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PUBLICATIONS

NBS TECHNICAL NOTE 1307

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

Limits to the

Precision of Electro-Optic and

Magneto-Optic Sensors

G. W. Day

P. D. Hale

M. Deeter

T. E. Milner

D. Conrad

S. M. Etzel

QC

100

U5753

No. 1307

1987

c2
Tm he National Bureau of Standards 1 was established by an act of Congress on March 3, 1901. The Bureau's overall ^L. goal is to strengthen and advance the nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research to assure international competitiveness and leadership of U.S.

industry, science arid technology. NBS work involves development and transfer of measurements, standards and related science and technology, in support of continually improving U.S. productivity, product quality and reliability, innovation and underlying science and engineering. The Bureau's technical work is performed by the National Measurement

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'Located at Boulder, CO, with some elements at Gaithersburg, MD
Katie, tdards ^~

GaitiierbLuiy and 20899 W

Limits to the Precision of Electro-Optic /n7

and Magneto-Optic Sensors t,v

G. W. Day

P. D. Hale*

M. Deeter**

T. E. Milner**

D. Conrad***

S. M. Etzel

Electromagnetic Technology Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

*Also with the Department of Physics, Colorado School of Mines, Golden, Colorado

**Also with the Optical Sciences Center, University of Arizona, Tucson, Arizona

***Also with the Department of Electrical and Computer Engineering, University of Colorado,

Boulder, Colorado

w

65

/

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

National Bureau of Standards, Ernest Ambler, Director

Issued March 1987
National Bureau of Standards Technical Note 1307

Natl. Bur. Stand. (U.S.), Tech Note 1307, 128 pages (March 1987)

CODEN:NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1987

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

Research in the Optical Electronic Metrology Group at the NBS Boulder Laboratories

aimed at understanding the characteristics and limitations of sensors for electromagnetic quantities began in 1982 and has continued under the auspices of NBS and

several other government and private agencies. The work reported in this document

was undertaken with the specific support of NBS, the U.S. Department of Energy

through Bonneville Power Administration (BPA), and, through BPA, the Electric

Power Research Institute (EPRI) and the Empire State Electric Energy Research

Corporation (ESEERCO). However, in some respects, it is inseparable from related

research conducted presently under the support of the Department of Energy through

Los Alamos and Sandia National Laboratories and previously supported by the

Department of Defense through the Calibration Coordination Group.

Numerous people have contributed to the authors' understanding of these topics in

recent years. Of these, Lynn Veeser, George Chandler, and Franz Jahoda of Los

Alamos National Laboratory, Richard Cernosek of Sandia National Laboratory, Dennis

Erickson of Bonneville Power Administration, and Gordon Frank of British Columbia

Hydro Research Labs deserve special mention. We are also greatly indebted to Edie

DeWeese for ably and patiently assembling this manuscript.

Where trade names are mentioned in this manuscript, they should not be considered

a recommendation or endorsement by the National Bureau of Standards or an indication that other, similar items may not perform equally well or better. This

report will be published subsequently by EPRI as part of an EPRI Report.

m

CONTENTS

Section

Page

1 INTRODUCTION 1-1

2 CONCEPTS OF PRECISION AND ACCURACY IN ELECTRO-OPTIC

AND MAGNETO-OPTIC SENSORS 2-1

Generic Transfer Functions 2-1

Transfer Function Distortions 2-2

Instantaneous Versus rms Measurements 2-10

3 ELECTRO-OPTIC AND MAGNETO-OPTIC SENSOR CONFIGURATIONS

SUITABLE FOR CURRENT AND VOLTAGE MEASUREMENTS 3-1

Electro-optic Voltage Sensors 3-1

Polarimetric Electro-optic Voltage Sensors 3-1

Interferometric Electro-optic Voltage Sensors 3-6

Magneto-optical Current Sensors 3-6

Optical Fiber Current Sensors 3-7

Bulk Glass Current Sensors 3-10

4 CRITICAL EVALUATION OF ELECTRO-OPTIC SENSOR TECHNOLOGY 4-1

Factors Limiting the Precision of Bulk Electro-optic Sensors 4-1

Properties of Electro-optic Materials 4-1

Properties of Waveplates 4-6

Birefringent Waveplates 4-7

Reflection Waveplates 4-9

Polymer Waveplates 4-11

Summary of Waveplate Properties 4-11

Properties of Polarizers 4-11

Prism Polarizers 4-13

Dichroic Polarizers 4-16

Dielectric Film Polarizers 4-16

Source Properties 4-16

Detector Characteristics 4-13

Fiber Characteristics 4-13
Factors Limiting the Precision of Planar Waveguide Sensors 4-19

Temperature Compensation Techniques 4-20

Waveplates 4-20

Electro-optic Crystals 4-22

Prognosis for High Precision Voltage Sensors 4-23

References 4-23

5 CRITICAL EVALUATION OF MAGNETO-OPTIC SENSOR TECHNOLOGY 5-1

Factors Limiting the Precision of Bulk Magneto-optic Sensors 5-1

The Verdet Constant of Bulk Materials and

its Temperature Dependence 5-1

Stress-Optic Effects in Bulk Materials 5-5

Source Properties: Spectral Stability 5-6

Other Components 5-8

Factors Limiting the Precision of Optical Fiber

Magneto-optic Devices 5-8

Relevant Properties of Optical Fiber 5-8

Other Fiber Components 5-16

Source and Detector Considerations 5-16

Temperature Compensation Techniques 5-17

Prognosis for High Precision Current Sensors 5-17

References 5-19

6 SUGGESTED APPROACHES TO THE DEVELOPMENT OF HIGH PRECISION

OPTICAL CURRENT AND VOLTAGE SENSORS 6-1

7 SUMMARY 7-1

APPENDIX A NOISE ANALYSIS FOR ELECTRO-OPTIC OR MAGNETO-OPTIC SENSORS A-l

APPENDIX B OPTICAL DESIGN FOR BULK SENSORS B-l

Maximizing Launched Power B-l

Coupling Between Fibers B-2

Reference B-4

APPENDIX C PROPERTIES OF SELECTED ELECTRO-OPTIC CRYSTALS

OF POINT GROUP 43m C-l

APPENDIX D PROPERTIES OF SELECTED DIAMAGNETIC GLASSES D-l

APPEN^x E THE CHARACTERIZATION OF WAVEPLATES E-l

APPEND!) BIREFRINGENCE MEASUREMENTS IN SINGLE MODE OPTICAL FIBER F-l

APPENDIX G PROGRESS IN THE DESIGN OF OPTICAL FIBER SENSORS FOR

THE MEASUREMENT OF PULSED ELECTRIC CURRENTS G-l

VI
LIST OF FIGURES

Figure

2-1. Transfer functions corresponding to Eq. 2-2 for four

values of *: (a) 0, tt/2; (b) +tt/4.

2-2. Transfer function corresponding to Eq. 2-3 for $ = tt/4.

2-3. Generalized calibration curve for a sensor with a transfer

function of the form of Eq. 2-3 ($ = tt/4) and Figure 2-2. 2-4

2-4. Three waveforms used for testing the sensitivity of the

calibration curve to waveform shape. Solid curve is a true

sinusoid, dotted curve is a distorted sinusoid, dashed curve represents a dc measurand. Each is normalized to an rms value of one. 2-5

2-5. Computed calibration curves for the three waveforms shown

in Figure 2-4. Solid curve is the same as Figure 2-3.

Dotted and dashed curves refer to the respective waveforms

in Figure 2-4. 2-6

2-6. Illustration of the effect on the transfer function of an increase in the parameter A. Solid curve is the unchanged

curve. Change in slope at the origin is directly proportionate to the change in A. 2-6

2-7. Illustration of the effect on the transfer function of an increase in the parameter xo. Solid curve is the unchanged

curve. Change in slope at the origin is directly proportionate to the change in xo. 2-8

2-8. Illustration of the effect on the transfer function of a change in the parameter $. Solid curve is the unchanged

curve. The result is the appearance of an average value,

a shift in phase, and a change in the calibration curve. 2-8

2-9. Result of small changes in * on the calibration curve for

sinusoidal signals. Labels indicate differences in

radians from tt/4. 2-9

2-10. Fractional errors in the distorted curves of Figure 2-9.

Specifically, the differences between each of the

distorted calibration curves and the undistorted curve divided by the undistorted curve. 2-9

vn
2-11. Illustration of a complex distortion of a transfer function arising from nonideal characteristics of a current

sensor described in Section 3. 2-11

2-12. Calculated calibration curve for a true rms reading

sensor for the 3 waveforms of Figure 2-4. 2-11

3-1. Basic configuration of an electro-optic voltage sensor.

