2 Applied weight vs. resulted retardation for a suprasil

fiber (circles). The straight line is the best linear

fit to these data.

95
CHROMATIC MEASUREMENTS OF GRADIENT INDEX MATERIALS BY

MULTIPLE WAVELENGTH INTERFEROMETRY

Danette P. Ryan

Gradient Index Laboratory

The Institute of Optics

University of Rochester

Rochester, New York 14627

Gradient index materials have been studied at the University of

Rochester. The samples studied are several centimeters in aperture

and are applicable to high performance lens systems. The design of

components using these materials requires accurate measurement of the

index of refraction profile and the dispersion.

Models"*" predict the existence of achromatized gradient index materials

.

These materials would make possible the manufacture of color corrected

fibers and single element lenses (Wood lenses) . Accurate dispersion

measurements are required to verify the existence of these materials.

Multiple wavelength a.c. interferometry has been used to obtain the

index of refraction profile and the chromatic properties with a single

measurement. Two simultaneous wavelengths are used for any single

measurement.

The theory has been developed for a Mach-Zehnder interferometer. The

standard two beam interference equation can be written out for each of

the two wavelengths incident upon the interferometer. The final irradiance is given by

I(x # y # Xlf X

2

) = I1X

+ I21+ I12+ I 22 + 271^ cos 6 X + 2J\2T2~2 C°S 6 2

(1)

where I-jj/ an<^ ^± are dePendent upon x, y and and 1^2' ^22 an<^

6 2 are dependent upon x, y and X^.

Using a standard trigonometric identity, one obtains

I(x,y,A

1

,A

2

) = iu

+ I21+ i + I22

+ 2(v^i^ -v^i^Jcos 6 2 + 4,/ I 11

I 21 cos 1/2 (6 - 6 2

) cos 1/2 (6 ± + 6 2

) (2)

The term of interest is the term containing the product of the two

cosines. The cosine whose argument contains the sum of the phases at

the two wavelengths is at a relatively high frequency. The cosine

96
whose argument contains the difference of the phases at the two wavelengths is at a relatively low frequency and is the envelope function.

It contains the dispersion of the gradient as a function of the spatial

coordinates

.

In order to automate the data acquisition process, one mirror of the

interferometer is modulated. The phase is then a function of both

space and time. For two wavelength a.c. interferometry , the phase is

written as a function of spatial coordinates and time for each of the

two wavelengths

6(x,y,A

1

,t) = 6 1 + 6(X

1

,t)

6(x,y,X

2 ,t) = & 2 + 6U2 ,t) (3)

Assuming S U^t) = 6(A

2 ,t) = 6 (t) , I = and I 21 = I , equation 1 becomes

r Kx,y,X

1

,X

2 ,t) = 21.^ + 2I

21 + 2vI

l;L I 21 jcos 6 (t) j cos 6 1 + cos 6 2 - sin 5 (t) j sin 6^ + sin 5 2 j | (4)

Using standard trigonometric identities this becomes

I(x,y,A

1

,A

2 ,t) = 2I

±1

+ 2I

21 + 4,1^1^ cos 1/2 (&1 -

cos[l/2(6 + 6 ) + 6(t)J (5)

Only one term of this equation has time dependence. The amplitude of

this a.c. signal is given by

4 ^ I 11

I 21 COS 1/2 (6 1 " 6 2

} (6)

The amplitude of the a.c. signal contains the information of importance

for the dispersion measurements . It corresponds to the envelope function of equation 2 which gives the dispersion of the gradient as a function of the spatial coordinates.

Figure 1 is a schematic of the a.c. Mach-Zehnder interferometer used

for the measurements. Two colinear laser lines enter the interferometer. The sample is conjugate to detectors 1 and 2. The light is

filtered at detectors 2 and 3. The signal at detector 2 is a measure

of the index profile at one wavelength. Detector 3 is used as a phase reference at that same wavelength. The signals from detectors

2 and 3 are processed in hard-wired electronics and analyzed by a minicomputer to yield the index of refraction profile. Detector 1

detects the sum of the irradiance patterns due to the separate wavelengths. The signal is processed electronically to yield the amplitude of the a.c. signal given by equation 6. This signal is then

97
analyzed by the minicomputer to yield the dispersion of the gradient

as a function of position.

Figures 2 and 3 show the experimental results for a gradient index

sample. Figure 2 is the index of refraction profile obtained from

detectors 2 and 3. Figure 3 compares an experimental plot of the

amplitude of the a.c. signal to a theoretical plot of that same quantity. The experimental plot is modulated due to an intensity mismatch between the two laser lines. This modulation is predicted by

equation 2. The envelope of the experimental curve is found to be in

good agreement with the theoretical curve. These results are consistent with the results obtained by Moore and Ryan using a conventional

a.c. interferometer .

The multiple wavelength a.c. interferometer has an advantage over the

conventional a.c. interferometer. It yields the index profiles for

two wavelengths in a single measurement. In addition, a direct

measure of the dispersion can be obtained.

References

:

1. Stephen D. Fantone, Design, Engineering and Manufacturing Aspects

of Gradient Index Optical Components, Ph.D. Thesis, University of

Rochester, 1979.

2. Duncan T. Moore and Danette P. Ryan, Measurement of the Optical

Properties of Gradient Index Materials, J. Opt. Soc. Am. 68 , No. 9, pp 1157-1166.

Figure 1

98
Q -0.16 1

I I I

I I I I

I

I I I 0.00 0.10 020 0.30 0.40 050

DISTANCE INTO SAMPLE IN cm

Figure 2

VISIBILITY

DISTANCE INTO SAMPLE IN mm

Figure 3

99
OPTICAL COUPLING COEFFICIENTS FOR PULSED C02 LASER

RADIATION ON BARE AND PAINTED ALUMINUM SURFACES

S. C. Seitel, J. 0. Porteus, and W. N. Faith

Michelson Laboratory, Physics Division

Naval Weapons Center, China Lake, California 93555

Introduction

The response of a material sample to laser radiation is specified by

the coupling coefficient, defined as the fractional energy absorbed in

a given time interval. The coupling of 10.6 urn radiation to planar

aluminum samples has been studied extensively; reference 1 contains a recent bibliography. In all cases, the coupling coefficient was determined by observing the temperature rise or rise rate of an appropriately

instrumented sample. In this paper, a fundamentally different method

of measurement, based on thermal expansion of the laser-heated sample,

is reported. Coupling coefficients for bare and painted aluminum are presented for pulsed laser fluences up to 145 J/cm2

.

Theory

The total energy absorbed is given by the volume integral of the temperature rise AT in the material; it does not depend upon the details of

the temperature distribution. In a sample of length L and constant

cross-sectional area A, the absorbed energy E(t) depends only on the

irradiation time t: L(t)

E(t) = pCA / AT(z,t)dz . (1) o Here z represents position along the length of the sample. Equation

(1) presumes that the sample area A, specific heat C, and mass density

p are constant, and that thermal losses to radiation and convection are negligible. After irradiation, the sample length satisfies Eq. (2):

L(t) = L

Q +

F(t^A

L( ° + r /

L

AT(z,t)dz , (2) o where LD is the unstretched length. The remaining terms represent

sample elongation due to tensile load F(t) and to thermal expansion.

Young's modulus Y and the thermal expansion coefficient r are presumed

constant. Before irradiation (t = 0), elongation is determined only by

the applied tensile load F(0), since AT = 0. The net length change

AL(t) is taken up by the load cell, which has elastic compliance Yl = -AL(t)/AF(t) . Thus, the instantaneous tensile relaxation AF(t) = F(t)-F(0) must satisfy

100
O

The second term in brackets is negligibly small if the experimental

parameters F, L, and yl are chosen carefully. Equations (3) and (1)

together yield the desired expression for total optical energy absorbed

as a function of the observed peak tensile relaxation:

E(t) = - i pCA(y

L + Ys )AF(t) . (4)

Here ys

= 1(0) /YA is the elastic compliance of the sample. The coupling

coefficient is the slope of the curve obtained when E(t) is plotted

against the total energy incident on the sample. In the experiments

reported here, values for C, p, and r were taken from tables of physical data, while A, Yl> and Ys were measured directly.

Experiment

Samples 1.0 mm wide by 50 mm long were cut from the .030 mm thick 2024-

T3 aluminum [2], using a pair of slitting saws on a common mandrel in a milling machine. Earlier attempts to shear samples to size induced

distortion and caused paint delamination. Sample thickness was reduced

to 0.15 mm (including paint, if any) in a single pass with the edge of

a milling cutter. This increased the energy per unit (sample) volume

deposited in a single pulse and, hence, system sensitivity by a factor

of two. The samples were cleaned carefully with acetone to remove machining residues.

The sample was clamped between the jaws of a tensioning device, shown

schematically in Fig. 1; a static tensile load, approximately 50% of

the elastic limit, was applied by increasing the jaw separation. The

elastic limit was established for each sample from a measurement of

elongation vs. applied load; it is the maximum load which caused no permanent deformation. For virgin samples, the elastic limit was approximately 4.4 N (8 pounds). Pulsed 10.6 urn laser radiation of 100 nsec duration was focused on the sample center with a ZnSe lens. The

spatial profile at the target, inferred from pinhole scans, was very

nearly Gaussian, but elongated (with a Ge prism) to overfill the narrow

sample dimension. The 1/e 2 full widths in the elongated direction, and

normal to it, were 1.399 and 0.393 mm, respectively. Approximately

half of the total energy was intercepted by the sample.

The total optical energy delivered to the sample was determined by

deflecting a known fraction of the incident radiation onto a calibrated

reference detector with a beamsplitter. That portion of the incident

laser pulse which was absorbed was converted into heat, causing the

sample to expand thermally. The expansion was taken up internally by a fast load cell which, together with bridge circuit and chart recorder,

sensed and displayed the resultant tensile relaxation. System response

101
to a typical thermal pulse was limited by the recorder to 20 msec. Sensitivity was 8.8 x 10-Lf N (2 x 10 -lt pounds). Recovery to ambient

temperature and tension was governed by the rate at which absorbed

laser energy was removed. The dominant mechanism was heat conduction

to the massive sample supports, with a characteristic time of approximately 1 sec. This is long compared to the time required to diffuse

heat across the sample (1 msec); thus the linear integrations in Eqs.

(1) and (2) are justified.

Results

Figure 2 shows the energy absorbed by an unpainted sample as a function

of intercepted incident energy. The slope, which is the coupling coefficient, increases dramatically at the flash threshold (~ 17 mJ) , from

0.03 to 0.25, in agreement with published values obtained by direct

temperature measurements [1,3,4]. Coupling above threshold is dominated by the laser-produced plasma, which absorbs more strongly than

the reflective bare metal. Unpainted samples show little evidence of

damage above threshold in spite of the large amount of energy absorbed.

Plasma expansion evidently enlarges the area over which energy is

transferred to the aluminum, so that the effective fluence is reduced.

At very high incident fluences, the slope decreases; this is consistent

with more rapid plasma expansion or detachment, with reduced transfer

to the sample [1,5]. No permanent laser- induced deformation was observed, even in samples stretched to the elastic limit. The maximum

fluence (145 J/cm2 ), which was sufficient to produce an intense flash

and crater the sample surface, is well above that required to produce

the slip phenomena reported previously [6]. It is concluded that

laser-induced slip has no significant adverse effect on mechanical

strength under load. Shock effects from individual pulses produce no measurable reduction in strength under these conditions.

Also shown are similar results for a painted sample. The peak absorption coefficient occurs at very low incident energies and was measured

as 1.15. This remarkable result is, in fact, consistent with an overall

energy measurement accuracy of 20%. No significant change in slope occurs at the flash threshold, since absorption already is near total.

The roll-off above threshold is attributed to plasma shielding as above, except that the painted surface produces a rapidly expanding

plasma at lower energies. This is consistent with the observation that

the painted samples are damaged severely above threshold.

References

[1] J. A. McKay et al. , J. Appl. Phys. 50, 3231 (1979).

[2] Sample materials were supplied by G. F. Thomas of Vought Corporation.

[3] S. Marcus, J. E. Lowder, and D. L. Mooney, J. Appl. Phys. 47, 2966

(1976).

102
[4] W. E. Maher and R. B. Hall, J. Appl. Phys. 4_9, 2254 (1978).

[5] J. 0. Porteus et al. , NBS Spec. Publ. 509, 204 (1977).

[6] J. 0. Porteus, M. J. Soileau, and C. W. Fountain, NBS Spec. Publ.

462, 165 (1976).

LOAD CELL

Figure 1. Experimental apparatus.

t i i i i i i r o

INCIDENT ENERGY (mJ)

Figure 2. Absorbed versus incident energy.

103
THERMOMODULATION SPECTRA OF HIGH-ENERGY INTERBAND

TRANSITIONS IN Cu, Pd, Ag, Pt, AND Au

C. G. Olson and D. W. Lynch

Ames Laboratory-USDOE and Department of Physics

Iowa State University, Ames, Iowa 50011

and

R. Rosei

Ames Laboratory-USDOE and Department of Physics

and

Istituto di Fisica del ' Universita , Rome, Italy*

Many f.c.c. metals exhibit a rise in the reflectance at about 18eV,

leading to a broad peak. Thermomodulation spectra in this region re- veal a richly-structured spectra. We have made thermotransmission

measurements [1] on unsupported thin films of Cu, Pd, Ag, and Au, and

thermoref lectance measurements on Pt in the 15-30eV spectral region.

The temperature-modulated transmittance spectrum can be shown to be

simply -dAu, the sample thickness multiplied by the negative of the

temperature-induced change in the absorption coefficient. No data

treatment is necessary. For Pt the thermoreflectance spectra were

Kramers-Kronig analyzed to get Ay. The data obtained for these metals

is given in Fig. 1. The spectra do not change appreciably when the

ambient temperature is changed.

There are no core electron excitations in this spectral region. The

structures in Ay arise from excitations of the 3d, 4d, or 5d electrons.

Band structures for many of these metals have been calculated by

Christensen, [2,3,4] all with the same method and potential, so com- parisons between metals are meaningful. Figure 2 shows his band

structure for Au. The region of structure beginning around 18eV

corresponds to excitations from the top of the 5d band complex to the

relatively flat bands centered around r, about lleV above the Fermi

energy. These flat bands are based on 5f wave functions at T with

mixing of p components away from r. The shifts in the structures from one metal to another correlates with the shift in the d-bands as can

be seen in Fig. 1. The phase space associated with T is very small and

critical points at r should not contribute strongly to either the

absorption spectrum or the modulated absorption spectrum. However

one can see, even in Fig. 2, many places where possible initial bands

and final bands are parallel, especially along E and A, and these

may produce critical points very close to those at r, critical points

at nearly the same energies and with more associated phase space.

Present address.

104
We fit Christensen' s bands for Au to a parametrization scheme and

sought interband critical points along E and A, finding over 40 such

points, all rather close to the zone center. Of these, we eliminated

a few by selection rules, then looked for those which involved the same band pairs as the interband critical points at V, assuming that

they all would be modulated by the same mechanism, since nearly the same states were being considered. The critical point transitions

may be modulated by a thermal-expansion-induced shift of the energy,

a thermally-induced broadening, or both. Each type of critical point

has a characteristic line shape for each mechanism. [5] We synthesized

the expected spectrum for each of the T interband critical points and

for the nearby E and A critical points involving the same bands.

Figure 3 is an example. It is clear that the T critical points contribute little, but the E and A points dominate. The line shapes are such that either a red shift or a broadening with increasing temperature

or both is consistent with the data for all of the major structures

seen.

The spectra for the metals other than Au, e.g., Ag, show less fine

structure in the corresponding region. This appears to be the result

of more overlapping of the structures. A mapping of all the V critical points expected from the band calculations onto the measured

spectra, the letters u-z in Fig. 1, shows this to be the case. Critical

point transitions at L, shown as letters a-r contribute some structure

and a background, while critical point transitions at X contribute as well, but not just in the region of prominent structure. Note that

the calculated critical points have not been shifted before plotting.

Pt has a different spectral feature at about 15eV, a positive peak

followed by a negative peak. This is the characteristic shape of a transition from the Fermi level to a relatively flat band [6] and it

agrees in energy with the energy of the flat band at T above Ep. A

similar transition is not present in Pd, although it might be expected,

because the density of d states at Ep is lower.

The sharpness of the structures in the thermoreflection spectrum for

Au, about O.leV, implies that these excited states, over 15eV above

Ep have relatively long lifetimes, long compared with those for electrons in free electron-like bands just below them in energy . [7 ,8, 9]

This long lifetime probably is the result of selection rules for electron-electron scattering.

This work was supported by the U.S. Department of Energy, contract No.

W-7405-Eng-82 , Division of Materials Sciences budget code Ak-01-02-02-2

.

It was carried out at the Synchrotron Radiation Center of the Physical

Sciences laboratory of the University of Wisconsin. The storage ring

was operated under NSF contract DMR-77-21888 . We wish to thank N. E.

Christensen for tables of energy eigenvalues for Au at several lattice

spacings, and for partial joint densities of states for Au and Ag. We

105
also acknowledge assistance from B. N. Harmon and D. J. Peterman in

the use of the interpolation program and a program to produce plots

of interband energies vs. wave vector.

References

1. R. Rosei, M. Meuti, C. Coluzza, and C. Quaresima, Opt. Letters !L, 217 (1977).

2. N. E. Christensen, Phys. Rev. B 13, 2698 (1976).

3. N. E. Christensen, Phys. Stat. Solidi (b) 54, 551 (1972).

4. N. E. Christensen, Phys. Rev. B 14, 3446 (1976).

5. E. Matatagui, A. G. Thompson, and M. Cardona, Phys. Rev. 176 , 950 (1968).

6. R. Rosei and D. W. Lynch, Phys. Rev. B 5_, 3883 (1972).

7. J. A. Knapp, F. J. Himpsel and D. E. Eastman, Phys. Rev. B 19 , 4952 (1979).

8. P. Thiry, D. Chaudesris, J. Lecante, C. Guillet, R. Pinchaux,

and Y. Petroff, Phys. Rev. Lett. 43, 82 (1979).

9. P.S. Wehner, R. S. Williams, S. D. Kevan, D. Denley, and D. A.

Shirley, Phys. Rev. B 19, 6164 (1979).

106
AT

T

AT

T

AT

T

AT

T

Au II be 4*1 111 II vA/X_„ 1.

^ In

\ II

J \ I III / \

\ P N P v.

p1 r \

A Ag / \ be

1 \ TTT

mi iii A—1 / \

1

1 1 Pd

I

'

if "'\ /

1 It \ / \

Cu

i

ell/ \

\

1 'v \

« » j,

Figure 1. Thermo transmission spectra

(AT/T = -dAy) for Au, Ag, Pd and Cu, and

-Ay for Pt. The ambient temperatures are 52K for Au and about 200K for the other

metals. AT/T is in arbitrary units and

the magnitudes of two spectra cannot be

compared

.

10 15 20 25 30 ENERGY (eV)

1 u I I n' 1 / I // \ 7 \ / ^i

//

1

/' J

jf\

\ yd \

v,v' \ w,w' UVv

1 1 1 1 1

1

19.5 20.0 20.5 2IO 215 22X5 ENERGY (eV)

Figure 2. Energy bands of Au obtained

by a Fourier series fit to the eigenvalues of Ref. 2.

Figure 3. Line shapes for -Ae2(n-Ay)

spectra for an M (V) and Mg(w) critical

point at T and the associated critical

points along Z and A (v' and w')

upper: Modulation by a red shift of

the critical point energy. Lower:

Modulation by thermal broadening.

107
ELLIPSOMETRIC OBSERVATIONS ON THERMALLY GROWN OXIDE

FILMS ON TITANIUM

Alia H. Musa and W. E. J. Neal

Physics Department

University of Aston in Birmingham

Birmingham, B4 7ET, U.K.

Apart from the use of oxide films of titanium as transparent antireflection coatings (Fan and Bachner 1

, Yoshida2), recently there has

been increased interest in their possible application in the photoreduction of water to produce hydrogen. The work reported here on optical properties of oxide films on titanium forms part of an on going investigation into properties of materials for solar

applications. The equipment used for the optical studies was the two

angle ellipsometer described by Neal 3 but in this investigation only

one angle of incidence (63.8°) was employed. The wavelength range was in the visible region from 397.1 nm to 576.6 nm. Details of the

el 1 ipsometric technique have been adequately described elsewhere; see for example Neal 4

.

The basic equation of ellipsometry is:

R /R = tan i|/ exp(iA). (1)

In general, film growth on a surface changes the values of both t|> and

A. The magnitudes of the changes depend on film thickness, the

optical constants of the substrate and film material and the

radiation wavelength. For the growth of thin films on a pure clean

substrate (up to 10 nm thick) the changes 6i|< and 6A can be assumed to

be proportional to thickness for a given substrate and film. For

thick films this approximation is not valid and exact equations

proposed by Drude must be used. The exact equations have been used

for all calculations in this work. Winterbottom5 drew attention to

the fact that a polar diagram plot of tan ijj against A, for film

growth on a surface, produced a closed loop for nonabsorbing films

but the curve for an absorbing layer was not closed. In this work

plots of tan 4< against A for different thermally grown oxide layers

on titanium have been compared with computer generated values using

assumed optical constants n and k for the oxide and measured

constants for the titanium substrates which were mechanically

polished in air.

The titanium substrates were examined optically prior to the grow

of oxide films and were characterised by the instrument angle

settings *)< and A as previously mentioned. The values were measured

108
for light radiation of five wavelengths in the range 397.1 nm to

576.6 nm. Because of the wavelength spread the Beattie-Conn method

was employed as opposed to the use of the compensator method. The

values obtained are given in Table 1 together with the corresponding

optical constants n and k for the clean substrate. Figure 1 shows

plots of computed values of tjj and A as a function of n for values of

k ranging from 3.22 to 3.28. Experimentally determined values of t|> and A at a given wavelength for the surface of a clean titanium

substrate are shown as horizontal lines. The points of intersection

giving the same value of n and k are the values taken to characterise

the substrate prior to oxide growth.

Table 1. Optical constants of titanium substrate.

(nm)

4> degrees

A

degrees

n 2k

2

576.6 32.48 139.29 2.52 3.36

546.1 32.62 137.76 2.36 3.28

499.7 33.65 134.29 2.01 3.26

454.1 32.60 131.08 1.94 2.96

397.1 32.46 127.34 1.76 2.78

Figure 2 shows an example of a plot of tan i|i against A at a wavelength of 546.1 nm for the growth of an oxide film on bulk titanium

in air at 750 K as measured at stages during the growth. Computed

values of and A are also shown for films of different thickness on

a substrate with optical constants determined experimentally as indicated above. In the example shown the computed values were

generated by using optical constants n = 2.40, k = 0.24 for the

titanium oxide on a titanium substrate having n = 2.36, k = 3.28

(from fig. 1). The values of n and k were determined as indicated

above and the optical constants obtained at the various wavelengths

are given in Table 2, together with substrate reflectances.

The reflectance of the (Ti02

- Ti) system was calculated from the

expression as given by Heavens 6 for an absorbing surface covered by

an absorbing layer. Figures 3A and 3B show reflectance against wavelength for differing thickness of oxide on titanium and reflectance

against oxide thickness for the two extreme wavelengths.

The optical constants obtained by other workers for titanium films

and bulk titanium can be compared with the present values given in

109
Table 2. The optical constant of titanium free film,

titanium oxide and the calculated reflectances.

A\ ( nm 1 ^ Mill J Optical Constant ofmetal free film (Ti)

Optical Constant of

Film (Ti0

2

) n 2 h

n l

k

l

Substrate

0 / D . D 2.52 3.36 2.45 0.23

546.1 2.36 3.28 2.40 0.25 57.1

499.7 2.01 3.26 2.39 0.25 59.2

454.1 1.94 2.96 2.38 0.24 55.9

397.1 1.76 2.78 2.38 0.23 54.1

Table 1. In the region of 580 nm the present values lie between

those of Smith 7 for films deposited in UHV and those of Winterbottom8

for mechanically polished material. At a wavelength of 540-550 nm published values of n lie between 1.78 for mechanically polished

surfaces in air to 3.09 for bulk material polished in UHV. 5 ' 8 11 The

highest value of n for films deposited in UHV is 3.03. It can be

assumed in general that the cleaner the surface the higher will be

both the n and k values. Published values for k over the same wavelength region vary from 3.73 for films prepared in UHV to 2.46

for mechanically polished bulk. The optical constants of n = 2.36

and k = 3.28 at a wavelength of 546.1 nm are lower than the best

values reported for UHV prepared films and much higher than bulk

samples polished in air indicating a good quality substrate for oxide

growth.

Hass and Bradford 12 in 1957 assuming that k = 0 for the oxide

obtained a value of n = 2.7 at a wavelength of 546 nm on evaporated

titanium film. Menard 13 gives values of n = 2.4 and k = 0.17 in the

wavelength range 588.9 nm to 589.5 nm for Ti0 2 thermally grown in

oxygen at 755 °K. The corresponding values for air grown Ti02 are n = 2.40 and k = 0.25, obtained in the present work shows only a small

variation in n from 2.45 to 2.38 over the wavelength range 576.6 nm

to 397.1 nm and a variation in k from 0.23 to 0.25. The present work

clearly shows slight absorption of Ti0 2 in the visible region and is

in close agreement with the work of Menard 13 at 589 nm.

Plots of oxide thickness (t) against log time (T) for a given temperature showed linear relationships relating to the expression

110
t = A + B log T (2)

suggested by Vermilyea (14) for oxide growth on tantalum where A and

B are constants at a given temperature.

REFERENCES

1. J. C. C. Fan and F. J. Bachner, Applied Optics 15, 1012 (1976).

2. S. Yoshida, Thin Solid Films, 56, 321 (1979).

3. W. E. J. Neal, Surface Technology 6, 81 (1977).

4. W. E. J. Neal, Applications of Surface Science 2, 445 (1979).

5. A. B. Wi nterbottom, Optical Studies of Metal Surfaces, Bruns

Bokhandel , Trondheim, (1955).

6. 0. Heavens, Optical Properties of Thin Solid Films (Dover, New

York), (1955).

7. T. Smith, Surface Science 38, 292 (1973).

8. A. B. Winterbottom, Trans. Farad. Soc. , 42, 487 (1946).

9. A. B. Winterbottom, J. Opt. Soc. Am. 38, 38 (1948).

10. A. B. Winterbottom, J. Iron & Steel Ind. (London) 165, 9 (1950).

11. A. B. Winterbottom, Ellipsometry in the Measurement of Thin

Films.

12. G. Hass and A. P. Bradford, J. Opt. Soc. Am. 47, 125 (1957).

13. C. R. Menard, J. Opt. Soc. Am., 52, 427 (1962).

14. D. A. Vermilyea, Acta Metal! . 6, 166 (1958).

FIG. 1 ANGLES $ AND A VERSUS n FOR DIFFERING VALUES OF k.

Ill
90m.n #

(Clean surface)

FIG. 2 TAN $ VS. A FOR (Ti0

2

-Ti) SYSTEM

x - Experimental, • - computed, <j> = 63.6°,

x = 546.1 nm

546 1 Irani 576Mml

CNnmP ol TIO,

20lnml o(TiO,

30(nmloCnO,

FIG. 3A REFLECTANCE AGAINST WAVELENGTHS FOR DIFFERING THICKNESSES OF

TITANIUM OXIDE ON TITANIUM

112
r-im Thickness inmi

FIG. 3B REFLECTANCE CURVES FOR (TiOg-Ti) SYSTEM

138 -

Tinw m (min t

FIG. 4 A AGAINST TIME DURING OXIDATION OF BULK TITANIUM IN AIR AT

VARIOUS TEMPERATURES FOR X = 546.1 (nm)

113
OPTICAL PROPERTIES OF A-15 THIN FILMS AND SINGLE CRYSTALS

R. C. McKee, D. W. Lynch, C. G. Olson, and J. W. Osmun

Ames Laboratory-USDOE and Department of Physics

Iowa State University, Ames, Iowa 50011

and

J. H. Weaver

Synchrotron Radiation Center, University of Wisconsin

3Z25 Schneider Drive, Stoughton, Wisconsin 53589

Much interest has been paid to A-15 compounds in recent years but not a great deal of work has been done on their optical properties. There

have been some reflection studies in the optical range [1] on V^Si,

V"3Ge, V3 Pt and Ti 3 Sb and in the infra-red on V-Ga alloys [2] and Nb-Sn

alloys. [3] Ellipsometry measurements [4] have been made on several A15 compounds in the near i.r. in an attempt to extract effective Drude

parameters . [5, 6] There is a question if these parameters are meaningful since calculations [7] on ten A-15 compounds having Nb and V as the A element show possible interband transitions in the optical range.

This problem seems to be solved for V^Si [8] by doing far i.r. transmission studies which are below any interband transitions.

Our work has two parts. Most of the work has been on optical absorptance studies. These have been made on sputtered thin films of M^Ge,

Nb3Al, Nb3lr, and V^Ga; polycrystalline bulk samples of V3Ga, V3Ge,

V^Si, and single crystal Cr3Si. The measurements were made in the

energy range of 0.2 eV to 4.0 eV using a calorimetric technique operating at 4.2K. Reflectance measurements on NboGe, Nb3lr and Nb3Al in the

range 4.0 eV to 30.0 eV were done using synchrotron radiation at the

University of Wisconsin. The second part of our work is to modulate

thermally the sputtered films and measure the change in reflectance in

the range 0.4 eV to 3.5 eV. The optical absorptance data is KramersKronig analyzed and compared to existing band structures. [7,8]

The films were sputtered onto heated (850°C) sapphire substrates (5.0 mm x 12.5 mm x 0.05 mm) using the getter sputtering technique. [10]

Transition temperatures and superconducting onset widths for M^Ge,

Nb3Al and V3 Ga were respectively; (18. 4K, 1.1K), (16. 7K, 0.9K), and

(14. 6K, 0.1K). These samples have a surface roughness the same size

as that of the substrates which are hundreds to several thousands of

Angstroms. This appears in S.E.M. pictures and in non-specular reflection from synchrotron radiation data above 6.0 eV. This roughness will cause trouble in the visible also.

The calorimetric data was K-K analyzed using a Drude extrapolation for

energies less than 0.2 eV with parameters chosen to match the slope anc magnitude of the data. The vanadium compounds and the single crystal

114
Cr^Si use vanadium absorption data [11,12] for the energy range 4.0 to

300.0 eV and an E~x (x between 3.5 and 4.0) function used as a high

energy extrapolation.

The optical absorptance data are shown in Fig. 1. The single crystal

Cr3 Si has the sharpest structure with a peak in the absorptance at 0.85

eV. Spectra from sputtered films of V3 Ga show a small peak at 0\85 eV

and structure at 0.3 eV, while data from a polycrystalline bulk sample

yielded a shoulder at 0.85 eV but not the low energy structure, otherwise being the same. Bulk samples of V^Si and V3 Ge produced spectra

which are in agreement with some of the literature [1,4] with the main

structure being a shoulder at 0.75 eV. This is shifted from the peak

in the Cr3 Si and V3Ga spectra.

The absorptance data obtained from the sputtered films of the niobium

compounds show structure which is smeared when compared to the vanadium

and chromium compounds. Spectra from Nb^Ge shows broad structures at

1.0 eV and about 1.6 eV. Data from Nb^Ir appears as a shoulder at 0.45

eV and a peak at 1.3 eV, while Nb 3Al spectra yields small shoulders at

0. 45 eV, o.75 eV and 2.0 eV.

Figure 2 graphs the conductivity obtained from the K-K analysis. The

conductivity shows a peak for V

3 Ge and V3 Si at 1.0 eV which shifts for

V3 Ga to 1.1 eV and to 1.45 eV for Cr3 Si. Nb 3 Ge has structure at 1.3 eV.

A peak at 0.55 eV and one at 0.95 eV constitute most of the structure

for Nb3 Al.

