NBS TECHNICAL NOTE 993

*<''>fAU O*

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

ptical Material

Characterizatio

inal Technical Repoi

"

February 1, 1978

ember 30, 197'
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j^ NalidnaT Bureau of Standards /^\.- I ivii X - I i^u * • -.- ^^^^ 2 197§

Optical Materials Characterization ,^^ ^^ ^ .,_ Final Technical Report Gx:.\oc3

February 1. 1978-September 30, 1978 , \js^^, 3

\ '^^^

Albert Feldman, Deane Horowitz, _ Roy M. Waxier, and Marilyn J. Dodge

Center for Materials Science

National Measurement Laboratory

National Bureau of Standards

Washington, D.C. 20234

Prepared for

Advanced Research Projects Agency

Arlington, Virginia 22209

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Director

Issued February 1979
National Bureau of Standards Technical Note 993

Nat. Bur. Stand. (U.S.), Tech. Note 993, 71 pages (Feb. 1979) CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1979

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Stock No. 003-003-0203 1-1 Price $2.40

(Add 25 percent additional for other than U.S. mailing)
OPTICAL MATERIALS CHARACTERIZATION

Albert Feldman, Deane Horowitz, Roy M. Waxier, and Marilyn J. Dodge

Ceramics, Glass and Solid State Science Division

Center for Materials Science

National Bureau of Standards

ARPA Order No '. . . 2620, 3343*

Support obtained through Department of the Navy,

Naval Weapons Center

Program Code Number 4D10 ,

Effective Date of Contract January 1, 1974

Contract Expiration Date September 30, 1978

Principal Investigator Albert Feldman

(301) 921-2840

Partial support for the work on piezo-optic constants of the »

alkaline-earth fluorides was provided by the Air Force Office of

Scientific Research, Air Force Systems Command, USAF, under Grant No.

AFOSR-ISSA-78-0026.

The views and conclusions contained in this document are those

of the authors and should not be interpreted as necessarily

representing the official policies, either expressed or implied,

of the Advanced Research Projects Agency or the U.S. Government.

Ill
TABLE OF CONTENTS PAGE

List of Tables v

List of Figures vii '

Abstract 1

1. Technical Report Summary 2

1.1 Technical Problem 2

1 .

2

General Methodology 2

1.3 Technical Results 3

1.4 Department of Defense Implications 4

1.5 Implications for Further Research 4

2. Technical Report 5

2.1 Introduction 5

2.2 Refractive Index 5

2.3 Linear Thermal Expansion Coefficient 7

2.4 The Thermo-Optic Constant 15

2.5 Piezo-Optic Constants 15

2.6 Publications I

2.7 Acknowledgements 24

2.8 References 24

2.9 Tables 26

iv
LIST OF TABLES PAGE

Table la. Constants of Dispersion Equation for KCl near 20 °C 26

Table lb. Constants of Dispersion Equation for CaF near 20 °C 26

Table Ic. Constants of Dispersion Equation for Fusion Cast SrF near 20 °C 27

Table Id. Constants of Dispersion Equation for Chemical Vapor Deposited (CVD)

ZnS near 20 °C 27

Table le. Constants of Dispersion Equation for Chemical Vapor Deposited (CVD)

ZnSe near 20 °C 28

Table 2a. Refractive Index of Commercial KCl at Discrete Wavelengths (T=19.9 °C) . . 29

Table 2b. Refractive Index of RAP KCl at Discrete Wavelengths (T=20.2 °C) 30

Table 2c. Refractive Index of KC1:KI (1.5% KI) at Discrete Wavelengths (T=19.9 °C) . 31

Table 2d. Refractive Index of Hot Forged CaF at Discrete Wavelengths (T=20.8 °C) . . 32

Table 2e. Refractive Index of Fusion Cast CaF at Discrete Wavelengths (T=21.7 °C) . 33

Table 2f. Refractive Index of Fusion Cast SrF at Discrete Wavelengths (T=20.0 °C) . 34

Table 2g. Refractive Index of CVD ZnS Specimen #1 at Discrete Wavelengths

(T=21.6 °C) 35

Table 2h. Refractive Index of CVD ZnS Specimen #2 at Discrete Wavelengths

(T=21.9 °C) 36

Table 2i. Refractive Index of CVD ZnSe Specimen #1 at Discrete Wavelengths

(T=20.3 ^C) 37

Table 2j. Refractive Index of CVD ZnSe Specimen #2 at Discrete Wavelengths

(T=20.8 °C) 38

Table 2k. Change in Refractive Index of CaF :Er with Increase in Percentage

of Er 39

—fi —1 Table 3. Linear Thermal Expcinsion Coefficients (10 K ) 40

Table 4a. dn/dT of Al O (10~ K~ ) 42

Table 4b. dn/dT of BaF^ (lo"^ k""*") 43

Table 4c. dn/dT of CaF (10~ k"""") 44

Table 4d. dn/dT of CdF^ (10~^ k'""") 45

Table 4e. dn/dT of KBr (10~ k""*") 46

Table 4f. dn/dT of KCl (lO"^ k"""") 47

Table 4g. dn/dT of LiF (10~ K~ ) 48

Table 4h. dn/dT of MgF (10~ k""'")

'. 49

Table 4i. dn/dT of NaCl (10~^ k"""") • 50

Table 4j. dn/dT of NaF (10~ K~ ) 51

V
Table 4k. dn/dT of SrF^ (10~ K~ ) 52

Table 4Z. dn/dT of CVD ZnS (10~ K~ ) 53

Table 4m. dn/dT of CVD ZnSe (10~ K~ ) 54

Table 5. Data Used for Computing dn/dT 55

Table 6. Piezo-Optic Constants, q and q and Elastic Compliance, s , of

-12 -1 As S Glass and a Chalcogenide Glass in Units of 10 Pa 56

-12 -1 Table 7a. Piezo-Optic Constants of Alkaline-Earth Fluorides (10 Pa ) 57

Table 7b. Comparison of Piezo-Optic Data in the Visible Region for Alkaline-Earth

-12 -1 Fluorides (10 Pa ) 58

Table 8. Photoelastic Constants of Ge 59

-12 -1

Table 9a. Piezo-Optic Constants of KCl (10 Pa ) 60

Table 9b. Elasto-Optic Constants of KCl 61

Table 10. Photoelastic Constants of Fused SiO 62

Table 11. Photoelastic Properties of CVD ZnSe 62

Table 12. Elastic Compliances Used in Computation of Piezo-Optic and Elasto-Optic

Constants (lo"''"^ Pa"""") 63

vx
I

LIST OF FIGURES PAGE

Figure 1. (a) Schematic of spectrometer used for visible region refractometry.

(b) Schematic of spectrometer used for non-visible region refractometry.

Symbols: A = source, B = divided circle, C = prism table, D = collimator, E = telescope, F = collimating mirror, G = movable - mirror, H = detector 6

Figure 2. Fizeau interferometer for measuring linear thermal expansion 8

Figure 3. Apparatus for measuring linear thermal expansion and thermo-optic

constants as a function of temperature over the range -180 °C to 200 °C . . 9

Figure 4. Linear thermal expansion coefficient of NaCl as a function of

temperature. The triangles are our experimental data and the circles

B are from the AIP Handbook [13] 11

Figure 5. Linear thermal expansion coefficient of NaF. The triangles are our experimental data and the circles are from the AIP Handbook [13] .12

Figure 6. Linear thermal expansion coefficient of CdF as a function of

temperature. The triangles show our experimental data and the

single circle is from S. S. Ballard and J. S. Browder, Appl. Opt.

« S_, 1873 (1966) 13

Figure 7. Linear thermal expansion coefficients of single crystal MgF as a function of temperature . The upper curve is for ot i i ,- the lower curve

is for ai .

| | and J_ refer to parallel and perpendicular to the

c axis, respectively. The curves and triangles are our data;

the squares are from Ref. [11], the circles from Ref. [10], and

the x's from [14] 14

Figure 8. Stressing apparatus. A = adjustment screw. with domed tip, B = adjusting

member threaded into push rod, C = lever arm, D = coil spring, E = axis,

F = frame, G = spacer, H = ball bushing, I = stressing screw with domed

tip, J = push rod, K = specimen cup, L = steel ball, M = load cell,

N = specimen 17

Figure 9. Modified Twyman-Green interferometer for measuring the piezo-optic

constants at 10.6 ym 19

Figure 10. Modified Dyson interferometer for measuring piezo-optic constants in

the visible 20

Figure 11. Double pass arrangement for measuring piezo-birefringence at 10.6 pm. . . 22

I

vxx

Optical Materials Characterization

Abstract

Data obtained as part of the Optical Materials Characterization Program are summarized

in this report. Room temperature values of refractive index as a function of wavelength are presented for the following materials: commercially grown KCl, reactive atmosphere processed

(RAP) KCl, KCl nominally doped with 1.5% KI , hot forged CaF , fusion cast CaF , CaF doped

with Er (0.001% to 3% Er) , SrF , chemical vapor deposited (CVD) ZnSe (2 specimens), and ZnS

(CVD, 2 specimens) . Data for the thermo-optic constant (dn/dT) and the linear thermal

expansion coefficient are given for the following materials over the temperature range -180 °C to 200 °C: Al O , BaF , CaF , CdF , KBr , KCl, LiF, MgF NaCl, NaF, SrF , ZnS (CVD), and

ZnSe (CVD). The piezo-optic constants of the following materials are presented: hs S glass,

CaF , BaF2 , Ge, KCl, fused SiO , SrF , a chalcogenide glass (Ge 33%, As 12%, Se 55%) and

ZnSe (CVD).

I

Key words: Al O ; As S glass; BaF ; CaF ; CdF ; chalcogenide glass; elastic compliances;

elastic constants; elasto-optic constants; fused silica; Ge; hot forged; KBr; KCl; KC1:KI; LiF; MgF ; NaCl ; NaF; piezo-optic constants; refractive index; SiO ; SrF ; thermal expansion coefficient; thermo-optic constant; ZnS; ZnSe

I

I

I
Optical Materials Characterization

1. Technical Report Summary

1 .

1

Technical Problem

Windows subjected to high-average-power laser radiation will undergo optical and mechanical distortion due to absorptive heating. If the distortion becomes sufficiently severe,

the windows become unusable. Theoretical calculations of optical distortion in laser windows

depend on the following material parameters; absorption coefficient, refractive index, the

thermo-optic constant (change of index with temperature) , linear thermal expansion coefficient,

stress-optical constants, elastic compliances, specific heat, thermal conductivity and

density. Our program has been established to measure refractive indices, thermo-optic

constants, piezo-optic constants, elastic compliances, and linear thermal expansion coefficients

of candidate laser window materials.

1.2 General Methodology

Laboratory experiments are conducted for measuring refractive indices, thermo-optic

constants, piezo-optic constants, elastic compliances and linear thermal expansion coefficients.