In addition to the electro-optic crystal, normal components

include polarizers, a waveplate (retardation plate) shown

as a quarter-wave plate, and lenses required to transmit

light efficiently from one optical fiber through the bulk

components and back into another fiber. Many modifications

of this basic geometry can be used, including, particularly

a double-pass arrangement in which light is reflected back

through the crystal and either into the input fiber or another fiber. 3-2

3-2. Linear birefringence induced in the crystal by an electric

field causes the polarization state of light to change as

it passes through the crystal. The changes in polarization

state can be converted to changes in transmittance with

polarizers. 3-2

3-3. Illustration of the change in polarization with r for the case of light that is initially linearly polarized at

45 deg to the axes of linear birefringence. 3-3

3-4. Illustration of a Mach-Zehnder interferometer used as an electric field or voltage sensor. An electro-optic crystal

is placed in one arm of the interferometer. A change in

refractive index of the crystal causes a fringe shift in

the interferometer. The transfer function can span the

full range of functions shown in Figure 2-2 depending on how closely matched the arms of the interferometer are in zero field. 3-4

3-5. A planar waveguide (integrated optic) version of the MachZehnder interferometer. The substrate would be of an electro-optic material in which a permanent waveguide

structure could be created by locally changing the

refractive index. By applying a voltage to electrodes

(black areas) near the guide the optical path length of one path can be changed relative to the other in the same manner

as in Figure 3-5. 3-5

3-6. Basic configuration of an optical fiber current sensor. 3-5

3-7. An optical fiber current sensor in which two orthogonal

output polarizations are detected using a Wollaston

prism polarizer. 3-9

3-8. Polarizer arrangement for detecting two output polarizations oriented at 45 deg to each other. 3-9

3-9. Rotating polarization technique for observing Faraday

rotation in an optical fiber coil. The rotating input

polarization is created by passing two orthogonally

polarized optical beams at slightly different optical

frequencies through a quarter-wave plate. The phase

of the rotation is shifted in proportion to the current. 3-9

VI 1 i
3-10. The Sagnac interferometer. Light entering the input

port is split by the fiber coupler, half propagating

through the coil in the clockwise direction and half in

the counter-clockwise direction. In the absence of

current through the conductor all light exits by the

input port, but if current flows, the magnetic field causes the fiber coil to become nonreciprocal and light

is shifted to the output port. The transfer function is

that of Figure 2-1 with * = 0. 3-11

3-11. A Faraday rotation current sensor based on a design by

Kanoi, et al . IEEE Trans. Power Delivery, 1986, vol.

PWRD-1, p. 91-97. Two complementary reflections are used

at each corner to cancel phase shifts that occur in reflection. 3-11

3-12. Illustration of the principle of polarization-independent

beam steering using complementary reflections. The component of the optical field that is perpendicular to the plane

of incidence in the first reflection is parallel to the

plane of incidence in the second and vice versa. 3-12

3-13. A bulk-glass current sensor that can be placed around a conductor without breaking either the conductor or the

optical path. 3-12

4-1 Retardance of a 100-order quartz quarterwave plate (approximately 1 mm thick) versus temperature for a coherent source

(solid) and an incoherent source (dashed). 4-10

4-2. Representation of a Fresnel romb quarter-wave plate (after

( 4-11 )). Light undergoes two total internal reflections,

each time incurring a 45 deg phase shift between components

parallel and perpendicular to the plane of incidence. For

commonly used BK-7 glass the angle e is 54.6 deg. 4-10

4-3. Representation of a Glan prism polarizer. For the component parallel to the plane of incidence, total internal

reflection occurs at the internal surface. The optic

axes of the two pieces are parallel to each other and to

the entrance and exit surfaces. 4-14

4-4. Representation of a Wollaston prism polarizer. The optic

axes of the two pieces are orthogonal. Orthogonal components are refracted by different amounts when passing from

the first segment to the second. Output beams are nearly

symmetric but the angle of deviation is wavelength dependent. 4-14

4-5. Current mode (or transimpedance) operational amplifier

following a photodiode detector. Principal noise sources,

shot noise associated with the average detector current,

Johnson noise associated with the feedback resistor, and

amplifier input voltage and current noise, are shown.

Signal input and output are related by Eq. 4-12. 4-19

4-6. Design for a temperature-compensated quarterwave plate

using quartz and magnesium fluoride. Each segment is

assumed to be a compound zero-order waveplate. 4-21

5-1. Measurement system for determining dV/dT. C--Chopper,

P--Polarizer, M--Mirror, BS--Beam Splitter, D--Detector.

Light makes two passes through the sample, doubling the

rotation. 5-3

IX
5-2. Rotation versus magnetic field for a sample of SF-57 glass

at 25°C. Sample was approximately 10 cm long. 5-3

5-3. Verdet constant versus temperature for a sample of SF-57

glass. Error bars represent a one standard deviation

uncertainty in the slope of curves of the form shown in

Figure 5-2. 5-4

5-4. Configuration for studying the stress-optic effect in isotropic materials, such as glass. A uniform pressure is

applied normal to the direction of propagation resulting in

a change of refractive index both for light polarized

parallel to the direction of the pressure and perpendicular

to it. The difference in these refractive indices under

applied stress is the induced birefringence. 5-7

5-5. Measurement system for determining the Verdet constant of

optical fiber. It is based on a 1-m long solenoid having

approximately 3000 turns and operated at 30 A. Polarizers

are oriented manually to determine rotation, the identification of a null being facilitated by the use of a dither

coil and a lock-in amplifier. 5-9

5-6. Geometry of form birefringence in an optical fiber. The

fast axis is the minor axis of the ellipse. The magnitude

of the birefringence increases with the ellipticity and

with the difference in refractive index between the core

and cladding. 5-9

5-7. Geometry of bend- induced birefringence in single mode

fiber and a numerical illustration for 125 ym diameter

fiber at a wavelength of 633 ran. 5-11

5-8. Transfer functions for two fiber current sensor configurations showing the effect of bend birefringence. Dotted

curves assume no birefringence; solid include only bend

birefringence, (a) 1 cm diameter coil, 1 turn; (b) 10 cm diameter coil, 10 turns. Both cases: 125 urn diameter

fiber, wavelength 633 nm. 5-13

5-9. Transfer functions for the two coils of Figure 5-8, but

with twisted fiber, (a) Twist rate 40 turns/meter;

(b) twist rate 10 turns/meter. All other parameters

same as Figure 5-8. 5-14

5-10. Possible configuration of an all-fiber current sensor. 5-15

A-l. Noise equivalent current for a single turn current sensor of

fused silica and noise equivalent for a bismuth germanate

voltage sensor with a length to thickness ratio of 5, both

operated at a wavelength of 633 nm, as a function of amplifier feedback resistor size and average detector current. A-2

B-l. Illustration of optical coupling from one multimode fiber,

through a series of sensor components, and back into an identical multimode fiber. In this case the light is collirnated through the sensor. Dotted lines show acceptance

cone of output fiber. B-3

B-2. Same as B-l, except that the output end of the input fiber

is imaged at a point somewhat greater than midway between

the lenses. This results in a greater collection efficiency

into the output fiber. B-3
E-l. Measurement system for the determination of the temperature

coefficient of the retardance of various waveplates. E-2

E-2. Retardance versus temperature for a mica quarter wave plate

(a) and an acromatic polymer waveplate (b). E-3

XI
LIST OF TABLES

Table Page

4-1 Temperature Derivative of the Refractive Index for Several Crystals 4-4

4-2 Thermal Expansion Coefficients of Several Crystals of Class 43m 4-4

4-3 Properties of Materials Commonly Used in Birefringent Waveplates 4-8

4-4 Temperature and Angular Dependence of Various Retarders at

Three Wavelengths 4-12

5-1 Temperature Dependence of the Verdet Constant for Several Materials 5-2

5-2 Temperature Dependence of the Verdet Constant for Two Glasses 5-5

5-3 Values of the Stress-Optic Coefficient for Several Common Glasses 5-7

x n
Section 1

INTRODUCTION

The material in this report has been prepared in response to a seemingly simple

question, "What precision (thai: is to say stability, or reproducibility) can be

achieved with an electro-optic voltage sensor or a magneto-optic current sensor?"

The basic principles of the linear and quadratic electro-optic effects (sometimes

known as the Pockels and Kerr effects, respectively) and the Faraday magneto-optic

effect have been known, studied, and occasionally used, for nearly a century. The

decade of the 60s, following the discovery of the laser, saw substantial research

on these effects, mostly motivated by their potential for optical modulation, and

the development of numerous materials with enhanced properties. Beginning in

1970, with the development of cw, room temperature, semiconductor lasers that are easily modulated and nicely compatible with low loss optical fiber developed at about the same time, interest in electro- and magneto-optic materials waned. Now,

however, the pendulum seems to be swinging again with interest revived by two

applications areas. One is the naed for high speed switching, control, etc. in

the advanced optical communications systems now being developed. The other is the

topic of concern here, namely the potential for nonconducting, noninvasive sensors

for electromagnetic quantities.

Throughout their history, very little attention has been paid to the stability of

electro- and magneto-optic devices, so that when the question stated above was originally posed, no reliable answers could be provided. This was particularly

the case in view of needed precisions of the order of 0.1 percent over very broad

temperature ranges (100°C). True, the temperature dependence of the Faraday

effect in paramagnetic materials is well known and the temperature dependence of

the static birefringence in certain electro-optic materials has been studied, but

these cases are not applicable to high precision devices. It seemed clear then,

that a critical review of the technology, with a view both to the precision that

could be obtained with present technology and to tnat which might be achieved with

further development, v/as in order. This represents the motivation and background

for the present study.

1-1
Our intent in this report is to follow the approach that one attempting to design

a high precision current or voltage sensor would follow, namely to examine the

transfer functions of such devices (i.e., their terminal characteristics), then to

relate the properties of those functions to individual components of a sensor, and

finally to examine the properties of those components in sufficient detail to project eventual performance.

It became apparent in the early stages of this study that the transfer functions

of optical sensors are sufficiently different from those of measurement devices

familiar to most power engineers that significant discussion of that topic was needed, hence a fairly lengthy treatment in Section 2. An important example in

this regard is that most optical sensors of the sort that may have applications in

the power industry provide an instantaneous response over a high bandwidth. They

are thus very different from transformer based systems and provide substantially

enhanced capability for measuring high frequency or distorted signals. The intent

of Section 2 is to be generic, that is, not to relate the transfer functions to

any particular sensor or sensor parameter but to examine the implications of the

transfer function shape and anticipated changes in shape for the precision of such

a sensor.

In Section 3 we begin to relate the transfer functions of Section 2 to specific sensor types and to the components of those sensors. Numerous examples of current

or voltage sensor configurations are briefly described as a basis for the more detailed and critical reviews later. It has not been our intent to describe or examine all possible sensor designs, but to cover the basic principles.

Section 4 is a review of the limitations that the properties of various components

pose to the precision of electro-optic voltage sensors. The treatment is at a fundamental level, without much attention to the manner in which the sensor would

be used. Wherever possible, we have attempted not only to point out problems, but

to discuss possible solutions and future developments. The section concludes with

a prognosis for the development of high precision voltage sensors. Similarly,

Section 5 is a review of the limitations to the precision of magneto-optic current

sensors, and also concludes in a prognosis.