Figure 3 shows a band structure calculation [7] for V3 Ga showing the

complication of bands caused by the transition metal. The broad 1.1 eV

structure in the conductivity of V3 Ga has possible origins at M and

along parallel bands in the S, T and A directions.

Spectra obtained from thermomodulation studies of these films show signals one part in 10^ to 10^, smaller than that of Cr which are one part

in 10 . This is expected since these films have low resistance ratios

between one and three.

This work was supported by the U.S. Department of Energy contract No.

W-7405-eng-82, Division of Materials Sciences budget code AK-01-02-02-2.

Most of the work was carried out at Ames Laboratory-USDOE and the

Department of Physics at Iowa State University. The remainder of the

work was done at the Synchrotron Radiation Center of the Physical Sciences Laboratory of the University of Wisconsin. The storage ring was

operated under NSF contract DMR-77-21888

.

References

1. J. A. Benda, T. H. Geballe and J. H. Wernick, Phys . Letters, 46A , 389 (1974).

115
2. A. I. Golovashkin, I. S. Levchenko , T. A. Leskova, V. M. Sokolov,

and N. S. Vorob'yeva, Fiz . metal, metalloved 36, 1187 (1973).

3. A. I. Golovashkin, E. D. Donner, I. S. Levchenko, and G. P.

Motulevich, Soviet Physics JEPT 32, 1064 (1971)

.

4. B. Y. Yao Ph.D. thesis (Princeton, 1978) (unpublished).

5. I. Tutto, L. M. Kahn, and J. Ruvalds, Phys. Rev. B 20, 952 (1979)

.6. M. H. Cohen, Phil. Mag. 3, 762 (1958).

7. B. M. Klein, L. L. Boyer and D. A. Papaconstantopoulos , Phys. Rev

B 18, 6411 (1978)

.

8. S. W. McKnight, S. Perkowitz, D. B. Tanner, and L. R. Testardi,

Phys. Rev. B 19, 5689 (1979).

9. W. E. Pickett, K. M. Ho and M. L. Cohen, Phys. Rev. B 1_9, 1734

(1979)

.

10. H. C. Theuer and J. J. Hauser, Transactions of the Metallurgical

Soc. of A.I.M.E. 233, 588 (1965).

11. B. Sonntag and R. Haensel, Solid State Comm. 7_, 597 (1967).

12. D. W. Lynch, J. H. Weaver and C. G. Olson, Phys. Rev. B 10, 501

(1974)

.

116
Figure 1. Optical absorptance of Nb3 Ge, Nb3Al, Nb3lr, V3Ga sputtered

films; single crystal Cr3Si; and VoGe and V3Si bulk samples.

Figure 2. Conductivity of A-15 compounds obtained from K-K analysis

Note the main feature, the peak shift at 1.0 eV in going

from V

3 Ge and VoSi to 1.1 eV in ^Ga and to 1.45 eV in

single crystal C^Si.

r UffL4

ri i.ocuSji.y.ySSjUs

Z 02S~0.yC,04,5-0.7

A o.-7,/.©,i.y

Figure 3. Band structure calculation [7] of V-^Ga and listing of ener- gies (eV) of allowed direct interband transitions at

symmetry points.

117
IE ABSORPTION BANDS IN MULTILAYER THIN FILMS OF SOME

II/VI, V/VI MATERIALS

J.S. Seeley, R.Hunneman, A.Whatley

Department of Cybernetics

University of Eeading

Reading, England

In an empirical investigation of materials for use in FIR interference

and/or absorption filters we have given attention to the thin layer

forms of familiar bulk materials. These comprise ZnS, ZnSe, CdSe

and CdTe (II/VI) and As~S^, As_Se^ (V/VI). A. prerequisite of the

materials is that they be available in pure and stoichiometric

evaporable form* % and that their dissociation (if any) during

evaporation be recoverable during deposition in the manner described

by Ritter and Hoffman*^. The deposition surface comprises polished,

non-oriented polycrystalline substrates the temperature of which is

precisely controlled by a thermal contact technique; at about 100°C

for single layers, at about 180°C with bled-in O2 for "hard" multilayers on silicon substrates, at 20°C for "soft" multilayers on KRS-5 or 6 substrates.

Many of the materials have been investigated in the configuration of

the optical multilayer , for the dual purpose of demonstrating

interference possibilities and minimising the specific thickness of

each contributory layer of the material: the significance of this

latter being that thick, single, layers become excessively rough and,

.

are known to yield inadequate delineation of the reststrahlung band^

06

Wavenumber (cm"')

Fig. 1 CdSe/PbTe multilayer on Si substrate

containing about 3 M- equivalent of CdSe

The possibility that a sharp and fully absorbed reststrahlung band

could be obtained from one constituent in a multilayer initially came

to our attention in CdSe/PbTe-based interference filters transmitting

118
to kO |i. The CdSe band at 185 cm" is shown in Fig.1, where the onset

of PbTe absorption beyond 100 cm-1 can also be clearly seen: the CdSe

band appearing classical in shape. The cut off in ZnS (Fig. 2), and

in ZnSe (Fig. 3) and CdTe also appear classical; their occurrence being found at longer wavelengths than was formerly supposed and being

sufficiently abrupt to provide definitive filtering action when a suitable continuum of absorption is provided for the longer wavelengths.

Microns 11

Fig. 2 Double-beam ratio spectrum of thick layer

of ZnS on Si substrate

The cut on in ZnS (Fig. k) occurs at kO u and was suspected in a study

from an earlier period(5). We are at present using it to strengthen

filter action at ^+0 \i where it is complementary to thin quartz also

cutting on there.

In comparison with these classical profiles thin-layer As_Se_, (Fig.

2 t> 5(a) and (b)) shows a pronounced rectangularity having transmission

less than 0.01% in its band but still retaining good transparency

adjacent to the band indefinitely in both directions. As^Se^ reverts

to a classical profile and in neither this or the sulphide glass does

the thin layer absorption relate to the known bulk spectrum.

These studies continue and we are presently engaged in examining the

thin layer reststrahlung at k deg K for use in cooled filters where

various continuum of absorption are required in the region 20-100 |i.

119
MICRONS

25

MICRONS U

35 50

80

60

,UUI o

z

40

20

WAVENUMBER cm'

1

Fig. 3 Cut off of ZnSe in

ZnSe/KRS-6 multilayer on thin KRS-6 substrate:

about 8 |i total thickness

ZnSe

400

Fig. k

300 200

-i

WAVENUMBER cm

Cut on of PbTe/ZnS

multilayer on Si

substrate containing

in excess of 8 ji ZnS

120
WAVENUMBER cm"1 WAVENUMBER cm"

1

Fig. 5(a) As^S^rvjl^ |i thick in (b) Intermediate thicknesses

As

2

S

3

/KRS-6 multilayer on of As

2§

3

KRS-6 substrate

eferences

1. ZnS, ZnSe, CdTe procured from Eastman Kodak.

2. CdSe, As_S , As_Se procured from BDH Chemicals Ltd.

d. 5 d 3

3- Hitter E, Hoffman R. J. Vac Sci Technol 3^+ (1967) 803.

*f. Evans C.S., Hunneman R. , Seeley J.S. J. Phys _D: Appl Phys £

(1976) 309.

5- Smith S.D., Seeley J.S. Final Rep, May 1968, USAF Contract AF61

(052) -833.

121
MULT I WAVELENGTH LASER RATE CALORIMETRY ON VARIOUS

INFRARED WINDOW MATERIALS

G. S. Coble, D. V. Dempsey, J. A. Detrio, N. C. Fernelius, J. A. Fox,

P. R. Greason, G. T. Johnston, D. B. O'Quinn

University of Dayton Research Institute

Dayton, Ohio 45469

Over a period of several years we have measured the optical absorption

coefficient, 3, using the slope method of laser rate calorimetry^ on

a variety of materials for the Air Force Materials Laboratory. The

lasers used to obtain these results include a modified Nd:YAG laser at

1.319 ym, an HF laser at 2.7 ym, a DF laser at 3.8 ym, a CO laser at

5.3 ym and a CO,, laser at 9.27 ym and 10.6 ym. The purpose of this

work was to provide 6 values at various wavelengths on a sample in which

the sample received similar mountings in a calorimetry box, received

similar data analysis, and which did not undergo the rigors of shipping

to another location for measurement.

The NaC£ samples were single crystals grown by Harshaw Chemical Company.

Some samples were grown by the Stockbarger technique while others were

Kyropoulos grown. Raytheon fabricated the six-inch CaF^ ingot by

remelting CaF2 P ieces - ^ rom tnis 38 mm diameter discs were cut. The

RAP-grown (Reactive Atmosphere Processed) Rb-doped KQ samples were

made by Hughes. Note the large absorption value in this material at

2.7 ym. The LiF samples were grown by Harshaw. One sample was forged

by Honeywell. The Aj^1^* sapphire, samples were made by Crystal

Systems, Inc. Fused silica, S i 0

2 » samples were obtained from a variety

of vendors. The Suprasil samples were obtained from Heraus-Amersi

1

122
and BK-7 from Zygo Corporation. The samples were prepared by

Optovac. Gadolinium gallium garnet, Gd^Ga^O-^ (GGG) is a material

developed as a substrate for magnetic bubble memories. We obtained

samples from Lambda/Airtron and Allied Chemical. Since GGG is not

normally regarded as an infrared material we include a Perkin-Elmer

180 transmission curve in Figure 1. The ZnSe samples were from CVD

(chemical vapor deposition) plates grown by Raytheon for the Air Force

Materials Laboratory Manufacturing Technology program MT-11 . The

silicon sample was cut from an ul trahigh-purity boule grown by Texas

Instruments. The 6 slope results are listed in Table 1 in the order of

increasing value at 1.3 ym.

Acknowledgment

We wish to acknowledge the support of the Air Force Materials Laboratory, Wright-Patterson Air Force Base, Ohio for this work.

References

1. M. Hass, J. W. Davisson, P. H. Klein and L. L. Boyer, J. Appl . Phys.

45, 3959 (1974).

123
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124
125
OPTICAL CONSTANTS OF

BORON CARBIDE IN THE INFRARED

James L. Lauer and Hedy Adari

Rensselaer Polytechnic Institute

Troy, New York 12181

I. INTRODUCTION

Boron carbide has been suggested as a material suitable for obscuration

against thermal imaging. It has an absorption band peaking at about

9.5 ym, which is fairly wide and therefore potentially able to block a substantial portion of the 8 - 14 ym atmospheric window. Since the CO2

laser emits at 9.6 and/or at 10.6 ym, a material absorbing strongly at

these wavelengths is more effective than an aerosol spray with only

general absorption and scattering.

The optical constants n and k determine the behavior as an obscurant.

They depend on many variables in addition to chemical composition,

however, and are difficult to determine. Particle size and shape are among them. Perhaps the most direct way of measurement is unsymmetrica

1

Michelson interf erometry (UMI) in which the phases of reflection spectra

are directly and independently recorded. This procedure has been very

successful with liquids and appears to be applicable to fine powders or compacted powders, provided both theory and procedures are properly

modified

.

While UMI would still be our preferred method, the availability of com- pacted material of flatness and surface finish better than 1.0 ym made

specular reflection a promising initial step for background information.

This procedure has many well-known drawbacks, especially since boron

carbide is hexagonal or rhombohedral and the bulk density was less than

the crystal density, but it nevertheless gives some information on the

location, relative strength, and width of the infrared bands and helps

pinpoint problems to be overcome by UMI later. This paper describes

the reflection method used and preliminary results .

II. MATERIAL

Compacted Norbide (boron carbide plates) was obtained from the Norton

Company. Pieces of 10 x 10 x 5 mm size were cut with a diamond saw and

diamond-polished. A representative piece was coated with a thin layer

of gold and examined under the scanning electron microscope (SEM) . A

particle size of average diameter of 2.0 ym was noted. Surface examination by X-rays in the SEM apparatus revealed the presence of iron,

presumably as iron oxide on the surface. An estimate of the surface

126
area potentially covered is 1 - 5%, which is considerably above the 0.9%

by weight of Fe for the bulk material. Therefore it could be a factor

influencing the optical constants.

III. APPARATUS

The instrument used for the reflectance measurements was a Model £21

Perkin Elmer double-beam grating spectrophotometer with a Harrick

reflectance adapter (VRA and VARA) containing a mirror system automatically equating angles of incidence and reflection. Different attenuating screens could be put into the reference beam to balance the instrument for a gold reference surface. A wire grid polarizer of fine

mesh size (0.4 ym) could be inserted in front of the sample slit.

IV. PROCEDURE

Measurements were made at several angles of incidence £or both unpolarized^, and p-polarized radiation in the 700 - 1200 cm wavenumbers

range. The standard gold surface and the boron carbide surface were

examined under identical conditions . Careful attention was given to

having the surfaces clean.

V. DATA PROCESSING

2 The processing procedure adapted was that of Simon } although^the form

of the Fresnel equations used by Rusch, Koehler, and Lagowski proved

to be more readily programmable. For every 10 degrees of incidence,

plots, of which Figure 1 is an example, were drawn to supplement those

of Simon for 20 and 70 only. Furthermore the computer program and

plotting routine can generate plots at any angle. It was found to be

best to compare R } R , and R at one angle only and find the best com- bination of n and^k to satisfy at least two R' s simultaneously. This

is the method of Heilmann.^ The advantage is that no change need be

made in the area irradiated; it proved to be difficult to maintain a constant area , especially at large angles of incidence. The experimental arrangement was optimized at 60 incidence ^ although other angles were also used.

VI. RESULTS

Figure 2 shows n and k for the 700 - 120(J cm ^ region. There are two

absorption bands ; a minor one at 810 cm and major one at about

1050 cm . Figure 3 shows typical reflectance spectra from which

Figure 2 was derived.

127
VII. DISCUSSION

The limitations of the reflectance method are quite clear as the comparison given by Huffman^ has shown. An "absorption" spectrum of a KBr

disc containing suspended particles of a very limited size range appears

to be more direct. This author is, however, well aware of many difficul

ties of the pressed KBr technique in quantitative infrared spectroscopy

and some of them would seem to be applicable here as well. As our SEM/

X-ray measurements have shown, contaminants prefer to accumulate on interfaces. The interface area of suspended particles is extremely

large. Infrared-invisible contaminants may affect the scattering characteristics of other materials.

We tried to correct for the differences between bulk and particle densities by assuming a proportion of "black" holes on the reflecting surfaces. However, it turned out to be impossible to get consistent

results. Judging from the SEM photos, it would seem that the holes were

"filled in" in the polishing operation.

ACKNOWLEDGEMENT

This work was supported in part by Naval Air Systems Command under

Contract No. N00164-79-M-2522

.

REFERENCES

1. Harrick, N. J., "Internal Reflection Spectroscopy". Second Edition

1979. Harrick Scientific Corporation, Ossining, N.Y. 10562.

2. Simon, I., J_. Opt . Soc . Am. , 41, 336 (1951).

3. Rusch, P. F. , Koehler, W. H. , and Lagowski, J. J., Spectrochim . Acta

25A, 1537 (1969).

4. Heilmann, G. , Z. Naturforsch. 18, 1103 (1962).

5. Huffman, D. R. , Adv. in Physics , 26, 129 (1977).

128
1

Figure 1: Complex refractive index versus absorption at one angle of incidence.

1 f \ » ( » t

1 —t » 1/.0 766 P6Q 90O (OOO 1(00 (200

Figure 2: Complex refractive index spectrum.

129
100 &o fooo

t~ r //oo /Joo

Figure 3: Reflectance spectra

130
CRITICAL POINT ANALYSIS OF MULTIPHONON

INFRARED ABSORPTION IN ZINC SELENIDE

Claude A. Klein and Robert N. Donadio

Research Division, Raytheon Company

Waltham, Massachusetts 02154

Multiphonon lattice-absorption processes in cubic ZnSe have been the

subject of a number of investigations, beginning in 1961. Infrared

reflectance and transmittance measurements by Aven et al . [1] first

led Mitra [2] to attempt an interpretation in terms of characteristic

phonon energies and , subsequently , to carry out a partial critical point

analysis [3]. Inelastic neutron- scattering [4] and second-order Raman

scattering [5] data having since become available, it should now be

feasible to interpret multiphonon infrared absorption in ZnSe on a much

sounder basis. Furthermore, the development of chemically vapordeposited (CVD) ZnSe has stimulated a great deal of interest in obtaining absorption spectra covering a range of multiphonon regimes [6,7,8],

primarily for the purpose of characterizing the nature of light-absorption processes of relevance in a C0 2~laser environment. In this context, Bendow et al . [9] succeeded in demonstrating that, even in the

three- and four-phonon regions, ZnSe exhibits structure, which appears

to be consistent with the results of calculations that emphasize the

effect of phonon density of states. For this reason, it will be the purpose of the present paper to take advantage of the availability of CVDZnSe specimens of widely differing thickness in order to examine the

room-temperature infrared spectrum over the entire wavelength range of

interest and, in particular, to identify significant features of the absorption and assign them to phonon summations at critical points of the

Brillouin zone.

Figure 1 shows the far-infrared transmission profile of a thin specimen

of CVD ZnSe (t = 0.0225 cm), which illustrates the type of structure

that this material can exhibit in the two-phonon absorption regime

[LO(D< v < 2 LO(D]. Twelve features have been identified and

assigned to critical-point phonon combinations as indicated in column 2 of Table I. In this connection, we note that, of the three sets of roomtemperature zone-edge mode frequencies presently available [4,5,10],

only those of Irwin and LaCombe were found to be compatible with both

infrared lattice absorption and Raman spectral characteristics. Further

comments are in order:

(a) At frequencies above the one-phonon cutoff [LO(T) = 250 cm~l]

,

electric-dipole allowed two-phonon summations occurring at stations X

and L all have been assigned to specific features of the spectrum, with

the exception of the TO(L) + LA(L) combination.

(b) On assuming that three-phonon processes can be ruled out , it appears necessary to assign two of the features to events occurring at station W; feature 5 then must be attributed to an acoustic phonon

131
overtone, which violates the usual dipole selection rule but confirms

that, for ZnSe as for ZnS [11], electric quadripole moments indeed play

a significant role in the multiphonon absorption mechanism,

(c) Most of our assignments also apply to Irwin and LaCombe's secondorder Raman features and properly describe their polarization characteristics [12].

Since the highest-frequency zone-boundary phonons [LO(X,L)] are at approximately 224 cm~l, it follows that the absorption edge shown in

Fig. 2, and which refers to an 0.264-cm thick specimen of CVD ZnSe,

must be attributed to three-phonon processes operating up to a cutoff

at 3 x LO ^ 670 cm~l. There are many such processes that are infrared active thus giving rise to considerable complexity if one attempts

to elucidate the details of the spectrum in this frequency range; also,

structural features are seen to be much less prominent than earlier.

For this reason, it should be more meaningful to describe the gross

features of the absorption in terms of combinations of four characteristic phonons , or in other words , on the basis of assigning a single

phonon energy to each of the main branches of the dispersion. In this

regard, it is interesting that the density-of-states distribution generated by means of neutron diffraction [13] has four major peaks, which

are indicative of weighted average populations at the Brillouin-zone

boundary and, hence, might provide a set of suitable characteristic

phonons: LO = 222, TO = 204, LA = 131, and TA = 65 cm" 1

. In this

approximation, and following Bendow [9], we may assume that for highmultiplicity (n > 3) phonon events selection rules are of little consequence. In this manner, we arrive at assignments as specified in

Table I, which points to some impressive correlations in terms of

shoulder positions (see Fig. 2) and reemphasizes the importance of

optical phonon overtones in shaping the absorption profile of zincblende type semiconductors [11].

Work in progress involving 1-in. thick specimens has allowed us to identify four-phonon summations in the infrared transmission, at frequencies

up to 750 cm~l. In this connection, we note that both Fourier transmission spectroscopy [14] and thermal emittance work [15] performed

at Hanscom AFB disclose that structure persists in the absorption spectrum of CVD ZnSe, over the entire four-phonon region. Figure 3

illustrates the situation as recorded by Lipson [14] together with relevant assignments as obtained from our previous set of characteristic

phonon energies. Evidently, this procedure confirms the contention

that structure in the absorption spectrum of CVD ZnSe, at wavelengths

above 11 ym, can be attributed to the phonon dynamics and reflects

the main features of the phonon density-of-states distribution.

REFERENCES

1. M. Aven, D. Marple, and B. Segall, J. Appl. Phys. 32, 2261 (1961).

2. S. S. Mitra, Phys. Rev. 132, 986 (1963).

3. S. S. Mitra, J. Phys. Soc7~7apan 21, supplement, 61 (1966).

4. B. Hennion, F. Moussa, G. Pepy, and K. Kunc, Phys. Letters 36A , 376 (1971).

132
5. J. Irwin and J. LaCombe, Can. J. Phys. 50, 2576 (1972).

6. T. F. Deutsch, J. Phys. Chem. Solids 34, 2091 (1973).

7. J. M. Rowe and J. A. Harrington, in Optical Properties of Highly

Tranparent Solids (Plenum Press, New York, 1975), p. 109.

8. P. Miles, in Proc. Fifth Conf. Infrared Laser Window Materials

(AFML, Wright -Patterson AFB, 1976), p. 8.

9. B. Bendow, H. Lipson, and S. Yukon, Phys. Rev. B16, 2684 (1977).

10. B. A. Weinstein, High Pressure Sc. and Tech. 1, 141 (1979).

11. C. A. Klein and R. N. Donadio, J. Appl. Phys., to be published.

12. W. G. Nilsen, Phys. Rev. 182, 838 (1969).

13. R. Beserman, M. Zigone, W. Drexel, and C. Marti, Solid State

Comm. 18, 419 (1976).

14. H. G. Lipson, Appl. Opt. 16, 2902 (1977).

15. L. Skolnik, A. Kahan, R. Brown, H. Lipson, A. Golubovic, and

J. Engel, in Proc. Fifth Conf. Infrared Laser Window Materials

(AFML, Wright -Patterson AFB, 1976), p. 806.

Table I. Two- and Three-Phonon Summation Bands in Cubic ZnSe

Feature^ a ^ Assignment Position (cm 1

) (b) Ac) Comment

J A ( Y ) -t-T A f Y \ 2Q2

2 TD { Y 1 4-T A ( Y \ £10 P

3 L0(L)+TA(L) 282

4 L0(X)+TA(X) 293 R

5 2A

1 (W) 300 Dipole forbidden

6 o

1 (vn+A2

(v>) 329 Also 02 (W)+A

2 (W)

7 2LA(L) 362 R

8 2LA (X

)

380 Dipole forbidden; R

9 T0(X)+LA(X) 401 Also LO(L)+LA(L);R

10 2TO(X) 412 2T0(L);L0(X)+LA(X);R

11 LO(X)+TO(X) 430 Also LO(L)+TO(L) ;R

12 2L0(L) 448 R

13 TO+2LA 466 R

14 2T0+TA 473

15 LO+2LA 484

16 LO+TO+TA 491 17 2L0+TA 509

18 2T0+LA 539

19 LO+TO+LA 557 20 2L0+LA 575

21 3TO 612

22 LO+2TO 630

23 2LO+TO 648

24 3LO 666

(a) See Fig. 1 and Fig. 2. (b) Based on critical-point mode frequencies as listed in Ref. 5 and

characteristic zone-edge phonons derived from a density-of-states

distribution reported in Ref. 13. (c) R means Raman active as observed in Ref. 5. 133
WAVELENGTH (,/j.m) 20 25 30 40 50

500 400 300 200 WAVENUMBER (cm"1 )

Fig. 1. Optical transmittance of

chemically vapor-deposited ZnSe in

the two-phonon absorption regime.

WAVELENGTH (^m)

14 16 !8 20 25 30

1

I 'l

1

I

1

I

1 'l1 I1 V 'I' " !'

1 "! CVD ZnSe

t= 0.264cm

800 600 400

WAVENUMBER (cm"1 )

Fig. 2. Optical transmittance of

chemically vapor-deposited ZnSe in

the three-phonon absorption regime

Fig. 3. Room-temperature absorption spectrum of chemically vapordeposited ZnSe in the three- and four-phonon absorption regimes.

Assignments are based on a set of characteristic phonons specified

in text. 134
MULTIPHONON ABSORPTION IN INFRARED GLASSES

BASED ON ZIRCONIUM AND HAFNIUM FLUORIDES

Herbert G. Lipson, Bernard Bendow and Martin G. Drexhage

Solid State Sciences Division, Rome Air Development Center

Hanscom AFB, MA 01731

There has been considerable interest in recent years in highly transparent mid-IR glasses for applications such as IR-domes , laser windows

and guided-wave optics (1). The preparation of one such class of

glasses based on zirconium (2-5) and hafnium (6) fluorides has been

reported recently. These glasses possess high densities (^4.5-6 gm/

cm3), fairly low refractive indices 0^1.53) and low glass transition

temperatures C^600-620°K) , and are highly resistant to attack by water

or acids. Most importantly, they offer the potential for high transparency (absorption coefficient a < 0.1cm ) throughout the visible,

out to IR wavelengths in the vicinity of 6ym and beyond. In the

present work we conduct experimental investigations of the vibrational

edge absorption of these glasses and compare the results with theoretical predictions. In particular, we perform detailed frequency ( (0 ) and

temperature (T) dependence studies of a for one zirconium fluoride

based glass, and interpret the results in terms of intrinsic multiphonon absorption. The analysis also yields parameters which can be utilized to predict a in ranges which are not usually accessible to experiment .

The glasses utilized for the present study were synthesized using

reagent grade Zr02 , Hf02 , BaO, Th02 , La203 and NH4F' HF as starting

materials. The preparation techniques were similar to those reported

previously- (2-6). The required amounts of the oxides were thoroughly

mixed with twice the stoichiometric amount of NH^F-HF needed to fluorinate them and placed in a vitreous carbon crucible loosely covered with

platinum foil. Batches of ^25g were fired under argon atmosphere,

first at ^40000 for 1.5h to achieve fluorination and then briefly at

°J 800°C to melt the glass and to assure the removal of any excess NH4 F

- HF. Melts were cast into room temperature b^ass molds and then annealed at ^J 300o C, yielding clear vitreous discs %2.5cm in diameter by

2-4mm thick.

The glass compositions, selected from the center of the glass formation

regions reported in references 2-5, are as follows (mol %) : Glass ZBT,

57.5 ZrF4, 33.75 BaF2 , 8.75 ThF4 ; Glass HBT, 57.5 HfF4, 33.75 BaF2 , 8.75 ThF4; Glass HZBT, 28.75 Hf F^ , 28.75 ZrF4 , 33.75 BaF2 , 8.75 ThF4

,

Glass HBL, 57.5 Hf F4 , 33.75 BaF2 , 8.75 LaF3

135
The absorption coefficient was deduced from transmission measurements

conducted utilizing a Digilab FTS-14 Fourier spectrophotometer. A

small furnace was added for measurements above room temperature.

Readers interested in details of the measurement technique are directed to Ref. 7.

Room temperature absorption spectra for glasses with the four compositions indicated above are displayed in Fig. 1. The results are in

good agreement with spectra obtained previously for a > 0.1cm- -1- utilizing a Perkin-Elmer 221 spectrophotometer (6). The values obtained here for a below ^O.lcm"! are sensitive to corrections for

background noise, and to the values used for the reflectivity for

each oo and T. A measure of confidence in the data for this range is

provided by the very good agreement between theory and experiment obtained in a detailed analysis of ZBT glass data, as described below.

ZBT and HBL display an overall exponential-like decrease in a (see

Fig. 1) characteristic of intrinsic multiphonon absorption over the

frequency range under consideration (8) ; HZBT departs somewhat from

such behavior, while HBT departs markedly. The absence of structure

in the ZBT spectrum, combined with the similarity in bonding between

Zr and Hf , strongly suggests that the observed structure in the other

spectra are due to extrinsic processes. This is likely the result of

utilizing 0.97 purity Hf02, as compared to 0.999 purity Zr02> Hfbased samples with improved purity are currently in preparation. We

note that a smooth, structureless spectrum is indeed a familiar characteristic of intrinsic multiphonon absorption in most ionic materials

(8). The shift in the exponential-like portion of the curves may, as shown previously (6) , be attributed to differences in reduced mass between Hf and Zr in the present glasses.

Since its spectrum appeared closest to intrinsic, ZBT was chosen for

more detailed investigations over a range of elevated temperatures.

Experimentally determined values of a are displayed in Fig. 2, along

with a theoretical fit based on Ref. 9. The latter theory fits the

absorption in the exponential-like regime with just three parameters

via the approximate formula

where N is the Bose-Einstein function and oo0 an appropriate average

phonon frequency. The overall good agreement between theory and

experiment suggests that the observed absorption is due to intrinsic

multiphonon processes. Departures between theory and experiment may

be due to deviations in the data from the purely exponential dependence assumed in the theory. The value utilized for oo0 is consistent

with Raman (various peaks between 350-600cm~l) and reststrahl reflectance (peaking near 500 cm~l) (10). Thus the shoulder in the data

spanning the 1300-1700 cm~l may well be due to three-phonon conbination bands involving these vibrations. One also notes a weakening

a

136
FIGURE 1

Measured absorption coefficient vs. frequency for four

fluroide glasses.

HBL^*"\ \WHZBT

\ \ (J(cm-l)-^

1000 1400 1800

_l I I I I l_

FIGURE 2

Absorption coefficient versus

temperature at selected frequencies for ZBT glass; circles

are experimental points and

the curves a theoretical fit

(see text) with Wq = 500 cm~l,

A = 0.00908, a0 = 452091 cm"l.

(jj (em-1

)

I

lO _J200_^ —

•

1300 - •

•

• -J400__*-

•

i50O_« "*

• J620—*

•

XTOO.

0.1

300

_l_

T(°K)-

400 500

I

137
of the spectral structure at elevated temperatures, as expected from

the increase in phonon linewidth as a function of temperature.

The authors thank M. Clark for assistance with the computations, and

C.T. Moynihan and M. Saleh of Catholic Univ. for useful discussions.

References

1. See, e.g., "Optical Properties of Highly Transparent Solids,"

S.S. Mitra and B. Bendow, eds. (Plenum, N.Y. , 1975).

2. M. Matecki, M. Poulain, M. Poulain and J. Lucas, Mat. Res. Bull.

13, 1039 (1978).

3. A. Lecoq and M. Poulain, J. Non-Cryst. Solids 34, 101 (1979).

4. M. Poulain and J. Lucas, Verres Refract. 32_, 505 (1978).

5. M. Poulain, M. Chanthansinh and J. Lucas, Mat. Res. Bull. 12 , 151 (1977).

6. M.G. Drexhage, C.T. Moynihan and M. Saleh, Mat. Res. Bull., in press.

7. See, e.g., B. Bendow et al, Phys. Rev. B, 20 1747 (1979).

8. B. Bendow, in "Solid State Physics", H. Ehrenreich et. al. , eds.

(Academic, N.Y. , 1978) Vol. 33.

9. B. Bendow, Appl. Phys. Lett. 23, 133 (1973).

10. Unpublished data, courtesy of S.S. Mitra, Univ. of R.I.

138
OPTICAL CHARACTERIZATION OF BULK GRADED INDEX MATERIALS

Duncan T. Moore

Gradient Index Laboratory

The Institute of Optics

University of Rochester

Rochester, New York 14627

The implementation of the large gradient index materials into optical

systems relies on the development in four areas. These are the design

and analysis algorithms for including gradient index optics in lens

systems, the fabrication and modeling of glass materials with these

index variations, the measurement of the optical properties, and the

fabrication of the materials into finished lens elements. This paper

is restricted to the discussion of the measurements of gradient index

materials; in particular, the materials whose geometries are larger

than 1 mm. In the systems which are being developed and produced at

this time, the gradients may be as large as 10 mm. In the next few

years the size will increase to multiple centimeter geometries.