The refractive indices of prismatic specimens are measured on precision spectrometers by

the method of minimum deviation. Two spectrometers are used. One instrument, which uses glass optics, is used for measuring refractive indices in the visible with an accuracy of

several parts in 10 . The other instrument, which uses mirror optics, is used for measuring

refractive indices in the ultraviolet and the infrared to an accuracy of several parts in 10 . Using both spectrometers we can measure refractive indices over the spectral region 0.2 ym

to 50 ym.

We measure the linear thermal expansion coefficient, a, by the method of Fizeau

interferometry. The interferometer consists of a specially prepared specimen which separates

two flat plates. Interference fringes are observed due to reflections of HeNe laser radiation at 0.6328 ym from the plate surfaces in contact with the specimen. We obtain a by

measuring the shift of these interference fringes as a function of temperature. We can measure a from -180 °C to 800 °C.

The thermo-optic constant, dn/dT, is measured by two methods. In the first method, we measure the refractive index with the precision spectrometers at two temperatures, 20 °C and 30 °C, by varying the temperature of the laboratory. This provides us with a measure

of dn/dT near room temperature. In the second method, which may be used for measuring dn/dT

from -180 "C to 800 °C, we obtain dn/dT from a knowledge of the expansion coefficient and by

measuring the shift of Fizeau fringes in a heated specimen as a function of temperature.

The Fizeau fringes are due to interferences between reflections from the front and back

surfaces of the specimens. Measurements are made with discrete spectral sources, such as lasers or spectral lamps, in the infrared, the visible, and the ultraviolet.

We measure piezo-optic constants and elastic compliances using a combination of

Twyman-Green and Fizeau interferometers. The coefficients for piezo-birefringence are measured by polarimetric techniques. From the shift of fringes in specimens subjected to uniaxial or hydrostatic compression, we obtain the data necessary for determining all the

piezo-optic constants and elastic compliances. The measurement are made with discrete

spectral sources.

In materials with small piezo-optic constants or in materials that cannot withstand

large stresses, we use interferometers designed to measure fractional fringe shifts. At

10.6 ym a modified Twyman-Green interferometer, which has a sensitivity of 0.01 A, is used.

At 632.8 nm, a modified Dyson interferometer, which has a sensitivity of 0.002 X, is used.

When using these interferometers to measure piezo-optic constants we must know the elastic

constants of the material under test.
1.3 Technical Results

The purpose of this report is to collect in one publication all the data obtained under

the Optical Materials Characterization Program. In addition to data found in our previous

reports, we present data not yet reported. The data are tabulated in Section 2.9.

Section 2.1 discusses the measurement of refractive index by the method of minimum

deviation. Tables of room temperature values of refractive index are presented as a function

of wavelength. Also given are the parameters for a three term Sellmeier equation for

refractive index. Data are given for the following materials: commercially grown KCl;

reactive atmosphere processed (RAP) KCl; KCl nominally doped with 1.5% KI ; hot forged CaF,

fusion cast CaF ; 0.03%, 0.1%, 0.3%

ZnS (2 specimens)

CaF doped with the following percentages of Er: 0.001%, 0.003%, 0.01%,

1% and 3%; chemical vapor deposited (CVD) ZnSe (2 specimens); and CVD

2'

The measurement of linear thermal expansion coefficient is discussed in Section 2.2. A table of linear thermal expansion coefficients as a function of temperature over the temperature -180 °C to 200 °C is given for the following materials: AI2O3, BaF, CaF, CdF^, KBr, 2' ""^2'

KCl, LiF, MgF , NaCl, NaF, SrF , ZnS (CVD), and ZnSe (CVD). The data are a synthesis of

values from the literature and values obtained under this program. Our data are presented

when disagreement with the literature was found. Graphs are shown to demonstrate the discrepancies.

The measurement of thermo-optic constants is discussed in Section 2.3. Tables of

thermo-optic constants as a function of temperature over the temperature range -180 °C to 200 °C are presented. In the following table, the materials and wavelengths for which data

are presented are denoted by x's:

Material/Wavelength 0.458 ym 0.6328 ym 1.15 pm 3.39 ym 10.6 ym

AI2O3

BaF,,

CaF,

CdF^

KBr (RAP)

KCl (RAP)

LiF

MgF^

NaCl

NaF

SrF^

ZnS (CVD)

ZnSe (CVD)
The measurement of piezo-optic constants and elastic compliances is discussed in

Section 2.4. The piezo-optic constants of the following materials are given: AS2S0

glass, BaF2, CaF , Ge , KCl, fused SiO , SrF , a chalcogenide glass (Ge 33%, As 12%, Se 55%)

and ZnSe (CVD)

.

1 .4 Department of Defense Implications

The Department of Defense is currently constructing high-power laser systems. Criteria

are needed for determining the suitability of different materials for use as windows in

these systems. The measurements we perform provide data that laser system designers can use for determining the optical performance of candidate window materials.

1.5 Implications for Further Research

While extensive measurements of refractive properties have been made in the infrared,

there remains a significant lack of data in the ultraviolet. A review of the literature

indicates that piezo-optic data in the ultraviolet are virtually nonexistent and although

some thermo-optic data are available, they are scant. These data would be particularly

important for materials to be used in conjunction with excimer lasers (XeF , KrF, ArF)

.
2. Technical Report

2.1 Introduction

With the development of new laser systems of ever increasing average-power levels, the

optical elements in these systems, even if they possess extremely small absorption coefficients, can experience a significant temperature rise. The temperature distribution in the

element will generally be nonuniform; hence, an optical beam propagating through the element

will experience a wavefront distortion due to the thermally induced optic path variation

across the aperture of the element. Theoretical analyses [1-4] have shown that the variation

of optic path will depend on: (1) the change of refractive index with temperature, (2) the

change of element thickness due to thermal expansion, (3) the change of refractive index due

to stresses produced by thermal gradients and, (4) the change of thickness due to these

stresses. In order to predict the magnitude of these effects, the optical designer requires

certain material parameters which include absorption coefficient, refractive index n, thermooptic constant dn/dT, piezo-optic constants q-j^-; / linear thermal expansion coefficient a, and elastic constants c. . or s. .. The purpose of the Optical Materials Characterization

i: 11 Program at the National Bureau of Standards has been to measure n, dn/dT, q^ -; / ot / and, when

necessary s . . of important optical materials of potential application in high-power laser

systems. An earlier examination of the literature had shown that data on dn/dT and q. . of

important optical materials were almost nonexistent outside the visible region of the

spectrum [5]; hence, our program has emphasized measurements in the infrared at 10.6 pm and

3.39 pm, wavelengths close to the output of CO and DP lasers, respectively.

' This report discusses the various techniques we use for measuring n, dn/dT, a, q. . , and

s- .. It then summarizes, principally in tabular form, data we have obtained on a wide

variety of infrared transmitting materials.

2.2 Refractive Index

Several techniques are used for measuring the refractive indices of optical materials;

however, as part of this program, the measurements of n have been conducted on two precision

spectrometers by the method of minimum deviation [6,7]. Schematic diagrams of both spectrometers are shown in Figure 1. The first spectrometer, which contains glass optics, is

capable of measuring n in the visible and in the near infrared to an accuracy of several

parts in 10 . The second spectrometer, which contains mirror optics, is capable of measuring

n from 200 ran in the ultraviolet to 50 ym in the infrared to an accuracy of several parts in

10 . The accuracy depends on specimen quality and size. All values of refractive index

are measured relative to the refractive index of air, n , that is we measure n/n . The

value of n is about 1.0003 over the full wavelength range of measurement.

When determining the refractive index by the minimum deviation technique, collimated

radiation is passed through a specimen which is in the form of a triangular prism. The

prism is rotated about an axis parallel to the prism apex until a position is found where

the angular deviation of the beam at a chosen wavelength is a minimum. In terms of the

minimum deviation angle D, the angle between the emergent beam and an undeviated beam, and

the prism angle A, the refractive index is given by

D+A

s in 2 ,,. n = —

(1) sin -

Measurements are performed at discrete wavelengths which are selected from the emission

spectra of Hg , Cd , He, Cs, and Zn and from calibrated absorption bands of HO, polystyrene,

methycyclohexane , and 1,2-4 trichlorobenzene. A series of calibrated narrow-band filters

is also used in the infrared region. Each set of experimental data is fitted by a least

squares solution to a three term Sellmeier-type dispersion equation of the form [8]

3 A.A^

n^ - 1 = E -^ r- (2) j=l X -X.

3
Figure 1,. (a) Schematic of spectrometer used for visible region

refractometry. (b) Schematic of spectrometer used for nonvisible region refractometry. Symbols: A = source,

B = divided circle, C = prism table, D = collimator,

E = telescope, F = collimating mirror , G = movable mirror,

H = detector.
I

where X is the wavelength of interest, A . is the wavelength position of an oscillator, and

A. is the oscillator strength. The X.'s and A.'s are not intended to have any physical

significance because they can be influenced by the wavelength range of the experiment data.

Primary emphasis is given to procuring a mathematical fit to the measured data useful for

interpolation. Equation (2) is not adequate for fitting data close to an absorption edge.

It is possible to obtain dn/dT by measuring n at two temperatures, usually near 20 °C and 30 °C (strictly speaking we obtain An/AT) . What we actually obtain is d(n/n ) /dT where

3.

. A dn

d n '\^ dn a dT ^n ' = d? - " dF" '2^ a dn _ _ where -r; is about 1.1 x 10 K [9] . The particular application of the data will determine

dT

whether the corrections in eq. (3) should be considered. For example, if the optical component is always in thermal equilibrium with the surrounding air, the correction is unnecessary.

In Tables la through le (Section 2.9) we tabulate coefficients for computing refractive

index from equation (2) for the following materials: Table la - commercial KCl, RAP KCl , and

KC1:KI (KCl nominally doped with 1.5% KI) ,- Table lb - hot forged and fusion cast CaF ; Table

Ic - SrF • Table Id - CVD ZnS (2 specimens), and; Table le - CVD ZnSe (2 specimens).

In Tables 2a through 2f we present tabulations of refractive index at convenient wavelength intervals for the following materials: Table 2a, 2b, 2c-commercial KCl, RAP KCl, and

KC1:KI; Table 2d, 2e- hot forged and fusion cast CaF • Table 2f - SrF ; Table 2g, 2h - CVD

ZnS (2 specimens); Table 2i, 2j - CVD ZnSe (2 specimens); and Table 2k - CaF doped with

the following percentage of Er: 0.001%, 0.003%, 0.01%, 0.03%, 0.1%, 0.3%, 1%, 3%. The values

given apply to the specific specimens measured. Differences in the fourth decimal place may

occur in nominally identical materials, as can be seen, for example, in the data for CVD

ZnS and ZnSe.

2 .3 Linear Thermal Expansion Coefficient

Different techniques have been used to measure linear thermal expansion. The most

common technique employs a quartz dilatometer, but this measurement is not of great accuracy.