In Section 6 we offer our opinions on the steps that should be taken to accelerate

the development of high precision current and voltage sensors. These include specific research to be undertaken and other developments that should be pursued.

1-2
Finally, Section 7 summarizes the results and recommendations.

Several appendices that should be useful to the designer of electro-optic and

magneto-optic sensors are included. The publication of several archival papers on the subject covered here is anticipated.

1-3

Section 2

CONCEPTS OF PRECISION AND ACCURACY IN ELECTRO-OPTIC AND MAGNETO-OPTIC SENSORS

In the introduction to this report, we pointed out that the use of optical sensors

in the power industry will require entirely different ways of thinking about the

relationship between the quantity to be measured (the measurand) and the output of

the sensor. In this section we will examine the factors that determine the

reproducibility of an optical sensor quantitatively, but in a generic sense, that

is without relating the changes in the transfer function to specific material or component properties.

GENERIC TRANSFER FUNCTIONS

In most cases, where a sensor is to be used to determine the instantaneous value

of a measurand (i.e., a waveform), the most desirable transfer function is a linear function,

R(x) = K x, (2-1)

where x is the measurand, R(x) is the output of the sensor, and K is a constant.

In some cases, specifically the measurement of dual polarity measurands, the antisymmetric nature of the waveform is important. Unfortunately, in the field of

optics, one is rarely able to obtain truly linear functions.

In all of the cases described in this report and in many others, the output of an optical sensor, understood usually to mean either optical power at a detector or the detector output, is related to a measurand (current, voltage, electric or magnetic field) by a function of the form

R(x) = A sin 2 (x/x + *)» (2-2)

where R(x) is the instantaneous output corresponding to a value, x, of the measurand, xo is a constant typically depending on the type of sensor, the material used

and the wavelength, A is a constant related to the amount of optical power

2-1
available from the source and the optical losses in the sensor, and $ is a con- stant characteristic of a particular configuration. Note that a single value of

R(x) corresponds to multiple values of x, that the function is nonlinear, and that

it is always positive—characteristics that are generally undesirable in a sensing

device.

The four choices of * illustrated in Figure 2-1, (0, it/2, and ±ir/4) are the most

useful. For greatest sensitivity (i.e., maximum dR/dx) and linearity, * = ±ir/4 are obviously the best choices. When very large signals are to be measured (those

that exceed xo) or when the rms value of the waveform rather than the waveform

itself is to be determined (see below), it may be advantageous to choose $ to be or u/2.

A further possibility is to utilize both the + and -it/4 choices and to take their

difference. This yields a transfer function of the form (Figure 2-2)

R(x) = A sin [2x/xo + 2(* - n/4)] (2-3)

where the second term in brackets is obviously equal to zero if the value of * is

chosen accurately. This function now represents a reasonable approximation to the

ideal transfer function, at least over a range of positive and negative values of

x. It can, however, be improved one step further by noting that the sum of the

$ = ±tt/4 choices is identically equal to A. The A dependence, which is a significant factor in determining precision, can thus be removed by division. This additional complexity, which probably requires a computer, may or may not be appropriate in a specific application.

TRANSFER FUNCTION DISTORTIONS

Having identified what is probably the most useful transfer function available

from an optical sensor, Eq. 2-3, we are now in a position to examine how that

function can be distorted and the impact those distortions will have on the performance of the sensor. Various specifications of sensor precision could be

chosen. For present purposes, we choose to compare the rms value of the sensor

output waveform to the rms value of the measurand waveform.

We begin by noting that this ratio will be dependent on both the amplitude and

shape of the measurand waveform. The dependence on amplitude can be readily com- puted and is shown in Figure 2-3 for the case of a sinusoidal measurand waveform.

2-2
(•)

s—\

R( x) 1.00"

.'.900 •

.BOO •

.700 r

x

.600 -. f

.500 • 7

.400 I \

\ .300 / .200 7

l_ •!•' 1 >

YlOO

*r i i i '•!• I -1.60 -1.20 -.600 -.400 .000 .400 .600 1.20 1.60 2.00

x/xn. radians

(bl

1.00 rR(x) ^—

.900 • \ ..BOO

\ .700 / \

\ .600

\

,500

i \ .40^- " \

\ T°°

' \

\ /.200 - \ / . 100

i i i —^< ^ 1 1 ' 1 '' 1 1 1 -1.60 -1.20 -.800 .400 .000 .400 .800 1.20 1.60 2.00

x/x . radians

2-1. Transfer functions corresponding to Eq. 2-2 for 4 values of *: (a) 0, it/2;

(b) ±tt/4.

2-3
1.00 T

2.00

2-2. Transfer function corresponding to Eq. 2-3 for $ = it/4.

.100 .200 .300 .400 .500 .600 .700 .800 .900 1.00

x.'x . radians rms

2-3. Generalized calibration curve for a sensor with a transfer function of the

form of Eq. 2-3 (* = -rr/4) and Figure 2-2.

2-4
Q. <

.628 1.26 4.40 5.02 5.65 6.26

ust, radians

2-4. Three waveforms used for testing the sensitivity of the calibration curve to

waveform shape. Solid curve is a true sinusoid, dotted curve is a distorted

sinusoid, dashed curve represents a dc measurand. Each is normalized to an rms value of one.

Note that for small values of x/xo the ratio is 2 (actually 2A) which is equal to

the first derivative of Eq. 2-3 at the origin. Figure 2-3 thus represents a generalized calibration curve for such a sensor. From the point of view of precise measurements the fact that the ratio varies with measurand amplitude is not

important; only changes in the curve need to be considered.

In principle, the calibration curve must be determined for every waveform used.

It is therefore useful to determine the sensitivity of the calibration curve to

waveform shape. Figure 2-4 shows three waveforms used here for illustration. The

solid curve is a perfectly sinusoidal waveform. The dotted curve is a distorted

sinusoid, with the positive half-cycle being somewhat larger than the negative

half-cycle; it therefore has a dc component. The dashed curve indicates a dc

measurand. As shown, each has been normalized to have an rms value of one.

Figure 2-5 shows the calibration curves corresponding to these three waveforms.

It appears that for nominally sinusoidal waveforms with relatively small values of

x/xo the calibration curves are relatively insensitive to waveform shape.

2-5
.100 .200 .300 .400 .500 .600 .700 .600 .900 1.00

rtns Input

2-5. Computed calibration curves for the three waveforms shown in Figure 2-4.

Solid curve is the same as Figure 2-3. Dotted and dashed curves refer to the

respective waveforms in Figure 2-4.

2-6. Illustration of the effect on the transfer function of an increase in the

parameter A. Solid curve is the unchanged curve. Change in slope at the origin

is directly proportionate to the change in A.

2-6
The effect on the transfer function of an increase in the parameter A is shown in

Figure 2-6. The result is a proportionate change in the transfer function and

therefore in the calibration curve. That is, the parameter A must be maintained

constant with exactly the same precision as is required in the overall sensor, or the A dependence must be removed as described above.

The effect of an increase in the parameter xo is shown in Figure 2-7. The result

is a proportionate change in the periodicity of the transfer function, hence the

slope at the origin, and the calibration curve. Therefore, xo must also be maintained with the same precision as is required in the overall sensor.

The effect of a change in $ is different, and is shown in Figure 2-8. The shape

of the transfer function is unchanged, but the origin is shifted. This has three

significant effects, as follows: (1) The output now has an average value (i.e., a dc level); (2) for sinusoidal signals, there is a phase shift between the input

and output of magnitude 2$; and (3) if the change in $ is large enough or the

signal is large enough, the calibration curve will change.

If a sensor is to be designed so that it can measure dc components, then the most

serious of these three effects is the appearance of an average value which represents an offset in the measurement. Figure 2-9 shows the result of small changes

in $ on the calibration curve. From that analysis, we can determine, for example,

that to maintain a precision of 0.1 percent for dc coupled sensors with rms values

of x/xo no smaller than 0.1, one must maintain * to within 0.004 radians. Figure

2-10 shows a plot of the errors in the transfer functions for several values of

*. Of course, if the sensor designer is willing to forego information about the

dc component of a measurand waveform, this requirement can be relaxed.

Sometimes more than one of the three parameters in Eq. 2-3 can change at the same

time, yielding a more complex distortion of the transfer function. Figure 2-11

shows an example of such a case, derived for a particular sensor configuration

described in more detail in a later section.

The type of analysis described in this section is the first step in determining

the sort of precision that can be obtained for a particular sensor. Having determined, quantitatively, what level of distortion in the transfer function can be

tolerated, one can then associate the particular defects encountered with the properties of specific components of the sensor, and thus determine the effectiveness

of a design. These steps are taken in later sections of this report, but before

2-7
2.00

2-7. Illustration of the effect on the transfer function of an increase in the

parameter xo« Solid curve is the unchanged curve. Change in slope at the origin

is directly proportionate to the change in xq.

2-8. Illustration of the effect on the transfer function of a change in the

parameter *. Solid curve is the unchanged curve. The result is the appearance of

an average value, a shift in phase, and a change in the calibration curve.

2-8
.030 .060 .090 .120 .150 .180

x/x_, radians, rms

.210 .240 .270 .300

2-9. Result of small changes in $ on the calibration curve for sinusoidal signals. Labels indicate differences in radians from -nr/4.

.030 .060 .090 120 .150 .180 .210 .240 .270 .300

x/Xq, radians, rms 2-10. Fractional errors in the distorted curves of Figure 2-9. Specifically, the

differences between each of the distorted calibration curves and the undistorted

curve divided by the undistorted curve.

2-9
that, it is useful to consider, briefly in the next section, an alternative type

of transfer function to that described above.