In the telecommunications business, the important parameter is the

bandwidth that can be transmitted through a fiber. In the optical

systems design, it is more important to know the quality of an image.

Thus the types of testing equipment that one uses for telecommunications applications are not applicable to that for bulk materials.

Typically, the most important parameters for bulk gradient index ma- terials are: 1) the index of refraction profile of the material,

2) the derivative of the index of refraction profile (the slope)

,

3) the variation of the index of refraction with wavelength, 4) the

index of the variation of index of refraction profile with temperature, 5) the variation of thermal expansion coefficient with temperature, 6) the transmittance of the material, and 7) the three-dimensional variation of the gradient.

The geometries of the gradients are not as simple as they are in telecommunications. There are currently four types of gradients that are being investigated: 1) axial gradient in which the index of refraction varies in the direction of the optical axis, 2) the cylindrical

or radial gradient which varies perpendicular to the optical axis,

3) the spherical gradient which has symmetry about a point, and 4)

the conical gradient which has surfaces of a constant index which are

ellipses, parabolae, etc. Each of these geometries creates unusual

problems for the measurements , particularly in systems which have

spherical or conical symmetries.

The effect of each of these gradients on the aberrations of a lens

system are now well understood. The axial, spherical and conical

139
gradients have the same effect on aberrations as an aspheric surface

does. This implies that any aspheric surface can be replaced with

one of these types of gradients and have equal performance by proper

choice of the gradient profile and its depth. The radial gradient, on the other hand, is much more important from a design standpoint,

although it is much more difficult to manufacture in large geometries.

The principle advantage of radial gradients is in their ability to

correct field aberrations (particularly the field curvature) and

chromatic aberrations. Unlike homogeneous elements, where the focal

length of the lens depends upon the index of refraction^ a slab of

radial gradient material (called a Wood lens) has a focal length which

depends only on the gradient. Therefore, if a gradient profile can be

manufactured which is independent of wavelength, then this single element lens can be achromatized. Based on models predicted by Fantone^

glasses have been manufactured which exhibit no chromatic variation

of the gradient. Of course, there is a variation in the base index,

but the profile itself is unchanged as a function of wavelength. This

results in a chromatically corrected single element lens.

A number of techniques have been proposed for measuring the index of

refraction profile in bulk materials. These techniques include prism

methods, moire techniques, Schlieren, interferometry , auto-collimation

and holography. In some of these techniques, the index profile is not

measured, but rather the derivative of the index of refraction profile,

and thus they are not usable for characterization of the gradient index

profiles because the profile is needed. Furthermore, we are restricted

to techniques which provide accuracies of the index profile of the

order 10~5 in change in index. The most likely prospect is that of

interferometry . However, interferometry has the necessary drawback

that the readout is a series of contours, each of which represents a change in index determined by the thickness and the optical path difference in material. In typical examples, the number of fringes will

reach several hundred, and thus the measurement of a photographic

plate becomes very tedious. Furthermore, in standard interferometry,

there are ambiguities of hills and valleys, that is, you cannot tell

from a simple interferogram whether the phase, i.e. the optical path

and the index, is increasing or decreasing. To eliminate these problems a technique was developed called AC interferometry (also called

phase-locked interferometry , homodyne interferometry , and heterodyne

interferometry) which will allow for the automatic measurement of

phase into a computer or onto a x-y recorder. This technique was not

originally designed for measurement of index profiles, but was con- sidered a general technique for reading of phase maps of complicated

objects

.

For the last eight years the group at the University of Rochester has

used this AC interferometry technique for regular measurement of index

of refraction samples. The technique involves the modulation in time

of one path of a Mach-Zehnder interferometer. By introducing this

140
time variation in phase in one arm relative to the other, the output

of a detector varies in time depending upon the initial location of

the detector in the field. The actual phase of the optical wave can be determined.

The current problems of measurement of bulk gradient index materials

include the variation of the gradient with wavelength. While it can be argued that the measurement of the phase at one wavelength can then

be subtracted from the data at a second, this becomes a tedious operation and is subject to a series of registration and magnification

errors. Therefore, a two wavelength interferometry technique has

been developed and is described in a subsequent paper.

The most important type of gradient at todays writing is the axial

gradient. This gradient can replace an asphere in a lens system and

is readily manufactured by a number of different techniques. It is our

feeling that these gradients will be implemented in gradient index

systems in the next three years. We therefore need to be able to

measure the index of refraction in the lens blanks. In such a lens

blank the index profile is in the direction of light propagation.

Therefore, a standard interferometer will not make such a measurement.

To be able to measure non-destructively the index profile in each

blank it is necessary to develop a new type of instrumentation. This

instrument is based on AC interferometry techniques. As a sample is

rotated in a beam, the phase varies in a well-known way as a function

of rotation. If the general shape of the gradient is known, then

the index of refraction profile can uniquely be determined. Such an instrument has been developed and tested.

The next series of problems to be solved are those of the index of re- fraction measurements in the infrared and the measurement of thermal

properties of gradient index materials. In the infrared, the problems

become one of using the same phase modulation techniques where the

modulation has to be much larger than in the visible. Linearity of

the system becomes more important. The measurement of thermal properties is a very difficult one. It is necessary to measure not only

the change in index of refraction profile as a function of temperature,

but also to measure a thermal expansion coefficient as a function of

position. The latter is important in actual manufacturing of gradient

index materials at elevated temperature. A system using a Fabry-Perot

interferometer with multiple internal interferometers will be discussed for such a measurement.

The implementation of gradient index components into conventional optical systems relies heavily on the measurement technique. While it

is now possible to design with such materials and many materials have

now been made, the measurement technique ultimately will determine the

cost and use of bulk gradient index materials.

141
1 . S . D . Fantone , Design, Engineering and Manufacturing Aspects of

Gradient Index Components , Ph.D. Thesis, University of Rochester,

1979.

142
MEASUREMENT OF AXIAL / GAUSSIAN INDEX DISTRIBUTION

Glen W. Johnson

The Institute of Optics

University of Rochester

Rochester, New York 11*627

Two examples are presented that illustrate the

measurement capabilities of a modified Mach-Zehnder

interferometer (see Fig. 1), its support electronics and

computer programs. Presently, two types of measurements

are possible. First, two-dimensional scans of the sample

may be made. In this case, two galvanometer driven mirrors

are positioned such that successive points of the object

plane (at the sample) are imaged onto the detector. Second,

with the galvanometers fixed at preset positions, the

sample may be rotated to selected angles, either manually

or under program control.

Figure 2 illustrates the orientation of the sample

in the sample arm of the interferometer. When two-dimensional maps are made, the rotation angle w is (very nearly)

zero and the surface of the sample is imaged onto the

detector plane. When measurements of optical path length

versus angle are made, a point (along the axis of rotation,

for this study) is selected using the galvanometers.

Data derived from measurements of the latter type

are analyzed (with a specially written ray trace program

(1)) by simulating the optical system in the neighborhood

of the sample as follows. From a point on the exit plane,

a ray traveling towards the sample originates. Upon

passing through the sample, the ray terminates on the

offset plane. At this plane, the ray's optical path length

is compared with the experimentally derived optical path

length. The position of this offset plane is adjusted

automatically during the analysis.

The index profile of a class of gradient index

materials is described accurately by a Gaussian distribution (2) as in the equation

n(z) = n(0) + An exp(-a(z-d) ) where n(0) is the base index, An is the maximum index

change, a is the shape factor of the distribution and d

is a displacement representing the location (along the

z axis) of the peak of the Gaussian. These four Gaussian

coefficients are also construction parameters whose values

may be adjusted automatically by the ray tracing program

during the analysis of experimental data.

143
As in the various forms of tomography / In order to

compute information about the index as a function of

position within a sample region, a series of measurements

are made of a beam that probes the sample at different

angles. To show how this can be done with a system for

which a model of the refractive index distribution is

assumed, measurements made using the wavefront tracking

capabilities of the modified Mach-Zehnder interferometer

are analyzed.

For rays traced through a homogeneous glass plate

(1 cm. thick) over a range of incident angles a plot of

the optical path length versus angle of incidence shows

a characteristic parabolic shape. When a typical axial

Gaussian index distribution is introduced into the glass

plate, the shape of the curve (optical path length versus

angle) is slightly different. if measurements of such

a system are to be made over incident angles of plus and

minus 60 degrees, optical path length variations of the

order of two millimeters (approximately 4000 fringes) must

be tracked. In addition, to resolve the small differences

between the homogeneous and i nhomogeneous cases,

measurements of optical path length differences that are

of the order 0.1 micrometer must be made.

When a gradient sample or a homogeneous plate of

glass is mounted on the stepping motor driven rotary

stage and measured under program control, a plot of the

optical path length versus incident angle is generated.

Once the experimental data and the optical system have

been described to the ray tracing program, the construction parameters that are free to vary must be described.

For the measurements of the homogeneous plate, the thickness and the index are known fairly accurately. These

values are held fixed, initially, while the two quantities

(position of the offset plane and the offset angle) are

allowed to vary. After good estimates for these quantities

are generated by the program, all four construction parameters (offset angle, position of offset plane, glass plate

thickness and index) are allowed to vary.

For the homogeneous sample, the optimization proceeds

quite rapidly towards a solution. The thickness of the

homogeneous sample, as measured by a micrometer, is 1.001

+..001 cm. and the thickness, computed from measurements

made with the interferometer, is 1.0012 cm. The index of

refraction, computed from measurements using a Pulfrich

ref Tactometer, is 1 . 5206 +.. 0002 and the index computed

from the i n terf eromet r i ca 1 1 y measured data is 1.5205.

144
For the analysis of the measurements of the gradient

sample, a subset of data points was selected initially.

After the initial fit to the data was performed, the

residuals were plotted. From that plot, gross errors in

properly assigning the fringe count were obvious. To reduce

the time required to compute better estimates for the

construction parameters, a representative set of 10 data

points was selected for fitting. The residuals associated

with these initial points are plotted in Figure 3. After

optimizing using this subset of data, the residuals were

plotted again. Finally, optimization was performed on

the entire dataset. Most of the optical path differences

(between computed and measured values) lie within about

one fifth of a wavelength. Given the conditions of the

experiment, the magnitude of these residuals is attributed

primarily to errors made in the phase measurements. Using

a micrometer and a standard, an estimate of the thickness

was 1. 0028 +.. 0005 cm. After final optimization, the computed

thickness (1.0026 cm.) is found to lie within this range.

With the exception of d, good estimates for the values

of these Gaussian parameters are known. The table below

reviews the measured Gaussian coefficients.

Measured Gaussian coefficients (Sample: BL44)

Coef f i c i ent

n(0)

An

a

d (*)

wavelength of

measurement

(*)

Moore/Ryan

1.505

. 0294

8.140 cm

-.0303 cm

5145 ym

Due to unresolvable differences

procedures, the values for this

can not be compared.

present work

1.5044

.02876

8.149 cm" 2

.00005 cm

(-.015 cm

approx. removed

in preparation)

.5309 ym

in experimental

coef f i ci ent

Procedures for reconstructing index profile information from measurements of optical path length have been

given. These procedures have been applied in the reconstruction of an axial, Gaussian index profile.

References

1. G. W. Johnson, Measurement of Strongly Refracting

Th ree-D imens i ona 1 Index Distributions . Ph.D. Thesis, University of Rochester, 1979

2. D. T. Moore and D. P. Ryan, "Measurement of the

Optical Properties of Gradient Index Materials,"

J. Opt. Soc. Am., pp. 1157-1166 68 (1978)

145
UJ

146
GRADED- INDEX AR SURFACES FOR IMPROVED

LASER-DAMAGE RESISTANCE

W. H. Lowdermilk and D. Milam

Lawrence Livermore Laboratory

University of California

Livermore, CA 94550

Thin-film AR (anti ref 1 ecti on) coatings have traditionally been the most

easily damaged elements in laser amplifier chains. Their damage thresholds limit the output fluence of high power lasers for pulsewidths in

the 1-10-ns range. The 1-ns threshold for commercial thin-film AR

coatings of 4-6 J/cm2 has resisted numerous experimental attempts to

improve it. These attempts included variations of substrate materials

and surface finish, coating design, materials, and deposition processes.

In exploring alternate techniques for AR surfaces we found that gradedrefractive- index AR surfaces, which can be developed on certain types of

glass by acid etching, have median damage thresholds two and one-half

times greater than the electron beam evaporated, thin-film Si02 /Ti0 2 AR

coatings now used extensively in large Nd: glass laser systems.

M. J. Mi not 1 introduced the formation of a graded- index surface based

on separation of certain glass compositions into silica-rich and silicapoor phases. Acid etching the more soluble, silica-poor phase forms a microporous high-silica-content surface layer. The pores have typical

dimensions of 100 A , so scattering of visible and longer-wavelength

light is negligible. Reflectivity of the surface can be 0.1-0.2%

(comparable to thin-film coatings) over a very broad bandwidth (<l/2%

for 0.35-2.5-um light) and range of incidence angles. Such optical

behavior is characteristic of a graded refractive index as opposed to a homogeneous low- index layer.

Damage threshold measurements were made with 1.06-um, 1-ns, linearily

polarized pulses, focused to a 2-mm spot diameter on the sample. Before

and after irradiation, each site was examined and photographed using a Nomarski microscope at lOOx magnification. Sites were irradiated, once

each, at increasing fluence levels until physical change occurred. At

threshold, 1-10 spots, ~10 urn in diameter, of apparently melted material

were formed with random distribution over the irradiated surface.

The laser-damage thresholds of more than 60 graded-index samples have

been measured. The median threshold of 12 J/cm2 is 2.5-times greater

than the median threshold of state-of-the-art Si0 2 /Ti0 2 thin-film AR

coatings. Some samples were further irradiated at fluences of

20-50 J/cm2

. Even then, the extent of damage was not severe; in fact,

it was difficult for the unaided eye to detect. Such behavior is

distinctly different from thin-film coatings, where irradiation at

fluences only 10-20% above threshold causes catastrophic damage.

147
We believe the high damage thresholds of graded- index AR surfaces are due to the absence of the highly contaminated substrate/film interface

region where AR coatings normally damage, and/or the removal of surface

impurities by the acid etch.

In conclusion, research samples of graded- index AR surfaces have

exhibited a median, 1-ns damage threshold of 12 J/cm2

, compared to a median threshold of 5 J/cm2 for commercial thin-film AR coatings, and

some samples withstood fluence of 20-50 J/cm2 without catastrophic

damage. The transmission and scatter throughout the visible and near-IR

spectral regions were found to be acceptable for laser-transmitting

optical components.

REFERENCES

1. M. J. Minot, J. Opt. Soc. Am. 66, 515 (1976).

148
REFLECTANCE PROPERTIES OF PRESSED TETRAFLUOROETHYLENE POWDER

Jack J. Hsia and Victor R. Weidner

National Bureau of Standards

Washington, D. C. 20234

Good white diffusers are useful in diffuse reflectance spectrophotometry

both as diffuse reflectance standards and as coatings for increasing the

reflectance efficiency of integrating spheres used in measuring diffuse

reflectance. Historically, the most commonly used materials have been

magnesium oxide and barium sulfate powders or paints. Much has been

written on the optical properties of these materials, and the advantages

and disadvantages of their use in spectrophotometry applications have

been experienced by nearly anyone faced with the problems of reflectance

spectrophotometry.

This paper will describe some of the properties of tetrafl uoroethyl ene 1 powder that make it attractive as a substitute or replacement for the

commonly used magnesium oxide or barium sulfate coatings.

Basically, tetrafl uoroethyl ene powder exhibits the highest diffuse

reflectivity of any known material in the wavelength range 200 nm to

2500 nm, its reflectance being above 96% in this wavelength range and

greater than 99% over the wavelength range 400 nm to 1800 nm. It is

manufactured in such high purity that samples prepared from different

lots over a 5 year period are found to have the same reflectance to

within ±0.2%. Its reflectance properties are not affected by changes in

humidity. Exposure to intense ultraviolet radiation causes little or

no change in its reflectivity in the visible and infrared and only slight

degradation of the ultraviolet reflectance2

. The mechanical properties

of pressed tetrafl uoroethyl ene powder are excellent from the standpoint

of using it as an integrating sphere coating.

The absolute 6°-hemispherical spectral reflectance of tetrafl uoroethyl ene powder for sample densities of approximately 0.8 g cm"3 has been determined by means of the NBS Reference Spectrophotometer3 for diffuse

reflectance and the reflectance accessories used in conjunction with

this instrumentation. These reflectance accessories include integrating

spheres for measuring 6°-hemispherical reflectance, directional -hemi

spherical reflectance, and a specular refl ectometer which can be used

to measure bidirectional reflectance in the plane of the incident beam.

The term "6°-hemispherical " refers to a geometry in which the incident

sample beam is 6° from the normal to the sample plane and the hemispherical reflectance of that beam is measured. This is a commonly used

geometry in many commercial spectrophotometers equipped with integrating

spheres for measuring diffuse reflectance. The geometry allows the

149
specular component of the reflected sample beam to be included in the

hemispherical reflectance measurement, a condition which would not be

possible with the sample beam normal to the sample plane.

Measurements of the absolute reflectance of tetrafl uoroethylene powder were made by means of the reference spectrophotometer, using the auxiliary sphere or Van den Akker method4

. Briefly, the technique utilizes

a measuring integrating sphere equipped with a suitable detector and a second sphere (auxiliary sphere) which is attached as a sample to the

sample port of the measuring sphere. The auxiliary sphere is lined

with a coating of the material to be measured (in this case, tetrafl uoroethyl ene powder). The auxiliary sphere, and several flat samples

of the same material used to line the auxiliary sphere, are measured.

These flat samples are prepared in the same manner and with the same thickness and surface finish as the auxiliary sphere coating. Calculations from these measurements will yield the absolute reflectance of

the sphere coating for the bi hemispherical geometry represented by this

double sphere geometry. The 6°-hemispherical reflectance will be

slightly lower than the bihemispherical value. In order to make this

adjustment to the 6°-hemispherical geometry, the directional -hemispherical distribution of the tetrafl uoroethyl ene powder reflectance must be

determined by means of a special integrating sphere which will be

described.

Measurements of the hemispherical reflectance of tetrafl uoroethyl ene powder as a function of angle of incidence (directional -hemispherical

)

are made with an integrating sphere in which the sample is suspended

in the center of the sphere3. A stepping-motor-dri ven turntable located on top of the sphere can control the angle of incidence of the

sample beam by rotating the suspension rod on which the sample is

mounted. The detector is located at the bottom of the sphere where it

is baffled so as to prevent direct viewing of the sample or sphere port.

Di rectional -hemispherical reflectance measurements are made at angles

of incidence in 5° increments between 5° and 75°. All measurements

are then normalized to the value at 6° incidence, thus showing the

relative diffuse reflectance of the sample at the selected angles of

incidence.

In addition to the 6°-hemispherical reflectance and the directional

hemispherical reflectance, measurements were also made of the directional

directional or bidirectional reflectance of tetrafl uoroethyl ene powder

for the plane of the incident sample beam. The tetrafl uoroethyl ene powder samples were prepared with both smooth and rough finishes for

this measurement. Angles of incidence of -10°, -30°, -50°, and -70° were selected and the reflected signal was measured at viewing angles

of -80° to +80° in increments of 10°. The limiting aperture of the

detector system for these measurements subtended an angle of 3.6° at

the sample. The measurements were made at 300 nm, 600 nm, and 1500 nm.

Among the other optical properties of tetrafl uoroethyl ene powder that

have been investigated at NBS are its reflectance as a function of

150
thickness, and its fluorescence properties. It was found that the maximum reflectance of tetrafluoroethylene powder was obtained for densities

of approximately 0.8 g cm

-3 and thicknesses of 6 mm or more, for the

wavelength range of these investigations. The reflectance of tetrafluoroethylene powder as a function of density is reported in reference

2.

Although there is no direct evidence that tetrafluoroethylene powder

itself fluoresces, there is an indication that there is some weak

fluorescence associated with contaminants, possibly introduced into the

powder from the plastic bag in which the material is shipped. It is

known that tetrafluoroethylene powder can be contaminated by tobacco

smoke and that this introduces a weak fluorescence effect. The observed

excitation wavelengths are in the wavelength range 270 nm to 290 nm with very weak emission in the wavelength range 300 nm to 330 nm. For

most spectrophotometry application where the sample is illuminated

with essentially monochromatic sources the fluorescence does not introduce a problem. No fluorescence has yet been observed for the visible

or infrared spectral range.

A detailed description of the diffuse reflectance properties of tetrafluoroethylene powder and the techniques used in their determination is

being prepared for publication. An Information Sheet describing techniques for using tetrafluoroethylene powder and tabulated results of

the absolute reflectance measurements of the powder is available from

the authors. The absolute 6°-hemispherical reflectance is given at

10-nm intervals over the spectral range 200 nm to 2500 nm. Data is

also given for the measurements of directional-hemispherical reflectance

and bidirectional reflectance.

REFERENCES:

1. Tetrafluoroethylene resin is manufactured by Allied Chemical Co.,

under the trade name Halon. This product is mentioned by trade

name for purposes of identification, but in no way implies recom- mendation or endorsement by the National Bureau of Standards.

2. Grum, F. and Saltzman, M.; P-75-77 New White Standard of Reflectance, Compte Rendu 18 e Session, Londres 1975, CIE Publication

No. 36, 91 (1976).

3. Venable, William H. Jr., Hsia, Jack J., and Weidner, Victor R.,

Development of an NBS reference spectrophotometer for diffuse

reflectance and transmi ttance , Nat. Bur. Stand. (U.S.), Tech.

Note 594-11, 47 pages (October 1976).

4. Venable, William H. Jr., Hsia, Jack J., and Weidner, Victor R.

,

Establishing a scale of directional -hemispherical reflectance

factor I: The Van den Akker Method, J. Res. Nat. Bur. Stand.

82, 29, (July-August 1977).

151
MEASUREMENTS OF LARGE OPTICAL ABSORPTION COEFFICIENTS BY DIFFUSE

REFLECTANCE

R. K. Waring

Central Research and Development Department

E. I. du Pont de Nemours & Co.

Experimental Station

Wilmington, Delaware 19898

INTRODUCTION

The dilution method of diffuse reflectance"'" is, in principle, suited to

the measurement of large absorption coefficients (ou > 10^ cm

- -'-) . A

small concentration, on the order of 0.01, of the unknown is mixed with

a white diluent powder of very low absorption coefficient, but of known

scattering function, S. Then, the Kubelka-Munk theory yields,

(1 -Roo> 2 K

(1) 2R S'

00 where R^ is the diffuse reflectance of a thick layer of powder, and K

is the Kubelka-Munk absorption coefficient of the mixture. Then, making

the assumption that the small amount of absorber has negligible effect

on S, but dominates the absorption,

1 K

a

= tt —. (2)

p 2 v

P Here Vp is the fraction of the powder volume (including air space)

oecUpied by the unknown. The factor 1/2 implies that the optical path

length between two points in the diffusing medium is twice the linear

distance between them. This has been justified on theoretical grounds^

for the relatively high reflectance (R > 0.26) of the diluted samples

used in this work. The technique has been applied to measure the absorption coefficient of airborne particulates^ . The diluent used in

this work was Eastman #6091 BaSO^ White Reflectance Standard^. The

scattering power, for this material has been published5.

EXPERIMENTAL DETAILS

It is implicit in the Kubelka-Munk theory that the absorber is molecular ly dispersed. For particles of diameter d, the condition d <0t - 1

should be approximated for K to be linear in a. For d > > a, K will

become insensitive to changes in 0t. In this work, stable water sus- pensions of powders were centrifuged to remove particles with a Stokes

radius, r s > 10~5 cm. The fines were then heteroagglomerated with the

BaSO, under conditions that prevented homoagglomeration of absorbing

152
particles with each other. The mixture was then dried and pressed into

low density pellets at 2.4x10^ Pascals (350 pounds/in. 2) . Reflectance

of loose BaSC>4 powder is not reduced at this pressure^. To improve

strength, a few drops of a 1% water solution of polyvinyl alcohol were

diffused into the pellet and dried. This also did not measurably

affect reflectance or scattering power. Diffuse reflectance was measured on a Cary 14 fitted with a #1411 diffuse reflectance attachment. Eastman BaSC>4 White reflectance Standard was used as a reference.

To correct for finite absorption in the diluent, intrinsic or possibly

introduced during sample preparation, the following formula was used:

a =-S_{F[R -

- V

P )F[R (3)

p 2v 00 abs v, 00 abs

p d

where R^Cmix/abs) is the absolute reflectance of the pigment/diluent

mixture, R^Cdil/abs) is the absolute reflectance of the diluent alone,

and vj is the fraction of the volume occupied by the diluent in the

sample of diluent alone. Equation (3) reduces to equation (2), if

absorption by the diluent is negligible. Further, if we imagine the

colored pigment to be replaced by white diluent, (3) reduces to the

intrinsic absorption coefficient of the diluent.

In a measurement R (dil/st) is determined according to the relation CO ° Rjdil/abs) = Roo (dil/st)-Roo (st/abs) (4)

where R (dil/st) is the reflectance of the diluent alone measured CO relative to the standard, and Roo (st/abs) is the published absolute

reflectance of the standard. ^ R^tmix/abs) is then measured according

to the relation:

R^Onix/abs) = R^Onix/dil) -R^dil/abs) (5)

where R^Onix/dil) is the reflectance of the pigmented mixture measured

relative to the diluent.

For minimum dependence of a p on errors in measured reflectance, the

colored pigment loading in the mixture should be sufficient to insure

that 0.2 < R < 0.6 in the spectral region of interest^.

RESULTS

As an example of spectra obtained with this technique, Fig. 1 shows the

absorption coefficients of PbCrO^ and BaCrO^ . The shoulder in the

visible, which accounts for the exceptionally strong, pure yellow color

of PbCrO^ is not seen in BaCr04. The additional transition has been

attributed^ to Pb2+(6s)-Cr6+(3d) charge transfer. SzabolO has suggested

a similar interpretation of a qualitative diffuse reflectance spectrum.

A detailed band theory calculation^ indicates that the transition

153
occurs between a filled hybrid 0 ^~ (2p)+Pb2+(6s) state and an empty

Cr6+ (3d) state.

12

Zumsteg has measured the absorption coefficient of PbCrO^ by ellipsometry. While the spectrum is qualitatively similar, the absolute values

are substantially higher. It is of interest to consider possible

sources of error in the diffuse reflectance measurement. Unexpected

difficulties were encountered in measurement of Vp, where

v = c Pp /p (6) P P d p

Here Cp is the mass concentration of colored pigment in the mixture, P

is the volume packing fraction, and p^ and p are the intrinsic

densities of the diluent and pigment, respectively. While, in principle, Cp could be determined from the mass of a dried aliquot of the

stable suspension of fines, the measurement is complicated because the

relative concentration of dissolved contaminants such as surfactants

is enhanced in the classification step. Therefore, in this work, X-ray

fluorescence was used with known mixtures of unclassified pigment and

diluent as standards. Using this technique, we should obtain a value of

c correct to within ±10%.

P

Other sources of error reside in assumptions implicit in the KubelkaMunk theory. While a > 10^ cm

-

! for a strongly colored solid, particle

diameters less than 10" 5 cm are not readily obtainable by grinding.

Colorant concentrated in a particle will be less effective in absorbing

light than an equal amount molecular ly dispersed^. No adequate particle size correction for light diffusing systems is known to this

author. In any event, the difference between ellipsometric and diffuse

reflectance values persists for a < d~l.

An experimental plot of the remission function (1) v_s. Cp(cp < 0.02)

for constant particle size distribution displays slight downward concavity. This indicates a failure in the assumptions of the Kubelka-Munk

theory or of the dilution method. If the curves for different parts of

the spectrum, and thus different absorption are normalized to superpose

them at one concentration, they are nearly identical, indicating that

the non-linearity is a function of concentration, not of ot in the ranges

tested. Accordingly, the non-linearity does not appear to be a particle

size effect. Further, it cannot account for an error larger than 2%

in our results.

None of the identified sources of error seems adequate to

account for the differences (^X2) between diffuse reflectance and ellipsometric determinations. A remaining possibility is that the cause can be found in the abrupt change in refractive index at the surface of

the strongly absorbing solid particles.

The collaboration of J. A. Perry in developing the data analysis is

gratefully acknowledged.

154
1. G. Kortiim, Reflectance Spectroscopy (Springer-Verlag New York,

Inc. 1969) p. 175 f f

.

2. K. Klier, J. Opt. Soc. Am. 62, 882 (1972).

3. J. D. Lindberg, Appl. Opt. 14, 2813 (1975).

4. Eastman White Reflectance Standard #6091, Eastman Kodak Co.,

Rochester, NY.

5. E. M. Patterson, C. E. Shelden, and B. H. Stlckton, Appl. Opt.

16, 729 (1977).

6. E. A. Schatz, J. Opt. Soc. Am. 56_, 389 (1966).

7. F. Grum and T. E. Wightman, Appl. Opt. 16, 2775 (1977).

8. G. Korttlm, op. ext., p. 250.

9. A. W. Sleight, private communication.

10. Z. G. Szabo et al., Spectrachimica Acta 64A, 607 (1978).

11. R. V. Kasowski, submitted to Bull. Amer . Phys. Soc, for March 1980

meeting of APS.

12. F. C. Zumsteg, next paper, this conference.

13. G. Kortlim, op. cit., p. 59ff.

u

z

111 I—

I

u

I—

u.

IdOU

zo

ClO

</> CD<

X 10 2.50-

2.25-

2.Z0-

1

\.SZ1 .25^

1 .00-

0.75-

0.50

0.25H

0.00-

200.

I i i i . I i i i I i i

i i I i '

I ' ' I ' ' 'I ' ' ' 'I ' ' ' ' I ' '

PbCrO^

BeCr04

mTTTTTTP I

i i i i I

i i i i f

i i i i

|

i i iT |

i i i i

i

"

i i i i l

i i 250 . 300 . 350. 400. 450 . 500 . 550 . 600 . 650 . 700. WAVELENGTH. NM

Fig. 1. intrinsic absorption coefficients of PbCrC>4 and

BaCrO^ obtained by diffuse reflectance.

155
ELLIPSOMETRIC MEASUREMENTS OF THE OPTICAL PROPERTIES OF

COMPACTED POWDERS

F. C. Zumsteg

Central Research and Development Department

Experimental Station

E, I. du Pont de Nemours & Company

Wilmington, Delaware 19898

Transmission and normal incidence reflection spectroscopy

are the most common methods for determining optical constants. Both have serious drawbacks when used for many

highly absorbing ( i > 104 cm~l) materials. Both techniques

require moderate size single crystals that may not be

readily available. Transmission measurements require

samples so thin that only micaceous materials can seriously

be considered for measurement. In addition, these measurements do not provide refractive index information. Normal

incidence reflection measurements require spectral data

over an extremely broad range so that an accurate KramersKronig transformation can be made.

Spectroscopic ellipsometry provides a partial solution to

these problems. When single crystals are available, the

optical constants of even anisotropic crystals can be

determined at any given wavelength without the need for

additional spectral information!. In addition, we have

found that ellipsometry can be used to obtain semiquantitative values of the optical constants of powders which have

been compressed into specularly reflecting pellets.

Pellets with densities near 100% were produced by compressing a powdered sample between the faces of a small Bridgeman anvil at pressures ranging from 100-600 atmospheres.

The powder was contained by a 30 mil-thick washer of

Teflon® fluorocarbon resin. The tungsten carbide faces of

the anvil were highly polished, so that in most cases the

resulting pellets needed no additional treatment before

measurements were made.

Ellipsometric measurements were made using a Rudolph Model

200E ellipsometer setup in a standard polarizer-compensatorsample-analyzer configuration. The light source was a

Perkin-Elmer 112 monocnrometer illuminated with a quartzhalogen lamp. A Babinet-Soliel compensator was used so that

1/4 A retardation could be used at all wavelengths.