A second technique involves the measurement as a function of temperature of lattice parameters by x-ray techniques flO] . In a third technique, a is obtained from a measurement

of the capacitance of a parallel plate capacitor, where the plate spacing is a function of

the specimen thickness [11] . We measure a by an interferometric technique [12] . A specially prepared specimen is placed between two optic flats as shown in Figure 2. Fizeau

interference figures are observed when monochromatic radiation from a helium-neon laser

(A=0.6328 pm) is reflected from the two surfaces in contact with the specimen. These

fringes are observed to shift as a function of temperature due to the thermal expansion of

the specimen.

Figure 3 shows a schematic diagram of the apparatus used for measuring both a and dn/dT.

This apparatus will operate over the temperature range -180 °C to 200 °C. The furnace is

constructed from a cylinder of copper 37 mm in diameter by 75 mm high with walls 6 mm thick

to permit rapid transfer of heat. A commercial band heater, which is clamped around the

furnace generates 175 W of heat with an input of 120 VAC.

The furnace rests at the bottom of an evacuable chamber 100 mm in diameter by 150 mm

tall. Protruding from the bottom is a copper rod, 12 mm in diameter by 150 mm long, that

conducts heat away from the furnace to the liquid nitrogen reservoir. Thus, we can stabilize the temperature in the furnace by balancing the heat input from the heater with the

heat leak to the liquid nitrogen.
OPTIC

FLATS

SPECIMEN

Figure 2. Fizeau interferometer for measuring linear thermal expansion,
ELECTRICAL FEEDTHROUGHS

i

WINDOW

LOW PRESSURE

HELIUM

WINDOW

COPPER FURNACE

SPECIMEN

HEATER THERMOCOUPLES

COPPER ROD

CRYOSTAT

Figure 3. Apparatus for measuring linear thermal expansion and thermooptic constants as a function of temperature over the range

-180 °C to 200 "C.

9
The specimen rests within the furnace over a depression that is milled at an angle of

1° with respect to the furnace axis in order to deflect extraneous laser beam reflections

to the side. Holes are drilled at several locations within the furnace to allow placement

of thermocouples in contact with the specimen and to allow the pressure within the furnace

to equalize with the pressure outside the furnace. Two thermocouples measure the temperature at the top and at the bottom of the specimen. A copper cover with a window allows access of laser radiation to the specimen in the furnace while maintaining a uniform thermal

environment around the specimen. All windows in the system are tilted at a 1° angle to eliminate unwanted reflections.

We find that the system operates well when filled with a helium exchange gas of several

millimeters Hg pressure. The helium environment has several advantages over air or vacuum. During cool-down, products in the air condense on the system optics and hence interfere with

the laser beam. With vacuum, the thermal response of the system is sluggish because of poor

heat transfer between the furnace, the heat leak, and the specimen. In addition, there is

a large temperature difference between the two thermocouples. With the heliiom present, the

maximum temperature differential measured with the two thermocouples across a 12 mm thick

specimen is less than 1 K at a given mean temperature.

The procedure used for measuring a consists of first cooling the specimen to approximately liquid nitrogen temperature. Sufficient time is allowed for the two thermocouple

readings to agree to within 1 K. The furnace is then heated very slowly until a fringe

minimum is observed on a strip chart recorder monitoring the Fizeau intensity. The temperature is then recorded. Subsequently, the furnace is heated rapidly and after a convenient

number of fringes has been observed, power to the furnace is cut back to allow the thermocouple readings to equilibrate while the temperature is slowly rising. At a fringe minimum,

the temperature is recorded. The heating process is repeated until the maximum desired

temperature is achieved.

The linear thermal expansion coefficient is defined by

1 dt

a = — -— (4) t dT ^ ' o where t is the room temperature specimen thickness and t is the specimen thickness at temperature T. In terms of a fringe count N. at a temperature T. we calculate a (T) by the

formula

, N.-N. ,

O 1 1-1

where T = (T.+T. )/2. A graph is then made of a as a function of T. On this graph we also plot either the accepted handbook values of a(T) when they are available, or else values

from the literature. A curve is then visually drawn through the data and from this curve,

we abstract a set of data points. These points are then fitted by computer to a polynominal.

The purpose of the fit is to obtain an analytical expression for a{T), which is needed for

computing dn/dT as a function of temperature.

In Table 3, we present values of a from -180 "C to 200 °C at 20 ° temperature intervals

for AI2O2 (only perpendicular to c-axis, ai), BaF , CaF , CdF , KBr, KCl, LiF, MgF (both

a

I I and ai), NaCl, NaF, SrF , CVD ZnS , and-H;VD ZnSe. In the cases of NaCl and NaF there is

disagreement between published values [13] and our values (see figures 4 and 5) ; we list only

our values. We have confidence in our values because our results are in excellent agreement

with the bulk of the measurements reported in the literature. We did not measure the linear

thermal expansion coefficient of Al Oo; hence, the numbers shown were computed from values

in the American Institute of Physics Handbook [13]

.

Figures 4 and 5 show the discrepancies betweeen our values (triangles and dashed lines)

and values in the literature (circles and solid lines) for NaCl and NaF, respectively. In Figures 6 and 7, we show curves of a as a function of temperature for CdF and MgF , respectively. The triangles and solid curves are our data. In the case of CdF , there has been

virtually no earlier published data. In the case of MgF , we find excellent agreement with

recently obtained low temperature data [11] but agreement with others [10,14] is poor above room temperature.

10
100

TEMPERATURE ("0

Figure 4. Linear thermal expansion coefficient of NaCl as a function

of temperature. The triangles are our experimental data and

the circles are from the AIP Handbook [13]

11
-200 -100 TEMPERATURE fC)

100 200

Figure 5. Linear thermal expansion coefficient of NaF. The triangles

are our experimental data and the circles are from the AIP

Handbook [131.

12
I

25

1 1 I 1

i^ _

20 — ^.^^^^^^^'^ —

T

itb

'5 - X

^ —

a /

10 — —

5

CdF2

1 1 1

1 -200 -100 100 200

TEMPERATURE CO

Figure 6. Linear thermal expansion coefficient of CdF2 as a function

of temperature. The triangles show our experimental data

and the single circle is from S. S. Ballard and J. S. Browder, Appl. Opt. 5, 1873 (1966).

13
b^ 10-

200

TEMPERATURE CO

Figure 7. Linear thermal expansion coefficients of single crystal MgF,

as a function of temperature. The upper curve is for a i i

;

the lower curve is for ai .

|

| and J_ refer to parallel and

perpendicular to the c axis, respectively. The curves and

triangles are our data; the squares are from Ref . [11] , the

circles from Ref. [10], and the x's from [14].

14
2.4 The Thermo-optic Constant

The thermo-optic constant, dn/dT, is measured by an interferometric technique at discrete laser wavelengths over the temperature range -180 °C to 200 °C. With this technique,

we observe as a function of temperature the shift of Fizeau interference fringes formed from

reflections off the surfaces of an optical specimen polished plane parallel. The same apparatus and experimental technique used for measuring a is used for measuring dn/dT, The

change of index from room temperature to temperature T. is given by

At- -1

(6)

where M. is the fringe count from room temperature to temperature T. , n is the room temperature refractive index, and At/t is computed at temperature T, from the linear thermal expansion data. We obtain dn/dT (strictly speaking An/AT) from

dn(T) ^'^^^i) - ^'^'Vl)

^^^

T. - T. , 1 1-1

where T = (T.+T. ,)/2.

X 1-1

Table 4 presents thermo-optic constants of the following materials over the temperature

range -180 °C to 200 °C tabulated at 20 °C increments:

A1,0^ - Table 4a

BaF - Table 4b

CaF^ - Table 4c

CdF^ - Table 4d KBr - Table 4e KCl - Table 4f

LiF - Table 4g

MgF^ - Table 4h

NaCl - Table 4i

NaF - Table 4j

SrF^ - Table 4k

ZnS(CVD) - Table 4£

ZnSe (CVD) - rable 4m

An intercomparison of some of these data with data in the literature has been made and

reasonably good agreement was found [15]

In Table 5 we present refractive index and thickness data used for calculating dn/dT of

the above-mentioned materials.

2 .5 Piezo-optic Constants

The piezo-optic constants are the components of a fourth rank tensor that describe the

effect of stress on the refractive index of a material [16] . The relationship is expressed

by

_^ ^^^"'^ij =%jk^ \£ («^ where ic is the reciprocal of the optical dielectric tensor, a is the stress tensor,

q. . . are the components of the piezo-optic tensor, and the indices, i, j, k, and i take

values 1, 2, and 3. Repeated indices indicate summation. Because both the stress and

dielectric tensors are symmetric under interchange of indices, a contracted notation (also

called the Voigt notation) has been adopted so that equation (8) becomes

A(k~-^) = q o (9) m Tnn n

where m and n take on values 1-6 corresponding to ij ^ m, kX. -» n with 11 -»- 1, 22 -> 2, 33 ^ 3,

23 and 32 -^ 4, 13 and 31 -* 5, and 12 and 21 ^ 6. Nye [16] discusses in detail the relationship between components in the full notation and in the contracted notation.

k 15
The elasto-optic constants relate the change of refractive index to strain in a material.

These coefficients are related to the piezo-optic constants by

P.^ = q-i„c (10) ij im mj

where p. . is a component of the elasto-optic tensor and Cj^.: is a component of the elastic

stiffness tensor, both expressed in contracted notation. In this presentation, only the

measurement of piezo-optic constants is discussed; however, by use of equation (10), it is

a simple matter to convert to the elasto-optic constants.

In a crystalline material with the least symmetry there exist 36 independent piezo-optic

coefficients. However, the materials that have been of interest to the NBS program have been

of cubic or isotropic symmetry; hence, the discussion is limited to these materials. Most

cubic materials possess three independent piezo-optic constants, q^ ^ , q, , q .; isotropic

materials have two independent constants, q and q, „ , where q = q,

, -q . Thus, we can

A. J. J. ^ ^T _LXX^

measure all these coefficients by measuring changes of n when stresses are applied along

certain symmetry directions. If we apply a uniaxial compressive stress, P, along the [100] , axis of a cubic material (any axis of an isotropic material) , the change of n will depend on

the state of polarization of the radiation and is given by

3 An = 2_ q p (11)

where q = q for radiation polarized parallel to the stress axis and q = q^ for radiation

polarized perpendicular to the stress axis. This convention will be used throughout the

following discussion.

The stress-induced birefringence (piezo-birefringence) for P along [100] is given by

3 An

I I -An, = ~ (^11-^12^ ^ ^^^^

and for P along [111] is given by

3 An||-An^= |-q^^ P. (13)

Here |

| and J_ refer, respectively, to polarization parallel and perpendicular to the stress

axis. Equations [11-13] provide more than enough conditions for obtaining all the piezooptic coefficients.