INSTANTANEOUS VERSUS rms MEASUREMENTS

The assumption that instantaneous measurements of current or voltage waveforms are preferred should not be viewed as a requirement. Another interesting possibility

is that of a sensor designed to give directly a response proportional to the true

rms of an arbitrary input waveform. Such a device can be produced, based on

Eq. 2-2 with $ = (see Figure 2-1). That is,

R(x) = A sin2 x/xo = A[(x/x ) 2 - (x/xo)V3 + ...], (2-4)

where the quantity in brackets is a Taylor series expansion. To the extent that

the second term in brackets in Eq. 2-4 is negligible, one can obtain the true rms value of the waveform by determining the average output of the sensor over the

period of the waveform.

Since this is not a true parabolic function, the ratio of average output to the

rms value of the measurand will depend, as with the case described above, on both

the amplitude and shape of the measurand. For the three waveforms used for

illustration above (Figure 2-4), the computed calibration curves are shown in

Figure 2-12.

2-10
2-11. Illustration of a complex distortion of a transfer function arising from

nonideal characteristics of a current sensor described in Section 3.

1.10

1.05

7:aO

.950

.900 •

.850 '•>v ***

E .800 •

.750

.700

.650 •

1 — 1 i 1> 1 1 1 1 1 ,100 .200 .300 .400 .500 .600

x/Xq, radians, rms

.700 .800 .900 1.00

2-12. Calculated calibration curve for a true rms reading sensor for the 3 wave- forms of Figure 2-4.

2-11

Section 3

ELECTRO-OPTIC AND MAGNETO-OPTIC SENSOR CONFIGURATIONS

SUITABLE FOR CURRENT AND VOLTAGE MEASUREMENTS

A very large number of optical approaches to the measurement of current and voltage have been discussed in the literature. Of these, there are a relatively small

number that have been examined in sufficient detail that we might expect them to

yield at least a first generation of useful devices. In this section we describe

some of the more promising approaches, which will allow us, in later sections, to

relate specific sensor properties, such as those described in the previous sec- tion, to particular component and material properties.

ELECTRO-OPTIC VOLTAGE SENSORS

Numerous effects involving a change in the optical propagation characteristics of

a material in the presence of an electric field have been reported in the literature. Of these the two most widely studied and developed are the linear electrooptic effect, sometimes known as the Pockels effect, and the quadratic electrooptic effect, sometimes known as the Kerr effect. Both of these effects may be

described as an induced linear birefringence, that is to say an induced anisotropic change in the refractive index of the material. The linear electro-optic

effect appears only in crystalline materials and of those, only crystals that do

not have a center of symmetry. The quadratic electro-optic effect appears in all

materials. Unfortunately, it is very small in glass, though that is the material

in which it was discovered, so except perhaps for extremely high fields, it is

probably not practical to use fiber itself as the sensing element for a voltage

sensor. We therefore concentrate here on sensors based on the linear electro-optic

effect though most of the discussion applies also to quadratic devices.

Polarimetric Electro -optic Volta ge Sensors

The basic configuration of an electro-optic voltage sensor using polarimetric

techniques is shown in Figure 3-1. A suitable crystal is chosen and oriented so that, when an electric field is applied in a certain direction, light passing

through the crystal experiences a linear birefringence or change in linear

3-1
\*

3-1. Basic configuration of an electro-optic voltage sensor. In addition to the

electro-optic crystal, normal components include polarizers, a waveplate (retardation plate) shown as a quarter-wave plate, and lenses required to transmit light

efficiently from one optical fiber through the bulk components and back into

another fiber. Many modifications of this basic geometry can be used, including,

particularly a double-pass arrangement in which light is reflected back through

the crystal and either into the input fiber or another fiber.

elliptical polarization

linear polarization

3-2. Linear birefringence induced in the crystal by an electric field causes the

polarization state of light to change as it passes through the crystal. The

changes in polarization state can be converted to changes in transmittance with

polarizers.

3-2
birefringence proportional to the field. (Precisely, linear birefringence is the

difference between the refractive indices that apply to two specific orthogonal

linearly polarized components of the transmitted light.) When the transmitted

light contains components parallel to both the axes of birefringence, the polarization state at the output is dependent on the magnitude of the birefringence

incurred. Changes in polarization state can be converted to changes in transmittance using a polarizer.

More specifically, consider the case illustrated in Figure 3-2. The axes of lin- ear birefringence are taken to be the x and y axes. Light incident on the material at 45° to these axes gives equal components parallel to the x and y axes. If

the refractive index for these components is taken to be n x and ny

respectively,

the two components will differ in phase at the output by an amount given by

r = 2ir(n x

- ny)h/x, (3-1)

where h is the crystal length and x is the wavelength. The polarization state at the output as a function of r is depicted in Figure 3-3. The quantity r may be

expressed as a function of the electric field as follows,

2TrBh eo

(3-2)

r=o 7T/2 37T/2

3-3. Illustration of the change in polarization with r for the case of light that

is initially linearly polarized at 45 deg to the axes of linear birefringence.

3-3
where Bh is the value of n

x

- ny

at zero field and Ce0 may be called the effective

electro-optic coefficient. C eo depends on the specific material, its crystalline

(point group) symmetry, and both the orientation of the electric field and the

direction of propagation relative to the crystalline axes.

When the device is placed between crossed polarizers, the transmittance is given by

R(E) = sin2 (r/2). (3-3)

If Bh = 0, we obtain

R(E) = sin2(C

eoE/2) (3-4)

which, when Cpn/2 is identified as 1/xo and E as x, is the function shown as the 'eo solid curve in Figure 2-la. When the polarizers are aligned, the function shown

as the dotted curve in Figure 2-la is obtained.

mirror

msrror beamsplitter

3-4. Illustration of a Mach-Zehnder interferometer used as an electric field or voltage sensor. An electro-optic crystal is placed in one arm of the interferometer. A change in refractive index of the crystal causes a fringe shift in the

interferometer. The transfer function can span the full range of functions shown

in Figure 2-2 depending on how closely matched the arms of the interferometer are

in zero field.

3-4
3-5. A planar waveguide (integrated optic) version of the Mach-Zehnder interferometer. The substrate would be of an electro-optic material in which a permanent waveguide structure could be created by locally changing the refractive

index. By applying a voltage to electrodes (black areas) near the guide the

optical path length of one path can be changed relative to the other in the same manner as in Figure 3-5.

rro>

Polarizer

Single mode fiber

Polarizer

Conductor

3-6. Basic configuration of an optical fiber current sensor.

3-5
Functions in between these two cases may be obtained when Bh is not zero. Specifically, the functions shown in Figure 2-lb are observed when 2TrBh/x is equal to

±90 deg. These can also be obtained when Bh = by placing a quarter-wave plate

(a device that introduces a 90 deg phase shift) in series with the electro-optic

crystal

.

Interferometric Electro-optic Voltage Sensors

An alternative to the use of polarimetric techniques with an electro-optic sensor

is to place the active material in one arm of an interferometer, for example the

Mach-Zehnder interferometer shown in Figure 3-4. In this case the polarization of

the light is oriented along one of the axes of induced birefringence in the crystal. The effect of the electric field then is to change the optical path length

of the interferometer arm containing the crystal relative to the other. The

change in output power is then again given by a function in the form of Eq. 2-1.

The value of A is determined by the total power transmitted by the interferometer.

The value of $ is the difference in phase between light transmitted through the

two arms of the interferometer with no applied field, and the value of xo is

related to the material, symmetry, and orientation of the crystal.

Interferometric devices constructed of bulk components are not particularly

attractive for measurement purposes because a high degree of mechanical and thermal stability is required for a stable output. However, such devices have been

constructed using planar waveguide technology (integrated optics) and these show more promise of yielding useful devices (Figure 3-5). A particular advantage of

this approach is that much more sensitive devices can be constructed and also that

the number of components is minimized. The causes of instability in planar

devices are similar to those in polarimetric devices, and therefore the discussion

of stability in electro-optic devices presented in a later section will largely

apply.

MAGNETO-OPTICAL CURRENT SENSORS

Magneto-optic current sensors are based on the Faraday magneto-optic effect, a rotation of the plane of polarization of linearly polarized light propagating

through a material in the presence of a magnetic field. The Faraday effect is

present to some degree in all materials, but is most often exploited in glass,

either bulk glass or single mode optical fiber. Utilization of the effect in

fiber allows great freedom in configuration and requires a minimum number of com- ponents and fabrication steps. On the other hand, a greater choice of materials

3-6
is available in bulk, bulk materials are more stable, physically, and it is easier

to design for certain configurations using bulk materials. Both choices have been

examined in detail in this study; their basic design and performance is described

here.

Optical Fiber Current Sensors

The basic configuration of an optical fiber current sensor is shown in Figure 3-6.

One or more turns of single mode fiber is looped around the conductor. The principles of the Faraday effect predict that the plane of polarization of linearly

polarized light propagating through the fiber will be rotated by an angle e given

by

9 = V / 6 . dl, (3-5)

where V is a constant characteristic of the material in the fiber, called the

Verdet constant, B = uH is the magnetic flux density, and di. is a differential

vector in the direction of propagation. From Ampere's law the integral of the

magnetic field (H) along any closed path around a conductor is equal to the current (I) passing through the path, i.e.,

/ H . dl = I. (3-6)

Thus we obtain a linear relationship between the rotation and the current,

e = yVNI, (3-7)

where N is the number of turns of fiber around the conductor. In typical fiber,

the ratio of rotation to current is small; for a single turn sensor and an operating wavelength of 633 nm it is approximately 265 deg/MA. It is shown in an appendix, however, that it is possible to detect very small rotations.