156
Figs. 1 and 2 show the absorption coefficient, a , and the

refractive index of BiV04 as a function of wavelength.

Absorption data is shown for ellipsometric measurements on

a single crystal and a compressed powder, as well as

R. K. Waring' s data obtained by diffuse reflectance . 2 one

can see that there is excellent agreement between the

ellipsometric data while the diffuse reflectance values of

a are appreciably smaller. Although the ratio is not always

the same, the ellipsometric value is always larger than that

determined by diffuse reflectance. This difference mav result from particle size effects in the diffuse reflectance

method where, for large values of a, light does not interact with the entire volume of the crystallites.

To a certain extent, the agreement between single crystal

and compressed powder is fortuitous. Inasmuch as BiV04 is

anisotropic, one would not necessarily expect agreement

between data obtained from a single crystal and a powder

of randomly oriented crystallites. Fig. 2, in fact, shows

a substantial difference between the single crystal refractive index data and that of the compressed powder.

Ellipsometry is particularly useful for measuring the

optical properties of thin surface layers. As a result,

surface layers, whether they be of a second phase, adsorbed

liquid layers, or irregularities, can cause appreciable

errors. Most of the materials we have examined have been

stable oxides, so our primary concern has been with adsorbed water and surface roughening. In both cases, errors

caused by either appear to be less than a = 3 x 10^ cm~l.

One should note that ellipsometry is limited to measurement of relatively large absorption coefficients,

a > 1()4 cm~l. For values of a less than this, sensitivity

is greatly reduced and surface effects play an increasingly

important role. An example of this can be seen in Fig. 1

where there appears to be a residual absorption of 3 x 104

cm~l for A > 550 nm in the ellipsometric data. From other

measurements, however, we know that B1VO4 has an absorption

coefficient of <.l cm~l in this wavelength region. Similar

discrepancies have been seen in our measurements on other

materials

.

Although there are some limitations to the technique

described here, it provides a method by which optical properties can be obtained when only very small crystallites or

powders are available. One can determine the shape and

location of absorption peaks with a moderate degree of precision and determine the refractive index and the magnitude

of the absorption to a lesser degree.

157
1. M. Elshazly-Zaghloul , A. M. A. Azzam, and N. M. Bushara,

Surface Science 56_, 281 (1976).

2. R. K. Waring, preceeding paper, this conference.

v-V

0) oU

c

o

.Ja

L

a<

X 10 4.0-p-1

3.5-

3.0-

2.5-

2.0-

1.5-

1 .0-

0.5-

0.0-

I j I i i i i L J I I I I J 1—1 I I I L_l I 1—1 I I I I I I I L.

X-A

#

X Xx

X x

/ *

\\\

\

wX

\X

B1VO4

single crystal

^ co mp ressed powder

x diffuse reflecleoce

300.

~i—i—r~1—r-r 350.i—

|—i—I—I—I—I—

r

400. 450. 500. 550. 6C0. 650. 700

Uio velength (nm)

Fig. 1. Absorption coefficient vs. wavelength of BiV04

158
o

c

cLV

»

4.0-

3.5-

3.0-

2.5-

2.0-

1.5-

1.0

J I I I I I I I I 1 I I I I I I I I I I L_

*' *.

****** **** * * * *****

*.

BiV04 * single crystal A compressed powder

T—i—i—i—

|—i—i—i—i—

|—i—i—i—i—

|—i—i—i—I—|—I—I—I—i—|—i—I—i—r- 350. 400. 450. 500. 550. 6C0. 6B0.

Uo velength (nm)

Fig. 2. Refractive index vs. wavelength of BiVO

159
MATERIAL PROPERTIES BY SPECTROSCOPIC ELLIPSOMETRY

D. E. Aspnes

Bell Laboratories

Murray Hill, N. J. 07974

An ellipsometer is an optical device that measures the change in

polarization state which occurs when light is reflected at non-normal

incidence from a surface."'- The polarization state is a complex

quantity having both amplitude and phase, and is independent of the

average light intensity. As a result, ellipsometry offers several significant advantages with respect to reflectance or transmittance

techniques for determining the basic optical properties of materials.

First, two parameters are determined in a single measurement instead of

one. These two parameters can be used to calculate both real and

imaginary parts of the dielectric function of a uniform sample at a single wavelength; extended wavelength measurements and Kramers-Kronig

analyses are not needed. Laminar or otherwise nonuniform samples

which are too complicated to investigate in single-wavelength measurements can be analyzed more definitively for structure and composition

because two spectra are available for interpretation instead of one. Alternatively, the values of parameters in models describing such

samples can be determined more precisely. This is particularly

important if material properties are to be deduced from their measured

visible-near uv optical response.

Second, accurate ellipsometric measurements can be made on surfaces

that are too rough for reflectance spectroscopy . ^ Ideally, samples

should be prepared with undamaged, atomically clean, and specular

surfaces. It is relatively easy to obtain clean, undamaged surfaces by

cleaving, ion bombardment and annealing, or chemical processing techniques. But quite often these surfaces are macroscopically rough,

causing light scattering which leaves them unsuitable for reflectance

spectroscopy although quite adequate for ellipsometric spectroscopy.

Third, the fast measurement and analysis capabilities of automatic

ellipsometers allow cleaning procedures to be monitored and surface

conditions to be assessed essentially in real time. This is almost

trivial to do with spectroscopic instruments that can be tuned to the

wavelength corresponding to the peak in the spectrum of a sample.

At this wavelength, surface sensitivity is maximized because light

penetration is least, and surface overlayers (including microscopic

roughness) almost invariably act to reduce the apparent value of £2

by reducing the impedance mismatch between substrate and ambient.

This leads to a "highest is best" rule that can be applied with

virtually no modeling assumptions or a prior knowledge of sample

160
properties, but which nevertheless insures that the subsequent data are taken with the sample in its cleanest possible state. Using these

techniques the dielectric functions of materials as diverse as Nb^ and

GaAs^ were recently revised by as much as 20% and 30%, respectively,

in the visible-near uv spectral range relative to values previously

determined by reflectance measurements and Kramers-Kronig analysis.

Because instrumentation and the determination of the intrinsic

dielectric properties of materials in their pure bulk form are now

basically solved problems, attention is turning to the determination of

properties of heterogeneous samples from their visible-near uv optical

response. Spectroscopic ellipsometric techniques can go much further

than simply measuring thicknesses and refractive indices of films, as

a recent analysis of the interface between Si and its thermally grown

oxide has shown. ' For example, we recall that the dielectric function

is defined as a polarization per unit volume. Thus it is clear that

ellipsometry can also be used to estimate the density of bulk

materials.^ Noting that a microscopically rough surface layer can be

considered as density-deficient bulk material, it is not surprising

that ellipsometric measurements can yield information about microscopic

roughness that is virtually impossible to attain any other way.

9

Likewise, the sensitivity of the dielectric response to long-range

order makes it an ideal probe for detecting the presence, or determining the fraction, of crystallinity in otherwise amorphous

materials

.

^

The determination of the properties of a heterogeneous sample from its

optical response is a three-step process. ^ First, accurate dielectric

function data must be acquired for the pure bulk forms of its constituents as well as accurate ellipsometric data for the sample itself.

Second, the physical microstructure must be mathematically represented

in some way, for example by n-phase models^ for laminar structures or by effective medium theories for heterogeneous materials. Third, the

model parameters must be determined from the data. By analogy to

circuit analysis, the sample can be viewed as a black box but with the

usual frequency-independent parameters of resistance, capacitance, and

inductance replaced by thicknesses, compositions, and void fractions.

The modeling of heterogeneous materials requires some comment. It is

generally assumed that the characteristic length of inhomogeneities is

much less than the wavelength of light, but that this length is

sufficiently large so the inhomogeneities themselves possess their own dielectric identity. This avoids the local-field problem even while

recognizing that everything is heterogeneous on an atomic scale. The

macroscopic (observable) dielectric function is now obtained by solving

the microscopic problem exactly for the microscopic electric field

e~(r) and polarization density p(r) , then spatially averaging the microscopic quantities to calculate the observed macroscopic equivalents

<E> and <P> from which <e><t> = <t> + 4Tr<Pr>. 11 It is clear that

internal boundaries and the distribution of the resultant screening

161
charge will play an important part in determining <e>. Either the

boundaries are known in detail or suitable approximations to them must

be made. The latter approach is usually taken because internal

structure is not generally known, or else requires far too many

parameters to describe, except in idealized models. We simply use

the self -consistent Bruggeman effective medium model, which differs

from the more common Lorentz-Lorenz and Maxwell Garnett models only in

the choice of dielectric background. 9 The advantage of so doing is

that the number of parameters are minimized; the disadvantage is that

the parameters that remain are effective averages whose values may

differ somewhat from those corresponding to the actual compositions.

The parameters themselves can be determined by linear regression

analysis^ (LRA) . LRA yields not only the best-fit values and the

residual mean-square deviations on a systematic basis, but it also

provides correlations and confidence limits. The latter are important

if meaning is attributed to the best-fit values, for it establishes

which parameters are being determined by the data and which are not.

Because correlations are included, the confidence limits also prevent

abuses such as using too many parameters. While adding another parameter

always reduces the mean square deviation, it can also cause catastrophic increases in confidence limits if it is not being determined

independently by the data.

14

The above approach has been applied in detail to Au. Representative

dielectric function spectra are shown in Fig. 1. Data include those

taken on bulk materials (Winsemius, Pells and Shiga) unannealed thin

films deposited in moderate pressure (Johnson and Christy, "this

work"), and annealed thin films deposited in ultrahigh vacuum (Theye)

.

The spectra at energies above the interband transition threshold at

2.5eV differ almost entirely because the samples contain different

void fractions, as shown in Fig. 2. Here, using the locally prepared

film data as a basis, void fractions were calculated in a one- parameter Bruggeman effective medium approximation using linear

regression analysis. The model describes the major differences

satisfactorily in the interband transition region not only in terms

of absolute values but also with regard to spectral variations.

Below 2.5eV the E2 spectra are dominated by the Drude tail, which

provides a measure of the importance of bulk and surface scattering.

The former can be related to grain size, and the latter to microscopic

roughness

.

REFERENCES

1. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light

(North-Holland, Amsterdam, 1977).

2. M. D. Williams and D. E. Aspnes, Phys. Rev. Letters 41, 1667 (1978).

3. D. E. Aspnes, in Proceedings of the Conference on Non-Traditional

Methods to the Study of Solid-Electrolyte Interfaces, ed. by T.

Furtak and D. W. Lynch (North-Holland, Amsterdam, 1980) (in press).

162
4. D. E. Aspnes and E. G. Lluesma (to be published).

5. D. E. Aspnes and A. A. Studna (to be published).

6. P. S. Hauge, in Proceedings of the Fourth International Conference

on Ellipsometry , ed. by R. H. Muller, R. M. A. Azzam, and

D. E. Aspnes (North-Holland, Amsterdam, 1980) (in press).

7. D. E. Aspnes and J. B. Theeten, Phys . Rev. Letters 4_3, 1046

(1979).

8. D. E. Aspnes and A. A. Studna, in ref. 6 (in press).

9. D . E . Aspnes, J. B. Theeten, and F. Hottier, Phys. Rev. B20 , 3292 (1979).

10. B. G. Bagley, D. E. Aspnes, A. A. Studna, A. C. Adams, and

F. B. Alexander, Jr., Bull. Amer. Phys. Soc. 24_, 363 (1979).

11. J. Sipe and J. S. Van Kranendonk, in Progress in Optics , vol. 15,

ed. by E. Wolf and A. C. Jones (Academic, New York, 1977), p. 245.

12. 0. Hunderi, in ref. 6 (in press).

13. E. S. Keeping, Introduction to Statistical Inference

(Van Nostrand, Princeton, 1963), Ch. 12.

14. D. E. Aspnes, E. Kinsbron, and D. D. Bacon, Phys. Rev. B21

(in press)

.

FIGURES

Fig. 1. Representative

dielectric function spectra

for Au (after ref. 14).

Fig. 2. Comparison between

dielectric function spectra

and one-parameter (void

fraction) model calculations

for several spectra of Fig. 1.

163
DIELECTRIC FUNCTION OF SUPERLATTICE MATERIALS

P.J. Price

IBM T.J. Watson Research Center

Yorktown Heights, New York 10598

In a "superlattice" formed from alternating layers of GaAs and (Ga.Al)As alloy, the

conduction band edge of the alloy is higher than that of the GaAs by a few tenths of an

eV. Consequently an individual GaAs layer acts as a "potential well" for electron motion

in the growth (say, X) direction, with quantized energy levels En

. These levels are the

minima for the electron energy including motion in the YZ plane:

En + (h

2/2m*)(kj + \fy (1)

in the parabolic range. 1 A similar situation for holes applies with those levels that can be

formed in the shallower valence-band wells. The lowest level in (1) is

E, - (h

2/2m*)(i7/aj)

2 (2)

where to sufficient approximation aj may be equated to the layer thickness a. 2 (For

example, aj = 0.7 x 10-6 cm gives Ej = 0.1 eV.) The interconnection of wavefunctions through the alloy "barriers" between neighboring GaAs layers is believed to result in

the individual well states (with the same k

y and kz) combining into Bloch-like itinerant

states; but if the barrier thickness, b, is fairly large then this phenomenon may be disregarded here. At the same time, with wavelengths at optical and infrared frequencies large

compared to the layer spacing c = a + b, the response to an electromagnetic field

should be given by the dielectric function e(w) for a uniform electric field.

The contribution to e that is dealt with here comes from the dipole matrix elements

between electron and hole Bloch states, in GaAs, at energies near the band edges, and

compares with the corresponding contribution to e(<o) in homogeneous GaAs. The latter may be calculated on the assumption of constant momentum matrix elements [that is,

constant dipole matrix element times energy difference, <c | x | v> Ecv (k)] between all

164
the pairs of Bloch states with the same wavevector. The result is

ecv ( u) = e G G(h«/Eg

) (3)

where

G(u) - (4/u2 )(2 - (1 + u)

1/2 - (1 - u)

1/2

), (4)

so that G(0) = 1 and G(l) = 2.34 . This formula can be fitted to the measured values

of Marple,3 by assuming that the background e — ccv is a linear function of u over the

range of the data, and taking e 0 = 1.0 . (The value of e 0 that one obtains theoretically,

using experimental values of mass and energy and momentum matrix element,4 agrees well

with this empirical value.)

A similar analysis for the GaAs "potential wells" of the superlattice case gives

««>(«,) = e<» H(WE<») (5)

where

H(u) = -L/n(-l_) (6) u

z v l-uz/

The superscript "l" signifies that this contribution is from the two-dimensional continuum

associated with the lowest level, Ej in eq. (1). From the theory one has approximately

(neglecting the difference between Eg and Eg1 *, as well as spin-orbit splitting in the

valence band)

c e^/e0 * 2h/(mcvEg

) 1/2(7)

where m^ is the appropriate joint-density-of-states mass. With the latter approximately

0.1 times the free electron mass, the right hand side of (7) equals 1.3 x 10 -7 cm.

Accordingly, we expect e^

1 * ~ 10" 1 for the usual values of layer spacing c = a + b.

The infini ty in (6) should be not very pronounced in practice, even when the superlattice

band width is not appreciable; for example, at 1 — u = 10~ 3

, H is only 6.2 . There is a

possibility, however, of observation of the peak by the electroreflectance method. 5 In an

electric field <?, the quantization energy Ej changes by —Yia^8 , where orj is the polariza165
bility, and similarly Eg . It can be shown that (disregarding the difference between

and a)

a, = 7 x 10" 3 (e

2 me/h

2

) a

4

= (0.92 x 105 cm" 1 ) a

4 (8)

the second line of (8) being for GaAs. For a = 10~ 6 cm and & = 105 V/cm, this gives

Yi <xj S2 = 3.2 milli eV. In this idealized model, such a shift would give a maximum 5e

of about 0.5. For the next level, a2is calculated to be only about 8% of O], however. It

is not clear, at the time of writing, whether electron and hole in this system can bind into an exciton.

1. For example, R. Dingle, W. Wiegmann and C.H. Henry, Phys. Rev. Lett. 33, 827

(1974); R. Tsu, A. Koma and L. Esaki, J. Appl. Phys. 46, 842 (1975).

2. The correction, from the finiteness of the barrier height and from the atomic-scale

"mismatch" of wavefunctions in the two layer materials, is a few lattice constants

at most. (The mismatch effect is important, however, in the strength of the interaction between GaAs layers which is associated with the superlattice band.)

3. D.T.F. Marple, J. Appl. Phys. 35, 1241 (1964).

4. C. Hermann and C. Weisbuch, Phys. Rev. B J_5, 823 (1976).

5. M. Cardona, K.L. Shaklee and F.H. Pollak, Phys. Rev. 154, 696 (1967).

166
DETERMINATION OF THIN FILM OPTICAL DISPERSION

FROM SPECTROPHOTOMETER DATA

Arnold L. Bloom and Dennis Fischer

Coherent, Incorporated

3210 Porter Drive

Palo Alto, California 94304

This paper describes work being done on a project in which an attempt

is made to determine the dispersive characterstics of optical thin

films using relatively common laboratory instruments, such as a transmission spectrophotometer. It is well known that the real part of

the refractive index can be measured very accurately by ellipsometry

and the imaginary part can be measured by calorimetry, but these

techniques are time-consuming and the instruments are not always

available in the laboratory. The output of a spectrophotometer, on the

other hand, provides data rapidly over wide wavelength ranges and

should be particularly convenient for the purpose if the output data

can be analyzed properly.

In our laboratory the experimental procedure is as follows. The

material whose dispersion curve is to be measured is coated on a substrate whose refractive index is well known and which is highly

transparent over the wavelength range in question (for example, fused

silica in the visible and near UV) . The coating is monitored at a highly transparent wavelength for the material and the layer is made

relatively thick, for example 5 to 9 (an odd number) quarter waves at

the monitoring wavelength. The transmittance of the entire sample is

then measured over the entire wavelength range of the spectrophotometer,

along with zero and full-scale calibrations of the strip chart recorder.

Because the layer is many wavelengths thick, the chart will show rapid

oscillations between maximum and minimum transmittance as a function of

wavelength, with the average transmittance decreasing rapidly to zero

at the short-wavelength end of the chart. It is clearly desirable to

make the layer as thick as possible, in order to get rapid oscillations,

but not so thick that the short-wave transmittance decreases below 20 or 30 percent of full scale.

In initial experiments the values of refractive index, n, and

absorption, k, at various wavelengths were estimated by hand

calculations based on the oscillation frequency, maximum and minimum

values after correction for the back-surface reflection of the sample.

The values obtained from this relatively crude technique turned out to

be surprisingly good in predicting the behavior of multilayer stacks

using the material. However, it appeared desirable to improve the

method by using a computer program to reduce the data. The remainder

of this paper describes the computer data reduction and the results

167
obtained in this way.

To start with, we assume that the optical thickness at the monitoring

wavelength is known approximately, and that there is a wavelength

region around the monitoring wavelength in which the index is

relatively constant and in which there is negligible absorption. We

have available several computer algorithms that can adjust the thickness

and index of thin films to make a least-squares fit to a given

transmittance or reflectance curve. These algorithms are used normally

for optimization of multilayer designs, but here they are used

essentially as curve- fitting devices. The spectrophotometer output in

the monitoring range, corrected for back-surface reflection, is entered

into the program and the algorithm solves for accurate values of n and

of the physical thickness to fit the data. Experience has shown that

good fits to the data can be obtained consistently in this way and we believe the values of thickness and index that are obtained are reliable.

It is necessary to include, in the input data, enough values of

transmittance so that the sine wave variation of transmittance is

clearly delineated over part of a period including a minimum value

(hence the odd number of quarter-waves) . Transmittances near the curve maximum are essentially those of the bare substrate and convey no information to the program. In addition, the curve-fitting process can

be expedited considerably by a proper choice of variables in the

algorithm. The algorithm requires both the function (transmittance in

this case) and first partial derivatives with respect to the variables.

In initial experiments we used, as variables, the index and the physical

thickness. It was found that the optimization program did not work well

with this choice of variables and the reason is not hard to find: Over

a limited range of wavelengths a small change in thickness has nearly

the same effect on the transmittance curve as a small change in index.

A much better choice of variables is index and phase (or optical)

thickness. In this case the variables are nearly orthogonal, one varying only the amplitude and the other varying only the period of the

sine wave, and the optimization process proceeds efficiently.

With the thickness determined accurately, the next step is to use the

curve-fitting algorithm to determine n and k at other wavelengths. Our

present efforts are aimed at making transmittance curve fits by

determining single values of n and k for use in restricted wavelength

ranges, or pairs of values with linear interpolation in between for

longer wavelength ranges. Attempts to fit constants of Lorentzian or complex Sellmeier equations were unsuccessful because of difficulties

involved in making optimization algorithms work with complex variables.

Interpolation using polynomials of order higher than linear is

esthetically pleasing but not suitable for cases where k may vary

between small and large values. The reason is that such interpolations

may result in k changing sign unexpectedly over some wavelength ranges

(i.e., giving gain), which is extremely undesirable in thin film design

work. Experience with the curve-fitting has shown that the linear

interpolation is quite satisfactory in wavelength regions in which n and

168
k do not vary too rapidly over the region. Where there is. rapid

variation of k with wavelength, as near the absorption edge of the

material, linear interpolation can be used only over very narrow

wavelength ranges.

The problems that arise in using this method are as follows. First,

the strip chart data must be nearly noiseless and the data transcription

to numeric values must be done carefully (it is not necessary to make

baseline and back-surface corrections by hand as this can be done in the

program) . Secondly, when n and k values at each end of a wavelength

range have been computed, it would be nice to have the values of n and k

agree with those calculated in an abutting wavelength range, however

this will not always be the case. An additional problem that has arisen

is that the transmittance is not particularly sensitive to n in regions

where k is large, and small deviations in the initial conditions

presented to the curve-fitting program may result in widely different

final values for n, although the values for k will always be consistent.

EXAMPLE

A layer of Ti02 was coated on a fused silica substrate. The operator

was instructed to lay on 5 quarter waves at a monitoring wavelength of

633 ran. The thickness was computed from data between 590 and 650 nm. The results are as follows:

Physical thickness = 327.5 nm Refractive index = 2.3793

Quarter wave thickness = 3117 nm

(Note this differs slightly from the assumed quarter wave thickness of

3165 nm. ) The fit to the data curve was better than 1% over the entire

range and better than 0.5% over most of it.

Table I shows the calculated values of n and k over several wavelength

ranges

:

TABLE I.

Range, nm. wavelength n k

600 - 800 600 2.3781 0.

800 2.3371 -0.0069

500-600 500 2.4490 -0.0057

600 2.3905 -0.00072

400-500 400 2.6430 -0.0040

500 2.4539 -0.0018

360-400 360 2.8328 -0.0197

400 2.5648 -0.0060

169
CONCLUSIONS

The results given above show that the method has promise but there are also problems, particularly the need to get highly accurate

spectrophotometer data. The anomalous wandering of the k values in the

vicinity of zero is undoubtedly due to the fact that the calculated

value will be very sensitive to the value of the transmittance maximum,

and in this case could have been affected by very small errors in the

baseline correction. The differences in index for the same value of

wavelength calculated in different wavelength ranges is an effect of the

linear interpolation and could be reduced by using shorter wavelength

ranges.

Despite the relatively crude appearance of the results, this output

should be quite satisfactory for most thin films design work. Above all

it points out the fact that hand calculations, based only on maximum and

minimum values of transmittance, are not nearly as reliable as one might

be led to expect naively on the basis of equations that can be solved

from these data.

170
OPTICAL PROPERTIES OF DOPED-SILICA WAVEGUIDE

GLASSES IN THE 0.8-1.8 um REGION

Robert Olshansky

Corning Glass Works

Corning, NY 14830

In optical quality glasses prepared by conventional melting techniques,

the principal source of attenuation is absorption from transition metal

impurities. To attain the very low loss required for telecommunications

the transition element contamination must be kept below a few parts per

billion.

The vapor phase oxidation technique 1 provides a simple and practical

method for achieving these purity levels. High purity raw materials

such as SiCli+j GeCl^ , BBr3 and POCI3 are readily available and can be

oxidized and deposited under controlled conditions to form glass

preforms from which optical fibers can be drawn.

Once the absorbtive losses of transition metals are eliminated, these

doped-Si02 glasses exhibit a broad transmission window encompassing the

range from 0.8-1.8 urn of interest for optical communications. In the

region from 0.8 to 1.2 urn, Rayleigh scattering losses from intrinsic

density and concentration fluctuations of the glass matrix are the

dominant loss sources. These scattering losses decrease as the fourth

inverse power of wavelength. In the region between 1.2-1.8 urn losses

are dominated by 0-H absorption bands, Rayleigh scattering and, in the

case of B2O3 doped waveguides, the tail of the B-0 infrared vibrational

absorbtion bands.

1. Rayleigh Scattering

The Rayleigh scattering of optical waveguides and of bulk samples

appears to vary somewhat according to the details of sample preparations

It is convenient to characterize the Rayleigh scattering by the form

YRS

= a/X\ (1)

The lowest value reported for bulk Si02 is 0.63 dB/km-um4. 3 As shown

in Fig. 1 the scattering values observed in optical waveguides vary

with composition. 3-7

As there appears to be considerable variability among the various

techniques used for determining dopant concentration, it is useful to

compare data from different laboratories by using A, the relative

171
difference in refractive index between the core and fused Si02

A °

(I" ' no)

• (2)

Fig. 1 shows that as the A increases (or equivalently the Ge02

concentration) the scattering level also increases. This presumably is

the result of the increase in concentration fluctuations as dopant is

added

.

Many of the earliest waveguides were made with a low level of B2O3

added to reduce the sintering temperature of the glass and to

facilitate the deposition process. The scattering data of Yoshida

et al 6 clearly shows that substitution of a low level of P2O5 for the

B2O3 reduces the Rayleigh scattering by 40-50%. At 0.85 urn this is a significant difference, amounting to 1 dB/km.

Horiguchi and Osanai have reported 4 the lowest scattering value for any

waveguide. Their waveguide doped with 2 m/o P2O5 had a Rayleigh

scattering coefficient of 0.60 dB/km-um1*.

Because of the large viscosity difference between glassed doped with

higher P2O5 levels (>10 m/o) and fused Si02> fabrication of gradedindex multimode waveguides is very difficult in the P205~Si02 binary

system. Little work has been reported in this compositional system.

Blankenship et al 7 have reported a A=1.0%, P 2 05-Ge02-Si02 waveguide in

which the P2O5 level is high enough to contribute about 50% of the index

difference. The scattering coeffient of 1.0 dB/km-um1* is the lowest

reported for a graded-index multimode waveguide.

2 . Infrared Absorption Edge

All oxide glasses have very strong cation-oxygen vibrational bands

in 4-25 um region. Multiphonon excitation of these states 8 produces an absorptive tail of the form

YJR = CIR exp (-E/E0 ) (3)

where E is the photon energy and C-j-r and EQ are empirically determined

constants. Izawa et al 9 have measured this absorption in the 1.8 to

20 um region using both bulk and fiber samples of Si02 and B203~doped

Si0 2

. The Si02 edge is well represented by the constants

E0 = .0235 eV

'IR = 1.19 x 10 13 dB/km •

This edge falls off rapidly with increasing energy. At 1.6 um the

intrinsic absorption of fused-Si02 is 0.06 dB/km.

172
The position of the fundamental vibrational band depends on the reduced mass of the cation-oxygen pair. Because of the low atomic mass of

boron, the B-0 bands and the resulting band edge are shifted to shorter

wavelengths. As shown in Fig. 2 the B-0 infrared absorbtion edge is

apparent in any fiber doped with more than a fraction of a percent B2O3.

The large atomic mass of germanium is expected to shift the edge to

longer wavelengths. No direct observation of this in optical

waveguides has yet been reported.

The little available data 10 for the P 2 0 5 -Si02 absorption edge indicates no obvious shifts due to the presence of phosphorus.

The Rayleigh scattering and intrinsic absorption data can be combined to

predict the total intrinsic losses of doped-Si02 waveguides 1

. For

SiC>2 slightly doped with GeC>2 the minimum loss is predicted to be 0.2

dB/km at 1.55 ym (see Fig. 3). Miyashita et al 12 have reported a singlemode waveguide which attains this minimum value.

3 . 0-H Absorption Bands

The other important sources of attenuation which must be considered

are the harmonics and sidebands of the fundamental 0-H vibrational band

at 2.75 um 13 > 11+. As shown in Fig. 4, the first and second harmonics

occur at 1.39 ym and 0.95 ym respectively. Sidebands due to

simultaneous excitation of a Si-0 vibrational mode and an 0-H band

occur at 2.25 ym and 1.25 ym.

The operating wavelength of 1.3 ym is a desirable choice for a telecommunication system because of the low intrinsic scattering losses

(0.3-0.5 dB/km) and the proximity of the zero-dispersion wavelength

(1.27-1.35 ym depending on the Ge02 dopant level). As 1.3 ym is in the

minimum between the 1.39 ym harmonic and the 1.25 ym sideband the OH

absorbtion at 1.3 ym is usually significant. Approximately 0.7 dB/km

absorbtion occur at 1.3 ym for each ppm 0-H.

In P205~doped Si02 a very broad P-O-H absorbtion band occurs at

3.05 ym 15. The first harmonic is a broad band centered at 1.65 ym 16. Absorbtion from this harmonic extends beyond 1.3 ym and even in low OH

content glasses the contribution at 1.3 ym can be as large as 1 dB/km

if the P2O5 level is high 7

.

Because of this P-O-H band, the very low intrinsic losses in the 1.5-

1.6 ym region are more easily achieved in P 2 05-free compositions.

4. Refractive Index Dispersion

Refractive index dispersion is of great importance for understanding

waveguide bandwidth. The difference in index dispersion between the on173
axis and the cladding composition is a key parameter for determining the

index profile shape required for highest information bandwidth 17

. Further discussion of this aspect of dispersion can be found elsewhere2

> 22 .

Refractive index dispersion is also important because of the pulse

broadening it produces in proportion to the source spectral linewidth.

For a source of width AX the pulse spreading At is given as L , , i , d

2 n i x AT =

c AA|A IT2 ' (3)

where L is the fiber length and C is the speed of light.

The refractive index of any glass possesses an inflexion point

(d 2 n/dX 2 = o) somewhere between the electronic absorbtion bands and the

infrared vibrational bands. At this zero-dispersion wavelength very

high bandwidth can be achieved even with LED sources having linewidths

as large as 50 nm.

The zero-dispersion wavelength varies with composition.

Bulk sample index measurements show that for fused Si02 it occurs at

1.27um 18

. For Ge02-doped silica it shifts to longer wavelengths, and

for B20 3~doped silica to shorter wavelengths. This effect has been

confirmed by direct measurements of delay time as a function of

wavelength for Ge02~doped fibers 19 ' 20 ' 21 and B203~doped fibers 19

. The zero dispersion wavelength does not shift with P2O5 doping 20 » 21

.

In an analysis of all available data for GeQo-SiC^ glasses Adams et

al 22 find that the zero dispersion wavelength increases by about 6 nm

per mole % Ge02 doping.

References

(1) For a review see P. C. Schultz, Applied Optics 18, 3684 (1979)

(2) R. Olshansky, Review of Modern Physics 51, 341 (1979

(3) J. R. Schroeder, R. Mohr, R. B. Macedo and C. J. Montrose, J. Am.

Ceram. Soc. 5_6, 510 (1973)

(4) M. Horiguchi and M. Osanai , Electron. Lett. 12,310 (1976)

(5) W. A. Gambling, D. N. Payne, C. R. Hammond, and S. R. Norman, Proc.