A variety of techniques have been employed for measuring the photoelastic constants of

optical materials including acousto-optic scattering and Brillouin scattering. Many of these

techniques have been reviewed recently [17]. In this article, we discuss the techniques used

in the NBS measurements program. The techniques involve interferometric and polarimetric

measurements on specimens under static uniaxial and hydrostatic stress. These measurements

can provide data for obtaining not only the piezo-optic constants, but also elastic compliances.

Fizeau Interferometer ; A specimen in the form of a right rectangular prism with dimensions

approximately 12 x 12 x 36 mm is stressed parallel to the long dimension in a calibrated

stressing frame [18] (see Figure 8) . Two opposite rectangular faces of the prism are polished flat and parallel so that Fizeau interference fringes are observed when laser

radiation is reflected from them. These fringes are observed to shift as a function of

applied stress. If the stress is applied along the [100] crystallographic axis, the fringe

shift per unit applied stress is

AN 2t ,n^ -=- , ,,., (-q - n s^^)- (14)

where s is a component of the elastic compliance tensor and q is defined above. If the

specimen is subjected to a hydrostatic compression, the fringe shift per unit applied

pressure is

A?=- [r (^11^2q^2) - "(^ll-*-2^12y

(15)

16
t

Figure 8. Stressing apparatus. A = adjustment screw with domed tip,

B = adjusting member threaded into push rod, C = lever arm,

D = coil spring, E - axis, F = frame, G = spacer, H - ball

bushing, I - stressing screw with domed tip, J = push rod,

K = specimen cup, L = steel ball, M = load cell, N = specimen.

17
The extra terms containing the elastic compliances on the right of equations (14) and (15) occur because the fringe shift is due to the change of optic path in the specimen, which

depends both on the change of n and the change of specimen thickness.

Twyman-Green Interferometer : A specimen mounted in a calibrated stressing frame is placed

in one arm of a Twyman-Green interferometer. When a stress is applied to the specimen the

fringes at the output of interferometer are observed to shift. If the stress is applied

along the [100] crystallographic axis, the fringe shift per unit applied stress is

If all the measurements described by equations [14-16] are made, we can obtain not only q and q, _ , but also s and s . 11

Modified Twyman-Green Interferometer . For many cases, especially in the infrared, it is

difficult to obtain a shift of even one fringe by the above two methods. We then require

a modified interferometric technique which is capable of measuring fractions of a fringe

shift [19,20]. Figure 9 shows an interferometer that is capable of measuring 0.01 fringe

shift at 10.6 ym. The two arms of the interferometer are in close proximity in order to

minimize instabilities due to air currents and vibrations. The effects of vibrations are also minimized by mounting the diagonal mirror onto the same base as the beamsplitter and by

mounting the two end mirrors on a common base. The end mirror in the specimen arm of the

interferometer undergoes a sinusoidal translation along the optic axis, thus, modulating the

output intensity of the interferometer. The reference specimen at 10.6 ym is a crystal of

Ge in a compression appratus that we have calibrated by measuring the force necessary to

produce an integral number fringe shift. Fractional fringes are then obtained by linear

interpolation. In operation, the reference specimen is stressed until the interferometer

is at a null, which occurs when the fundamental harmonic of the output intensity is zero. A given stress applied to the unknown specimen will shift the interferometer away from null,

whereupon we compensate for this shift by applying an incremental stress to the Ge that brings

the interferometer back to null. From these data we can calculate q and q with eq. (16)

provided s is known. The state of the polarization is determined by the polarizer. The

variable wave plate is used to balance the intensities of the two arms of the interferometer

for a given state of polarization. It consists of a specimen of Ge placed in a stressing

apparatus with the angle of stress at 45° with respect to the vertical in a plane perpendicular to the beam axis.

Modified Dyson Interferometer . We have constructed a polarizing interferometer for measuring

photoelastic constants. This instrument is capable of measuring fringe shifts to a precision

of A/500 at 632.8 nm [21]. It is based on a design by Dyson [22] that was further modified

by Green [23]. A schematic diagram of the experimental apparatus is shown in Figure 10. This instrument operates on two beam interference, however, the two beams are orthogonally

polarized. Thus, an optic path change in one arm of the interferometer results in a change

of state of polarization of the combined beam at the output of the interferometer. Hence,

fringe shifts are analyzed with ellipsometric techniques which have great inherent precision.

This interferometer has several other advantages over conventional Twyman-Green

interferometers: it is more stable with respect to motion of system elements because both

beams traverse the same optics, hence, the optic path changes in both arms tend to be equal.

In addition, the close proximity of the arms minimizes the effects of thermal currents, which

are further reduced by placement of a cover over the interferometer part of the apparatus

.

In this interferometer, the expression for the piezo-optic constant in terms of the

fringe shift per unit applied stress is

n - -I Stress-Induced Birefringence (Piezo-Birefringence ) : The coefficients that determine stressinduced birefringence in most cubic materials are q,

, ^ -q, ^ and q^^. It is most convenient to

11 12 44 measure these coefficients on two separate samples, one oriented for stress along [100] and

the other oriented for stress along [111] , because in these orientations the crystal becomes

optically uniaxial and not biaxial; hence, small angular misorientations lead to only small

measurement errors.
LOCK- IN AMPLIFIER AC. AMPLIFIER

FOCUSING

MIRROR

REFERENCE

SPECIMEN

MIRROR ON

PZT DRIVE

VARIABLE

WAVE PLATE

I, , LASER

RADIATION

Figure 9. Modified Twyman-Green interferometer for measuring piezooptic constants at 10.6 ym.

19
SILICON MATRIX VIOICON

ANALYSER

LASER

SOLEIL-BABINET COMPENSATOR

SPATIAL FILTER AND

BEAM EXPANDER

MIRROR

WOLLASTON PRISM

LENS

LENS

' M/ I QUARTER WAVE PLATE

MIRROR

Figure 10. Modified Dyson interferometer for measuring piezo-optic

constants in the visible.

20
A variety of techniques have been used to measure piezo-birefringence [17]. In the

simplest technique, the specimen is placed between two crossed polarizers with the stress

axis at 45° with respect to the direction of polarization and perpendicular to the radiation

beam. As stress is applied, the output intensity will undergo a series of nulls corresponding

to a series of fringe shifts and the fringe shift per unit applied stress is

AP - 2X

"^ '^^'

where q' = q,

, -q, _ for stress along [100] and q' = q for stress along [111]. In the case

of noncubic materials, the expression for the fringe shift becomes much more complicated.

Frequently, it is either impossible or inconvenient to apply sufficient stress to obtain

the shift of even one fringe. In this case, a compensator is placed within the experimental

apparatus. Compensators used are Soleil compensators, de Senarmont compensators, or compensators consisting of a stressed specimen which acts like a Soleil compensator. Photometric

techniques are also employed [24] . Recently, Birnbaum et al. [25] have developed an interesting new technique for measuring piezo-birefringence in which a stressed specimen is

placed in a scanning Fabry-Perot cavity.

A simple variation of the basic crossed polarizer technique, is to double pass the

radiation through the specimen [20] . This technique which has the advantage of requiring

only one polarizer, has double the sensitivity of the single pass method. Figure 11 shows

a double pass arrangement for measuring piezo-birefringence at 10.6 pm.

In Tables 6 through 11, we present photoelastic constant data for CaF , SrF , BaF , As S glass, a chalcogenide glass (Ge 33%, As 12%, Se 55%), Ge , KCl , KC1:KI, fused SiO , and CVD ZnSe . The ZnSe is a polycrystalline material and, hence, is considered to be

isotropic. In Table 12, we present elastic constant data for BaF , CaF , Ge , KCl, fused

SiO , SrF , and ZnSe (CVD).

2.6 Publications

A. Feldman, D. Horowitz and R. M. Waxier, "Stress Optic Measurements in the Infrared", in the

Proceedings of the Third Conference on High Power Infrared Laser Window Materials, Nov. 12-14,

1973, Edited by C. A. Pitha and B. Bendow, AFCRL-TR-74-0085 (1), Special Reports, No. 174,

p. 403, February, 1974.

A. Feldman, I. Malitson, D. Horowitz, R. M, Waxier and M. J. Dodge, "Characterization of

Infrared Laser Window Materials at the National Bureau of Standards", in Laser Induced Damage

in Optical Materials: 1974 , NBS Special Publication 414, eds. A. J. Glass and A. H. Guenther

(U.S. GPO SD Catalogue No. 013.10:414, 1974), pp. 141.

A. Feldman, I. H. Malitson, D. Horowitz, R. M. Waxier, and M. J. Dodge, "Optical Properties

of Polycrystalline ZnSe", in proceedings of the Fourth Annual Conference on Infrared Laser

Window Materials, Tucson, AZ (Nov. 1974), pp. 117.

A. Feldman, D. Horowitz and R. M. Waxier, "Photoelastic Constants of Infrared Materials", in

Laser Induced Damage in Optical Materials: 1975 , NBS Special Publication 435, Eds. A. J. Glass

and A. H. Guenther, (US GPO, 1976), pp. 164.

M. J. Dodge and I. H. Malitson, "Refractive Index and Temperature Coefficient of Index of CVD

Zinc Selenide, in Laser Induced Damage in Optical Materials: 1975 , NBS Special Publication

435, Eds. A. J. Glass and A. H. Guenther, (US GPO, 1976) pp. 170.

A. Feldman and W. J. McKean, "Improved Stressing Apparatus for Photo-elasticity Measurements",

Rev. Sci. Instrum. 46_, 1588 (1975).

A. Feldman, R. M. Waxier and D. Horowitz, "Measuring Photoelastic and Elastic Constants of

Transparent Materials by Application of Static Stress", in Optical Properties of Highly

Transparent Solids , Edited by S. S. Mitra and B. Bendow (Plenum Publishing Corporation,

New York, 1975) , pp. 517,

21
FOCUSING MIRROR

MIRROR*

VARIABLE

WAVE PLATE \ /V

LASER -^ 1 ! ^|(r^F

RADIATION * 1 H -^

CHOPPER I

MIRROR

PYROELECTRIC

DETECTOR

BEAM STOP

BEAM SPLITTER

POLARIZER

COMPENSATOR

SPECIMEN

Figure 11, Doiible pass arrangement for measuring piezo-birefringence

at 10.6 ym.

22
A. Feldman, D. Horowitz and R. M. Waxier, "Piezo-Optic Constants in the Infrared", in Proceedings of the Fifth Annual Conference on Infrared Laser Window Materials, Las Vegas, Nev.

,

December 1975.

M. J. Dodge, "Refractive Index of High Purity KCl and KI Doped KCl", in Proceedings of the

Fifth Annual Conference on Infrared Laser Materials, Las Vegas, NV, Dec. 1975 (1976). pp. 215.

A. Feldman, "Measuring the Optical Properties of Infrared Laser Windows" , Electro-Optical

Systems Design 8_, 36 (1976) ,

A. Feldman, "Optical Properties of Infrared Laser Windows", in Proceedings of the Technical

Program Electro-Optical Systems Design Conference-1976, International Laser Exposition , New

York , New York, Sept. 14-16, 1976 (Industrial and Scientific Conference Management, Chicago

1976) , pp. 499.