The most common method of measuring the rotation induced by the current is to place polarizers at the input and output, as shown in Figure 3-6. The rotation

then results in a change in transmittance which is detected as a change in power

at an optical detector. Depending on the relative orientation of the polarizers,

any of the transfer functions shown in Figure 2-1 can be obtained. The case where

the polarizers are aligned for maximum transmittance at zero current corresponds

3-7
to * = w/2; alignment for zero transmittance at zero current to <s» = 0; the two

orientations giving 50 percent transmittance correspond to * = ±tt/4.

The transfer function shown in Figure 2-2 is obtained with a polarizing beam

splitter, such as a Wollaston prism, oriented so that both the + and -ir/4 components are detected and their difference taken. It is often convenient to incorporate a half-wave plate (a polarization rotator) into the system in order to simplify the orientation of the polarizer (Figure 3-7),

To obtain, simultaneously, transfer functions with $ = and ±n/4 or u/2 and ±ir/4,

to count fringes requires a beam splitter and two separate polarizers, as shown in

Figure 3-8. The beam splitter must be designed and used in such a way that the

polarization states of the transmitted and reflected beams are not altered.

Other configurations for determining the rotation can be considered. One is shown

in Figure 3-9. If the plane of polarization of the linearly polarized light

injected into the fiber is caused to rotate rapidly with time, the plane of polarization of the light at the output rotates at the same frequency, but with a phase

shift that is proportional to the induced rotation in the fiber. Standard phase

measurement instrumentation can thus be used to determine the current, as shown.

Any method of creating a rotating linear polarization state, such as a rotating

mechanical polarizer, can be used, but it is best if a very high rotation rate can

be used. A convenient method depicted in Figure 3-9 is to start with two orthogonally polarized beams at slightly different wavelengths (i.e., slightly different optical frequencies). When these beams are passed through a quarter-wave plate

oriented with its axes at 45 deg to the directions of polarization, the resulting

beams is linearly polarized with its orientation rotating at the optical difference frequency. The two beams can be obtained from a Zeeman-split gas laser,

where the difference frequencies &re of the order of 0.1 MHz or using acoustooptic modulators, where the difference frequencies are of the order of tens of

megahertz.

Another possibility is to incorporate the fiber coil into a Sagnac interferometer,

as shown in Figure 3-10. The Sagnac interferometer is the same device used in a fiber optic gyroscope, and many of its properties are well known. Light entering

the input fiber is divided with a 3 dB fiber coupler, the fiber equivalent of a 50/50 beamsplitter. Equal components thus propagate in opposite directions

through the sensing coil, and are recombined at the coupler. It is a property of

3-8
laser - f- 2

Wolianton

prism

o

pulse

generator oscilloscope

3-7. An optical fiber current sensor in which two orthogonal output polarizations

are detected using a Wollaston prism polarizer.

Two Polarization (sine, cosine) Detection

detector

Beam

Splitter

ector

3-8. Polarizer arrangement for detecting two output polarizations oriented at 45 deg to each other.

tm

A + A.A.

3-9. Rotating polarization technique for observing Faraday rotation in an optical

fiber coil. The rotating input polarization is created by passing two orthogonally polarized optical beams at slightly different optical frequencies through a quarter-wave plate. The phase of the rotation is shifted in proportion to the

current.

3-9
such couplers, as with beam splitters, that the two output components differ in

phase by tt/2 radians. One can then quickly show that, if the coil is reciprocal,

the two components arriving at the output port differ in phase by v radians and

interfere distructively, while the components arriving at the input port are in

phase. Because the Faraday effect is nonreciprocal (i.e., it depends on the sign

of the magnetic field) light is shifted from one port to the other by the presence

of a current though the coil. The actual transfer function is given by Eq. 2-1

with $ = 0.

Because there is no easy method of choosing another value of $, the Sagnac device

is not well suited to the measurement of small signals. It is extremely attractive for other reasons. It is a particularly simple device, involving no polarizers, and in fact works well with any input polarization state, including un- polarized light.

Bulk Glass Curre nt Sensors

While the fiber current sensors described above have many advantages, there are times when it is preferable to construct a device in which the sensing occurs in a bulk material, with light transmitted to and from the material using fiber. The

basic principles of such devices otherwise are identical to the all-fiber sensor. Advantages of this approach include the opportunity to use materials that are not

available in fiber form, the possibility of using certain geometries that are not

possible with fiber, and, for the present time, greater stability.

For high sensitivity current sensors, fused silica is not particularly attractive

because the Verdet constant is low. Other commercial glasses offer a Verdet con- stant that is as much as twenty times larger and some experimental glasses offer

the possibility of still higher values. Some crystalline materials have Verdet

constants about three orders of magnitude greater than fused silica.

Figure 3-11 shows the design of a bulk glass sensor that has been reported in the

literature. Light is transmitted to and from the sensor using multimode fiber.

Polarizers and lenses are placed between the fiber and the sensor. The sensor is

constructed of a single piece of glass faceted to reflect light around the conductor by complex path. The reason for the complex path is that when light is

reflected from a dielectric interface (in this case total internal reflection is

used) a phase shift between light polarized in the plane of the reflection and

that polarized perpendicular to the plane of polarization is encountered. This

3-10
OUT

IN Single mode fiber

3-10. The Sagnac interferometer. Light entering the input port is split by the

fiber coupler, half propagating through the coil in the clockwise direction and

half in the counter-clockwise direction. In the absence of current through the

conductor all light exits by the input port, but if current flows, the magnetic

field causes the fiber coil to become nonreciprocal and light is shifted to the

output port. The transfer function is that of Figure 2-1 with * = 0.

Path

3-11. A Faraday rotation current sensor based on a design by Kanoi , et al . IEEE

Trans. Power Delivery, 1986, vol. PWRD-1, p. 91-97. Two complementary reflections

are used at each corner to cancel phase shifts that occur in reflection.

3-11
3-12. Illustration of the principle of polarization-independent beam steering

using complementary reflections. The component of the optical field that is

perpendicular to the plane of incidence in the first reflection is parallel to the

plane of incidence in the second and vice versa.

Optical Current Probe

3-13. A bulk-glass current sensor that can be placed around a conductor without

breaking either the conductor or the optical path.

3-12
results in a change of polarization state at each reflection and a distortion of

the transfer function. The solution is to use two reflections wherever one is

needed, the two being designed so that the parallel component in the first reflection is the perpendicular component in the second and vice versa, so that the

phase shifts cancel. This use of complementary reflections for polarizationindependent beam steering is widely used in optics. It is illustrated schematically in Figure 3-12.

Figure 3-13 shows how a bulk current sensor can be designed to slide onto a con- ductor. In such a device the optical path does not completely surround the con- ductor, but when carefully designed only a small percentage of the total signal is

lost.

3-13

Section 4

CRITICAL EVALUATION OF ELECTRO-OPTIC SENSOR TECHNOLOGY

FACTORS LIMITING THE PRECISION OF BULK MAGNETO-OPTIC SENSORS

Properties of Electro-opt ic Materials

The effective electro-optic coefficient, Ceo defined in Eq. 3-2, depends on the

specific material, its crystal! ographic symmetry, its orientation with respect to

the directions of propagation and electric field, and its dimensions. A complete

description of the electro-optic effect is beyond the scope of this document; the

interested reader is referred to two books ( 4-1,4-2 ) that provide broad treatments

of the subject. Here, we focus on material properties and material selection.

Many of the best known electro-optic material s--LiTa0, LiNbO , and KDP and its

isomorphs, for example—are naturally birefringent; that is, even in the absence

of an applied electric field, different polarizations experience different refractive indices ( 4-1 , 4-2 , 4-3 ). As a result, in many configurations, the parameter B in Eq. 3-2 is non-zero and is often yery temperature dependent. This is particularly true in LiTaO when used in its optimum orientation. It is possible in some

of these materials to choose an orientation in which this natural birefringence is

not, in principle, a problem. In these cases, however, alignment and collimation

of the beam become critical and, furthermore, those orientations usually result in

a significantly lower electro-optic coefficient,

Our first suggestion in selecting materials for high precision voltage measurements therefore is to restrict the selection to crystals with cubic symmetry;

these are not naturally birefringent.

There is a second reason for choosing cubic crystals and that is related to the

pyroelectric effect. Certain classes of crystals, specifically 10 of the 32 point

symmetry classes, known as polar classes, have the property of developing an electric polarization when their temperature is changed. This represents an internal

4-1
electric field that can, by itself, cause changes in the birefringence of the

crystal. None cf the 10 polar classes is cubic ( 4-3 ).

Among the five cubic crystal classes--23, m3, 432, 43m, m3m--two have a center of

symmetry (m3m and m3) and therefore do not exhibit a linear electro-optic effect.

One other (432) also does not have a linear electro-optic effect, leaving only

classes 23 and 43m to be considered.

There is one further effect to be considered, namely optical activity. Optical

activity is a rotation of the plane of polarization of plane polarized light of

the same sort produced by the Faraday effect, except that both the sign and magnitude of the rotation are fixed by the material rather than a magnetic field. In the same way that linear birefringence tends to quench Faraday rotation, optical

activity tends to quench the electro-optic effect. Crystal class 23 exhibits

optical activity suggesting that crystals of class 43m are perhaps the best choice

for voltage sensors. (There is one possible exception to this, discussed under

temperature compensation techniques, below.)

Fortunately, a number of common crystals are. included in class 43m. These include

GaAs, CdTe, ZnS, ZnSe, GaP, and s \

Ge

3 12

« Foi centrate on the properties of these materials.GaAs, CdTe, ZnS, ZnSe, GaP, and Bi Ge . For the rest of this section we con

For crystals of class 43m, optimally oriented, the expression for induced birefringence is given by

r = CeoE =|^n3 r41 hE, (4-1)

where r is the induced phase shift between orthogonal linearly polarized components, \ is the wavelength, h is the length of the crystal, n is its refractive

index in zero field, r is an element of the electro-optic tensor applicable to

the specific material, and E is the electric field in the crystal.