Inst.Electr. Eng. 123, 570 (1976)

(6) K. Yoshida, Y. Furui, S. Sentsui and T. Kuroha, Electron. Lett 13,

609 (1977)

174
(7) M. G. Blankenship, D. B. Keck, P. S. Levin, W. F. Love,

R. Olshansky, A. Sarkar, P. C. Schultz, K. D. Sheth and

R. W. Siegfried, Post-deadline Paper Topical Meeting on Optical

Fiber Communications, March 6-8, 1979, Washington, D.C.

(8) For a review see T. C. McGill in Optical Properties of Highly

Transparent Solids ed. by S. Mitra and B. Bendow, Plenum Press

(1975)

(9) T. Izawa, N. Shibata, A. Takeda, Appl. Phys . Lett. 31, 33 (1977).

(10) S. Kobayashi, W. Shibata, S. Shibata and T. Izawa, Rev. Elect.

Comm. Lab. 26, 453 (1978).

(11) M. Osanai, T. Shioda, T. Moriyama, S. Araki, M. Horiguichi, T.

Izawa, M. Takata, Electron Letts 12, 549 (1976)

(12) T. Miyashita, T. Miya and M. Nakahara, Post-deadline paper Topical

Conference on Optical Fiber Communication, March 6-8, 1979,

Washington, D.C.

(13) D. B. Keck, R. D. Maurer and P. C. Schultz, Phys. Letts 22_, 307

(1973)

(14) P. Kaiser, A. R. Tynes, H. W. Astle, A. D. Pearson, W. G. French,

R. E. Jaeger and A. M. Cherin, J. Opt. Soc. Am. 63_, 1141 (1973)

(15) Y. Mita, S. Matsushita, T. Yanase and H. Nomura, Electron. Tett.

13 , 55 (1977)

(16) T. Edahiro, M. Horiguchi, K. Chida and Y. Ohmori, Electron. Lett.

15, 275 (1979)

(17) R. Olshansky and D. B. Keck, Appl. Opt. 15, 483 (1976)

(18) I. H. Malitson, J. Opt. Soc. Am. 55 , 1205 (1965)

(19) L. G. Cohen and C. Lin, Appl. Opt. 16, 3137 (1977)

(20) D. N. Payne and A. H. Hartog, Electron. Lett. 13, 627 (1977)

(21) C. Lin, L. G. Cohen and V. A. Foertmayer, Electron. Lett. JL4, 170

(1978)

(22) M. J. Adams, D. N. Payne, F. M. E. Sladen and A. H. Hartog,

Electron Lett. 14, 703 (1978)

175
RAYLEIGH SCATTERING VS A

20

1.5

10

0.5

OY0SHIDA ET AL (1977)

A GAMBLING ET AL (1976) • SCHROEDER ETAL (1973)

HORIGUCHI ET AL (1976)

BBLANKENSHIP ET AL

(1979)

P2 05 -Ge02 -Si02 P2 05 -Si02

,Si02 (BULK)

CT-P2 05 -Si02

_i i i i i_i i_ 0 0.5 10 A (%) RELATIVE TO SiO,

Fig. 1 Rayleigh scattering

loss versus relative index

difference is shown for

different optical waveguide

compositions.

CORE CLAD

l)Ge02-B203 -Si02 B203 -Si02

Fig. 2 Spectral attenuation

for three low-loss waveguides

reported by Osanai, et. al.

WAVELENGTH ( Mm)

176
Ge02 -Si02 INTRINSIC LOSS

WAVELENGTH ( ^m)

1.2 1.3 1.4 1.5 1.6 17 I f

Fig. 3 Intrinsic attenuation

predicted by Miyashita, et. al

.

for three GeCL - SiCL compositions. 1 L

I 2 1.0 0 9 0 8 0.7 PHOTON ENERGY (eV)

10.0- x

o

E\

CD

<3

010-

Fig. 4 Harmonics and sidebands

of the hydroxyl absorption

spectrum reported by Keck, et.

al

.

001

700 800 900 1000 1100 1200 1300 I4C WAVELENGTH (nm)

177
THE USE OF A SCATTERING CUBE TO

CHARACTERIZE THE SPECTRAL LOSS OF OPTICAL FIBERS

Dan L. Phil en and Frank T. Stone

Bell Laboratories

Norcross, Georgia 30071

In many instances, it is useful to separate the scattering loss of an optical fiber into a wavelength dependent component, Rayleigh Scattering

= a/A^, and a wavelength independent component, b, caused by scattering

mechanisms with dimensions large compared with the signal exciting

wavelength. These scattering components provide important data characterizing the fiber material system and manufacturing process. When they are obtained by curve fitting total loss data versus frequency, errors

are introduced because of band-edge and other forms of absorption.

These errors can be eliminated by measuring only the scattering loss

with a scattering cube. Using this technique with a laser source and

relatively short fiber samples, it is also possible to: (1) excite

different mode groups in multimode fibers, thereby determining the

scattering intensity from different regions within the fiber core, and

(2) obtain accurate data on single mode fibers that can be difficult to

get from two-point loss measurements. For example, by careful scrutiny

of the near field pattern of short (several meter) lengths of fiber

and appropriate adjustment of launch conditions, a single mode can be

excited even at wavelengths where the fiber supports several modes.

This avoids effects due to mode cut-off, and yields useful data on the

basic glass properties. Two-point loss measurements do not isolate the

scattering component, and require fibers so long that mode-mixing is

difficult to avoid.

The essential component to this measurement is the scattered light

detector. Since the scattered light exits in all directions, this

detector must surround the fiber completely to collect all the

scattered radiation. Two types of detectors have been used to do

this: an integrating sphere!, and a scattering cube^, which was used

in this work. This scattering cube is constructed of 1 -cm-square

silicon solar cells with a 0.25mm hole drilled through the center of

two opposite faces to allow the fiber to pass through the cube. One

side of the cube is removable to facilitate the insertion of the

fiber and allow the cube to be filled with index-matching fluid. The

sensitivity and impedance of all the cells are matched as closely as possible. Final matching is accomplished by trimming potentiometers

that equalize the outputs of the individual cells.

The linearity of the scattering cube at 633nm was determined by

launching a He-Ne laser beam into a fiber pigtail and inserting the

other end of the pigtail into the scattering cell. The input power

178
was varied over eight orders of magnitude using a set of calibrated

neutral density filters and the cell was found to be linear over six

orders of magnitude. During the experiments, the detector was always

operated well within the linear region.

Since the scattering cube is composed of silicon solar cells, its

sensitivity is wavelength dependent. This spectral dependence was obtained by using a He-Ne laser and a Krypton laser as sources and a Scientech calorimeter to measure the absolute optical power. The

sensitivity at 633nm was measured to be 100.5 yv per yw. The relative

sensitivity is given in the following figure.

1.6 r

0.2 -

! I 1 I L 560 620 660 720 760 820 WAVELENGTH IN nm

The experimental set-up is illustrated in the following figure.

MICROSCOPE

OBJECTIVE

SCATTERING

CELL -o FIBER -r\J^—

CHOPPER

S-SHAPED MODE STRIPPER

CLADDING MODE STRIPPER

LOCK-IN AMPLIFIER

Samples of fiber a few meters in length were selected for test,

stripped of their coating, cleaned to remove adhering dust particles,

and threaded through the scattering cell. Bends in the fiber

immediately before or after the cell were avoided. Scattering from

cladding, leaky, or marginal bound modes was suppressed to a high

179
degree by using an S-shaped mode stripper before the scattering cube.

To insure that no cladding modes had built up in the straight section

of fiber between the S-shaped mode stripper and the scattering cell,

an additional cladding mode stripper consisting of black paper

saturated with index oil was placed 1mm in front of the scattering

cube. The remaining power guided by the fiber into the scattering

cube was now largely confined to the bound modes of the fiber. The

scattering cube was filled with index oil to prevent any scattered

light from being trapped in the cladding, and the end of the fiber

was terminated in index matching fluid to prevent light reflected

from the fiber end from being scattered back into the scattering cube.

The input laser light was chopped mechanically and the output of the

silicon detectors was measured on a lock-in amplifier. The total

light incident on the fiber was measured on a Scientech calorimeter.

The scattering loss in dB/km for a particular wavelength is given by:

where V = signal from the lock- in in microvolts.

D = normalized spectral response of the scattering cube. (Fig. 1)

C = sensitivity of scattering cell = 100.5 yv/uw/cm at 633nm.

P = total incident power in microwatts.

By using several lines of the Krypton laser, the spectral dependence

of the fiber scattering loss could be obtained at well -spaced

wavelengths in the region from A = 0.568 urn to X = 0.799 urn. Since we model the scattering loss by an as = a/A^ + b relationship,

a linear least squares fit to the loss data on a 1/A 4 scale gives

the "a" coefficient as the slope and the "b" coefficient as the

intercept. The following figure is a plot of the average scattering

loss versus wavelength for a germanium-borosil icate-core, silicaclad multimode fiber that was measured many times to determine the

experimental repeatability.

a,

|dB/km|

14 -

12

10

2 —

\/\4

( Mr»-«) 180
The fiber was excited using a 5x microscope objective to focus the

Krypton laser beam to a spot positioned at the center of the core where maximum compositional fluctuations should occur. The repeatability was of the order of + 1-2%, even when measurments occured several

weeks apart and were taken on different 1 -cm-long regions of the

fiber. The correlation coefficient for the a/A^ + b curve-fit was

0.9995. The "a" coefficient obtained this way was approximately 0.2

pnrdB/km lower than the value obtained by curve-fitting to total loss

data, as might be expected from the effect of band-edge absorption.

We have examined a number of other multimode and single mode fibers.

The next figure gives an interesting example of a single mode fiber

(borosilicate core, borosilicate inner cladding, silica outer cladding)

that had high total loss. 12 _

(dB/km)

c c c c c

1/X

4 (^n.-

4

! The plot of the scattering loss, however, is what is expected from a good fiber, indicating the source of the added loss is absorption.

This was confirmed calorimetrical ly.

In summary, the direct measurment of the scattering component of the

spectral loss of an optical fiber is a useful diagnostic technique.

It can be used to eliminate the errors in the a and b coefficients due

to absorption, and to determine whether scattering is the cause of excess fiber loss.

REFERENCES

1. D. B. Keck, P. C. Schultz, and F. Zimar, Appl . Phys. Lett.

n, 215 (1972).

2. A. R. Tynes, Appl. Opt. 9_, 2706 (1970).

181
TRANSITION ELEMENT ABSORPTION IN

MOLECULARLY- DOPED OPTICAL FIBER GLASSES

Aaron Barkatt, Dahn C. Tran* and Joseph H. Simmons

Vitreous State Laboratory

The Catholic University of America

Washington, DC 20064

The presence of transition elements in fiber optic waveguide

glasses, even at trace levels, causes high absorption losses

(in some cases, higher than ldB/km for each ppb of impurity)

in the wavelength range of most interest in the development

of long-range communication systems (600-1300nm) . Controlling the resulting absorption losses is hard because of the

difficulties encountered in identifying and determining the

levels of the important absorbing impurities. Chemical

analysis is complicated because of the trace concentrations

involved, while the absorption spectra in the region of

interest often consist of broad bands and often reflect the

presence of a transition element in several oxidation or

coordination states. The relative amounts of different

states are determined by the conditions of preparation.

It is therefore desirable to develop methods of characterizing the various species which are likely to contribute to

absorption losses in the near-IR region by searching for

intense, sharp, characteristic features in other spectral

regions such as the visible and the UV. The molecular

doping method is particularly suitable for such studies because it can be used to produce large, uniformly doped samples at relatively low temperatures (<_ 850° C) , where

individual oxidation states can be isolated by means of controlling the atmosphere under which the doped porous preform

is sintered.

Glasses prepared by this method, with a base composition of

approximately 92mol% Si02 / 4.5mol% B 2 0 3 , 3.5mol% CS2O, 0.03

mol% Na 2 0 and 0.0 3mol% K2O, were doped with several transition elements at a level of 0.0 5wt% (only in the case of Ru

a concentration of 0.008wt% was used). Samples doped with

each of these elements were consolidated in each of three

atmospheres: oxygen (oxidizing), helium (intermediate) and

5% hydrogen in nitrogen (reducing) . The samples had a diameter of about 0.6cm and were 0.1-5cm long, polished at both

ends. The spectra of each of the doped glass prepared under

these conditions were analyzed in order to identify the important absorbing species in each case. The findings are

summarized in the following Table.

182
Spectra of Transition Elements in

Molecularly Doped High-Silica Glasses

Approximate

Spectral Principal Absorbance,

Transition Features Chemical 1060nm,

Element Atmosphere nm Species dBkm ! ppb 1

Fe 0 2 ,He 375,412,437,

470

Fe (III) 0 . 008

H 2 820 ,950 Fe (II) 3. 0

Cu 0 2 ,He 785,1050,1080 Cu(II) 0. 90

H 2 cud) < 0. 01

Co o 2 778,1552 Co (III) 0. 80

He / H 2 547,600,648

,

1329 .2556 .1750

Co(II) tet 0. 21

MiIN _1_ \j 2 f lie 512 56 8 640

1158,1500

Ni (u±; TT ) tet 1 1

H 2 430,1125 Ni(II) oct 0. 05

Cr o 2 435,600,750,

1000

Cr (VI) 0. 13

He 435,587,723,

XUUU (lo JU

Cr (IV) 1. 4

H 2 354,499,700,

1075,1850

Cr (III) 1. 2

Mn o 2 363,520 fin (III) 0. 27

H 2 325,358,370,

422 ,435,470 , 515,650

Mn (II) < 0. 006

Rh o 2 312,470 Rh(III) 0. 03

H 2 Rh (III) 0. 08

Ru He 480,815 Ru(VI) 0. 19

Ag 0 2 ,He Ag(I) < 0. 005

H 2 229,300,399 < 0 . 01

Zr 0 2 /He ,H 2 Zr (IV) < 0. 005

183
The results show that the molecular doping method is very

suitable for the isolation of individual oxidation or coordination states and obtaining characteristic "fingerprints" consisting of a series of well-defined spectroscopic

features in the near-IR, visible or near-UV regions. In

particular, detailed band structures are evident in the

cases of Fe(III), Co (II), Ni(II) / Mn(II) and the various

forms of Cr. Such "signatures" can serve as convenient,

sensitive methods of identifying transition metal species

which cause absorption losses in fiber optic glasses.

Moreover, identification of the oxidation state makes

it possible to try to reduce losses by changing the redox

conditions of the environment during the preparation of

the glasses. Of the species identified, Fe(II) and Cu(II)

are of major concern because of their ubiquity and their

high specific absorption in the near-IR. Fe(II) can be

eliminated by oxidation, Cu(II) by reduction. Cr is a

problem under all conditions. Oxidized Cr absorbs to a

smaller extent than Cr doped under He or H2/N2 around

1060nm (by one order of magnitude) , but bands in this region are still observed, probably due to the difficulty in

oxidizing all traces of the lower oxidation states (Cr(III)

and Cr (IV) ) to Cr (VI)

.

The results also show that because of the presence of a relatively large concentration of the highly basic oxide

CS2O and the low temperature of preparation these glasses

provide a unique opportunity, especially when produced

under an oxygen environment, of isolating and characterizing the spectra of species accessible only at unusually

high basicities, such as the high oxidation states Co (III),

Cr(VI) and Mn(VII) and the low coordination state Ni(II) tet in a high-silica matrix.

*Present address: Battelle Laboratories, Columbus, Ohio

184
MEASURED POCKELS COEFFICIENTS AND PREDICTED

STATIC PRESSURE SENSITIVITY FOR INTERFEROMETRIC FIBER OPTIC HYDROPHONES

R. Hughes, N. Lagakos , H. Dardy and J. Bucaro

Naval Research Laboratory

Code 5133

Washington, D.C. 20375

Introduction ; Optical phase modulations induced in glass fibers have

been investigated-'-, especially since potential use of fibers for detecting sound was established 2. in sound detection, efforts were concentrated on describing theoretically and experimentally pressure induced

effects in step index, single mode fused silica cored fibers positioned

in interferometers More recently, consideration is being given to

fibers with numerical apertures larger than that found in fused silica

cored fibers because microbend loses are reduced

Variations in optical phase induced by an externally applied sound

field have been examined by several groups 2~5

# The primary causes of

phase variation for an applied static pressure have been attributed to

certain effects: axial strain alters the physical length of the fiber

waveguide and axial and radial strains alter the refractive index of

the fiber waveguide. For purposes of calculating pressure (sound)

sensitivities of fiber optic hydrophones, experimental values for mechanical elasticity and Pockels coefficients are needed 5,

Predicted static pressure sensitivity of particular fiber optic hydrophones depend directly on the values of Pockels coefficients for the

specific fiber used. Measurements were made on two glass specimens to

determine values of their respective Pockels coefficients. Using these

determined values, predictions of pressure sensitivities for the two

types of fibers are presented.

Experimental Technique : Cylindrical fiber preforms including one with a fused silica core and the other with a Ge02 doped silica core were

polished on the ends normal to the symmetry axis of the preforms.

The two preforms were approximately equal in diameter (7mm diameter).

Both preforms were of the "w" index profile. The smaller numerical aperture (NA=0.1) preform was composed of a fused silica core with less

than 0.1% Ge0 2 impurity; a clad of 5% B2O3 + 95% Si02 ; and a substrate

of the same material as the core. The other preform (NA=0.15) included

a 3% Ge02 +97% Si02 core; 15% B2 03+ 85% Si02 clad; and a fused silica

substrate.

Brillouin scattering techniques ° were used in determining Pockels

coefficient values. The preforms were immersed in parafin oil and

185
positioned in the focused beam of an Argon ion laser (A=0.5145um)

.

Light scattered at 90 degrees with respect to the incident light was analyzed with a Fabry-Perot interferometer at room temperature.

Experimental Results : Calculated values of the Pockels coefficients,

P44 and ?i2 of the studied preforms are given in Table I. The method

of calculation involves analysis of the observed Brill ouin Spectra.

As given in Table I, the P44 value of the NA=0.15 preform is approximately 2 % less than P44 for the NA=0.1 preform. The P^2 coefficient

for the NA=0.15 preform is smaller than Pj^ f° r tne NA=0.1 preform by

approximately 13%. The Pockels coefficients determined for the NA=0.1

preform are in close agreement with reported values ^ of Pockels

coefficients for fused silica.

Calculated Fractional Phase Change: An analytical model for predicting

the static pressure sensitivity for a two layered fiber has been derived

previously 5. The model assumes the fiber composite to be a right

circular cylinder having a length which is much greater than its diameter. Additionally, each material in the composite is assumed to be

isotropic, homogeneous and of uniform diameter. Further, the applied

hydrostatic pressure is symmetric. For these considerations it was shown that for an interferometric fiber optic hydrophone the fractional

phase change, A(|)/(J>, for a change in pressure, Ap, could be expressed as:

A<t>/<J> = (e

z -n

2 /2(e

r

(P44+P 12 )+e 2 P

12 )) Ap (1)

where $ = rikl

The quantities in Eq. 1 include the axial strain, e z , radial strain, e r , wave number of the light, k, length of the fiber, 1, and refractive index, n. The static pressure sensitivity for a given fiber is defined

as A(J)/Ap.

Calculated fractional phase changes for an applied static pressure of

1 dyne/cm^ for the two specimens studied are given in Table II. Diameters of materials for the various layers in the fibers used in the

calculations are: 1) NA=0.1: substrate 80um, clad 30um and core 4.5um;

2) NA=0.15: subtrate 80um, clad 30um and core 2.2um. The fractional

phase change of the NA=0.15 fiber is approximately 1.3 times larger

than that calculated for the NA=0.1 fiber. This difference is due not

only to values of the Pockels coefficients but also to the elastic

properties of the glasses in the fibers. The signs of the fractional

phase change are negative for both specimens considered. This indicates

that the optical path length of the test arm is reduced compared to

that of the reference fiber.

Conclusions

:

Values of the Pockels. coefficients Pn and P12 f°r single

mode preforms were determined. The numerical apertures of the fibers

drawn from the preforms were 0.1 and 0.15. Calculated values of the

fractional phase change per unit of applied pressure show the fiber

186
with numerical aperture .15 has the larger sensitivity of the two specimens studied. Judiciously selected materials for the glass layers in

single mode fibers could be combined to enhance pressure sensitivity in

interferometric fiber optic hydrophones.

References

1. FOSS Workshop (NRL Washington, D.C.) Dec. 12-14, 1979

2. J. A. Bucaro, H.D. Dardy and E.F. Carome, JASA 62, 1302 (1977);

J.H. Cole, R.L. Johnson and P.G. Buta, J ASA 62^ 1136 (1977)

3. P. Shajenko, J. P. Flatley and M.B. Moffett, JASA 64, 1286 (1978)

4. G.B. Hocker, Appl. Opt. JJ5, 1445 (1979)

5. R. Hughes and J. Jarzynski, Appl. Opt. Jj?, 98 (1980)

6. H.Z. Cummings, in Proceedings of the Second International Conference

in Light Scattering In Solids, ed. M. Balkanski (Flammarion Sciences,

Paris, 1971) p.

3

7. J. Schroeder, PhD Thesis, Catholic University of America (unpublished)

TABLE I

Numerical

Aperture

0.1

Core

Material

Fused Silica

(less than 0.1 % Ge02 )

Pock el '

s

Coefficients

p 44 Pl2

-0.0718±6% 0.270±2%

0.15 3 % Ge0 2 + 97 % Si0 2 -.0736 ± 6% 0.236 ± 2%

TABLE II

Numerical

Aperture

0.1

0.15

Fractional Phase

Change , A (J) / <$>

-2.79 x 10* 13

-3.73 x 10-13

187
ABSORPTION AND SCATTERING IN THIN-FILM AND BULK MATERIALS

Marshall S. Sparks

Pacific-Sierra Research Corporation

1456 Cloverfield Blvd.

Santa Monica, California 90404

The past ten years have seen great improvements in the materials used

as reflectors and windows for high-power lasers. Polarizers, gratings, switches, modulators, and partially transmitting reflectors have

also benefited, although indirectly, from the search for better optical

materials. This review discusses optical attenuation, absorptance, and

scattering, considering transparent materials, reflectors, thin films

(coatings), and fibers, in the infrared, ultraviolet, and visible re- gions.

Bulk attenuation, represented by the extinction coefficient 3 , is the

exponential decay constant in the Beer law I = I 0 exp (-6 z),

ewhere I 0

is the irradiance at z = 0 and I the irradiance at z. It is the sum

of absorption and scattering (8 = 8 + 8 ). Absorption is of prime

importance here because it produces heat, which can limit an optical

material's application.

In a transparent material there is also optical attenuation at the sur- face due to surface absorptance and surface scattering. Total absorptance is determined by bulk absorption 8 = 8, surface absorptance

A

g

, and sample thickness £.

The lowest measurable absorptance obtained by using transmission

methods is 0.01. Absorption is now measured directly by calorimetry,

emissivity, and photoacoustics ; attenuation less than 0.01 is measured

by modulation spectroscopy and attenuated-total-internal reflection.

The absorption coefficient can be measured from 10 5 or 106 cm'^-at

absorption peaks--to as low as 0.5 dB/km for optical fiber materials

or ^10~5 cm

-1 for window materials.*

The required absorptance and absorption coefficient varies with the

application, but values much less than 10"4 would be useful in highpower studies, spectrometry, and fiber optics. Optical material 8's

have been reduced from 10"2 cm-1 to near the current measurable limit

of ~10"5 to 10"6 cm-1. Measured values far below 10~4 are still sus- pect, however, and maintaining such low values has not been proved feasible. Temple [1], Hass [2], Harrington and coworkers [3], and Deutsch

[4] have measured bulk and surface absorptance separately.

*1 dB/km = 2.3 x 10~6 cm"1

.

188
Intrinsic attenuation mechanisms include absorption-mul tiphonon,

multiphoton, direct one-phonon (across the bandgap), or by thermalequilibrium concentration of vacancies; and scattering—Brillouin, or

by random molecular structure in glassy or amorphous material. Extrinsic attenuation comprises absorption by molecular ions (on surfaces or within materials), electron absorption by impurity ions, and absorption by microscopic inclusion.

Intrinsic limits establish the maximum obtainable absorption. Knowing

that, neither of the following material-improvement plans could possibly decrease absorptance: reducing the 10.6-um absorption coefficient of potassium chloride below its current minimum (~10~4 cm

-1 )

because it is already at the intrinsic limit; or obtaining 1 percent

absorptance in a metal at 250 nm—because it is unlikely that a metal

with a lower intrinsic absorptance than aluminum (20 percent at 250 nm

[5]) will be found.

For frequency iu greater than several times the fundamental reststrahlen frequency to f

, p decreases nearly exponentially as tu increases. For

alkali halides at room temperature, the coefficient varies smoothly with

frequency. The exponential frequency dependence of p was first observed

by Rupprecht [6], who suggested it resulted from mul tiphonon absorption. Horrigan and Deutsch [7] studied the effect in detail; Sparks

[8] rediscovered its theoretical multiphonon source.

The temperature dependence of (3 is considerably weaker than the T

predicted [9,10]. Sparks and Sham [11] obtained good agreement between

theory and experiment by including the temperature dependence of the

other parameters in the calculation of the absorptance dependence.

Multiphonon absorption is now considered to explain the exponential

frequency dependence of the absorption coefficient.

The highly transparent region of optical materials is bounded by vibrational (phonon) absorption at low frequencies and electron absorption at high frequencies. Electron promotion from a valence band to

the conduction band, which often produces an exciton, is primarily

responsible for the high-frequency absorption edge. In this region

(the Urbach), (3 increases steeply and exponentially with frequency.

Extrapolating the two boundary exponents would yield an intersection

at a value of p typically below 10~5 ° cm"1

. At frequencies where the

intrinsic £ is less than, say, 10"2 to 10"6 cm

-1

, extrinsic mechanisms

determine the absorption coefficient.

Extrinsic absorption mechanisms include point imperfections (e.g., impurities such as molecules in anion sites); extended imperfections

(e.g., voids, inclusions, dislocations); electrical carrier absorption

(e.g., interband transitions of holes or electrons); and surface effects (e.g., contamination).

189
Extrinsic_absorption_due to molecular ions [12] is exemplified by N02 , HC03 , S0| , and CrO| , which substitute for the halide ions in

al kal i-hal ide crystals, vibrating relatively freely of the host/ion

environment. Matrix-isolation spectroscopy reveals that a typical impurity absorbed in the infrared region has a large cross section at

resonance of a -10~17 cm2

. Thus, p = 10-4 cm-1 is obtained from an impurity concentration N = p/a = 10 13 cm

-3 (a few parts per billion).

Impurity ions or molecules on a sample surface give rise to absorptances of 0.1 percent per surface [13]. Such large effects follow from

an order-of-magni tude argument. For a surface layer 0.5 nm thick having p = 10 s cm

-1 at resonance, the absorptance is p£ 5 x 10~3

, or

0.5 percent absorption per surface. Ions that absorb as a result of

electron transitions have absorption bands spanning wide frequencies

in the visible and ultraviolet regions, with large cross sections a =

p/N of a — 10~17 cm2. Only a few parts per billion of strongly absorbing ions can thus yield p ^ 10""4 cm-1 (the infrared absorption

lines are generally more strongly peaked than the visible and ultraviolet) .

Isolated-region absorption is the best understood type of absorption

(surface or bulk) for transparent materials. The phenomenon has been

studied experimentally by Boling and Dube [14], theoretically by Hopper

and Uhlmann [15] and also by Sparks and Duthler [16], who found that

volume fractions of strongly absorbing inclusions as low as 10"8 yield

P = 10~4 cm

-1

. The frequency and temperature dependence of the absorption depends strongly on the type of inclusion (strong or weak absorber, metal or dielectric, large or small).

A local increase in absorption can cause fracture, vaporization, melting, or other material failure. Damage almost always occurs in small

regions in the laser beam, rather than being uniform across the beam.

Such damage is known to occur from polishing compounds embedded in the

surface of materials. Other possible sources include polishingcompound inclusions, thermally isolated flakes on metallic surfaces,

clusters of microscopic inclusions, scratches, Bloembergen field en- hancement, surface contamination, or airborne particles that burn near

the surface.

Obtaining low optical attenuation in thin films and optical fibers

entails difficulties. The extinction coefficient of both is limited to an optical value much greater than for corresponding bulk materials.

When material is deposited as a thin film, its absorption coefficient

is almost always three to six orders of magnitude greater than that

of the same material in bulk [17]. The reason is not clear, but the

most likely cause is contamination—which could occur at the interfaces, in the pores or bulk of the film, or on the surface of the coating. It could occur during deposition—e.g., from residual gas; after

deposition—e.g., by surface absorption or by absorption into the

190
pores; or before deposition—e.g., from substrate or material contamination.

Water is the most important of many contaminates in the 2-to-5 pm wavelength region. Donovan [18] has verified that water accounted for most

of a 10-order-of-magnitude increase in the absorptance of thin films

of sodium fluoride. At 10.6 pm, only two molecular layers of water (a

packing density of 99.95 percent) will give an absorptance of 10~ 4. Even if films are deposited water-free, water is absorbed by the film

pores shortly after removal from the deposition chamber.

Sparks [17] has suggested that a working ultrapurif ication deposition

process would greatly improve all types of optical coatings over all

wavelength regions. Though it is unlikely that all sources of extra

absorptance could be eliminated, ultrapurif ication deposition processes

have had some success.

Protective coatings are required to prevent degradation by water, other

contaminants, and hostile environments. Glassy arsenic-trisulf ide

films thicker than the maximum diameter of scratches on the surface of

the material to be protected have been found to protect sodium chloride

from water vapor [19] (the edges would have to be protected for long

exposures)

Plasma-polymerized polymers have successfully protected alkali halides

from water vapor, despite the fact that the thin, unsupported, pin-holefree films of polymers transmit much more water vapor than would destroy the halides. Flannery and Sparks [20] explain that plasma deposited by the polymer formed a protective coating on the surface of

the sodium chloride.

An otherwise adequate coating may nevertheless have excesssive absorptance. That of most polymers exceeds 10-4

, even for extremely thin

coatings. However, Braunstein [21] measured 6 = 4 to 7 cm

-1 at 10.6 pm

for polyethane films that were plasma-deposited by Shen [22], and

the lowest measured 10.6 pm absorptance of thin-film arsenic trisulfide

is 0.8 cm

-1

. Thus, 0.5 pm films of those materials would have absorptances of 2 x 10~4 to 4 x 10~4 and 4 x 10-5

, respectively.

Scattering as a function of surface roughness of metallic reflectors

has been studied extensively [23]. In crystalline fibers, it is one

of the most likely sources of attenuation, the lowest measured value

being 100 dB/km. A lower bound in transparent materials is established

by Brillouin scattering. In glassy materials, total scattering is

typically 20 times the Brillouin value. It is theoretically possible

to approach the Brillouin limit in crystals. However, any of four or five extrinsic mechanisms could cause excessive scattering.

191
Of the nonlinear and parametric absorption processes, we now appear to

have a viable theory of electron-avalanche breakdown [24]. Multiphoton

absorption is clear in principle, but multiphoton rates still cannot be

calculated accurately for most solids because the energy bands are not

well understood. By assuming they are spherically symmetrical and that

the oscillator strengths have reasonable values, surprisingly good

agreement (within a factor of 2) between experimental and theoretical

two-photon cross sections can be obtained [25]. Estimates of higher

orders are scant and become more unreliable as the order increases.

REFERENCES

1. P. Temple, this volume.

2. M. Hass et al . , "Infrared Absorption in Low-Loss KC1 Single Crystals Near 10.6 urn," J. Appl. Phys. 45, September 1974.

3. J. A. Harrington, D. L. Bobbs, and M. Braunstein, Ninth Annual

Damage Symposium on Optical Materials for High-Power Lasers,

Boulder, Colorado, 4 October 1977 (NBS Spec. Publ. 509).

4. T. Deutsch, "Lattice Absorption in Zinc Sulphide," Proc. of Internat. Conf. on the Physics of Semiconductors, held at Exeter, July

1962; published by the Institute of Physics and the Physical

Society, 1962.