A. Feldman, D. Horowitz, and R. M. Waxier, "Effect of Temperature and Stress on the Refractive

Index of Window Materials", in Laser Induced Damage in Optical Materials: 1976 , NBS Special

Publication 462, Eds. A. J. Glass and A. H. Guenther (US GPO SD Cat. No. 13.10:462, 1976),

pp. 58.

M. J. Dodge, "Refractive Index and Temperature Coefficient of Refractive Index of Hot-Forged

Calcium Fluoride", in Laser Induced Damage in Optical Materials: 1976 , NBS Special Publication

462, eds. A. J. Glass and A. H. Guenther (US GPO SD Cat. No. 13.10:462, 1976) pp. 64.

R. M. Waxier, D. Horowitz and A. Feldman, "Precision Interferometer for Measuring Photoelastic

Constants", Appl. Opt. 16, 20 (1977).

A. Feldman, D. Horowitz, and R. M. Waxier, "Refractive Properties of Infrared Window Materials",

in Laser Induced Damage in Optical Materials: 1977 , NBS Special Publication 509, Edited by

A. J. Glass and A. H, Guenther (US GPO, 1978) , pp. 74.

A. Feldman, D. Horowitz and R. M. Waxier, "Photoelastic Constants of Potassium Chloride at 10.6 Mm", Appl. Opt. 16, 2925 (1977).

M. J. Dodge, "Refractive Properties of CVD Zinc Sulfide", in Laser Induced Damage in Optical

Materials: 1977 , NBS Special Publication 509, eds. A. J. Glass and A. H. Guenther (US GPO,

1978) , pp. 83.

C. K. Kim, A. Feldman, D. Horowitz, and R. M. Waxier, "Temperature Dependence of Szigeti

Effective Change of Alkali Halides", Solid State Communications, 25_, 397 (1978).

A. Feldman, R. M. Waxier and D. Horowitz, "Photoelastic Constants of Germanium", J. Appl.

Phys. 49, 2589 (1978)

A. Feldman, "Measurement of the Photoelastic Constants of Optical Materials", Optical Eng.

17^, 453 (1978) .

M. J. Dodge, "Refractive Index of SrF " , in Laser Induced Damage in Optical Materials: 1978 , m to be published.

R. M. Waxier, A. Feldman and D. Horowitz, "Piezo-Optic Coefficients of Some Neodymium Doped

Laser Glasses and Single Crystals of CaF , BaF and SrF " , in Laser Induced Damage in Optical

Materials: 1978 , to be published.

A. Feldman and M. J. Dodge, D. Horowitz and R. M. Waxier, "The National Bureau of Standards

Optical Measurements Program: Refractive "^ndex, Thermo-Optic Constants and Photoelastic

Constants", to be published.

2 3 1
2.

7

Acknowledgements

We would like to thank the following for supplying materials for measurement: Carl Pitha m of RADC, John Fenter and Colonel William Goldberg of AFML, Perry Miles of Raytheon, Ra.y Hilton, | Philip Klein of NRL, E. Bernal G. of Honeywell, John Fontanella of the U. S. Naval Academy and , B. Sherman of the Servo Corporation. We thank William McKean and Howard Layer of NBS for k valuable assistance with instrumentation. t

ii We appreciate encouragement provided for our program by A. H. Guenther of the Air Force i| Weapons Laboratory, A. J. Glass of the Lawrence Livermore Laboratory, H. E. Bennett and J. M. i Bennett of the Naval Weapons Center, M. Stickley of the Department of Energy, H. Winsor of I the Defense Advanced Research Projects Agency, and M. Swerdlow of the Air Force Office of i Scientific Research.

|

2 .8 References |

1. M. Sparks, J. Appl. Phys. 42_ 5029 (1971).

2. J. R. Jasperse and P. D. Gianino, J. Appl. Phys. 43_, 1686 (1972). \

I 3. B. Bendow, P. D. Gianino, A. Hordvik and L. H. Skolnik, Optics Comm. 7, 219 (1973). I

I 4. B. Bendow and P. D. Gianino, Appl. Phys. 2_, 1 (1973). j

I

! 5. C. S. Sahagian and C. A. Pitha, Compendium on High Power Infrared Laser Window Materials 1 (LQ Program), AFCRL-72-0170, 9 March 1972, Special Reports No. 135. j

6. L. W. Tilton, J. Res. Natl. Bur. Std., (U.S.), 2_, 909 (1929), RP 64. j

7. C. Weir, S. Spinner, I. H. Malitson and W. J. Rodney, J. Res. Natl. Bur. Std., (U.S.),

58, 189 (April 1957) , RP 2751.

8. L. E. Sutton and 0. N. Stavroudis, J. Opt. Soc. Am. 5]^, 901 (1961).

9. American Institute of Physics Handbook, (McGraw-Hill, 1972), p. 6-111.

10. K. V. Krishna Rao, S. V- Nagender Naidu and P. L. N. Setty, Acta Cryst. 15_, 528 (1962).

11. J. S. Browder and S. S. Ballard, Appl. Opt. 16_, 3214 (1977).

12. J. B- Saunders, J. Res. Natl. Bur. Std. (U.S.), 35_, 157 (1945) RP 1668.

13. American Institute of Physics Handbook, Dwight E. Gray, ed. (McGraw-Hill Book Company,

1972) pp. 4-119.

14. Yep. Artyukh and V. N. Reytorov, Sov. J. Opt. Tech. 40_, 523 (1973) .

15. A. Feldman, D. Horowitz and R. M. Waxier, "Refractive Properties of Infrared Window

Materials", in Laser Induced Damage in Optical Materials :1977 , NBS Special Publication

509, Edited by A. J. Glass and A. H. Guenther, (US GPO 1977) , pp. 74.

16. J. F. Nye, Physical Properties of Crystals (Oxford University Press, London 1957),

pp. 243-254.

17. A. Feldman, Optical Eng. 17^, 453 (1978).

18. A. Feldman and W. J, McKean, Rev. Sci. Instrum. 46, 1588 (1975).

19. A. Feldman, R. M. Waxier and D. Horowitz, "Measuring Photoelastic and Elastic Constants

of Transparent Materials by Application of Static Stress" in Optical Properties of

Highly Transparent Solids , Edited by S . S. Mitra and B. Bendow (Plenum Publishing

Corporation, New York, 1975) pp. 517.

24
20. A. Feldman, D. Horowitz and R. M. Waxier, Appl . Opt. 16, 2925 (1977).

21. R. M. Waxier, D. Horowitz and A. Feldman, Appl. Opt. 1£, 20 (1977).

22. J. Dyson, Inter ferometry as a Measuring Tool , (The Machinery Publishing Co., Ltd.,

Brighton, 1970)

23. F. Green, in Optical Instruments and Techniques, 1969 , edited by J. H. Dickson (Oriel

Press Limited, Newcastle upon Tyne, England, 1970) , pp. 189-198.

24. A. J. Michael, J. Opt. Soc. Am. 58, 889 (1968).

25. G. Birnbaum, E. Cory and K. Gow, Appl. Opt. 13, 1660 (1974).

25
2.9 Tables

Table la. Constants of Dispersion Equation for KCl near 20 °C,

Specimen

Temperature

Commercial

19.9 °C

RAP^

20.2 °C

KC1:KI^

19.9 °C

'^i 0.74783561 0.80902239 0.78085271

*2 0.42626630 0.36511458 0.39493953

^

4.6867104 2.2323342 2.2662238

X^ (ym) 0.083633417 0.08828162 0.08611153

^2 (ym) 0.15389978 0.15737774 0.15600595

A (ym) 95.063422

No. of Wavelengths 79

Wavelength Range (ym) 0.22-14.4

65.870423

58

0.25-15.5

66.360157

54

0.25-15.5

Average Absolute

-5.

Residual of n (10 ) 2.3 2.9 3.2

a . b . Reactive atmosphere processed. KCl nominally doped with 1.5% KI

Table lb. Constants of Dispersion Equation for CaF near 20 °C.

Specimen Hot Forged

Temperature 20.8 °C

^

0.98594551

^

0.05290246

^3 4.2816899

X^ (ym) 0.07218116

^2 (ym) 0.14114719

A^ (ym) 36.465937

No. of Wavelengths 69

Wavelength Range 0.25-8.03

Average Absolute

Residual of n (10 ) 1.9

Fusion Cast

21.7 °C

0.34393190

0.6948269

3.8902192

0.0127821

0.0936663

34.8259

60

0.21-8.7

2.1

26
Table Ic. Constants of Dispersion Equation for Fusion Cast SrF near 20 °C.

Specimen

Temperature

Fusion Cast

20 °C

A (um)

^2 (um)

X (ym)

No. of Wavelengths

Wavelength Range (ym)

Average Absolute

-5, Residual of n (10 )

0.67805894

0.37140533

3.3485284

0.05628989

0.10801027

39.906666

53

0.21-11.5

2.1

Table Id. Constants of Dispersion Equation for Chemical Vapor

Deposited (CVD) ZnS near 20 °C.

Specimen

Temperature

#1

21.6 °C

^1 0.33904026

^2 3.7606868

^3 2.7312353

X (ym) 0.31423026

A (ym) 0.17594174

A (ym)

No. of Wavelength

Wavelength Range

Average Absolute

s

(ym)

33.886560

25

0.55-10.6

Residual of n (10 ) 5.4

#2

21.9 °C

0.24199447

3.8575584

2.5433609

0.33005445

0.17899635

32.849275

30

0.55-10.6

4.6

27
Table le. Constants of Dispersion Equation for Chemical Vapor

Deposited (CVD) ZnSe near 20 °C.