With regard to material properties and their effect on precision, we see from

Eq. 4-1 that we must focus on the quantity n

3 r h. The fractional change in this

quantity with temperature is

1 d(n3r»i h) 3dn 1 dr ^i Idh

C n

3 r.,h dT " n df

+

rv. dT

+

h dT* TM~2 ' Hi 41

4-2
Because it appears as the third power, the variation of refractive index with temperature is the first consideration. In most semiconductor materials the temperature derivative of the refractive index is of the order of 10" 5 /°C. Accurate data

are available for only a few of the cases of interest here. What data can be

obtained are summarized in Table 4-1.

For the materials shown in Table 4-1 the quantity 3(dn/dT)/n is between 10~V°C

and 10~ 5 /°C in each case.

The next parameter of concern is dh/dl". .For cubic crystals, thermal expansion is

isotropic. Representative values of a = (dh/dT)/h are given in Table 4-2.

The final parameter of concern in Eq. 4-2 is r . The temperature dependences of

H" 1 the electro-optic tensor elements of a few crystals have been measured but no data

appear to be available on any of the 43m crystals listed above* (See reference

( 4-4 ) for one of the most extensive compilations of data on the electro-optic properties of materials.) We suspect that, r will not be the major contributor to

the temperature dependence of the electro-optic effect, but cannot at this point

be sure.

While it does not appear explicitly in Eq. 4-1 or 4-2, another property of materials that can effect their thermal stability is the stress-optic effect, Stress

applied to any material causes an anisotropic change in its refractive index which

may yield a non-zero value of An in Eq. 3-2. In a sensor, stress could occur

because of differential thermal expansion in a mounting structure. Materials with

small stress-optic coefficients are therefore desirable. For those class 43m

crystals in which the stress-optic effect has been studied, the cceffecients are similar ( 4-1 ).

During this study we have begun to focus on bismuth germanate, Bi Ge 0„„, as perh 3 12 haps one of the most attractive of the materials listed in Tables 4-1 and 4-2. It

is widely used in nuclear scintillation and therefore readily available, And it

has been suggested (4-5) that the temperature dependence of its electro-optic

coefficient is smaller than that for other crystals. We have obtained samples of

bismuth germanate for complete testing of its properties. These studies have thus

far yielded the preliminary data presented in Tables 4-1 and 4-2; work on the complete electro-optic coefficient continues along with work on the stress-optic

coefficients. Gallium phosphide is another attractive choice but high resistivity

crystals are difficult to obtain.

4-3
Table 4-1

TEMPERATURE DERIVATIVE OF THE REFRACTIVE INDEX FOR SEVERAL CRYSTALS

Crystal n

3.3

x(nm) (dn/dT)/n

10-5/°C

Ref.

GaAs 5000 1.7 b ZnSe 2.5 850 3.1 a ZnS 2.3 850 2.1 a GaP 3.2 850 1.3 b

B \

Ge 3°l2

2.1 633 2. c

a A. Feldman, D. Horowitz, R. M. Waxier, M. J. Dodge, Optical Materials Character!

zation, Nat. Bur. Stand. (U.S.) Tech. Note 993 (1979).

b

Y. Tsay, B. Bendow, S. S. Mitra, Theory of the temperature dependence of the

refractive index in transparent crystals. Phys. Rev. B. _8, 2688-2696 (1973).

C

G. W. Day, D. Conrad, K. S. Lee, P. D. Hale. "Optical electro-optical and

stress-optical properties of bismuth germanate, Bi Ge ," unpublished.

Table 4-2

THERMAL EXPANSION COEFFICIENTS OF SEVERAL CRYSTALS OF CLASS 43m

Crystal g(10~ 6 K' 1

) Ref.

GaAs 5.7 c ZnSe 7.3 a ZnS 6.8 a GaP 5.3 c

B \

Ge 3° 12 10. b

a A. Feldman, D. Horowitz, R. M. Waxier, M. J. Dodge, Optical Materials Character!'

zation, Nat. Bur. Stand. (U.S.) Tech. Note 993 (1979).

bG. W. Day, D. Conrad, K. S. Lee, P. D. Hale. "Optical electro-optical and

stress-optical properties of bismuth germanate, Bi Ge ," unpublished.

c William L. Wolfe. "Properties of optical materials," in Handbook of Optics . Optical Society of America/McGraw Hill, 1978.

4-4
Summaries of the properties of several of the more promising electro-optic materials for use in electro-optic voltage sensors can be found in an appendix.

There is one further concern with electro-optic materials. It is that all materials that possess a linear electro-optic effect are also piezoelectric ( 4-3 )

Direct piezoelectricity is the property that when stress is applied to a crystal,

an electric polarization is developed. Converse piezoelectricity is the property

that when an electric field is applied to a crystal, its dimensions change. The

consequence, for the study of the electro-optic effect is that the electro-optic

coefficients are dependent on the modulation frequency of the applied field and on the manner in which the crystal is mounted.

If a crystal is not physically constrained and if the applied field is electrostatic or varying slowly, the piezoelectric effect causes a small dimensional

change that through the stress-optic effect causes a refractive index change in

addition to that produced directly by the electric field. The symmetry characteristics of the two processes are identical so that the effects add algebraically.

The resulting effective electro-optic tensor elements are often identified with

the superscript T.

If the crystal is constrained so that its dimensions cannot change with the electric field, or if the electric field is changing fast enough so that the crystal

cannot change dimensions fast enough to follow the field, the piezeoelectric con- tribution vanishes and the resulting electro-optic tensor elements are often identified with the superscript S. It should be noted clearly that while the symmetry

of the piezoelectric and electro-optic contributions is the same, the magnitudes

of the effects can be opposite so that S values may be smaller than T values or vice versa.

At certain frequencies, depending on the properties of a crystal and its dimensions, a crystal will exhibit piezoelectric resonances, that is frequencies at which the dimensional changes dre enhanced. At these same frequencies, the

electro-optic effect is also typically enhanced.

There is little that can be done about piezoelectric effects in electro-optic

sensors other than to ensure that the signals to be measured are at frequencies

significantly below any resonances. Generally, for most applications in the power

industry, this can be achieved.

4-5
Further concern relates to the establishment of the electric field in the crystal.

In all of the foregoing discussion it has been assumed that the electric field in

the crystal is uniform in magnitude and direction. This is a good approximation

if electrodes are applied to the crystal and the field established by applying a voltage to the crystal. It may not be a good approximation if a crystal without

electrodes is simply placed in a field.

In the latter case the field in the crystal will depend on the dielectric constant

of the crystal, the shape of the crystal, and the field distribution outside the

crystal. Exact field distributions inside a dielectric material are very difficult to calculate except where simplifying geometries are chosen ( 4-6 ). This

makes calibration of such a device difficult. Furthermore, the dielectric con- stant of a material is known to be a function of temperature, thereby introducing

an additional source of imprecision.

Generally, therefore, it seems advisable to consider sensor geometries that

involve electrodes on the crystal. In a power system application this may require

the use of voltage dividers to reduce the voltage at the electro-optic crystal to

an acceptable value.

One final concern related to materials is that all materials exhibit a Faraday

effect, and if a magnetic field component in the direction of propagation exists,

noise, or distortion in the transfer function could result. The problem is somewhat less severe when, as would typically be the case, light propagating through

the crystal is circularly polarized, on which the magnetic field has no effect.

Design of the sensor so that anticipated magnetic field components are perpendicular to the direction of propagation is also desirable and magnetic shielding could

be used if necessary.

Properties of Waveplates

The second most important component in a voltage sensor is the waveplate. The

function of the waveplate is to establish the desired value of $, as for example,

$ = u/2 to achieve the transfer function described in Eq. 2-3, when An = in

Eq. 3-2. Three types of waveplates may be considered--birefringent waveplates,

reflection waveplates (rhombs), and polymer waveplates. Reference (4-7 ) provides

an extensive review of waveplate designs and properties. Recent work in our laboratory on the characterization of waveplates, in particular

4-6
the issue of their stability, is presented in an appendix to this document and in

a forthcoming paper by the authors ( 4-8 ).

Birefringent Waveplates . Birefringent waveplates are perhaps the best known type

of waveplates. They are usually made from uniaxial crystals, such as quartz or magnesium fluoride, cut so that the direction of propagation is normal to the

optic axis. In this case, light polarized parallel to the optic axis experiences

one refractive index, called n e

, and light polarized perpendicular to the optic

axis experiences a different refractive index, called n Q

. Either n e or n Q may be

larger. A phase shift between these two polarizations of magnitude

6 = — (n - n )h = — Bh (4-3)

X

v e o' X

v '

occurs as light propagates through the crystal.

Generally one is interested in a waveplate for which 6 = ir/2 (i.e., a quarter-wave

plate), though in double pass sensor configurations, a value of tt/4 (i.e., an eighth-wave plate) may be desired. With n e

- n Q

determined by the material, one may construct a waveplate with the desired retardance at a given wavelength by

choosing the thickness correctly.

A waveplate with a retardance of 6 is, in some respects, indistinguishable from a waveplate that differs in retardance by 2m. Waveplates with 6 < 2tt are called

zero order waveplates; those with n > are called multiple order waveplates of

order n. If n is large, a multiple order plate is much less stable than a zero order plate.

For many materials, a true zero order plate would be very thin and thus difficult

to fabricate. As a result, the components usually sold as "zero order waveplates"

are actually compound waveplates, composed of two multiple order waveplates differing in retardance by the desired value. In most respects such a plate behaves

almost exactly the same as a true zero order plate.

The fractional stability of a birefringent waveplate is seen from Eq. 4-3 to be

given by

_ 1 ds 1 dB . 1 dh ,„ „x

4-7
Table 4-3

PROPERTIES OF MATERIALS COMMONLY USED IN BIREFRINGENT WAVEPLATES

Material y Ref

.

Quartz -1.4 x 10

_1+ a

MgF -3.9 x 10~ 5 b

Mica -2.3 x 10" 4 c

a T. Toyoda and M. Yabe. "The temperature dependence of the refractive indices of

fused silica and crystal quartz." J. Phys. P ., 1983, vol. 16, p. 97-100.