5. M. Sparks, "High-Power Ultraviolet Materials and Components," invited paper, Tenth Annual Damage Symposium on Optical Materials

for High-Power Lasers, Boulder, Colorado, 12-14 September 1978.

6. G. Rupprecht, Phys. Rev. Lett. 12, 508 (1964).

7. F. A. Horrigan and T. F. Deutsch, "Research in Optical Materials

and Structures for High-Power Lasers," Raytheon Research Division,

Final Technical Report, Contract DAAH01-70-C-1251, 1971.

8. M. Sparks, National Materials Advisory Board Ad Hoc Committee

Meeting, March 1, 1971; "Theoretical Studies of High-Power Infrared Window Materials," Xonics, Inc. Quarterly Technical Progress

Report No. 1, Contract DAHC15-72-0129, March 1972.

9. J. A. Harrington and M. Hass, Phys. Rev. Lett. 31, 710 (1973).

10. A. J. Barker, J. Phys. C 5, 2276 (1972).

11. M. Sparks and L. J. Sham, "Theory of Multiphoton Absorption in Insulating Crystals," Phys. Rev. B 8, 3037 (1973).

12. C. J. Duthler, "Extrinsic Absorption in 10.6 pm Laser Window Materials Due to Molecular-Ion Impurities," J. Appl. Phys. 45,

2668 (1974).

13. T. F. Deutsch and R. I. Rudko, "Research in Optical Materials and

Structures for High-Power Lasers", Raytheon Research Division,

Final Technical Report, Contract DAAH01-72-0194, January 1973.

14. N. L. Boling and G. Dube, Appl. Phys. Lett.

15. R. W. Hopper and D. R. Uhlmann, J. Appl. Phys. 41, 4023 (1970).

16. M. Sparks and C. J. Duthler, "Theory of Infrared Absorption and

Material Failure in Crystals Containing Inclusions," J. Appl. Phys.

44, 3038 (1973).

192
17. M. Sparks, "Materials for High-Power Window and Mirror Coatings and

Multilayer-Dielectric Reflectors," Eighth NBS-ASTM-ONR-ERDA-DARPA

Symposium on Laser Induced Damage in Optical Materials, Boulder,

Colorado, 13-15 July 1976 (NBS Spec. Publ. 462).

18. T. Donovan, this volume.

19. P. A. Young, Thin Solid Films 6, 423 (1970).

20. M. Flannery and M. Sparks, in [17].

21. M. Braunstein, private communication to M. Shen, 1978.

22. M. Shen, Eighth NBS-ASTM-ONR-ERDA-DARPA Symposium on Laser Induced

Damage in Optical Materials, Boulder, Colorado, 13-15 July 1976

(NBS Spec. Publ. 462).

23. H. E. Bennett, "Validity of the Drude Theory for Ag, Au, and Al

in the Infrared," Optical Properties and Electronic Structure of

Metals and Alloys , edited by F. Abeles, Amsterdam, 1966.

24. M. Sparks et al . , "Theory of Electron-Avalanche Breakdown in

Solids," 1979 Symposium on Optical Materials for High- Power

Lasers, Boulder, Colorado, 30-31 October 1979 (NBS Spec. Publ.).

25. M. Sparks, "Nonlinear Absorption in Optical Materials," in Physics

of Transmissive Optical Materials , edited by Marvin Hass, to be

published by Springer Verlag.

193
THE MEASUREMENT OF INTERFACE AND BULK ABSORPTION

IN THIN FILMS AND BARE SUBSTRATES

P. A. Temple

Michelson Laboratory, Physics Division

Naval Weapons Center, China Lake, California 93555

Introduction

In recent years, with the availability of large cw infrared lasers,

there has been much interest in the problem of optical absorption in

highly transparent materials. Early effort was aimed at determining

and then lowering the bulk absorption in available optical materials.

However, as purer materials were developed, it became clear that absorption at the two surfaces, which was introduced by the required polishing

and grinding, frequently dominated the bulk absorption of the optic.

Additionally, many of the optical components of a low absorption system

require thin-film coatings. These coatings serve as environmentally

protective coatings, as antireflection or partially reflecting coatings,

or, finally, as highly reflecting coatings for either enhanced metal

mirrors or dielectric mirrors. In many cases the absorption introduced

by the coating is larger than the optic's bulk absorption. The lowering

of this surface and thin-film absorption remains a challenge to the

optics industry.

This paper is concerned primarily with the measurement of the absorption

which takes place at bare surfaces or, for coated optics, the absorption

which takes place within the various coating layers and the interfaces

between those layers. Ideally, for bare surfaces, one would like to

measure the absorption at the surface for all wavelengths of interest,

and in a manner which separates the surface contribution from the bulk

contribution. For coated optics, we wish to measure the bulk absorption

coefficient, a-j_, of the film of a stack and the interfacial specific

absorptance, a^j , between the 1^ and 3^ layers, again for all wavelengths of interest. By determining these quantities, we hope to

proceed in an orderly fashion to construct an understanding of the causes and cures for the high absorptance of bare surfaces and thinfilm coatings.

Absorptance Measurement Techniques

The bulk of coated windows and mirrors designed for use at one of the

laser wavelengths in the 1- to 10-ym range which we have looked at over

the last two years at the Naval Weapons Center (NWC) have exhibited

absorptances , that is (total absorbed power) / (incident power), of

from 2 x 10~ 3 to 2 x 10_I+

. An exception to this has been very carefully

194
polished and cleaned fused silica, which exhibits, at 1.06 urn, an absorptance of ~ 2 x 10-5

. This includes contributions from both

surfaces and one-quarter inch of bulk material. The measurement of

such low absorptance requires substantial effort.

Several techniques have been developed to measure absorptances as low

as those listed above. Two excellent review articles, one by Skolnik

[1] published four years ago, and a later one by Hordvik [2] published

two years ago, discuss the state of the art in absorptance measurement

as of that time. Since that time some of these techniques have been

refined or supplemented. Harrington et al. [3] reported on a wavelength modulation scheme which, when calibrated with laser calorimetric

data, yielded spectral absorptance data in the 10-5 range. A particularly simple technique, that of photoacoustic spectroscopy (PAS) [4-6],

has also been used in conjunction with laser calorimetry. The strength

of the PAS signal is proportional to the absorptance of the sample but

is not directly calibrated. This problem can be overcome by measuring

identical samples calorimetrically [7] or by electrical calibration

[8]. If this calibration is performed, PAS offers the potential of

very rapid evaluation of similar samples. In addition, the PAS response

is sufficiently great that a high intensity lamp and monochromator may

be used as a source, allowing spectral absorptance measurements to be

made. PAS also has the potential of separating surface and bulk contributions [7-10], although this feature has not been extensively exploited

as yet. Recently, Farrow [11] described a Fourier-transform PAS technique which improves the signal-to-noise ratio of the PAS signal and

also allows rapid data collection. A fundamentally different absorption

measurement technique has been reported by Seitel et al. [12] wherein

the absorptance of a metal surface is determined by noting the elongation of a long, thin sample due to heating by laser irradiation. Unlike

the other techniques, this method uses pulsed laser radiation and is a technique for learning absorptive properties of a surface under dynamic

conditions

.

In spite of the advantages of the various systems discussed above,

there are probably more laser calorimeters in operation at this time

than all other instruments combined. In laser calorimetry, the absorptance of a sample is determined by measuring the temperature rise of

the sample caused by a timed laser radiation of known power [1], The reasons for the popularity of laser calorimetry are its mechanical

simplicity, reasonable sample turn-around time, and adaptability to

various sample sizes. Laser calorimetry is potentially capable of

yielding absolute absorptance values and can be electrically calibrated.

Finally, not to be discounted is the fact that laser calorimetry is

essentially a prototype setup where one measures the actual temperature

rise of a sample under actual laser irradiation of the exact same wavelength which will be used in the full size system. It is just this

temperature rise which worries the system designer and which has

prompted so much activity in the area of absorptance measurement.

195
Surface Versus Bulk Absorption

Two calorimetric techniques have been employed to differentiate surface

absorption from bulk absorption in uncoated samples. In the first [13]

,

the absorptance of rods of various lengths are compared, with the

shorter rods showing lower absorptance due to the decreased path length.

When a plot of the absorptance data versus sample length is made, the

slope of the data is the bulk absorption coefficient, and the extrapolated zero-thickness absorptance is the contribution made by the two

surfaces. The problem with this straightforward technique lies in the

difficulty of obtaining uniform and repeatable surface absorptance from

the various samples.

The second technique, which also uses a long, rod-shaped sample [14]

,

uses the fact that heat generated at the rod's ends must travel half

the length of the rod to reach a centrally located temperature sensor while heat generated in the center of the rod by bulk absorption will

reach the sensor almost immediately. By analyzing this "prompt" signal, one can determine the bulk absorption coefficient of the rod, while the

delayed signal indicates the magnitude of the surface absorption present

This latter technique has also been used to measure the absorption of

surfaces coated with thin films to determine the change of absorptance

caused by the film [15].

The most common way of measuring coating absorptance is to measure the

absorptance of the bare substrate, and then measure its absorptance

again after coating. By comparing the two measurements, one can determine the absorptance of the thin-film coating. It is recognized,

however, that the increased absorption of the filmed substrate is due

not only to absorption in the bulk of the film, but also to absorption

in the newly introduced film-substrate interface and the film-air

interface. It is not possible to distinguish among these three sources

of absorption by any of the measurements discussed above. The remainder

of this paper will be concerned with the technique we have been using

at NWC to determine these three quantities.

Standing Waves and Optical Absorption

The absorptance of a filmed or unfilmed sample of thickness L under

normal incidence radiation is given by the general expression

L

A = / p(x)a(x)dx , (1) o where a(x) is the absorption coefficient at x, and p(x) = n(x)|E2 (x)|/ n0

|E^| is the time averaged relative energy density at position x.

|Eq| is the time average of the square of the incident electric field

external to the sample, and n(x) is the index of refraction of the

material at position x.

196
In the absence of reflections caused by index discontinuities, p(x) is

constant, and each portion of a sample contributes to the absorptance

in direct proportion to the absorption coefficient at that location.

In the usual case, however, there are index discontinuities which cause

a portion of the incident light beam to be reflected. This reflected

beam combines coherently with the incident beam, resulting in a spatially modulated relative energy density, p(x). It is this varying

p(x) which weights regions of the sample to contribute proportionately

more or less to the total absorption of the sample. By proper construe

tion of a sample, it is possible to accentuate the contribution of one portion of a sample over another portion and thus enhance that portion'

contribution to the absorptance.

At NWC we have been using wedge-shaped single-layer films on uniform

substrates to produce samples whose absorptance can be measured at

several film thicknesses [16,17]. A portion of the coated surface is

left bare to allow the uncoated substrate absorptance to be measured.

The adiabatic calorimeter [18] used to make these measurements allows

absorptance measurements to be made at any point along a selected

diameter. Each film thickness selected on the wedge produces a unique

relative energy density at the film-substrate interface, within the

film, and at the film-air interface.

We characterize the absorptance at the air-film interface by a specific

absorptance a r = a r h r , where the air-film interface is a sheet of

af af af

thickness A _ with absorption coefficient a Similarly, the filmaf af

substrate interface is characterized byJ a, = A,, a- . We assume that

fs fs fs

the bulk absorption coefficient of the film, a^, is constant throughout

the remaining thickness of the film. Under these conditions, the

f ilmed-substrate absorptance [using Eq. (1)] becomes

A =

P af

aaf

+ PfVf + P fsafs + (T

l

/T

o )Ao

(2)

where p^ is the spatially averaged relative power density within the

film,'1T-, is the first surface transmittance with the film in place, T

o is the unf ilmed-substrate first-surface transmittance, and A is the

o unf ilmed-substrate absorptance. The physical thickness of the film is

p^, as well as p - and p.. (the relative power densities at the

f f af fs

air-film and film-substrate interfaces) , are calculable from boundary

value considerations. The first three terms in Eq. (2) are the contributions to the absorptance made by the film bulk and its two interfaces

and the last term is the substrate contribution.

197
The four quantities p^, p

f

, p , and T are dependent on the film

thickness. By choosing appropriate film thicknesses, a set of independent equations can be generated from Eq. (2). Then, in principle, four

measurements of absorptance are required to determine the four quantities a _ , ar , a r , and A . The four measurements we generally make on af fs t o b j a wedge sample are at the bare substrate (which determines Aq) and at

film thicknesses of 1/4A, 1/2A, and 3/4A optical thickness. Further

measurements at A, 5/4A, ... are redundant and serve to improve the

quality of the data.

Figure 1 shows previously published data [17] from a As2Se3 film on CaF2 measured on the bare substrate and at 1/4A, 1/2A, 3/4A, and A optical thicknesses at 2.72 and 2.87 urn. The slopes of the two solid

lines determine af. These data, when analyzed using Eq. (2), indicate

that most of the observed absorption can be attributed to water at the

film-substrate interface, and very little to the film itself or to the

air-film interface. We have found, in fact, that quite frequently a substantial portion of the observed absorption takes place at the first

film-substrate interface. The existence of hydrogen at this interface

has been verified by a completely independent, nuclear resonance technique [19]. If one assumes that the presence of hydrogen indicates the

presence of water, there is very good agreement between the calorimetric

data and the nuclear data.

14

12

10

-5

2

- V 2.87 jum O 2.72 Aim

0.4 cm

-1

= -0.4 x 10"

= 4.2 x 10"

a S o.O cm

-1

= -0.4

= 2.3 X 10" X 10"

4"

0.25 0.50 THICKNESS, mi

0.75 1.0

Figure 1. The absorptance of an As2Se3 film on CaF2 measured at

0, 1/4, 1/2, 3/4, and 1A optical thicknesses at two laser wavelengths. A film of 1/2A optical thickness is ~0.5-ym thick.

198
As of this time we have looked only at single-layer films at the HF/DF

laser wavelengths (2.7 to 2.9 ym and 3.8 to 4.0 ym) . We have used

single-line wavelengths in the 2.7 to 2.9 ym band to verify the presence

of water. Ideally, one would like to extend this technique to the case

of two films to measure the absorption present at the film-film interface. In addition, there is evidence that the single-layer film properties are not always representative of that materials behavior in a complicated stack. In particular, hygroscopic materials such as ThF^

show the presence of substantial amounts of water when measured in

single-layer form, while these same films do not contain nearly as much

water when sealed by an overlayer of such materials as ZnS. It is

hoped that through techniques such as the wedged-film method we can learn enough about the absorptive properties of thin films and their

interfaces to make use of the method developed by Bennett and Burge

[20,21] for calculating the expected absorptance of both highly reflective and antiref lective multilayer stacks from the explicit knowledge

of the individual interface and bulk properties of all films in the

stack. We would like to point out, as a concluding remark, that while

we have used calorimetry to make these measurements, Eqs. (1) and (2)

apply in general. Another technique, such as PAS, might be used as an absorptance measurement technique just as well as, and possibly even better than, laser calorimetry.

Conclusion

In this paper we have discussed some of the more recent advances in

the measurement of absorption in optical materials. We have put particular emphasis on the problem of measuring the separate contributions

of the film interfaces and the film bulk to the overall absorption of a coated sample. The measurement technique developed at NWC, a scheme

which uses a wedged-film sample for calorimetric measurement, has shown

that, at least in many cases, there is substantial absorption at the

first film-substrate interface. We conclude the paper by indicating

that this wedged-film technique may be adaptable to two-layer film

stacks.

References

[1] L. Skolnik, in Optical Properties of Highly Transparent Solids,

S. S. Mitra and B. Bendow, Eds. (Plenum, New York, 1975), p. 405.

[2] A. Hordvik, Appl. Opt. 16, 2827 (1977).

[3] J. H. Harrington, B. L. Bobbs, M. Braunstein, R. K. Kim, R. Stearns,

and R. Braunstein, Appl. Opt. 17, 1541 (1978).

[4] L. K. Kreuzer, J. Appl. Phys. 42, 2934 (1971).

[5] A. Rosencwaig, Opt. Commun. 7_, 305 (1973).

[6] E. L. Kerr, Appl. Opt. 12, 2520 (1973).

[7] A. Hordvik and L. Skolnik, Appl. Opt. 16, 2919 (1977).

[8] J. M. McDavid, K. L. Lee, S. S. Yee, and M. A. Afromowitz, J.

Appl. Phys. 49, 6112 (1978).

199
[9] A. Hordvik, J. Opt. Soc. Am. J56, 1105 (1976).

[10] H. S. Bennett and R. A. Forman, in Digest of Topical Meeting on Optical Phenomena in Infrared Materials (Optical Society of

America, Washington, DC, 1976).

[11] M. M. Farrow, R. K. Burnham, and E. M. Eyring, Appl. Phys. Lett.

33, 735 (1978).

[12] S. C. Seitel, J. 0. Porteus, and W. N. Faith, "Optical Coupling

Coefficients for Pulsed CO2 Laser Radiation on Bare and Painted

Aluminum Surfaces," this conference.

[13] T. F. Deutsch, J. Electron. Mater. 4, 663 (1975).

[14] M. Hass, James W. Davisson, Herbert B. Rosenstock, and Julius

Babiskin, Appl. Opt. 14, 1128 (1975).

[15] J. A. Harrington, M. Braunstein, and J. E. Rudisill, Appl. Opt.

16, 2893 (1977).

[16] P. A. Temple, D. L. Decker, T. M. Donovan, and J. W. Bethke,

NBS Spec. Publ. 541, 37 (1978).

[17] P. A. Temple, Appl. Phys. Lett. 34, 677 (1979).

[18] D. L. Decker and P. A. Temple, NBS Spec. Publ. 509, 281 (1977).

[19] T. M. Donovan, P. A. Temple, Shiu-Chin Wu, and T. A. Tombrello,

"The Relative Importance of Interface and Volume Absorption by

Water in Evaporated Films," 11th Annual Symposium on Optical

Materials for High Power Lasers, Boulder, Colo., 1979 (to be

published)

.

[20] H. E. Bennett and D. K. Burge, NBS Spec. Publ. 541, 266 (1978).

[21] H. E. Bennett and D. K. Burge, "Simple Expressions for Predicting

the Effect of Volume and Interface Absorption and of Scattering in

High Reflectance or Antiref lectance Multilayer Coatings," to be

published in J. Opt. Soc. Am. (March 1980).

Added Note : The author is grateful to Dr. A. Feldman for bringing to

his attention the recent work of Tam and Patel [22] and its potential

usefulness in the measurement of absorption in optical materials. In

this technique, called optoacoustic (OA) spectroscopy, a pulsed laser

impinges on a sample to which is attached a piezoelectric transducer.

The transient acoustic signal is detected by a gated signal processor.

When properly gated, this technique has the important advantage over

the normal PAS scheme of rejecting the detector's spurious response to

scattered light. Such scatter now limits the sensitivity of PAS to

absorptances of ~ 1 x 10

-t+

.

[22] C. A. Tam and C.K.N. Patel, Appl. Phys. Lett. 35_, 843 (1979).

200
INFRARED OPTICAL PROPERTIES OF SILICON MONOXIDE

FILMS: APPLICATION TO RADIATIVE COOLING

A. Hjortsberg and C.G. Granqvist

Physics Department, Chalmers University of

Technology, S-412 96 Gothenburg, Sweden

Radiative cooling during clear weather occurs since the atmosphere can

be sufficiently transparent for wavelengths 8 < X < 13 ym that radiative

losses in this range are not balanced by reradiation from the sky. A

blackbody may reach a temperature which lies 10 to 15°C below that of

the ambient because of this effect, while temperature differences as large as 40°C are possible with a selective infrared radiator, whose

spectral emittance matches the atmospheric transmittance . Previously

suggested selectively emitting surfaces have used plastic films bonded

to aluminium ]j-~3] . Below we report on a more efficient approach, whose

basis is a determination of the infrared optical properties of silicon

monoxide from a novel technique. These data lead us to predict that SiO

films on a metallic substrate can give the spectral profile demanded

for efficient radiative cooling. This result is verified by measurements.

The optical constant n and k of SiO films were determined from transmittance and reflectance recordings with double beam spectrophotometry

in the range 2.5 to 40 ym. Initially, only results from SiO films vacuum

evaporated onto infrared transparent KRS-5 (thallium bromide-iodide)

plates were used. It was found that only k could be accurately determined, whereas experimental uncertainties affected n to an unacceptable

extent. This result is indeed expected, since curves for constant re- flectance and transmittance drawn in the n-k plane show branch points

in the pertinent intervals for n and k [4] . However, accurate values of n could be obtained by using the additional information from reflectance

spectra of SiO films on Al-coated smooth glass plates. Transmittance

measurements on films on transparent substrates combined with reflectance measurements on films on highly reflecting substrates in fact make

a powerful new technique for determination of infrared optical properties of absorbing films [5] .

The solid curves in Figure 1 show our results for £i = n

2 -k 2 and

£2 = Ink. A strong absorptance peak at X ^ 10 ym is noteworthy. For

X < 14 ym, these data agree rather well with an earlier evaluation [6]

.

The internal consistency in the results for £i and £2 was tested by

using the Kramers-Kronig relation to calculate £1 from the experimentally determined values of £2 (properly extended towards small wavenumbers; cf. the dotted line at the bottom of Figure 1). The circles in

the upper part of Figure 1 show good correspondence with the experimentally determined result for Ex.

201
Wavelength [ym]

Fig. 1. Real and -imaginary parts of the dieleetrio permeability of

SiO. Solid curves represent this work3 while dashed curves represent

data from Ref. 6. Circles denote results obtained via Kramers-Kronig

analysis

.

The infrared optical properties of SiO will now be used in a discussion

of surfaces for radiative cooling. The upper part of Figure 2 depicts

zenithal spectral emittance as obtained from an accurate model of a typical midlatitude summer atmosphere by use of published spectral

radiance data [7] . Low emittance is noted for the interval 8 < X £ 13 ym.

Cooling to low temperatures is possible for a surface which radiates

predominantly in this "window" range. The ideal spectral reflectance is

indicated by the dotted lines in the lower part of Figure 2. Reflectance

data which approximate the ideal behaviour could be obtained by computations based on the dielectric permeability of SiO. The dashed curve in

the lower part of Figure 2 pertains to a film thickness of 0.9 ym. The

202
Fig. 2. Upper part shows zenithal atmospheric emittance as derived from

Ref. 7. Lower part shows reflectance for SiO on Al as measured and as computed from the dielectric permeability given in Fig. 1.

strong minimum at A ^ 10 \m results from the dominant absorption band

in SiO combining with destructive interference. Hence the reflectance

data are strongly dependent on film thickness. The solid curve in the

lower part of Figure 2 represents a measurement on a SiO film, with an estimated thickness of 1.0 pm, deposited onto Al . Good agreement between theory and experiments in noted. Detailed reports on our work will

be given elsewhere [8,9]

.

REFERENCES

1. F. Trombe, Rev. Gen. Thermique 6, 1285 (1967).

2. S. Catalanotti, V. Cuomo, G. Piro, D. Ruggi, V. Silvestrini, and

G. Troise, Solar Energy 17, 83 (1975).

3. Ph. Grenier, Rev. Phys . Appl. 14, 87 (1979).

4. P.-0. Nilsson, Appl. Opt 7, 435 (1968).

5. A. Hjortsberg, to be published.

6. G. Hass and CD. Salzberg, J. Opt. Soc. Am. 44, 181 (1954).

7. P. Berdahl and M. Martin, Proc. 2nd Nat. Passive Solar Conf. 3 Philadelphia, 1978; Vol. 2, p. 684; Proc. 3rd Nat. Passive Solar

Conf. j San Jose, 1979; to be published.

8. C.G. Granqvist and A. Hjortsberg, Appl. Phys. Lett., in the press.

9. A. Hjortsberg and C.G. Granqvist, to be published.

203
THE PHOTOELASTIC EFFECT IN OPTICAL MATERIALS*

Albert Feldman and Roy M. Waxier

National Bureau of Standards

Washington, D. C. 20234

The photoelastic constants are components of a fourth rank tensor that

relates the change of the dielectric impermeability tensor Ak" 1 and,

hence, refractive index n to an applied elastic deformation. Pockels

[1] first formulated the relationship of A<

_1

to the stress tensor

a and the strain tensor n. Using group theory, Bhagavantum [2] cor- rected some errors that existed in the earlier formulation. In recent

years, Nelson and Lax [3] discovered that body rotations make an additional contribution to the photoelastic effect in naturally birefringent

materials and this effect has been shown to be significant in the

acousto-optic interaction of light with shear waves. In this paper, we

will not be concerned with the latter effect.

The earliest theories of the photoelastic effect were based on molecular

or atomic polarizabilities. The most comprehensive theory appears to be

due to Mueller [4] who considered the following stress dependent factors

for cubic and amorphous materials: change of density; change of the

local field correction (or the Lorentz-Lorenz field); change in the

crystal field (or Coulomb field); and change in the intrinsic polarizability of the atoms. Mueller appears to be the first to recognize the

importance of the last factor. His formulation considered only the

electronic polarizabilities of the ions, but did not include the effect

of stress on lattice polarization, which has been treated only in recent

years.

A large body of experimental work has dealt with the effect of hydrostatic stress P on refractive index. These results can be interpreted

on the basis of the density dependence of the Lorentz-Lorenz equation

pjjlU

[ {n 2 . 1)(n2 + 2 )/6n](l - \ Q) (1)

where p = the density and \ Q

= the strain polarizability parameter

introduced by Mueller. Values of x 0 have been published for a wide

range of materials and they have yielded qualitative information about

the amount of heteropolar binding and ionic overlap in crystals [5].

*This work supported in part by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Nos. AFOSR-ISSA-79-

0001 and -80-00002. The U. S. Government is authorized to reproduce and

distribute reprints for governmental purposes not withstanding any

copyright notation hereon.

204
However, they have not been derived on the basis of fundamental calculations. Recent results have shown that x 0

z 0 for molecular solids

[6]. A formulation based on the Drude equation has been shown to be

equivalent to the Lorentz-Lorenz formulation described above [7].

Several years ago, some materials were found to exhibit a nonlinear

piezo-effect, that is, the change of n was not a linear function of a. The explanation of the effect was dependent on the material. In ionic

materials, it was shown that the nonlinear dependence of n on hydrostatic pressure [8] was due to the nonlinear deformation. When the non- linear elastic constants were used to calculate the strain, it was found that n was a linear function of strain.

Intrinsic semiconductor materials were shown to exhibit a nonlinear

piezo-optic effect at wavelengths near the absorption edge [9,10]; the

coefficients for piezo-birefringence, qn - q 12 and q^, exhibited a large dispersion in this region as well. This nonlinear piezo-optic

effect was attributed to the complicated stress-dependence of the

valence-band splittings and interband oscillator strength.

Significant nonlinear piezo-optic effects were observed in highly doped

n-type Ge [9,11]. Schmidt-Tiedemann [12] was the first to observe

piezo-birefringence due to the transfer of free carriers in the highlyanisotropic conduction bands of Ge. Other workers [9,11] used this

effect to calculate the shear deformation potential E 2 of Ge. Working

at 1.4°K, Feldman [9] found a dramatic nonlinearity in the piezobirefringence in which the incremental stress-induced birefringence

reversed sign. This occurred when the stress was sufficient to transfer

all free electrons to a single conduction band minimum.

In the Mueller theory of photoelastici ty, dispersion effects had not

been treated. In order to account for dispersion, modern formulations

treat a material as consisting of oscillators due both to interband

band transitions and to the creation of lattice optical phonons.

Cardonna and coworkers have calculated the dispersion of the piezobirefringence of al kali-hal ide and semiconductor crystals based on band

structure models with certain phenomenological parameters fitted to

experimental data [13,14]. Wemple and DiDomenico [15] have fitted a wide range of piezo-optic data to a phenomenological oscillator model

for electronic transitions.

Van Vechten [16] developed a model for the pressure dependence of the

optical dielectric constant of a wide range of materials based on the

Penn model for the optical dielectric constant,

£oo = 1 + (g 0^2 /E

g

2 )(l " B + j

B

2

) (2)

where B = Eg/4Ep, Ep = Fermi energy, g 0

= oscillator strength, and Eg = average energy gap consisting of a homopolar part E^ and a heteropolar

part C related by

205
p 2 - p 2 + r2

(3)

Based on the band structure calculations of others, Van Vechten con- cluded that Eh was a function only of the interatomic spacing r, and

then postulated that there is a power law dependence of Eh on r; thus,

Eh « r~ s with s = 2.48. Biegelson demonstrated a shortcoming of the

model by showing that the s parameter calculated from his strain-optic

measurements on Si was at variance with the predicted value [17].

Until recently, almost no piezo-optic data in the infrared have been

available for ionic materials. A theory for piezo-optic dispersion due

to infrared lattice modes has been developed by Humphreys and Maradudin

[18] (HM) and extended by Bendow, Gianino, Tsay, and Mitra [19] to a wide range of zinc-blende and al kal i-hal ide crystals. Subsequently,

several experiments were conducted that suggested inadequacies in the

model [20,21]. However, the experimental data were obtained at few

wavelengths and were prone to large experimental errors, and, hence did

not provide a stringent test of the model. We have measured the piezobirefringence coefficients of CaF2 , SrF2 , and BaF2 over the wavelength

range 0.45 to 10.6 ym and have been able to fit the data to the basic

phenomenological equation

+ 3Gl /3r

>i ' 3 G2/3 n-j (2Go

/v T0 )(v/v T0 ) 2 8A

i /3ri

i 11 1 - (v/v Tn )2 [1 . (v/v Tn )2?

where i = index indicating uniaxial strain either along the [100] or

[111] crystal axis, k-j = photoe2astic constant derived from the piezobirefringence coefficient q., = high frequency photoelastic con- stant, ni = magnitude of strain, G

0

= zero-strain oscillator strength,

Gj = oscillator strength for polarization along strain direction,

G2 = oscillator strength for polarizaton perpendicular to strain

direction, v = optical frequency, vTM = transverse optic-mode frequency, a 4 = strain-induced optic-moae frequency splitting. This

equation is equivalent to the phenomenological expression of HM. In

Figure 1, we show experimental photoelastic constants of BaF2 plotted

as a function of wavelength, and a curve denoting a least squares fit

of equation (4) to the experimental data. Analogous results have been

obtained for CaF2 and SrF2

. The fit indicates that the strain-induced

oscillator strength anisotropy is negligible suggesting that the Szigeti

effective charge remains a scalar. In addition, the shear deformation

potentials have been calculated. To our knowledge, this has been the

first determination of the splitting of the transverse optic phonon

mode due to uniaxial stress (or strain). The complete interpretation

of these latest results will depend on the development of a microscopic

model for the strain dependence of the dielectric function in fluorite

structure materials. Clearly, a large amount of experimental work

remains in the measurement of dispersion of the piezo-optic coefficients of ionic materials in the infrared.

206
WAVELENGTH (jim)

Figure 1. Photoelastic constants of BaF2 derived from piezo-birefringence data. The curves are least-squares fits to equation (4) of the

data points denoted by pluses for k n - k 12 and squares for kt^.

References

1. F. Pockels, Lehrbuch der Kristalloptik , (Leipzig: Teubner) 941,

74 (1906).

2. S. Bhagavantam, Proc. Indian Acad. Sci. A16, 359 (1942); Acta

Cryst. 5, 591 (1952).

3. D. F. Nelson and M. Lax, Phys. Rev. Letters 24, 379 (1970).

4. H. Mueller, Phys. Rev. 47, 947 (1935).

5. E. Burnstein and P. L. Smith, Proc. Indian Acad. Science A28, 377

(1948).

6. M. Kastner, Phys. Rev. B 6, 2273 (1972).

7. K. S. Krishnan and S. K. Roy, Phil. Mag. 43, 317 (1952).

207
8. K. Vedam and E. D. D. Schmidt, J. Mat. Sci. 1_, 310 (1966).