Specimen

Temperature

#1

20.3 °C

#2

20.8 °C

^1 4.2980149 4.4639521

^

0.62776557 0.46132463

^

2.8955633 2.8828867

X^ (ym) 0.19206300 0.20107634

^2 (ym) 0.37878260 0.39210520

X^ (ym) 46.994595 47.047590

No. of Wavelengths

Wavelength Range (ym)

33

0.54-18.2

38

0.54-18.2

Average Absolute

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iH M iH rH .H nH iH (N CN ON r^j rsj CN CM CN CN CN (N CN

iH (N CO M rH (Ti IT) O in (J\ ^ 00 CN in 00 r-i '^ CO rH '^

<Ti iH (N ^ in in <D r- [~- r^ 00 CO cn en CTi o O d r-{ ,-{ iH iH M nH rH iH iH rH rH •-< rH •-\ :-i r-i CN r^j CM CN CN

O O O O o o O o O o o o o o o O O O o o

CO U3 ^ r\] o CO IX) ^ CN CM 'T 1^ 00 o CN '^ IXI 00 o

1 1 rH1 1 iH1

1 1 1 1 •-^ ^-^ ^ r-t •-\ tN

40
<uc

•H

-pcou

y; I

tn +Jc

0) HO

•H

4-1 IW

0)OUCo

•H

COc

(13 a,Xw

(T3 EM

0)

0)c

0)

U

(N

X

h (B

tr. 1 S u

(/5 (N -H

P4

X1o

rO ro

X

•H

O (C

U CM 1 <U n^ u

-P <;

fC s

V£> r~- CO cri "vT Ln -vT ro •-^ CTi VD CN CO ro en L/l o '^ 00 ^

en r-~ o CN ^ in vO r^ CO CO en

O o rH rH CN ro ro ro ^

CNJ CNn fo ro ro ro ro ro ro ro '^ '^ ^ "^ '^ ^ •<* 'T '^ o in in C7^ 1.0 CN v-O ^ r- 1^ O CT\ ^ ';r CN r^ o ro r- o

0^ •^ (Ti ro CO CO CO r- ^ O rO in CTi ro O) o ro vD o

rsi ^ IT) r-- CO a^ o r-\ CN ro ro ^ •^f '^ IT) in kO >Xi ^0 r~- rH •-\ ^ rH rH rH rH rH rH rH ,-\ <-i rH t-{

(N ro in ^ CO ID ro ro CN -^ CO CO inO ro CN en rH r-^ o

r-- ^ \D i^ IT) ^ CN (Ti LD

O '^J' CO CN VD (Ti CN •sC r~~ (Tl iH o iH CM 00 '^ in <o ^ r- CO 00 CO 0^ CTi cn o

rH o O

rH

O

rH

rHrH

'^ <Ti '^ LD CTi ro '* ro CO

O <Tl ^ 1^ inO rsj <-^ CTi un

O

CO VD nH ^ rH r^ rsi r- r-{ 1^ 0^ ro ^ CTi fN ^ U3 r- en rH o O iH r-( CN CM ro ro ^ ^ 'T m in LD \D ^ 'S) ^ vX) r^

KO r-- 1^ CN ^ o '3' r- cri rH rom V£> r- CO (Ti o r-{ rsi ro

CN on '^ LT) IT) ^ ^ ^D VD r~- r-- r- r- r-- r- r^ CO CO CO CO

(N (N rH (Ti \D iH in CTi ro ^o CO o (N ro ro ^ "^ in X) rrH CN n ro •^ LT) in LD 1^ vO VD r~- r^ r- r-- r- (^ t~~ 1^ r^

rO 03 ro "d- CO t-i r- CN >^ CTi rs] "^ r- (Ti r-\ ^ -X) (Ti CN

rO <-\ ro 'Tm v£) vo r-- r^ r- CO CO CO CO en en (T> CTi o

rH -H r-^ r-{ rH rH rH rH rH rH r-{ r-] r-\ rH r-{ ^ rH rH CN o o O O O o o o o o O o O o o o o o O o

00 <o ^ rsiO CO ^0 ^ rN CN "d* V£) CO o fN "^ \o CO o 1

•-i1 1 rH1 rH1 1 1 1 1 H rH rH r-i r-\ CN

41
Table 4a. dn/dT of Al (10~ K~ )

Temperature ( °C

)

Wavelength (ym)

0.4579

dn /dT

e dn /dT

o -180

-160

-140

-120

0.19

0.36

0.51

0.65

0.18

0.32

0.45

0.58

-100

-80

-60

-40

0.78

0.89

0.99

1.07

0.69

0.79

0.88

0.96

-20

20

40

1.15

1.22

1.28

1.33

1.04

1.11

1.17

1.23

60

80

100

120

1.38

1.42

1.47

1.51

1.28

1.32

1.37

1.41

140

160

180

200

1.55

1.59

1.64

1.69

1.44

1.48

1.51

1.54

0.04 0.03

Standard deviation from a third degree polynomial fit.

42
Table 4b. dn/dT of BaF (10~ K~ )

t

Wavelength (ym)

Temperature ( °(^\-) 0.4579 0.6328 1.15 3.39 10.6

-180 -0.78 -0.86 -0.81 -0.81 -0.73

-160 -0.92 -0.98 -0.96 -0.95 -0.85

-140 -1.04 -1.09 -1.08 -1.07 -0.96

-120 -1.15 -1.19 -1.19 -1.17 -1.05

-100 -1.24 -1.27 -1.29 -1.26 -1.13

- 80 -1.32 -1.35 -1.37 -1.34 -1.21

- 60 -1.38 -1.41 -1.44 -1.41 -1.27

- 40 -1.44 -1.47 -1.50 -1.47 -1.32

- 20 -1.49 -1.52 -1.55 -1.51 -1.37

-1.53 -1.56 -1.59 -1.56 -1.41

20 -1.56 -1.60 -1.62 -1.59 -1.45

40 -1.60 -1.63 -1.66 -1.62 -1.48

60 -1.63 -1.66 -1.69 -1.66 -1.51

80 -1.65 -1.70 -1.71 -1.68 -1.54

100 -1.68 -1.73 -1.74 -1.71 -1.57

120 -1.71 -1.76 -1.77 -1.75 -1.60

140 -1.75 -1.79 -1.80 -1.78 -1.63

160 -1.78 -1.83 -1.84 -1.82 -1.66

180 -1.83 -1.87 -1.88 -1.87 -1.70

200 -1.88 -1.92 -1.93 -1.92 -1.75

a

a 0.03 0.02 0.03 0.03 0.03

\

standard deviation from a third degree polynomial fit.

t

43
Table 4c. dn/dT of CaF (10 K )

Wavelength (ym)

Temperature (°C \

I 0.4579 0.6328 1.15 3.39

-180 -0.39 -0.40 -0.41 -0.40

-160 -0.53 -0.54 -0.56 -0.52

-140 -0.64 -0.66 -0.68 -0.63

. -120 -0.74 -0.77 -0.78 -0.73

. -100 -0.83 -0.85 -0.87 -0.82

- 80 -0.90 -0.93 -0.95 -0i89

- 60 -0.95 -0.99 -1.01 -0.95

- 40 -1.00 -1.03 -1.06 -1.00

- 20 -1.04 -1.07 -1.10 -1.05

-1.07 -1.10 -1.13 -1.09

20 -1.10 -1.13 -1.15 -1.12

40 -1.12 -1.15 -1.18 -1.14

60 -1.14 -1.17 -1.20 -1.17

80 -1.16 -1.19 -1.22 -1.19

100 -1.18 -1.21 -1.24 -1.21

120 -1.20 -1.23 -1.26 -1.23

140 -1.22 -1.26 -1.29 -1.25

160 -1.26 -1.30 -1.32 -1.27

180 -1.29 -1.34 -1.36 -1.30

200 -1.34 -1.40 -1.41 -1.34

a

a 0.01 0.02 0.02 0.03

Standard deviation from a third degree polynomial fit.

44
I

Table 4d. dn/dT of CdF (10 ^ k""'")

Wavelength (ym)

Temperature (°C)

0.4579 0.6328 1.15 3.39

»

-180 -0.43 -0.56 -0.57 -0.53

-160 -0.52 -0.64 -0.67 -0.64

-140 -0.59 -0.72 -0.76 -0.73

-120 -0.65 -0.75 -0.83 -0.81

-100 -0.71 -0.84 -0.90 -0.87

- 80 -0.75 -0.89 -0.96 -0.93

- 60 -0.80 -0.93 -1.00 -0.98

- 40 -0.83 -0.97 -1.05 -1.02

- 20 -0.86 -1.01 -1.08 -1.05

-0.89 -1.04 -1.12 -1.08

20 -0.92 -1.07 -1.15 -1.11

40 -0.94 -1.10 -1.17 -1.14

60 -0.97 -1.13 -1.20 -1.17

80 -1.00 -1.16 -1.23 -1.20

100 -1.02 -1.19 -1.27 -1.23

120 -1.06 -1.23 -1.30 -1.27

140 -1.09 -1.27 -1.34 -1.31

160 -1.14 -1.31 -1.39 -1.36

180 -1.18 -1.37 -1.44 -1.42

200 -1.24 -1.43 -1.51 -1.49

O^ 0.02 0.02 0.02 0.04

aStandard deviation from a third degree polynomial fit.

45
Table 4e

-5 -1

dn/dT of KBr (10 K )

Temperature (°C)

Wavelength (ym)

0.4579 0.6328 1.15 3.39 10.6

180

-160

140

-120

-2.85

-3.30

-3.19

-3.33

2.95

3.17

3.36

-3.53

3.05

3.26

3.44

3.59

-3.05

-3.26

-3.44

3.60

3,06

-3.24

-3.40

-3.54

100

80

- 60

40

3.46

3.56

3.66

3.74

3.67

-3.78

-3.88

-3.96

-3.73

-3.84

•3.94

4.02

3.74

-3.85

-3.95

-4.03

-3.66

-3.77

-3.86

-3.93

20

20

40

-3.81

-3.88

-3.93

-3.98

-4.02

-4.08

-4.12

-4.16

-4.09

-4.14

-4.19

-4.23

-4.10

-4.16

-4.21

-4.25

-4.00

-4.06

-4.11

-4.16

60

80

100

120

-4.03

-4.07

-4.11

-4.16

-4.19

-4.23

-4.27

-4.31

-4.27

-4.31

-4.35

-4.39

4.29

-4.33

-4.36

-4.40

-4.20

4.25

-4.29

-4.33

140

160

180

200

4.20

-4.25

-4.31

-4.38

-4.36

-4.42

4.49

-4.58

4.44

-4.49

-4.56

-4.63

-4.44

-4.49

-4.55

-4.62

-4.38

-4.43

-4.49

-4.56

0.04 0.03 0.03 0.03 0.06

Standard deviation from a third degree polynomial fit,

46
Table 4f. dn/dT of KCl (10 ^ K

"*)

Wavelength (ym)

Temperature (°C)

0.4579 0.6328 1.15 3.39 10.6

-180 -2.26 -2.32 -2.35 -2.39 -2.33

-160 -2.44 -2.52 -2.55 -2.58 -2.50

-140 -2.61 -2.70 -2.74 -2.75 -2.65

-120 -2.76 -2.86 -2.90 -2.91 -2.80

-100 -2.90 -3.00 -3.05 -3.05 -2.93

- 80 -3.02 -3.13 -3.17 -3.17 -3.04

- 60 -3.14 -3.24 -3.29 -3.28 -3.15

- 40 -3.24 -3.35 -3.39 -3.38 -3.24

- 20 -3.33 -3.43 -3.48 -3.47 -3.33

-3.41 -3.51 -3.55 -3.55 -3.41

20 -3.49 -3.58 -3.62 -3.62 -3.48

40 -3.55 -3.65 -3.68 -3.69 -3.54

60 -3.61 -3.70 -3.74 -3.75 -3.60

80 -3.67 -3.76 -3.79 -3.80 -3.65

100 -3.72 -3.81 -3.84 -3.85 -3.70

120 -3.77 -3.86 -3.89 -3.90 -3.74

140 -3.82 -3.91 -3.94 -3.94 -3.79

160 -3.87 -3.96 -4.00 -3.99 -3.83

180 -3.91 -4.02 -4.05 -4.04 -3.87

200 -3.96 -4.08 -4.11 -4.09 -3.91

a^ 0.02 0.02 0.02 0.02 0.04

Standard deviation from a third degree polynomial fit.