"A. Feldman, D. Horowitz, R. M. Waxier, M. J. Dodge. "Optical Materials Characterization." Nat. Bur. Stand. (U.S.) Tech. Note 993 , 1979.

C P. D. Hale and G. W. Day. "The selection of linear retarders (waveplates) for use in high precision electro-optic sensors and other polari metric appliations,"

to be published.

The quantity y is tabulated in Table 4-3 for quartz and magnesium fluoride.

It was suggested in Section 2 that the quantity * should be maintained stable to

about 1 mrad, at least for a sensor designed to measure dc quantities. From

Eq. 4-4 and the data in Table 4-3 we discover that, given a perfectly stable

source wavelength, a zero order quarter wave plate made from quartz will change

over 100°C by approximately 22 mrad, one made from magnesium fluoride by approximately 6 mrad, and one made from mica by 36 mrad. The temperature stability of a multiple order plate will be worse than that of a zero order plate, in proportion

to ratio of retardances. The temperature dependence of a compound plate will be

the same as that of an equivalent zero order plate.

Orientation is another problem with birefringent waveplates. If a waveplate is

rotated away from normal incidence, the optical path length increases, but in

uniaxial crystals n e also changes with angle. The net result for a zero order

plate is that when the rotation occurs about the optic axis the retardance

increases by the factor 1/cos e where 9 is the angle of incidence with respect to

4-8
the normal, but rotation about an axis normal to the optic axis causes a decrease

in retardance by the factor cos 9 ( 4-9 ). The change of retardance of a multiple

order plate with angle is larger than that of a zero order plate in proportion to

the ratio of the total retardances. The change in retardance of a compound

waveplate with angle is more complex to describe but is also large compared to a true zero-order plate ( 4-8 ). Careful alignment procedures and mechanical design

are thus essential parts of sensor design.

The apparent retardance of a waveplate is also dependent on the coherence of the source with which it is used. If the coherence length of the source is long with

respect to the thickness of the wave plate, multiple reflections within the wave

plate can cause a significant change in its effective retardance ( 4-10 ). Furthermore this effective retardance has a strong temperature dependence as shown in

Figure 4-1. One obvious solution is to coat the waveplate with an antireflection

coating. This substantially reduces the sensitivity to changes in temperature but

an extremely low reflection coating is required to completely eliminate the problem. A better solution is to use a low coherence source.

Reflection Waveplates . Reflection waveplates rely on the fact that in reflection

from a dielectric surface, the components of the incident light parallel to and

perpendicular to the plane of incidence undergo different phase shifts. The best

known reflection waveplate is the Fresnel rhomb quarter wave plate, shown

schematically in Figure 4-2. It is designed so that incident light is totally

internally reflected, twice, yielding a total retardance of tt/2.

From the expression for the retardance, A, that occurs in total internal reflection,

tan [A] = cos_e (n? sin 9 - lj^2

, L (4 } 2

J n sin2 9

v '

where n is the refractive index of the material and 9 is the angle of incidence

relative to the normal ( 4-11 ) and using data for the temperature coefficient of

the refractive index, it is possible to determine the change in retardance with

temperature. For a Fresnel rhomb made of BK-7 glass the normalized temperature

coefficient is found to be 3 x 10~ 6 .

4-9
140

CD Q

0)o

co

CO J

90

40

vV V^\

> M

- \\

1 1 1 1 1 1 1 1 l*V> -10 10

Temperature, C

4-1. Retardance of a 100-order quartz quarterwave plate (approximately 1 mm

thick) versus temperature for a coherent source (solid) and an incoherent source

(dashed)

4-2. Representation of a Fresnel romb quarter-wave plate(after (4-11 )). Light

undergoes two total internal reflections, each time incurring a 45 deg phase shift

between components parallel and perpendicular to the plane of incidence. For

commonly used BK-7 glass the angle e is 54.6 deg.

4-10
Also using Eq. 4-5, it is possible to determine the sensitivity of the Fresnel

rhomb to misalignment. The result is d6/de = 0.01 rad/deg.

From these results we see that the stability characteristics of a Fresnel rhomb

are significantly better than those of a birefringent wave plate. The obvious

disadvantages of the rhomb are that it is comparatively large and the input and

output beams are not collinear. These are significant considerations, particularly in the design of small sensors.

Polymer Waveplates . The retardance of polymer waveplates derives from the fact

that thin polymer films are significantly anisotropic. They have long been known

to provide a retardance that is insensitive to wavelength ( 4-12 )

, and are also

attractive because they can be made very thin, even with necessary supporting

substrates. Recent commercial literature suggests that they may be relatively

insensitive to temperature. Testing in our laboratory confirms these

characteristics to some degree, but also indicates that the maximum operating

temperature of a polymer waveplate must be kept below about 40°C. They are therefore probably unsuitable for use in power systems applications. Some data on polymer waveplates are presented in an appendix.

Summary of Waveplate Properties . Table 4-4 presents a summary of waveplate

properties useful in the design of voltage sensors. From this compilation, it

appears that the best choice for high precision sensors may be the Fresnel romb,

at least for those cases where its size and configuration can be tolerated.

Another possibility is discussed below in the section on temperature compensation

techniques.

Properties of Polarizers

A linear polarizer is a device that, when placed in a beam of light, produces a beam in which the electric vector is vibrating almost entirely in one direction.

If such a device is placed in a perfectly plane polarized light and rotated about

an axis parallel to the direction of propagation the transmittance is given by

T = (Tj - T

2

) cos 2 e + T

2 (4-6)

4-11
Table 4-4

TEMPERATURE AND ANGULAR DEPENDENCE OF VARIOUS RETARDERS

AT THREE WAVELENGTHS

Device,

material

,

wavelength, nm d6/dT, OQ-1

Y,

o C

_l ds/de, rad/deg

Fresnel rhomb

BK-7

1300 4.1 VA 10-6 2.6 X 10-6 9.3 x 10-3

850 4.6 X lO- 6 2.9 X 10-6 1.2 x 10" 2 633 4.7 X 10-6 3.0 X lO" 6 1.4 x lO" 2

Birefringent

retarder

MgF t 1300 -6.2 X 10-5 -3.9 X lO" 5 -0.098*

850 -6.2 X lO -5 -3.9 X lO" 5 -0.136*

633 -6.2 X 10-5 -3.9 X lO" 5 -0.186*

Birefringent

retarder

quartzt

1300 -2.7 X 10" 4 -1.7 X 10" 4 -0.086*

850 -2.3 X 10 -4 -1.4 X lo

- * -0.128*

633 -2.1 X io-t -1.3 X 10"4 -0.168*

tUncertainty in y and d6/dT for MgF is 5 x 10" 6 and 8 x lO" 6

, and for quartz

3 x 10" 5 and 4 x 10" 5

, respectively.

*In a Taylor series expansion the first angle dependent term is quadratic in

8. These values assume a total thickness of 6 mm. 8 is measured in degrees.

where J

l and T

2 are called the principal transmittances (usually T >> T ) and $

is the angle between the principal transmittance T and the plane of polarization

of the incident beam.

A few examples explain the performance and specification further. When a polarizer is placed in an unpolarized beam, the transmittance is

T = 0.5 (T

2 + T ). (4-7)

4-12
When two identical polarizers with their directions of transmittance oriented at the angle 9 to each other are placed in an unpolarized beam the resulting transmittance is given by

T(9) = 0.5(Tf + T|)cos 2

9 + V2 sin 2 9 (4-8)

from which one obtains

T(0) = 0.5(Tf + T|) (4-9)

when the polarizers are aligned and

T(90) = T

X T

2 (4-10)

when the polarizers are crossed. The ratio T /T is usually called the extinction

ratio E x and can be obtained by taking the ratio of T(90) to T(0),

T(90)/T(0) - 2T

2 /T1 = 2EX

. (4-11)

Prism Polarizers . Most prism polarizers are made from the crystal calcite, a uniaxial crystal with an extremely large birefringence. Innumerable prism

configurations have been used (4-4 ) , to separate orthogonally polarized components

of the beam.

The most popular designs, known as Glan-type prisms (also, Glan-Thompson, GlanTaylor, Glan-Foucault), function through the fact that when light is propagating

normal to the optic axis in a uniaxial crystal, the difference in refractive index

experienced by components parallel and perpendicular to the optic axis makes it

possible for one but not the other to undergo total internal reflection (Fig- ure 4-3).

Except when intended for high power laser applications, the reflected beam is

generally absorbed in the prism mounting. In those cases where the reflected beam

is available, one may find a significant component of the transmitted polarization

in the reflected beam, depending on how close the angle of incidence is to the

Brewster's angle. Glan-type prisms are generally superior to an older type known

as the Nicol prism, which also relied on total internal reflection but in which

4-13
absorber

e-ray

4-3. Representation of a Glan prism polarizer. For the component parallel to the

plane of incidence, total internal reflection occurs at the internal surface. The

optic axes of the two pieces are parallel to each other and to the entrance and

exit surfaces.

4-4. Representation of a Wollaston prism polarizer. The optic axes of the two

pieces are orthogonal. Orthogonal components are refracted by different amounts

when passing from the first segment to the second. Output beams are nearly

symmetric but the angle of deviation is wavelength dependent.

4-14
the entrance and exit faces were not perpendicular to the direction of propagation. Properly used, Glan prisms offer the best extinction ratios available in

polarizers— values of 10 5 to 10 6 are generally expected for well collimated light

and a well aligned prism.

Common imperfections in Glan prisms include a deviation of the output beam with

respect to the input beam and ellipticity of the output beam. Beam deviation can

be a very significant when the prisms are used with optical fibers, particularly

when the prism is rotated in a beam before the beam is focused into a single mode

fiber. Angular deviation of the output beam is translated into a transverse

offset at the focal point of the launch lens. The launch efficiency thus depends

on the orientation of the polarizer. For such applications it is useful to use polarizers with the smallest beam deviation available, about one arc minute.