9. Albert Feldman, Phys. Rev. 150, 748 (1966).

10. K. Vedam and E. D. D. Schmidt, Phys. Rev. 150, 766 (1966).

11. S. Riskaer, Phys. Rev. 152, 845 (1966).

12. K. J. Schmidt-Tiedemann, Phys. Rev. Lett 7, 372 (1961).

13. A. Gavini and M. Cardonna, Phys. Rev. 177, 1351 (1969).

14. P. Y. Yu, M. Cardonna, and F. H. Pollak, Phys. Rev. B3, 340 (1971).

15. S. H. Wemple and M. DiDomenico, Jr., Phys. Rev. Bl_, 193 (1970).

16. J. A. Van Vechten, Phys. Rev. 182, 891 (1969).

17. David K. Biegelsen, Phys. Rev. Letters 32, 1196 (1974).

18. L. B. Humphreys and A. A. Maradudin, Phys. Rev. B6, 3868 (1972).

19. B. Bendow, P. D. Gianino, Y. F. Tsay, and S. S. Mitra, Appl . Optics

13, 2382 (1974).

20. J. P. Szczesniak, D. Cuddeback, and J. C. Corelli, J. Appl. Phys.

47, 5356 (1976).

21. A. Feldman, D. Horowitz, and R. M. Waxier, Appl. Optics 16, 2925

(1977).

208
THE RELATION OF ELASTOOPTIC AND

ELECTROSTRICTIVE TENSORS

D. F. Nelson

Bell Laboratories

Murray Hill New Jersey 07974

BACKGROUND

Electrostriction is the deformation that is produced in a body by the application of an electric field and is proportional to the square of that field. Traditionally the applied electric field is a very low frequency or constant field and is applied by electrodes attached to the body. It is apparent that electrostriction must be characterized by a fourth rank tensor, two indices coupling to the two electric fields and two indices coupling to the relevant measure of deformation,

the strain. The elastooptic effect (also called the photoelastic or piezooptic effect) is the interaction

of an elastic deformation with an input light wave to produce an altered output light wave.

Since the light waves are determined by their electric fields, the elastooptic effect can also be

characterized by a fourth rank tensor with two indices coupling to the two electric fields and two

indices coupling to the relevant measure of elastic deformation. From the discovery of the

elastooptic effect by Brewster in 1816 through the extensive work of Pockels in the 1890's until 1970 it was believed that the appropriate measure of elastic deformation for the elastooptic

effect was the strain. It was thus quite natural to expect that the electrostriction and elastooptic tensors were closely related, the electrostrictive tensor being simply the low frequency limit of

the elastooptic tensor. Proofs of this equality, in fact, were given many times

1-4 based simply on reversing the order of partial differentiation of a thermodynamic potential. In 1970 it was shown 5 that the elastooptic effect had been misrepresented throughout its long history and that the proper measure of elastic deformation relevant to the elastooptic effect

is the displacement gradient which is a sum of strain and rotation. Measurements on strongly

birefringent crystals such as rutile 6 and calcite

7 showed that the contribution of rotation to the

elastooptic effect can be comparable to that of strain. If the proofs

1-4

cited above are correct,

then the electrostrictive tensor must also couple to rotation as well as to strain; that is, the

application of an electric field to electrodes on a body would cause the body to rotate. That,

however, would clearly violate angular momentum conservation. Thus, something must be

wrong with the phenomenological proof. 1-4 Since the mathematics of the proof is too simple to be wrong, it must be that the proof inadequately addresses the physics of the processes

involved. In order to avoid any confusion before proceding further let us point out that a converse

elastooptic effect in which two light waves are mixed to produce a deformation (such as an

acoustic wave) has sometimes been called electrostriction, in particular by Caddes, Quate, and

Wilkinson 8 who first observed this effect. We do not use the term electrostriction in this sense

here but rather in the traditional sense defined above. Clearly the converse elastooptic effect is properly characterized by the same elastooptic tensor that characterizes the normal elastooptic

effect.

209
Recently a new relationship between the low frequency limit of the elastooptic tensor and

the electrostriction tensor was obtained by comparing the results from the application of the same basic theory of long wavelength interactions in dielectric crystals 9,10 to the elastooptic

effect

5 and to electrostriction. 11 The difference between the two tensors was attributed to the

differing coordinates, spatial and material, that are appropriate in expressing the tensors for the

two interactions, the elastooptic effect and electrostriction. Since the length of those two

derivations may obscure this interpretation, it is worthwhile to distill from them the essential

physics into a compact derivation of the new relationship. It is the purpose of this paper to do

that. The choice of coordinates to which to refer the two tensors is determined by the methods

of measurement. In the elastooptic effect the electric fields of the input and output light waves

are known relative to the spatial (laboratory) coordinates since the light source and detector are

fixed in the laboratory. It is thus natural also to express the deformation with respect to the same coordinates. In the study of electrostriction as in the study of other phenomena in the low frequency

(quasielectrostatic) region electric fields and deformations are known relative to the material

coordinates anchored in the crystal. This results because electric fields are typically applied to and detected by electrodes evaporated onto the surfaces of the crystal and deformations are applied and detected by transducers bonded to the crystal surfaces. This means that the electric and deformation fields are known only relative to the crystal surfaces and not relative to the

laboratory because the crystal surfaces are moving and deforming relative to the laboratory as a

result of the applied influences.

DERIVATION

The deformed position of a matter point is given by the spatial position vector x and the

designation of a matter point is given by the material position vector X. The latter can be

regarded as the name of the matter point that remains with the matter point during deformation. The relation between these two positions is the deformation transformation x = x(X,t).

It is convenient to take the material coordinate vector as the undeformed position of the matter

point and to represent the deviation of the matter point from this position arising from deformation by the displacement vector u. Thus

x = X+u. (1)

Both the spatial and material positions are measured with respect to a rectangular coordinate

system. The deformation gradients bx/dXj and dXjdx, can be expressed in terms of the dis- placement gradient, for instance,

aX/dxj = 8ji - du/ax, (2)

The displacement gradient is a sum of strain u< kii ) and rotation U[k aui/dxj = uk)i = u (k)i) + U[kii], (3)

where

U(k,i) = (dui/dxi + c)u/dx k)/2 (3a)

and

u tk,i] = (duk/axj — Qu/9x k)/2. (3b)

The Jacobian of the deformation transformation is

J = det (dx/dX) = 1 + Uij + • • • (4)

210
Finally we note that a theory is said to be cast in the spatial description (or frame) if x, t are regarded as the independent variables and in the material description (or frame) if X, t are regarded as the independent variables. In the spatial description the polarization P relevant to the elastooptic effect is given by 5

Pi = eoXijEj + 2e, EjUk>1, (5)

where xy is the linear electric susceptibility, Ej is the spatial frame electric field, e 0is the permittivity of free space, and the elastooptic susceptibility Xij(ki) is related to the Pockels elastooptic tensor p^, by

2Xij(ki) = ~~ K imKjnp mnkl- (6)

being the dielectric tensor. The factor of two before Xij(ki) in Eqs. (5) and (6) results because xy(ki) applies to one Fourier frequency component (Stokes or anti-Stokes) and a low

frequency limit is taken here in which these two components coalesce. The Pockels term is symmetric upon interchange of k and 1 and so couples only to the strain part of u k>t

. The last two terms 5 are antisymmetric upon interchange of k and 1 and so couple only to the rotation

part of uk j. We now wish to transform Eq. (5) to the material frame. A study 12 of the Maxwell equations in the material frame shows that the material frame polarization P and the material frame

electric field £are related to the corresponding spatial frame quantities by

Pm = JPiSXjdxi , ^ = EndXjdx,. (7)

If Eqs. (5) and (7) are now combined with the use of Eqs. (2) and (4), we obtain

•Pm = e 0Xmn-En + eO^Xmnfkl) - Xm(kSl)n — Xn(kS|)m+XmnSkl)£n<)UkA)Xl. (8)

A material frame study of nonlinearities in the quasielectrostatic region 11 yields

* m *0X + €ol mn ( k i)£ ndu k/9X|, (9)

where l mn(ki) is the electrostrictive susceptibility. Since to first order duj/dx, = duJdX h comparison of the last two equations gives

Imn(kl) = 2Xmn(kl) — Xm(k8|)n — Xnd^Dm + Xmn8 kl (10)

for the final result. An alternate form of the last equation can be obtained if the expression 12 for the low fre- quency material frame electric displacement,

Z) k = e (>I(C- 1 ) klJE1 + Pk, (11)

where (C

-1

)^ = (9X/9x k) (9X/Qx k), is expanded to yield

Dm - €oK mn£n + eoUnGcD-EnWdX! . (12)

The expansion gives the electrostriction tensor I mn(k0 i n terms of the electrostrictive susceptibility by

Imn(kl) = lmn(kl) — 2S m ( kS 1)n + 8 mn8 k , (13)

and so allows an alternate form for Eq. (10) to be

Imn(kl) = 2Xmn(kl) — Kmd^Dn ~~ K n(l£\)m + K mn8 kl • (14)

211
We regard both the electrostrictive susceptibility and the electrostriction tensor as equally

important. The former, like the linear electric susceptibility, vanishes for a vacuum and so

characterizes the medium. The latter, like the dielectric tensor, is nonzero for a vacuum and is the tensor entering the differential equations. It also enters the stress expression as the

coefficient of the square of the material frame electric field. DISCUSSION

Let us note several things about Eq. (10) [similar remarks could be made about Eq. (14)].

First, we see that the essential difference between the electrostrictive susceptibility and the elas- tooptic susceptibility arises because the former is a material frame tensor and the latter is a spatial frame tensor. As pointed out in the Introduction this difference arises from the differing

methods of measurement. Second, the electrostrictive susceptibility couples only to strain, as expected from an angular momentum conservation argument, even though the elastooptic ten- sor can couple also to rotation. Note that the antisymmetric part of the elastooptic tensor that couples to rotation does not enter Eq. (10). Third, the terms by which the electrostrictive susceptibility and the elastooptic susceptibility differ are terms describing Maxwell stresses arising

from the presence of a polarizable medium. These terms are comparable in magnitude to the

elastooptic susceptibility in many materials.

REFERENCES

1. H. Osterberg and J. W. Cookson, Phys. Rev. 51, 1096 (1937).

2. J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1957), pp. 255-256.

3. W. P. Mason, Crystal Physics ofInteraction Processes (Academic, New York, 1966), p. 166.

4. K. Iamsakun, W. Elder, C. D. W. Wilkinson, and R. M. DeLaRue, J. Phys. D 8, 266

(1975).

5. D. F. Nelson and M. Lax, Phys. Rev. Lett. 24, 379 (1970); Phys. Rev. B 3, 2778 (1971).

6. D. F. Nelson and P. D. Lazay, Phys. Rev. Lett. 25, 1187, 1638 (1970).

7. D. F. Nelson, P. D. Lazay, and M. Lax, Phys. Rev. B 6, 3109 (1972).

8. D. E. Caddes, C. F. Quate, and C. D. W. Wilkinson, in Modern Optics J. Fox, Ed.

(Polytechnic Press, Brooklyn, NY, 1967), p. 219.

9. M. Lax and D. F. Nelson, Phys. Rev. B 4, 3694 (1971); 13, 1759 (1976).

10. D. F. Nelson, Electric, Optic, and Acoustic Interactions in Dielectrics (Wiley, New York,

1979).

11. D. F. Nelson, J. Acoust. Soc. Am. 63, 1738 (1978).

12. M. Lax and D. F. Nelson, Phys. Rev. B 13, 1777 (1976).

212
PHOTOELASTIC PROPERTIES OF MAGNESIUM FLUORIDE

Sunwhee Chung

EMR Photoelectric

P.O. Box 44

Princeton, New Jersey 08540

Herbert R. Carleton*

Department of Materials Science

State University of New York at Stony Brook

Stony Brook, New York 11794

Magnesium fluoride (MgF2) has the rutile crystal structure with a tetragonal space lattice (P4/mnm) 1

. The crystal is uniaxial positive with

nU)=1.378 and n£ =1.390 for sodium D light 2

. A single crystal of MgF2 grown by the Materials Research Corporation was used in this study. The

crystal was approximately 1 cm^ with polished faces in the (001) , (110)

,

and (110) crystal planes as verified by the back-reflection Laue method.

After preparation, the sample was bonded with salol to a fused silica

block on which an x-cut 20 MHz quartz transducer was bonded with epoxy

cement. A similar fused silica block was prepared with a y-cut 20 MHz

quartz transducer for shear wave measurements. Upon the completion of

measurements with this configuration, the crystal was cut at an angle

45±0.5° to [110] and [110] in order to obtain (100) and (010) faces.

Further measurements were conducted with this configuration, which were

followed by another cutting at an angle 45±0.5° to [100] and [001].

This orientation was verified by obtaining an angular separation of

11.6±0.5° between [101] and the direction perpendicular to the newly-cut

face as determined by the back-reflection Laue method.

The experimental arrangement for ultrasonic laser-diffraction used for

all measurements is similar to that previously reported 3

. The intensity

of light pulses diffracted from the MgF2 crystal and the fused silica

reference was measured on an oscilloscope after detection with a photomultiplier tube.

It can be shown 4 that the photoelastic constant p responsible for optical diffraction by an ultrasonic wave is related to experimentally

available parameters by the relation:

<p s> 2 - <i R> 1/2^>3 £>V> 2 u>

^27 r s where the subscripts r and s stand for reference and sample respectively, I R

is the measured intensity ratio, p is the density, V is the

* Research supported in part by NSF Grant GK28383.

213
sound velocity, and n is the refractive index. The photoelastic con- stants of the sample were calculated from the known piezooptic constants

of fused silica which were measured by Primak and Post 5

. These piezooptic constants at several wavelengths were converted to the photoelastic constants using the elastic moduli reported by Primak and Post, and

tabulated in Table I.

Table I. Photoelastic constants of fused silica.

Wavelength (nm) 436.0 546. 0 579.0 589.0 644.0

P12

0.121 0.121 0.121 0.121 0.122

0. 272 0. 270 0.270 0.270 0. 270

The ratio of sound velocities was obtained from a knowledge of the Bragg

angle 0 B which is one half the angle between incident and diffracted

beams. The sound velocities Vs are then calculated from 2Vs Sin8

B

=Af

where A is the laser wavelength in air and f is the frequency of the

sound wave.

Six of the seven independent photoelastic constants of MgF2 have been

determined and listed in Table II. The piezooptic constants q^j were derived using elastic constants obtained in this experiment. Since p3 could not be measured accurately with a longitudinal wave along [001]

because of low diffracted light intensity, p j3 was determined using

quasi-longitudinal and quasi-shear waves along a direction 45° from

[100] and [001] in the (010) plane. These results were also used to

assign the relative signs of pij( p 3

, and p . Diffraction involving

p is "abnormal" 6, i.e. scattering 3 between light beams with different

phase velocities requires very large "phonon" frequencies to conserve

k-vector. Since this experiment was conducted in the Raman-Nath regime,

p could not be measured.

Table II. Photoelastic and piezooptic constants of MgF 2 at 632. 8nm.

Photoelastic Experimental Piezooptic Calculated Value

Constant Result* Constant (10

1

3

cm

2 /dyn)

p +0.041±0.002 q -0.467

p

1 1 +0.119±0.002 q

11 +1.053

p

12

+0.07810.002 q +0.197

p

13 -0.099±0.003 q

13 -0.545

p

31 +0.01410.001 q

31 +0.409 ^3 3 3 3 p — q

p

44

-0.047510.0015 q

kk -0.498 ^66 6 6 *Signs are assigned with respect to p which is assumed positive.

The change of the refractive indices of rutile under hydrostatic pressure dn/dP was reported by Davis and Vedam7

. For the sake of comparison

dn/dP of MgF2 was calculated using the following relations (2) and com- pared with those of rutile in Table III where we find that dn^dP is

positive while dn£/dP is negative.

214
dni£c n£ — 3 11(0 = —(2q

31 + q 33 ), — = —(q^ + + q^) (2)

Using known relations for the photoelastic constants, p(dn/dp) of MgF2

was calculated using Equations (3) and (4) and is listed in Table III

along with the corresponding strain polarizabilities

.

dn,,. n,

dn, n,

0) 0) I 1 = —=-{-(P, +P ) (S +S +S ) + -p (2S +S )} (3)

2 S 11 12 11 12 13 S 13 13 33

p

dn£ n 3 2P

= { (S +S +S ) + dp 2 S 11 12 l 3

J p 33 ,„(2S +S

S 13 3 3 )} (4)

Here, Sj_j is the elastic compliance, and 3=23! 1 +2S 1

2

+4S x

3

+S 3

3

Table III Change of refractive indices for MgF2 and rutile.

Crystal Refractive Index A(nm) dn/dP _. (Mbar)~ ^P A0

MgF2 n(jJ=l. 377 632.8 0.102 0.104 0.754

n£=1.389 -0. 0915 -0. 0927 1.21

Ti02

* n0J=2.587 58 9.3 0.11 0. 25 0.92 ne=2. 902 -0.49 -0. 95 1.21

*Davis and Vedam . It is interesting to note that the ordinary and extra-ordinary refractive indices of MgF 2 and rutile change in opposite directions under

hydrostatic pressure.

A total differentiation of the Lorentz-Lorenz equation predicts a densi7 8 9 ty dependence of the refractive index, »

> dn

>dp"

(n

2 - 1) (n2 + 2)

6n

(1 " AJ, (5)

where A = -(p/a) (da/dp) is the strain polarizability

.

Detailed studies 10 have shown that the polarizability of a cation in- creases under compression while that of an anion decreases. This is

related to a decrease in ionicity of valence-pairs under compression.

It can be expected that shifts away from ionicity, and hence to directed

bonds, will produce anisotropic changes in refractive index where crystal symmetry permits. The contribution of different ions to changes in

refractive index can be considered by introducing an ionic strain polarizability A^,

Ai = -(p/a±) (daj/dp) , (6) so that the molecular strain polarizability is given, for binary systems, by

215
a+ a_

A„ = — A, + A , (7)

a++a_ + a++a_ ~' '

where the subscripts + and - represent the cation and anion, respectively. AQ is a phenomenological constant which attempts to explain those

changes in refractive index which cannot be explained by volume changes

alone. It must be interpreted as a tensor in the case of MgF2 . Since

the two terms appearing in (7) are of opposite sign, the observed values

of A D are consistent with a larger value of A+ for polarization in the

basal plane (nw) than for polarization along the c axis (n £

) . This is

plausible if one takes a close look at the irregular octahedron made by

six anions of MgF2

. Along the directions [110] and [110] , all ions are

in close contact with one cation for every two anions. However, along

the [001] direction, the anions are not in contact, leaving some space

for cations in the direction perpendicular to the c axis.

One can go a step further from this argument and say that dn/dP is negative for more covalent crystals because the former part of Equation (7)

is very small or non-existent compared to the latter part which is positive, thus making A Q greater than 1. This will in turn make p(dn/dp)

negative. The experimental results for MgO, C (diamond), Si, and Ge

support this argument. The values of A o are 1.1 for diamond7 and 1.2 - 1.4 for MgO 7

' 11

. Accordingly, p(dn/dp) and dn/dP for diamond and MgO

1 2 are negative. Gibbs and Hill reported the change of the static electronic dielectric constant due to pressure for diamond as (l/Ej (0)

)

(0)/3P) T=(-1.07±0.09)xlO~ 7 cm

2 /Kg. Cardona et al 12 reported (1/n) (dn/dP)

=(-3±2)xlO_7 cm

2 /Kg for Si and (1/n) (dn/dP) = (-7±2) xlO~ 7 cm

2 /Kg for Ge.

Davis and Vedam 7 related the larger values of A Q to the more covalenttype bonding and the smaller values to the more ionic-type bonding from

the experimental results. This is in agreement with the conclusion

derived in this report using the concept of the ionic strain polarizability.

References

1. R.W.G. Wyckoff, Crystal Structure Vol. 1, John Wiley New York (1963).

2. Handbook of Chemistry and Physics, 56th edition, CRC Press.

3. W.T. Maloney and H.R. Carleton, IEEE Trans, on Sonics and Ultrasonics

SU-14 , 135 (1967).

4. R.W. Dixon and M.G. Cohen, Appl. Phys. Lett. 8_, 205 (1966).

5. W. Primak and D. Post, J., Appl. Phys. 30, 779 (1959).

6. R.W. Dixon, IEEE J. Quantum Electronics QE-3 , 85 (1967).

7. T.A. Davis and K. Vedam, J. Opt. Soc. Am. 58, 1446 (1968).

8. H.R. Carleton in "Amorphous Materials", John Wiley New York (1972).

9. H. Mueller, Phys. Rev. 47_, 947 (1935).

10. S. Chung, "Photoelastic Dispersion of Alkali Halides and Alkaline

Earth Fluorides", Ph.D. Thesis (1976) State University of New York.

11. T.S. Narasimhamurty, Acta Cryst. 17_, 788 (1964).

12. J. A. Van Vechten, Phys. Rev. 182, 891 (1969).

216
A MICROSCOPIC APPROACH TO PREDICT REFRACTIVE INDICES

AND ELECTRO- OR STRAIN-OPTIC COEFFICIENTS

M.D. Ewbank, P.R. Newman

Rockwell International Science Center

1049 Camino Dos Rios

Thousand Oaks, California 91360

and

W.A. Harrison

Department of Applied Physics

Stanford University

Stanford, California 94305

Introduction - Research and development of solid state optical devices

has recently been increasing. Specific examples are tunable spectral

filters, modulators and beam steerers (both acousto-optic (AO) and

electro-optic (EO)). However, some devices exhibit unacceptable performance characteristics. This limitation is usually not device design

but rather the relevant materials properties of the few selective com- pounds being utilized. One solution to this problem obviously is to

find crystals which demonstrate superior materials properties. However,

the experimental investigation (including growth, fabrication, and characterization) of random compounds which satisfy the necessary criteria

is prohibitively expensive.

A more efficient approach entails theoretically estimating the virtues

of candidate materials. Several authors 1 " 3 have addressed the issue of

identifying promising compounds for both AO and EO applications. Other

authors** 5 have attempted to establish empirical "guidelines," which are based upon bulk macroscopic properties, for selecting new crystals. Our

method, by contrast, is a "first principles" scheme that commences at

the atomic level of the solid. The ultimate goal is to develop a com- pletely general (based solely on elemental composition, atomic configuration, and crystal symmetry) theoretical predictive methodology for

comparing materials properties of different compounds, to "prescreen"

candidate materials, and subsequently to assist in the selection of

optimal materials to be grown and characterized experimentally.

Approach - Initially, we have identified three relevant material parameters: 1) the refractive indices, 2) the electro-optic coefficients, and

3) the photoelastic constants. This selection is based, in part, on two

"f igures-of-merit" for EO 5 and AO 6 devices which are F = n?r.?/e. and

M« = n?n?P.?/pv 3

, respectively, where n^ is the optical i ndexJ ofJ refraction, rA H the electro-optic coefficient, e,- is the dielectric constant at the frequency of the external electric field, P

7

- • is the photoelastic component, p is the mass density and v is the acoustic velocity.

217
Briefly, the procedure for determining the refractive indices and the

electro-optic or strain-optic tensors is as follows: 1) calculate the

electronic susce ptibility tensor and hence the refractive indices

(n. = A + 4TM-..-), using a "first principles" method discussed below,

for the "unperturbed" crystal, 2) apply an external perturbation (an

electric field for EO or a strain field for AO) and calculate the

effects of this perturbation on the atomic configuration and/or chemical

bonds, 3) recalculate the susceptibility for the "perturbed" crystal.

The resulting change in the susceptibility tensor due to the external

electric or strain field can be related to the electro-optic or strainoptic coefficients, respectively. 7

The interaction between the electric field associated with light propagating in a material and its constituent electrons is manifest in the

dynamic electronic susceptibility. Specifically, we are concerned with

the spectral region above the lattice response modes (Reststrahl) and

below the interband or interatomic transitions. A novel approach for

the calculation of the principle (diagonal ized) components of the electronic susceptibility has been put forth by Harrison 8 in terms of a modified LCAO theory as:

X

11 = (4e

2

/v) I I [V a3]

2

(J e\)

2 /U3

- g

3

(1) a 3

where s is a summation over occupied states in the unit cell, I is a summation over coupled unoccupied states, e is the electronic charge,

v is the volume per unit cell, V ao represents the interatomic matrix

element (overlap) between occupied state a and unoccupied state 3, a is

the vector distance between bonding atoms, E. is the unit vector along

the i-th principal crystal axis, e ais the energy of the occupied state

a, and eg is the energy of the unoccupied state 3. The factors v and a depend only on the crystal geometry. The interatomic matrix elements,

V a3 , can be quantitatively evaluated by using the Slater-Koster LCAO

energy integral formulas 9 along with a parameterization by Harrison 10

for the two-center integrals. The energies, e a and e«, can be determined from band structure calculations which depend on elemental composition, crystal structure, and the same set of interatomic matrix

elements, V a3.

Results - The above formalism has been applied to the change in the

refractive indices due to variations in atomic positions, of the sulfosalt, Tl3AsSe3 (TAS). As one example, the variation of atomic positions caused by' a longitudinal acoustic wave (uniaxial strain) leads to

calculation of photoelastic constants. Another calculation involves the

effects of thermal expansion on the refractive indices. 11

The crystal structure of TAS at room temperature was determined by Hong,

et al. 2 The perturbed structure is generated by incorporating a strain

which is assumed to be anisotropic and microscopically inhomogeneous,

with the As-Se, Se-Se and Tl-Tl interatomic distances remaining constant

and the Se-Tl distances accommodating all of the strain. A detailed

study of the atomic configuration makes this assumption plausible.

218
Following the procedure outlined above, the unperturbed refractive

indices of TAS can be calculated. The ordinary index, n 0

, is dominated

by the As(p

z )-Se(p

z

) ir-bond since these two states constitute the bottom

most conduction band and top most valence band, respectively, which re- sults in a small energy difference (e

g

- e ).

13 However, since the

As-Se bonds essentially lie in the a_ - b_ pfane, they do not contribute

to the extraordinary index, ne

. Consequently, the main contribution to

n gis from the Se-Tl p state interactions.

The change in the refractive indices, due to thermal contraction or strain (e.g. uniaxial contraction), can be understood by examining

Eq. (1). Both nQ

and n e will experience the volume dependence; as con- traction occurs, both refractive indices tend to increase. For n Q

, this

volume effect is the only contribution because nQ is dominated by the

As-Se interaction whose interatomic distance remains constant despite

contraction elsewhere in the lattice. Therefore, n0 increases with

contraction. In contrast, n e has several competing factors. Most are specified directly by the change in Se-Tl bond length. A significant

contribution results from the change in the energy difference,

(e - e ), for the Se-Tl p state. As the interactomic distances con- tract,

athe wave function overlaps increase and the energy levels split

apart. This variation in energy difference can be approximated by con- sidering only two coupled states . Then the shift in (e

g

- e ) can be

expressed as ^(e, - e?

) 2 + 4V,£. In the case of TAS, and are the ionization energies of Se and Tl p states and ls tne interatomic

matrix element between the Se and Tl p states.

The seemingly anomalous experimental temperature dependences of the

refractive indices for TAS are explained in the context of the above

model, since the factor (e - e ) dominates over the volume for n

fi . A

comparison between theory and experiment is shown in Figs. 1 and 2.

Fig. 1 Comparison of the predicted

temperature dependence of the

ordinary refractive index of

TKAsSeo with experiment.

Fig. 2 Comparison of the predicted

temperature dependence of the

extraordinary refractive index

of TloAsSeq with experiment.

219
The strain-optic coefficients (P-jii^) are defined in terms of the change

in the dielectric impermeability tensor (B^,-) with respect to elastic

strain (^-j):

7

AB. . = I P. .. , e. t U k j

Ukl kl

optic axis,

<5)c where 6 To examine the effect of a uniaxial strain in TAS

the lattice parameter, c, is modified as follows:

is a small number. Then, since TAS has the point

AB, = = for ordinary polarized light and ^

ordinary light, where we have used the standard contracted0

! nd ices notaalong the

c' = (1 + group 3m,

AB-, = 6 for extration. 7 The strain-optic coefficients are then defined in terms of the

refractive indices as:

13 K

2 >s

" (%

2 >u /« and

33 (n;

2

) s - (n;

2

) u /«

where subscripts "s" and "u" refer to "strained" and "unstrained,"

respectively.

Conclusion - We have outlined a predictive methodology for calculating

refractive indices and electro- or strain-optic coefficients. To test

its fundamental basis, this theory was successfully employed in predicting the photoelastic constants and the temperature dependences of the

refractive indices of Tl3AsSe3.

References

1. N. Uchida and N. Niizeki, Proc. of the IEEE 61_, 1073 (1973).

2. R.W. Dixon, J. Appl. Phys. 38, 5149 (1967).

3. I. P. Kaminow and E.H. Turner, Proc. of the IEEE _54 , 1374 (1966).

4. D.A. Pinnow, IEEE QE-6 , 223 (1970).

5. I. P. Kaminow and E.H. Turner, in CRC Handbook of Lasers , p. 447

(1974).

6. I.C. Chang, IEEE SU-23 , 2 (1976).

7. J.F. Nye, Physical Properties of Crystals , (Oxford Univ. Press,

Oxford, 1976), p. 244.

8. W.A. Harrison, Electronic Structure and the Properties of Solids , (Freeman, San Francisco, 1980).

9. J.C. Slater and G.F. Koster, Phys. Rev. 94, 1498 (1954).

10. S. Froyen and W.A. Harrison, Phys. Rev. B20 , 2420 (1979).

11. M.D. Ewbank, P.R. Newman, N.L. Mot a, S.M. Lee, W.L. Wolfe,

A.G. DeBell, and W.A. Harrison, to be published.

12. H. Y-P Hong, J.C. Mikkelsen and G.W. Roland, Mat. Res. Bull. _9» 365

(1974).

13. M.D. Ewbank, E.A. Kraut, S.P. Kowalczyk, W.A. Harrison, to be

publ ished.

220
DISPERSION OF THERMO-OPTIC COEFFICIENTS

OF Nd LASER MATERIALS

K. E. Wilson and L. G. DeShazer

Hughes Research Laboratories

3011 Malibu Canyon Road

Malibu, CA 90625

We developed a double interferometer capable of measuring simultaneously both the coefficient of linear expansion a£ and the thermo-optic

coefficient an and also capable of measuring differences in dB/dT in

anisotropic materials to better than 2%. The experimental technique

consisted of having the sample in one arm of a Twyman-Green interferometer which formed the first interferometer and the second interferometer, a Fizeau type, was formed by the reflected beams from the

front and back faces of the sample. The measured phase shifts in the

Fizeau interferometer are caused by optical path length changes in the

sample, while the phase shifts in the Twyman-Green are caused by path

length changes between the two arms of the interferometer. The linear

expansion and thermo-optic coefficients are therefore determined from

the simultaneous solution of the equations for the phase shifts in the

two interferometers.

The thermo-optic coefficients an and the thermal expanion coefficient

a^ were determined for seven laser materials: YAG, YALO, BeL, ruby

(Cr:Al203), quartz, ED2 and Nd Kodak glasses using the double interferometer technique. For YAG and ED2 glass, the wavelength variation

of the thermo-optic coefficient was fitted to a single resonance

theoretical model from which the relative variation of the electronic

resonance frequency with temperature wg

1 dwg/dt was determined to be

-1.73xl0 5 /°C (undoped YAG), -1 . 77xl0

_5 /°C (Nd:YAG) and -1 . 39xl0_5 /°C

for ED2 glass. As a comparison, these values were determined for NaCl

and quartz and are -2.03xl0~ 5 /°C and -0.97xl0" 5 /°C respectively.

Fig. 1 shows the wavelength dependence of the electronic resonance contribution to the thermo-optic coefficient.