47
Table 4g. dn/dT of LiF (10 K )

\ Wavel(sngth (ym)

ieinpeiru.L.ux e y U;

i 0.4579 0.6328 1.15 3.39 ' -180 -0.33 -0.36 -0.38 -0.40

-160 -0.51 -0.63 -0.64 -0.50

-140 -0.85 -0.86 -0.86 -0.78

-120 -1.04 -1.05 -1.05 -0.93

-100 -1.20 -1.21 -1.21 -1.06

- 80 -1.32 -1.34 -1.34 -1.16

- 60 -1.42 -1.44 -1.45 -1.25

- 40 -1.49 -1.52 -1.53 -1.32

- 20 -1.54 -1.59 -1.60 -1.37

-1.58 -1.63 -1.65 -1.42

20 -1.60 -1.67 -1.69 -1.45

40 -1.63 -1.70 -1.73 -1.48

60 -1.65 -1.72 -1.75 -1.51

80 -1.67 -1.75 -1.77 -1.53

100 -1.71 -1.78 -1.79 -1.55

120 -1.75 -1.81 -1.81 -1.59

140 -1.82 -1.85 -1.84 -1,63

160 -1.90 -1.91 -1.88 -1.67

180 -2.02 -1.99 -1.92 -1.73

200 -2.16 -2.09 -1.99 -1.80

a 0.03 0.02 0.04 0.04

48
in13

y. I S

4-1o\c

^3

Xi^

3-c

rH

0)>

(0

00 c

EhT3

LD

00

T3

Eh

Ln

EhC

Ti

£h

U

4-> (d

^^0)

i^

0)

U o o

(N (N rH

CO

rH rH rH

in

iH

00 CMrH iH o

rH o

rH o

00o o o

ino

M" 00 o o o o o o o o o o o o o o o o o o o o o o d d m

rHo

CM

r-i o

CMrH

rHrHd od od

00od od1^odinod od00ooCNodrHoo orHoo1CM 00 o o o o 1 1

(Ti 00

CTi 00 rH

in

in

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CN

00

rH

rH

CNrH orH o

CO

COo o o

ino

00o

CM00orH

OMo orHo

rH 00 O rH o o O O o o o o o o ° o o o o o o o o o o o 1 1

"^ en ^ rn

<-{ rH

CM

rH o

rH

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cri eno

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ino

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CM00o oo oo

OMoo

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CN (N

rHo o

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0^

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00

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in

rH

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CN o oo o00o

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CN <-i o o O O o o o o o o o o o o o o o o o o o o

LD 'T

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CN CMrH

rH orH o

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in

CM

CM

in

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CN oCN rH

COrH

in

rH rH

00

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CO

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f-i

CTi eno

00o o o o o o o o o o o o o o o o o o o o o o o o o o

r- 00 rH rH

in rHin

CN ro

00rHCNrH fH

rH o

CO

(Ti oCOoCOo

CNo

00o

ino o

00o

CO

CNo

(Tl rH o o o o o o o o o o o o o o o o o o o o o o o o

CO V£) rH rH 1 1 o

-^rH1 o

(N

•-{1 oo1 o

CO1 o1 o1 o

CN1 o oCM o o o

CO oo

r-i o o

'a* o o o

CO o

rH CN oo

(NOOoo

iHOO

CMrHOO

cnoo

rHoo

cnoo

•Hu

0)ceo

l+HcoH

-p •H>

T)

TSU

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49
Table 4i, dn/dT of NaCl (10 ^ K

""")

Wavelength (ym)

Temperature

{°C) 0.4579 0.6328 1.15 3.39

-180 -2.06 -2.16 -2.22 -2.24

-160 -2.30 -2.40 -2.48 -2.49

-140 -2.51 -2.61 -2.70 -2.70

-120 -2.69 -2.79 -2.89 -2.89

-100 -2.85 -2.96 -3.06 -3.05

- 80 -2.99 -3.09 -3.20 -3.19

- 60 -3.11 -3.21 -3.32 -3.31

- 40 -3.30 -3.32 -3.42 -3.41

- 20 -3.29 -3.40 -3.51 -3.49

-3.36 -3.48 -3.58 -3.57

20 -3.42 -3.54 -3.64 -3.63

40 -3.48 -3.60 -3.70 -3.68

60 -3.53 -3.65 -3.74 -3.73

80 -3.57 -3.69 -3.79 -3.78

100 -3.62 -3.74 -3.83 -3.83

120 -3.67 -3.78 -3.88 -3.88

140 -3.72 -3.83 -3.93 -3.94

160 -3.78 -3.88 -3.99 -4.01

180 -3.84 -3.94 -4.06 -4.09

200 -3.92 -4.01 -4.14 -4.18

a

a 0.05 0.04 0.04 0.04

Standard deviation from a third degree polynomial fit.

50
Table 4 j

dn/dT of NaF (10 ^ k"""")

» Wavelength (ym)

lempcxacuxe \ \^/ 0.4579 0.6328 1.15 3.39

-180 -0.41 -0.42 -0.45 -0.45

-160 -0.55 -0.59 -0.63 -0.61

-140 -0.68 -0.74 -0.78 -0.75

-120 -0.79 -0.86 -0.91 -0.86

-100 -0.88 -0.96 -1.02 -0.96

- 80 -0.96 -1.05 -1.10 -1.04

- 60 -1.02 -1.12 -1.17 -1.11

- 40 -1.08 -1.17 -1.23 -1.16

- 20 -1.12 -1.22 -1.27 -1.20

-1.16 -1.25 -1.30 -1.23

20 -1.19 -1.28 -1.32 -1.25

40 -1.22 -1.30 -1.34 -1.27

60 -1.24 -1.32 -1.36 -1.29

80 -1.27 -1.33 -1.37 -1.31

100 -1.29 -1.35 -1.39 -1.32

120 -1.31 -1.37 -1.41 -1.34

140 -1.34 -1.40 -1.44 -1.37

160 -1.38 -1.43 -1.48 -1.40

180 -1.42 -1.47 -1.53 -1.44

200 -1.47 -1.52 -1.59 -1.49

a 0.02 0.05 0.05 0.05

Standard deviation from a third degree polynomial fit.

I

51
Table 4k. dn/dT of SrF (10~ K )

Wavelength (ym)

Temperature (°C) 0.4579 0.6328 1.15 3.39 10.6

-180 -0.54 -0.56 -0.55 -0.56 -0.35

-160 -0.67 -0.69 -0.69 -0.68 -0.49

-140 -0.77 -0.81 -0.81 -0.80 -0.61

-12 -0.86 -0.90 -0.91 -0.89 -0.71

-100 -0.94 -0.98 -1.00 -0.97 -0.79

- 80 -1.01 -1.05 -1,07 -1.04 -0.85

- 60 -1.06 -1.11 -1.13 -1.10 -0.90

- 40 -1.11 -1.15 -1.17 -1.15 -0.93

- 20 -1.15 -1.19 -1.21 -1.19 -0.96

-1.18 -1.22 -1.24 -1.22 -0.97

20 -1.20 -1.24 -1.26 -1.24 -0.98

40 -1.22 -1.25 -1.28 -1.26 -0.99

60 -1.24 -1.27 -1.29 -1.27 -0.99

80 -1.25 -1.28 -1.30 -1.28 -1.00

100 -1.26 -1.29 -1.31 -1.29 -1.01

120 -1.27 -1.30 -1.32 -1.29 -1.02

140 -1.29 -1.32 -1.33 -1.30 -1.05

160 -1.30 -1.34 -1.35 -1.31 -1.08

180 -1.32 -1.36 -1.37 -1.32 -1.13

200 -1.34 -1.39 -1.40 -1.33 -1.20

o^ 0.03 0.02 0.01 0.03 0.05

Standard deviation from a third degree polynomial fit,

52
t

Table 4£. dn/dT of CVD ZnS (10 ^ K

•)

Temperature (°C)

Wavelength (ym)

1.15 3.39 10.6

-180

-160

-140

-120

3.5

3.7

3.8

4.0

2.8

3.1

3.3

3.5

2.7

3.0

3.3

3.5

-100

- 80

- 60

- 40

4.1

4.2

4.3

4.4

3.7

3.9

4.0

4.1

3.7

3.8

3.9

4.0

»

- 20

20

40

4.5

4.5

4.6

4.6

4.1

4.2

4.2

4.3

4.0

4.1

4.1

4.1

60

80

100

120

4.7

4.7

4.7

4.8

4.3

4.3

4.3

4.4

4.1

4.1

4.2

4.2

140

160

180

200

4.8

4.9

4.9

5.0

4.4

4.4

4.5

4.6

4.3

4.4

4.5

4.7

0.2 0.2 0.2

Standard deviation from a third degree polynomial fit.

53
Table 4m. dn/dT of CVD ZnSe (10 K )

Wavelength (ym)

Temperature (°C]

0.6328 1.15 3.39 10.6

- -180 7.6 5.4 5.0 4.9

-160 8.2 5.7 5.2 5.1

-140 8.7 6.0 5.4 5.4

-120 9.1 6.3 5.6 5.5

-100 9.4 6.5 5.8 5.7

- 80 9.7 6.6 5.9 5.8

- 60 10.0 6.7 6.0 5.9

- 40 10.2 6.8 6.1 6.0

- 20 10.3 6.9 6.1 6.0

10.5 7.0 6.2 6.1

20 10.6 7.0 6.2 6.1

40 10.7 7.0 6.2 6.1

60 10.8 7.1 6.3 6.1

80 10.9 7.1 6.3 6.2

100 11.0 7.2 6.3 6.2

120 11.1 7.2 6.4 6.3

140 11.3 7.3 6.4 6.3

160 11.5 7.4 6.5 6.4

180 11.8 7.6 6.6 6.6

200 12.1 7.8 6.7 6.7

a

a 0.1 0.1 0.1 0.1

Standard deviation from a third degree polynomial fit.

54
X

CD TiCH

0)>H

+JU

(d

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56
-12 -1 Table 7a. Piezo-optic Constants of Alkaline-Earth Fluorides* (10 Pa )

A = 0.6378 ym X = 1.15 ym A = 3.39 ym

CaF,

^11

^12

(^ir%2^

I44

SrF,

^11

^12

(^ir%2^

^44

BaF,

^11

^12

(q,,-qi2)

M4

-0.38 ±0.03

1.08 ±0.03

-1.46 ±0.01

0.71 ±0.01

-0.64 ±0.04

1.45 ±0.04

-2.08 ±0.01

0.60 ±0.01

-0.99 ±0.03

2.07 ±0.04

-3.06 ±0.01

0.95 ±0.01

-0.40 ±0.06

1.09 ±0.05

-1.49 ±0.02

0.72 ±0.01

-0.63 ±0.05

1.50 ±0.06

-2.13 ±0.04

0.62 ±0.02

-0.91 ±0.07

2.13 ±0.07

-3.03 ±0.02

0.95 ±0.01

-0.52 ±0.11

1.00 ±0.11

-1.51 ±0.03

0.87 ±0.06

0.83 ±0.09

1.23 ±0.07

-2.05 ±0.06

0.72 ±0.04

-0.75 ±0.07

2.11 ±0.05

-2.91 ±0.08

0.99 ±0.07

*This work was supported in part by the Air Force Office of Scientific

Research under grant No. AFOSR-78-0026.