In the course of our experiments, we discovered a new technique for

precisely measuring the temperature dependence of the birefringence of

anisotropic materials. We call this technique "fringe beating" which

is the superposition of the interference fringes for the two orthogonal polarizations in the sample and is very sensitive for measuring

small values of dB/dT, capable of measuring values of dB/dT on the

order of 10

_7

/°C. Figure 2 illustrates the beating for both TwymanGreen and Fizeau interferometer fringes with increasing sample

temperature using ruby.

221
WAVELENGTH, (J

' 0 06 0 38 0.32 0.29 9 i96-4

L I I I I

I I 0

2 4 6 8 10 12 FREQUENCY SQUARED, »T2 -2 -2

Figure 1. Plots of (1-n )/A vs. X where A is the electronic

resonance part of the thermo-optic coefficients.

TEMPERATURE °C Figure 2. Beating of interferometer fringes for ruby (60° cut) for

increasing T where top trace is Fizeau fringes and bottom, TywmanGreen

.

222
TEMPERATURE DEPENDENCE OF THE OPTICAL PROPERTIES OF SOME

METALS AT VISIBLE AND INFRARED WAVELENGTHS

D. L. Decker and V. A. Hodgkin

Michelson/Lauritsen Laboratories

Naval Weapons Center, China Lake, California 93555

This paper briefly describes experimental techniques and apparatus

developed at the Naval Weapons Center for measuring temperaturedependent changes in the near-normal incidence reflectance (R) of a sample to a precision of a few parts in 10 5 [1], Reflectance results

obtained from this instrument are presented for Al, Cu, Ag, and Mo

films and bulk material over the 0.6 to 10.0 um wavelength range at

temperatures from 80 to 450°K. The sample and reference surfaces were

protected in ultrahigh vacuum for these measurements. These data

(dR/dT) are analyzed by a differential Kramers-Kronig technique to

yield the temperature dependence of the real and imaginary parts of the

index of refraction and dielectric constants [2],

The infrared optical properties of a "good" metal are described classically by the simple Drude model [3]. The temperature dependence of the

optical constants computed from this model primarily arises from the

temperature dependence of the dc conductivity (a) [4]. For the metals

considered in this paper, at temperatures near room temperature and at

wavelengths in the infrared, nearly wavelength and temperature independ

ent values of dR/dT are computed from measured values of a(T). In the

far infrared, the measured and computed values of dR/dT are in reasonable agreement and are on the order of -1 x 10-5 /°C. In detail, there

are discrepancies which are both time and temperature dependent.

Reflectance data taken with ascending and descending temperatures show

hysteresis with very noticeable time dependence. Especially at elevate

temperatures, permanent changes in reflectance do occur due to "annealing." Much of the time-dependent variation is very similar to that

previously seen in heat capacity, thermal conductivity, and electrical

resistivity and is broadly described under the title of "premelting

effects" [5].

At shorter wavelengths in the visible and ultraviolet, these metals

have an additional dispersion mechanism associated with electron interband transitions. This dispersion acts in addition to that provided by

intraband electron transitions, which is accounted for by the Drude

model. For example, in Al, a very pronounced dip occurs in reflectance

with a minimum at about 0.83 um, which has been identified with interband transitions near specific critical points in the Brillouin zone of

this face centered cubic metal [6]. In this region, both the magnitude

and sign of dR/dT fluctuate wildly, and at a given wavelength, dR/dT is

223
strongly temperature sensitive. This is especially true near 0.81 urn where dR/dT « 0. The detailed temperature dependence of the reflectance

near the region of the interband transition is also strongly dependent

upon the condition and method of preparation of the sample. Data are presented for both evaporated film and single-crystal samples. Another

class of non-Drude effects has been discovered for Ag in the near

infrared, which also causes a sign reversal in dR/dT. This effect occurs in a region where the reflectance is known to be very sensitive

to surface roughness and may be associated with a surface plasmon-like

excitation which is coupled to the incident light by very small slope,

spatially uncorrelated surface roughness.

The data presented in this paper is of immediate engineering value in

computing the performance of optical systems whose components necessarily operate at temperatures other than room temperature. It is also

hoped that it will stimulate theoretical interest in examining some of

the subtle and poorly understood dispersion effects such as those seen

in the near infrared in silver.

References

[1] D. L. Decker, "Measurement of the Optical Constants of Thin Films

of Silver and Other Metals at Temperatures Near Room Temperature,"

in High Energy Laser Mirrors and Windows, ARPA Semi-Annual Report

#2, ARPA Order 2175 (Mar 1973), pp. 34-49.

[2] D. L. Decker, J. Opt. Soc. Am. 61, 679 (1971).

[3] H. E. Bennett and J. M. Bennett, "Validity of the Drude Theory for

Silver, Gold, and Aluminum in the Infrared," Optieal Properties and

Electronic Structure of Metals and Alloys, ed. by F. Abeles (North

Holland Publishing Co., Amsterdam, 1966), pp. 175-188.

[4] G. A. Boloshin, Opt. Spectrosc. 18, 423 (1965).

[5] G. Borelius, "The Changes in Energy Content, Volume and Resistivity

With Temperature in the Simple Solids and Liquids," in Solid State

Physics, Vol. 15, ed. by F. Seitz and D. Turnbull (Academic Press,

New York, 1963), pp. 1-51.

[6] H. Ehrenreich, A. R. Philipp, and B. Segall, Phys. Rev. 132, 1918

(1963).

224
OPTICAL PROPERTIES OF Ti DIFFUSED

LiNbO„ WAVEGUIDES

W. K. Burns

Naval Research Laboratory

Washington, DC 20375

We will discuss measurements of the optical properties of LiNbO^ which

are pertinent to optical waveguiding applications. LiNbO^, which is

both electro-optic and piezoelectric, has many potential uses in integrated optic applications, including communications, signal processing,

and spectrum analysis. Typically, optical waveguides are formed in

LiNbO by the diffusion of thin films of Ti at high temperatures,^

resulting in an increased index of refraction in a surface layer. The

waveguide is then characterized by the diffusion length and the surface

index change. Since LiNbO^ is uniaxial, the diffusion coefficients are anisotropic and the index change depends on optical polarization. The

situation is complicated by the outdiffusion of Li which occurs simultaneously with the indif fusion of Ti, and causes a non-stoichiometric

surface layer with a corresponding increase in the extraordinary index

of refraction. Using a suitable dispersion theory to describe the

graded-index waveguide, it is possible to obtain the index changes and

diffusion coefficients from optical measurements of the effective

9 indices (phase velocity) of the propagating modes. By using a series

of waveguides which vary in a known manner, a fairly complete description of the diffusion process can be obtained. Alternatively, using

analyzing techniques such as secondary-ion mass spectrometry (SIMS)

,

the Ti and Li concentration profiles can be observed directly. In

channel waveguide devices, the extent of lateral diffusion from the

channel is sometimes of interest. This effect has been successfully

measured by the electron microprobe.

In integrated optical spectrum analyzer applications utilizing Ti diffused LiNbO_ waveguides, it is desirable to induce absorption in various parts of the waveguide and substrate. This would improve the signal

to noise ratio by reducing optical noise at the detector array. We will

discuss the creation of optically absorbing layers which result from

the implantation of H into bulk and Ti diffused LiNb0

3

. References

1) R. V. Schmidt and I. P. Kaminow, Appl. Phys. Lett. 25_, 458 (1974)

.

2) W. K. Burns, P. H. Klein, E. J. West and L. E. Plew, J. Appl. Phys.

50, 6175 (1979).

225
OPTICAL PROPERTIES OF THIN FILMS

BY GUIDED WAVES AND SURFACE POLARITONS

J. D. Swalen

IBM Research Laboratory

San Jose, California 95193

Guided optical waves, also called integrated optics, are optical waves

which propagate in a thin layer, usually a few micrometers thickpThese parallel plate waveguides, as in the microwave case, have

propagation characteristics which follow directly from a solution of

Maxwell's equations matching the boundary conditions at each

interface. The optical fields are highly localized within the film

and the polarization of the light can be either s or p. Coupling is

usually accomplished by high index half prisms^ as illustrated in

Fig. 1 or gratings. The mode characteristics, the number of nodes in

the optical field across the guide, their angle of propagation and

their attenuation, can be analyzed to give detailed information about

the film thickness and its refractive index, real and imaginary parts,

or its related dielectric function.^

Surface polaritons are surface waves which propagate along an interfaced Like guided waves they are also highly localized but in

this case decaying exponentially away from the surface. They exist

only for p polarized light and require that the sum of the real parts

of the two dielectric functions at the interface be less than zero. This can be accomplished either with a metal at energies below the

bulk plasmon energy or with a strong absorber where the real part of

the dielectric constant becomes sufficiently negative. For the case

of a metal the surface wave is called a plasmon surface polariton and

the polarization change at the interface of metal and dielectric comes from the oscillations of the pseudo-free electrons in the metal. For

the case of a strong absorber the surface wave is called an exciton

surface polariton when the absorption is from excitons and a phonon

surface polariton when the absorption is from phonons . The dispersion

curve is shown in the top of Fig. 2.

6,7 8

Coupling is again accomplished with high index prisms or gratings

but since the propagation is for only a very short distance, a few

micrometers in the visible region of the optical spectrum, the

reflected instead of the propagated light is observed, see Fig. 1. In

Fig. 2 a typical reflectivity curve is shown, 9C being the critical

angle for prism-air interface. Measurement of this reflectivity

minimum gives a measure of dielectric function (and the thickness in

226
the Kretschmann scheme shown in the lower left of Fig. 1) of the metal

or strongly absorbing layer. Overlay ers of transparent or absorbing

films shift the angle at which the reflectivity minimum occurs. This

shift is a function of both the thickness and the refractive index

(the real part) of the overlayer but from this measurement only one

can be determined. Absorption has the added features of broadening

and changing the depth of the reflectivity minimum. Detailed analysis

of this exciton - plasmon surface polariton interaction has explained n this anomalous dispersion behavior which is orientationally dependent. in 111? Absorption, fluorescence , Raman scattering, > lifetime, spatial

and orientational dependency, and scattering from surface roughness^ are some of the many observables which can be analyzed to

characterized a film and the species within it. Recently thick liquid

crystal cells next to metal electrodes have also been studied by

surface polaritons as a function of applied electric field to

determine the anchoring and reorientational characteristics.^

1. See for example D. Marcuse, Theory of Dielectric Optical

Waveguides, (Academic, New York, 1974).

2. P. K.Tien, R. Ulrich, and R. J. Martin, Appl. Phys. Letters 14, 291

(1969)

.

3. M. K. Dakss, L. Kuhn, P. F. Heidrich and B. A. Scott, Appl. Phys.

Letters 16, 523 (1970).

4. J. D. Swalen, J. Phys. Chem. 83, 1438 (1979).

5. E. Burstein, 'Introductory remarks on polaritons', Polaritons,

Proceedings of the First Taormina Research Conference on the

Structure of Matter, Edited by E. Burstein and F. de Martini,

(Pergamon, New York, 1974)

.

6. A. Otto, Z. Physik 216, 398 (1968).

7. E. Kretschmann and H. Raether, Z. Naturforsch. 23a, 2135 (1968).

8. A. Girlando, M. R. Philpott, D. Heitmann, M. R. Philpott, J. D. Swalen and R. Santo J. Chem. Phys. (in press).

9. I. Pockrand, J. D. Swalen, J. G. Gordon II, and M. R. Philpott, J. Chem. Phys. 70, 3401 (1979).

10. W. H. Webber and C. F. Eagen, Optics Letters 4, 236Z(1979).

11. G. Burns, F. Dacol , J. C. Marinace, B. A. Scott and E. Burstein,

Appl. Phys. Letters 22, 356 (1973).

12. J. F. Rabolt, R. Santo, and J. D. Swalen, J. Appl. Spectrosc. (in

press)

.

13. I. Pockrand, Optics Commun. 13, 311 (1975).

14. J. D. Swalen and G. J. Sprokel, 'Liquid crystal - surface

interactions by surface plasmons ' , Symposium on the Physics and

Chemistry of Liquid Crystal Devices, IBM Symposium Series

(Plenium Press, New York, 1979).

227
LaserBeam Aj r

Waveguide Configuration

Substrate

Kretschmann Configuration Otto Configuration

Fig. 1. The schematics for coupling light into guided waves and

surface waves. In the top figure for waveguide coupling the film

thickness is exaggerated and the angle <j> is changed to couple to

different modes. The middle figure is an enlargement showing the

optical rays. The lower figures illustrate the two methods for

coupling to surface waves. In the Kretschmann configuration the

metal film must be thin enough for the evanescent wave to

penetrate to the bottom side.

223
£ 0.6 >

<d 0.4

oc

0.2

IE i 40 44 48 52

Internal Angle 0

Fig. 2a The dispersion curve (u vs. k) for plasmon surface

polaritons (SP) and its intersection with a laser frequency U£

and propagation vector ko. The frequency w

p

is the bulk plasmon,

e Ais the dielectric function of the dielectric half space, and

Tip is the refractive index of the coupling prism. 2b A typical

reflectivity curve.

229
PROPERTIES OF LOW LOSS DIFFUSED OPTICAL WAVEGUIDES IN GLASS

T. Findakly, E. Garmire

Center for Laser Studies

University of Southern California

University Park, Los Angeles, California 90007

Graded index waveguides in glass are typically fabricated by ion ex- change from a silver nitrate melt. Residual losses observed in such

waveguides are from 0.5 to 2 dB/cm and are generally attributed to

either scattering from surface irregularities or loss due to silver

grains. In order to reduce the loss, and to investigate mechanisms for

loss in glass waveguides, we have investigated other techniques of fabrication. In particular, we have employed a dry process, diffusing

metallic silver into the glass substrates. In addition, we have investigated the effect of an electric field applied during diffusion.

We have observed losses so low as to be unmeasurable (0.1 dB/cm), and

have made both single mode waveguides and highly multimode waveguides

with large numerical aperatures. We report measurements of modedependent losses in these waveguides at several wavelengths and also of

absorption, measured calorimetrically . In addition, we report experiments on burying the waveguide below the surface.

Silver films several hundred angstroms thick were evaporated on sodalime silicate glass slides and diffusion was carried out at 500 C in

oxygen, for periods from 5 minutes to 7 hours forming waveguides at

6328A

5 of depths from 6 urn to 85 urn.

The waveguide losses of the thicker waveguides were lower than could be

measured by monitoring the decrease in scattered light as a function

distance along the waveguide, using the photomultiplier . This very low

loss was due to a combination of relatively thick waveguides and a low

concentration of silver, which reduced both absorption and scattering

from any possible aggregates. The losses increased somewhat as the

waveguides were made thinner, however. Figure 1 shows the loss as a function of the diffusion time, and would indicate that surface scattering is the dominant loss mechanism in this case (assuming an infinite diffusion source) . Although they have very low loss, these

waveguides have the advantage of having a very low index (An^O. 002)

.

It is interesting to note that the ions may diffuse very far (85 um)

,

but with a very low solubility. This is in contrast to the high con- centration of silver ions achieved with ion exchange.

In order to increase the index of the waveguides, we applied an electric

field during diffusion. Diffusion was carried out at 300°C in air with

an applied electric field of from 0 to 100 V/mm for periods ranging

from a few minutes to one hour. The ionic current ranged from micro230
amperes to a few milliamperes and was monitored throughout. The re- fractive index profile for the multimode guides could be determined

from the WKB method and is shown in Fig. 2. It can be seen that

large refractive index increases can be obtained. The large index

profiles obtained are very different from the erfc (x) profiles usually

observed in ion exchange. These flatter distributions do not concentrate the light so close to the surface and should have a smaller loss

contribution due to surface scattering than do those fabricated by

ion exchange.

These studies show that by applying an electric field it is possible

to drive as many silver ions into the glass as with ion exchange.

We observed index changes as large as 0.03. A monitoring of the ionic

current showed a decrease in exchange current as a function of time,

which we attributed to a buildup of sodium on the gold cathode. In

order to continue the diffusion for a long time and make deep waveguides, we have found it necessary to use NaNO^ as the cathode.

These waveguides typically show more loss than those fabricated without an electric field. This appears to be due to the much larger

silver content of the guides. The losses in these guides are

^1 dB/cm and are comparable to those quoted in the literature for

ion exchanged guides. The mode dependent loss was measured for a highly multimode waveguide and is shown in Fig. 3. The decrease in

loss with increasing mode number differs from the independence observed in ion exchanged guides. The reasons for this difference will

be discussed.

We have found that it is possible to reduce the loss below that shown

in Fig. 2 by annealing after electro-diffusion. Reductions to less

than 0.5 dB/cm for all modes was typical. Further reduction of the

loss is possible by burying the waveguide below the surface. We

fabricated an electro-thermally diffused waveguide, removed excess

silver oxide, applied new electrodes and reintroduced the sample into

the furnace. The loss was decreased by 70% and the fact that the

guide was buried below the surface was confirmed by the substantial

reduction in prism coupling efficiency.

In this paper we shall present detailed results on the losses for

single mode guides and highly multimode guides. In addition,

calorimetric absorption measurements and total loss measurements at

other wavelengths are presently underway and will be presented at the

conference

.

231
12 3

Diffusion Time (hrs)

Fig. 1. Measured losses in waveguides fabricated

by diffusion of evaporated silver at 500 C

as a function of diffusion time.

0. 02

° U

a b

N a \ ^c s

1 \ \

d n.

n

Fig. 2.

10 15 20 x (ym)

25 30 35

Refractive index profiles for waveguides

diffused in the presence of an electric

field. (a) and (b) were at 60 V/mm with

two metal electrodes for 15 and 60 min.

respectively (c) and (d) were at 12 V/mm

with a cathode of NaNO^ for 1 and 2 hrs

respectively.

232
2.0

1.0

0 5 10 15

Mode Number

Fig. 3. Mode-dependent loss for a highly

multi-mode waveguide

233
THICKNESS MEASUREMENT OF VERY THIN-FILMS

BY OBSERVING ANOMALOUS LIGHT ABSORPTION

t t 1t H. Kitajima, K. Hieda and Y. Suematsu

t Kyushu Institute of Technology

Tobataku Kitakyushu, 804 Japan

it Tokyo Institute of Technology

Ookayama Meguroku Tokyo, 152 Japan

1. Introduction

Rapid and accurate measurement of film thickness is important in many

applications 1 ' 2. The prism coupler called m-line method 3

, which is one

of the most convenient methods, can not be used when a film is too thin

or the refractive index of a film is too small to support a guided mode.

We report here a powerful technique for measuring very thin-film thickness. The method is based on observing anomalous light absorptions in

a metal-clad thin-film into which surface waves are excited through a prism4

. A metal-clad thin-film, a transparent film coated on metal,

can support the guided mode, number m=-l of a TM wave, even the film is

extremely thin 5 ' 6

. Metal-clad films possess a quasi discrete spectrum

of leaky modes 7 and a continuous spectrum of radiation modes. In contrast to the radiation modes which are observed by ellipsometry method 8

, the leaky modes are obseved using a prism coupler. Therefore, the ano- malous absorption characteristics strongly depend on the film thickness

and the incident angle.

2. Theory

In the layered structure shown in Fig.l, the four media are denoted by

subscripts j=l,2,3,4, respectively. Their refractive indices are n . Incident|:E wave : H" Reflected

wave

Prism

Metal Substrate

Fig.l. Prism-film coupling

structure.

0 n . = / e . / e„

J J

0

( J=l,2,3 )

(1)

k

Q = a) / y 0 e

Q = 2tt / A

0

exp [ibit ]

wavelength in vacuum space

time convention

Let us assume that we are dealing with a plane wave which is impinging

obliquely at the prism-gap boundary. The magnetic fields in each region

are written as follows.

234
H. = expt-ifrc] (A .exp [-iy .s]+B .exp [iy .z] ) , j=l,2,3,4

where = 1 (incidence) , 8^=0

6 = fe n^ -sin6 .

Y . = k n n .cos6 . 3

0 3 3

Real{y .} > 0

3

Imag{y • } < 0

3

(2)

(3)

(4)

The reflection coefficient, at the prism-gap boundary is obtained

exp[-£<j> 12 ] + B2/A2

B, =

1 1 + exp[-£<t> 12 ] *B 2 /A2

where (5)

B

2 -exp[i(j> 32 ] + R31t exp[i(<l>3 tt -2<|>^,) ] "A^ " 1 - R 34 expK(<|)3 2

+<j)3 ir 2<jy)]

•exp[-2a^]

y ./ z . - y, / e,

^12 = ^32 =» ^34 ^ ! exp[i<f>., ] = -exp [£<{>, .]

2<jy = 2y 3 <i^ ,

2a = i2y 0 d = 2|yJd

9

2 g

1 21 g

The norraalized film thickness (guided modes)

dj. <}> 32 + 4> 31( + 2m-rr

4Trn

3 cos8 3

( ^=-1,0,1,2,..- )

The no-reflection (B-^0) conditions are given as

Ap tan(

A<(y 2* Ap tan( -jd 1

1 1

X A 4tt n„cos6,

» 12 ) , A(d^/X Q

) =

'0 r-2

Ap = 1 - R

2sincf> 32

log <

- > > /Ap z + Acjy^

4iTn

3 cose 3

where

34

A(f>/

= *32 + *34 + 2W7T " 2(|) /

12'

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

235
Fig. 2. Film and gap thicknesses as functions of incident angles for the

no-reflection. d^/\ Qt dg/Xq versus 8^° . The broken line is corrected film

thichness for the no reflection. The

three dots (1,2,3) are experimental data.

Fig. 3. Light absorption character- Fig. 4. Vector trajectories of

istics as a function of incident reflection coefficient showing

angle. | B| 2 versus 8^°. The plots resonant absorption. versus

are experimentally measured values. 8. °. ( ® : guided mode point)

236
3. Experimental Results and Discussion

First, we determined the refractive index of sputtered silica films on

gold films which support several guided modes.

Refractive index of sputtered SiC^: 1.47+0.002 at 6328A

Next, we measured thickness of very thin silica films on gold, which is

sputtered on glass substrates. Relation between the incident angles

and the thickness are shown in Fig. 2. According to Fig. 3, the measured

absorption characteristic fits in well with the calculated curve using

the index of bulk gold. However, thickness differences between the bulk

and evaporated gold are within 3^ for all samples. We did not deal with

a serious matter here; the complex refractive index of the gold should

have been measured.

From the vector trajectories shown in Fig. 4, one can understand that

when a trajectory crosses the origin, the reflection coefficient becomes

zero. However, even when the reflection does not become zero completely,

the incident angles at which the reflection becomes minimum are not so different from the angles which satisfy the guided mode. Therefore,

rapid and accurate thickness measurement is possible.

Table 1. Measured samples.

Sample Determined

Thickness

Measured Thickness [£]

Evaporated* Bulkt

1 161±5 162.06 159.27

2 71±5 72.39 69.79

3 32+5 33.98 31.47

* 0.15-£3.2 , t 0.35-£3.16 at A

0 =6328a"

4. Conclusion

This work has demonstrated the feasibility of using anomalous light

absorptions in metal-clad thin-film systems, as a thickness measurement

method for very thin films. Complex refractive index of metal may also

be measured in this way. Unlike ellipsometry , this technique need not

to measure either the reflection ratio or the phase difference.

References

1. N. M. Bashara and D. W. Peterson, J. Opt. Soc. Am., 56, pp. 1320-1331,

1966.

2. P. K. Tien, Rev. Mod. Phys., 42, 2, pp. 361-420, 1977.

3. P. K. Tien, R. Ulrich and R. J. Martin, Appl. Phys. Lett., 10, 14,

pp. 291-294, 1969.

4. V. Shah and T. Tamir, Opt. Commun., 23, 10, pp. 113-118, 1977.

5. A. Otto, Zeit Phys., 216, pp. 398-410, 1968.

6. A. Otto and W. Sohler, Opt. Commun., 3, pp. 254-258, 1971.

.7. K. Furuya and Y. Suematsu, Trans. IECE Jpn., 57-c, 11, pp. 411-418,

1974.

8. R. J. Archer, J. Opt. Soc. Am., 52, pp. 970-977, 1962.

237
INTERFEROMETRIC WAVELENGTH MEASUREMENT OF INFRARED SURFACE WAVES

Z. Schlesinger and A. J. Sievers

Laboratory of Atomic and Solid State Physics

Ithaca, N. Y. 14853

We have developed an inter ferometric technique for accurately measuring

the wavelength of surface electromagnetic waves (SEW's) on coated metal

surfaces. A variable pathlength, two-beam interferometer is employed

in which the beam separation and interference take place entirely on

the coated surface. The SEW's comprise one arm of the interferometer

and bulk waves traveling just above the surface the other. The observed inter ferograms are in good agreement with model predictions.

Consider the propagation of a SEW across a partially coated surface

such that the coated region occupies an intermediate section of the SEW

path. The interference phenomenon involves the inhomogeneous nature of

the SEW in an essential way. The field amplitudes of a SEW decay exponentially with distance away from the surface. This distance is very

sensitive to small changes in the SEW wavelength which, in turn, depends

on the state of the surface. For example, at the free space wavelength

XQ = 10 microns, the SEW on a bare gold surface has a wavelength Xs = 9.999 microns and extends 60 microns in the air above the surface,

while the SEW on a gold surface with a 0.05 micron Ge over layer has a wavelength Xs = 9.992 microns and extends only 20 microns above the surface. This discrepancy in the SEW extent makes it impossible for the

bound SEW to maintain its integrity when it traverses a boundary between

coated and uncoated regions of surface. Specifically the electromagnetic boundary conditions require that the tangential E and H fields be

continuous at the boundary between the coated and uncoated regions at

all heights above the interface. When the SEW is incident at the first

coating edge this condition can be satisfied only if bulk (unbound) ra- diation is produced in transmission in addition to the transmitted

(bound) SEW. At the far edge of the over layer the SEW and bulk wave

packet both contribute to the transmission of a bare metal SEW; however, these two contributions will in general no longer be in phase.

The total intensity of the resultant SEW is

i<i> - iSEW(i) + v*) + NW^V^trV - i>] (i)

' o s where ^ogW

(^) an<* are the component intensities and I is the

length or the coatect region across which the beam travels. From the

third term in Equation (1), the spatial period of the interference is

X

A* =

X /X°- 1

• o s

238
Because ^

Q/^s

- 1 is small, large interference periods will be produced by relatively short wavelength radiation (e.g. — 3 mm at X —

10H).

'

To test these conclusions, evaporated Ag and Au films were deposited on

KC1 couplers. (1) Over part of these rectangularly shaped films thin Ge

over layers of a triangular shape were then deposited. Both the metal

and Ge film evaporations were carried out at a pressure of 4 x 10~6

torr. The SEW was launched from a laser beam at one edge of the

metal film by means of the edge coupling technique. The length, l,

of the over layer region probed by the beam was continuously varied by

translating the film assembly in the plane of the surface but perpendicular to the beam direction. The transmission was measured as a function of & for fixed over layer thicknesses, d, and CO2 laser wavelength, X0 .

Ge over layers ranging in thickness from O.Lu ^ d ^ 0.7|J were studied in

this manner in the range 9.2|_i ^ Xq ^ 10. 8\J-. In each case the observed

transmission characteristics and interference period were in agreement

with model predictions.

In conclusion the SEW interferometer provides a unique method for studying thin films on metal surfaces. Not only is the attenuation of the

SEW obtained but also, of equal spectroscopic significance, the wavelength of the SEW is measured, an undetermined quantity in ordinary

transmission measurements.

ACKNOWLEDGMENTS

The authors acknowledge valuable conversation with R. Warner and Y.

Chabal.

Work supported by AFOSR under Grant #AFOSR-76-3684. Additional support

was received from the National Science Foundation under Grant No.

DMR-76-81083 A02 and technical report #4210, to the Cornell Materials

Science Center.

REFERENCE

1. Y. Chabal and A. J. Sievers, Appl. Phys. Lett. 32, 90 (1978).

239
AUTHOR INDEX

Page

Adari, H. ..... . . 126

Allen, S. D 48

Andrews, J. B. . . . 63

Arakawa, E. T. . . . . 20

Ashley, J. C 20

160

Barkatt, A 182

Bass, M 48,77

Becker, W. M 59

44,135

Bi 1 lard, D 44

Bloom, A. L 167

Boyd, R. W. 81

, 185

Burns, W. K 225

213

Champness, C. H. 55

Chandrasekhar, H. R. 40

213

Church, E. L 51

Coble, G. S 122

Dardy, H 185

223

Dempsey, D. V. . . . . 122

DeShazer, L. G. . . . 85,221

Detrio, J. A 122

Donadio, R. N. . . . . 131

135

Ewbank, M. D 217

Faith, W. N 100

204

Fernelius, N. C. . 122

230

63

167

Fleming, J. W. . . . . 91

Fox, J. A. . . . . . 122

Gallant, D 48

230

Gibbs, H. M 9

Gossard, A. C. . . . 9

Granqvist, C G. . 201

122

13

217

Hieda, K 234

. 201

Page

Hodgkin, V. A. . . ... 223

Hsia, J. J . . .149

Hughes, R ... 185

Hummel, R. E. . . . ... 63

Hunneman, R. . . . ... 118

Imaino, W ... 59

Johnson, G. W. ... 143

Johnston, G. T. . . ... 122

Kitajima, H. . . . ... 234

Klein, C. A. . . . ... 131

Kramer, M. A. . . . ... 81

92,185

Lauer, J. L. . . . ... 126

Lipson, H. G. . . . 36,44,135

Lowdermilk, W. H. . ... 147

Lynch, D. W. . . . 16,24,104

114

Marshall, R. C. . . ... 44

McCall, S. L. . . . ... 9

McKee, R. C. . . . ... 114

Mead, D. G ... 40

Milam, D . ... 147

Mitra, S. S. . . . 13,71

Moore, D. T. . . . ... 139

Musa, A. H ... 108

Nastasi-Andrews, R. J. .63

Neal, W. E. J. . . ... 108

Nelson, D. F. . . . ... 209

Newman, P. R. . . . ... 217

Olshansky, R. . . . ... 171

Olson, C. G. . . . 24,104,114

O'Quinn, D. B. . . ... 122

Osmun, J. W. . . . ... 114

Painter, L. R. ... 20

Passner, A ... 9

Peterman, D. J. . . ... 24

Philen, D. L. . . . ... 178

Porteus, J. 0. ... 100

Price, P. J. . . . ... 164 ... 104

Ryan, D. P ... 96 ... 238 ... 118 ... 100 ... 63

Shih, I ... 55

Shyamprasad, N. G. ... 55

240
Page

Sievers, A. J 238

Simmons, J. H 182

Simpson, C. T 59

Smith, D. Y 28

Sparks, M. S 188

Spector, H. N 67

Stewart, A. F 77

Stone, F. T 87,117

Strom, U 32

Suematsu, Y 234

Swalen, J. D 226

Taylor, P. C 32

Temple, P. A 194

Tran, D. C 182

Vaidyanathan, A 13

Venkatesan, T. N. C. . . 9

Waring, R. K 152

Waxier, R. M 204

Weaver, J. H 24,114

Weber, M. J 3

Weidner, V. R 149

Whatley, A 118

Wiegmann, W 9

Williams, M. W 20

Wilson, K. E 85,221

Winsor, H. V 1 Wood, D. L 91

Zumsteg, F. C 156

241

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4. TITLE AND SUBTITLE

Basic Optical Properties of Materials, Summaries of Papers

(Topical Conference on Basic Optical Properties of Materials)

5. Publication Date May 1980

7. AUTHOR(S)

Albert Feldman, Chairperson, Editorial Committee

8. Performing Organ. Report No.

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of 62 papers which include 14

Nonl inear Optical Properties;

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rincipal topical areas are:

The purpose of the conference is to discuss the state of the art in the measure- ment of the optical properties of optical materials. The emphasis is primarily on materials properties rather than on optical devices. The primary focus of the con- ference is on the measurement and theory of basic optical properties of materials in

bulk, thin film and fiber form.

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