57
Table 7b, Comparison of Piezo-optic Data in the Visible Region for

-12 -1 Alkaline-Earth Fluorides (10 Pa )

.

0, 64

1, 45

•2 .08

0. 60

NBS Literature

-0.38 -0.29 , -0.41

1.08 1.16^, 1.04^

-1.46 -1.45^, -1.45^, -1.48'^,

-1.44^, -1.47^

0.71 0.70^, 0.89^, 0.81^

0.58^

c 1.77

-2.35^

0.59^

-0.99 -0.62^^

2.07 2.31^

-3.06 -2.93^

0.95 1.06^

F. Pockels, Lehrbuch der Kirstalloptik (B. G. Teubner, Leipzig und

Berlin, 1906). (A=0.5893 ym)

.

K. V. Rao, T. S. Narasimhamurty , J. Phys. Chem. Solids 31l' 876 (1970)

(A=0.5893 ym)

.

O. V. Shakin, M. F. Bryzhina, V. V. Lemanov, Sov. Phys. Solid State

13_, 3141 (1972). (A=0.6328 ym) .

K. S. Iyengar, K. B. Bansigar, Current Science 27_, 436 (1958).

(A=0.5890 ym)

.

^A. J, Michael, J. Opt. Soc. Am. 58, 889 (1968). (X=0.5461 ym)

.

V. G. Krishna Murty, Ph.D. Thesis (Osmania University, Hyderabad,

India, 1964). (X=0.5461 ym)

.

CaF^

^11

^12

^\l q,^)

^44

SrF^

^11

%2

(^11-%2'

^44

BaF^

%1

^12

<^11-q,,)

^44

58
Table 8. Photoelastic Constants of Ge.

X = 3.39 pm A = 10.6 \xm

-12 -1

"^11 ^^° ^^ ^

q^2 (10""'"^Pa"-^)

^44 (10-^^Pa-^

Pll

Pl2

P44

-0.79 -0.84

-0.51 -0.48

-1.07 -1.09

-0.151, -0.158^ -0.154

-0.128, -0.132^ -0.126

-0.072, -0.074^ -0.073

4.037^ 4.006^

Estimated accuracy approximately 2%. To calculate the elasto-optic

constants we used the elastic constants of H. J. McSkimin, J. Appl.

Phys. 2£, 988 (1953)

D- K. Biegelsen and J. C. Zesch, Phys. Rev. B 1£, 3578 (1976).

^H. W. Icenogle, B. C. Piatt, and W. L. Wolfe, Appl. Optics 15_, 2348

(1977)

59
-4.22 1.67 a -4.42 1.66 b

-4.94 1.47 c — 1.42 d

-4.74 1.57 e — 1.81 f

2.7 ±0. 8 -3.9 ±0.8 1.7 ±0.4 — -4.4 ±0.2 1.9 ±0.4

2.8 ±0. 2 -4.6 ±0.2

-4.7 ±0.2

1.9 ±0.2

1.9 ±0.1 — 2.0 g

-2.62 — h

2.8 ±0, 3 -3.4 ±0.4 1.8 ±0.4

2.6 ±0. 2 -3.6 ±0.3 1.8 ±0.2

-12 -1

Table 9a. Piezo-optic Constants of KCl (10 Pa )

.

0.589

0.589

0.589

0.480

0.589

0.633

0.633 4.6 ±0.2

0.644

*0.633 4.6 ±0.2

*0.644

10.6

10.6

10.6 4.3 ±0.3

*10.6 4.2 ±0.2

*Nomially doped with 1.5% KI.

F. Pockels, Lehrbuch der Kristalloptik (Teubner, Leipzig, 1906) , p. 408.

bBhagavantam and Y. Krishna Murty, Proc. Indian Acad. Sci. A46_, 399

(1957).

K. G. Bansigir and K. S. Iyengar, Proc. Phys. Soc. London 71B , 225

(1958)

.

R. Srinivasan, Zeit, f. Physik 155 , 281 (1959).

K. V. Krishna Rao and V. G. Krishna Murty, Proc. Indian Acad. Sci. 64 , 24 (1966)

.

W. W, Wilkening, J. D. Friedman and C. A. Pitha in Third Conference on High-Power Infrared Laser Windows, 1973 , AFCRL-TR-47-0085-I.

^C. S. Chen, J. P. Szcznesniak, and J. C. Corelli, J. Appl. Phys. 46_,

(1975)

.

C. A. Pitha and J. D. Friedman, in Proceedings of the Fourth Annual

Conference on Infrared Window Materials, 1974 , compiled by C. R. Andrews

and C. L. Strecker.

60
Table 9b. Elas to-Optic Constants of KCl

X(ym) p^^ p^2 p^^ p^^/p^^ Ref,

.589 -0.0276

.589 0.215 0.159 -0.024 -0.74

.589 0.246 0.192 -0.0298 -0.78

.633 0.21 0.15 -0.026 -0.70

.644 -0.029

* .633 0.21 0.15 -0.031 -0.72

* .644 -0.031

10.6 0.20 0.15 -0.023 -0.76

*10.6 0.19 0.14 -0.024 -0.71

*Nominally doped with 1.5% KI

F. Pockels, Lehrbuch der Kristalloptik (Teubner, Leipzig, 1906), p. 480,

b.

K. S. Iyengar, Nature 176, 1119 (1955).

'K. V. Kri

24 (1966)

^K. Krishna Rao and V. G. Krishna Murty, Proc. Indian Acad. Sci. 64,

61
Table 10. Photoelastic Constants of Fused SiO

2

X = 0.6328 ym 1.15 vim 3.39 ym

-12 -1

0.42 ±0.01 0.58 ±0.01 0.81 ±0.01

-12 -1

2.70 ±0.01 2.80 ±0.03 2.78 ±0.02

^11 0.120 ±0.001 0.136 ±0.002 0.154 ±0.001

Pl2 0.269 ±0.001 0.281 ±0.003 0.283 ±0.001

n 1.457 1.449 1.409

The errors are based on the standard deviation of the data and do not

take into account any errors in the elastic constants.

Table 11. Photoelastic Properties of CVD ZnSe

X - 0.5328 ym X = 10.6 ym

q (10~''"^Pa""'") -1.44 ±0.04, -1.48 ±0.05^ -1.46 ±0.07

q (10~"'"^Pa~''") 0.17 ±0.05, 0.22 ±0.05^ 0.51 ±0.07

q -q (lO'-'-^Pa""'") -1.60 ±0.01 -1.97 ±0.02

p -0.13 -0.10

p -0.04 0.007

L. F. Goldstein, J. S. Thompson, J. B, Schroeder and J. E. Slattery,

Appl. Optics 14, 2432 (1975)

62
Table 12. Elastic Compliances Used in Computation of Piezo-Optic and

-12 -1

Elasto-Optic Constants (10 Pa )

^11 ^12 ^44 ^2 = V3(s^^+2s^2-l/2 s^^)

-4.587

-3.639

BaF^^ 15.126 -4.708 38.941

CaF^^ 6.867 -1.451 29.764

Ge^ 9.75 -2.66 14.9

KCl'^ 25.8 -3.73 158.0

Fused sio/ 13.16 -2.16 —

SrF^^ 9.877 -2.553 31.969

^ ..e -3.738

-2.61" -3.66^

ZnSe (CVD) 13.9 ±0.6^ -4.4 ±0.2^ —

From tabulation by S . K. Dickinson, "Infrared Laser Window Materials

Property Data for ZnSe , KCl, NaCl, CaF , SrF , BaF " , Report No. AFCRLTR-75-0318, PSRP # 635, Air Force Cambridge Research Laboratories,

L. G. Hansom Field, Bedford, MA 01730 (1975).

H. J. McSkimin, J. Appl. Phys. 2£, 988 (1953).

^S. Haussiil, Zeits. fur Physik 159 , 223 (1960).

W. Primak and D. Post, J. Appl. Phys. 30, 779 (1959).

e Obtained in this laboratory and used for calculating the piezo-optic

constants.

63
NBS-114A (REV. 9-781

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. TN 993

2.Gov't Accession

4. TITLE AND SUBTITLE Optical Materials Characterization

Final Technical Report

February 1, 1978-Sept ember 30, 1978

5. Publication Date February 1979

$..l*««i^^ {^SmizatioR Co^

7. AUTHOR(S)

Albert Feldman, Deane Horowitz, Roy M, Waxier, Marilyn J. Dod|

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

18. Pro}ftrt/ta*/Work ifeilt fto.

11. Contract/Grant No.

12, SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS rS(ree(, City. st<,te. ZIP) Advanced Research Projects Agency

Arlington, VA 22209

13. Type of Report & Period Covered Final Technical Report

2/1/78 - 9/30/78

14. Spossonng Ag«jcy Code

15. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT (A 200~word or Ie33 [actual summary of most significant information. If document includes a significant bibliography or

literature survey, mention it here.) Data obtained as part of the Optical Materials Characterization Program are summarized in this report. Room temperature values of refractive index as

a function of wavelength are presented for the following materials: commercially

grown KCl , reactive a1:mosphere processed (RAP) KCl, KCl nominally doped with

1.5% KI, hot forged CaF2 , fusion cast CaF , CaF doped with Er (0.001% to 3% Er)

,

SrF , chemical vapor deposited (CVD) ZnSe (2 specimens), and ZnS (CVD, 2 specimens) . Data for the thermo-optic constant (dn/dT) and the linear thermal

expansion coefficient are given for the following materials over the temperature

range -180 °C to 200 °C: Al O , BaF , CaF CdF , KBr, KCl, LiF, MgF , NaCl , NaF

,

SrF , ZnS (CVD), and ZnSe (CVD). The piezo-optic constants of the following

materials are presented: As S glass, CaF , BaF , Ge , KCl, fused SiO , SrF , a chalcogenide glass (Ge 33%, As 12%, Se 55%) and ZnSe (CVD).

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons) Al ; As S glass; BaF ; CaF ; CdF ; chalcogenide glass; elastic

compliances; elastic constants; elasto-optic constants; fused silica; Ge ; hot forged;

KBr; KCl; KC1:KI; LiF; MgF ; NaCl; NaF; piezo-optic constants; refractive index; SiO ; SrF ; thermal expansion coefficient; thermo-optic constant; ZnS; ZnSe

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