Ellipticity of the output beam generally occurs because of strain in the output

half of the prism and is dependent on mounting. Ellipticity may not normally be

specified but should not be a problem with most high quality prisms.

Other specified parameters include the field angle and the length to aperture

ratio. The field angle in a Glan prism is determined by the minimum angle at which the unwanted polarization undergoes total internal reflection and the maxi- mum angle at which the wanted polarization is transmitted. It is strongly wavelength dependent, being larger at shorter wavelengths and having typical values of

a few degrees. This small angular aperture is in almost all cases smaller than

the exit radiation angle of a fiber making it essential to insert a lens between

the fiber and polarizer as shown in Figure 3-1. In some cases, the length to

aperture ratio can similarly limit the location of a prism polarizer in a sensor

configuration.

A second class of prism polarizers relies on a difference in refraction of two

orthogonal components to separate them spatially. These include the Rochon,

Senarmont, and Wollaston types. Of these, the Wollaston, is the best known and

most popular because the two beams emerge at symmetric angles, typically about

1 deg, to the axis of the input beam (Figure 4-4). Because of this geometrical

characteristic, it is often useful in sensor designs. There is, however, a potential problem with the Wollaston prism in that the deviation angles are wavelength

dependent making it important to insure, for example, that unexpected aperturing

does not occur. In principle, we should expect the deviation angle to also be

temperature dependent, though we have been unable to observe any significant

effect.

4-15
A potential problem with all prism polarizers is that the cements used to hold the

prisms together and which significantly affect their performance may not withstand

the full range of operating temperatures necessary in power system applications.

In some cases cements can be avoided. In others it may be necessary to choose

nonstandard cements.

Dichroic Polarizers . Dichroic polarizers are those that rely on a difference in

attenuation of orthogonally polarized components. Among the best known and widely

used types are the H and K sheet polarizers which consist of polyvinyl alcohol,

stretched and stained with iodine ( 4-4 , 4-13 ). Sheet polarizers are thin and can

be readily incorporated into sensor configurations without deviating the beam and

in the visible portion of the spectrum can have extinction ratios of 10 14 or greater, more than sufficient for most sensing application.

There are three problems with the use of sheet polarizers in sensors. One is that

they are inherently lossy, with T often being only about 0.6 to 0.7, thus limiting the transmitted power and often ultimately the signal to noise ratio. Second,

most types do not perform well in the near infrared, where most sensors are likely

to operate. Some sheet polarizer types are designed to function in the 800 to 900

nm region, but their extinction ratios and transmittances do not approach that

which can be achieved with prisms at that wavelength. Third, there is concern

about the performance of polymer films over the full temperature range required

for sensors in the power industry, particularly when the exposure to high

temperatures is prolonged.

Dielectric Film Polarizers . Another technique for constructing a polarizer is to

take advantage of the difference in reflectivity of a dielectric surface for

polarization components parallel and perpendicular to the plane of incidence.

Near the Brewster's angle, this effect is strong and is enhanced by using a multilayer coating. However, polarizing beam splitters that use this technique

generally have a specified extinction ratio of only about 100; they are therefore

probably not the best choice for high precision sensors.

Source Properties

In designing a high precision voltage sensor there are basically three considerations related to the source--ampl itude stability, wavelength, and coherence (spectral width).

4-16
Various sources may be used for the development and testing of electro-optic sen- sors, but it is assumed here that practical devices that can be used in the field

will utilize semiconductor sources, either lasers, light emitting diodes (LEDs),

or perhaps superluminescent LEDs. The latter are devices, intermediate between

lasers and LEDs, in which stimulated emission and some line narrowing occur, but

in which the optical feedback is weak, so that oscillation does not build up to

the same degree as in lasers and modes do not appear. They are therefore relatively efficient, low coherence devices.

As pointed out in Section 2, amplitude stability is related directly to sensor

precision, so that, for example, to achieve a sensor that is stable to 0.1 percent, one must stabilize the output power to 0.1 percent. This generally requires

temperature control and feedback control, but is well within present capability.

One is likely to choose a wavelength of operation in the range from 0.8 to 0.9 pm

where GaAlAs lasers are readily available and where high quality silicon detectors

are also available. There is little reason for choosing a specific v/avelength

within this range, though it might be pointed out that the electro-optic coefficient is inversely proportional to wavelength and the sensor will be more sensitive at shorter wavelengths. That functional dependence leads to greater concern

about source stability. A change in wavelength results in an inversely proportionate change in the parameter x in Eq. 2-3, so it seems necessary to achieve a source wavelength stability of the order of 0,1 percent. This is achievable with

the same level of temperature control necessary for amplitude stability.

In addition to concerns with amplitude and spectral stability, there is, assuming

that the fiber used to convey light to and from the sensing element is multimode

fiber, additional concern with the coherence properties of the source. This is

related to a phenomenon known in the field of optical communications as "modal

noise."

A multimode fiber of the sort commonly used in communications supports 10 or 20

mode groups each comprising many discrete modes having, in principle, the same phase velocity. If the coherence length of the source is long compared to the

product of the differences in phase velocity and the propagation time through the

fiber, the modes can interfere at the output of the fiber yielding a complex

intensity pattern. The details of that pattern are highly dependent on the

details of the differences in phase velocity. Because these differences change

4-17
with temperature and mechanical disturbances to the fiber, the details of the output near- and far-field patterns generally vary continuously.

If any mode-dependent loss mechanisms are present (coupling from a fiber through

various bulk components and back into another fiber is a prime example) the

variations in the output patterns will yield noise in the output signals, i.e.,

modal noise. Modal noise is avoided by using a source with a broad spectral characteristic (a low coherence source) and minimizing mode dependent losses. As a practical matter for high precision sensors it is likely that such systems must be

limited to the use of light emitting diodes.

Detector Characteristics

Properly used silicon PIN photodiode detectors are among the easiest and most

stable optical detectors available. Prime consideration in their use is with the

electronics used to control the operating point and load line on their currentvoltage characteristic. For measurement devices, where stability and linearity

are principal considerations, the proper operating point is the origin, with a vertical load line (zero resistance load). Under these circumstances the detector

can be considered to be a current source, directly proportional to the incident

optical power.

The desired conditions are most easily met using an operational amplifier in

transimpedance mode (Figure 4-5). The output voltage of this amplifier is related

to the input current by the expression

v out Un Rf (4-12)

where Rf is the feedback resistor. In this case there are three factors related

to stability—the responsivity of the detector, the feedback resistor, and the

input offset characteristics of the amplifier. All three of these can be adequately addressed by temperature control, and in the case of the last two, suitable choice of components.

Fiber Characteristics

One aspect of fiber selection has already been addressed above in the discussion

of modal noise. Others include design for efficient transmission of light through

the bulk components and the polarization properties of fiber.

4-18
'out

4-5. Current mode (or trans impedance) operational amplifier following a photodiode detector. Principal noise sources, shot noise associated with the average

detector current, Johnson noise associated with the feedback resistor, and amplifier input voltage and current noise, are shown. Signal input and output are related by Eq. 4-12.

Coupling of light from a fiber, through bulk components that are long compared to

their aperture, and into another fiber is the subject of an appendix. Basically,

the design is easier if the input fiber has as small a core as possible and the

output fiber as large a core as possible. Purely from the standpoint of transmitted light, using a single mode fiber for the input and a relatively large

multimode fiber for the output would thus be appropriate. Depending on the

source, however, other considerations, for example, the efficiency with which

light can be coupled into a single mode fiber from an LED may dominate.

Polarization properties of the fiber generally become important only when a polarized source is used, but this includes many laser diodes. Multimode fiber largely

depolarizes light, but not completely, so that when polarized light is passed

through a multimode fiber and then through a polarizer, significant amplitude

noise occurs. If a polarized source must be used, another choice is to use polarization maintaining single mode fiber between the source and the sensor and avoid

an input polarizer at the electro-optic crystal.

FACTORS LIMITING THE PRECISION OF PLANAR WAVEGUIDE SENSORS

In the long term, planar waveguide sensors, such as those described in Section 3, are likely to provide very attractive sensor characteristics. At the present

time, however, almost all devices of the sort shown in Figure 3-5 are being produced in LiNbO . As pointed out above, LiNb0

3 is a very unattractive material for

stable devices, because of its high birefringence, and strong temperature dependence, and because it is pyrcelectric.

4-19
High precision planar interferometric sensors will require the exploitation of

other materials, the most likely being the same group suggested here for bulk sensors. Of these, GaAs and related compounds are already the subject of substantial

research. If and when devices in these materials are developed, the fundamental

limits to performance should be the same as those described for bulk sensors of

the saine materials. The advantage in the avoidance of bulk components is significant; sensitivity and speed should be enhanced.

TEMPERATURE COMPENSATION TECHNIQUES

Waveplates

A 1970 patent (4-14 ) suggested that it should be possible to produce a temperature

compensated waveplate by using two different birefringent materials having

different temperature coefficients of their retardance. If the two materials have

temperature dependences of the opposite sign they may oriented with their

respective fast and slow axes aligned. However, since waveplates made from most common materials exhibit a decreasing retardance with increasing temperature, it

is necessary to align the fast axis of one with the slow axis of the other.

The proposal of reference ( 4-14 ) was incomplete in that it did not take into

account the thermal expansion of the material, a significant contribution to the

change in retardance with temperature, and apparently never resulted in an actual

device. We have recently revised the analysis and produced a specific design

using two readily available materials, quartz and magnesium fluoride.

The design is achieved by setting the difference in retardance of the two plates

equal to the desired value and the temperature dependence of the composite plate

to zero. Thus for a quarter-wave plate

S

l - 62 = it/2 (4-13)

and

Tl 6! - Yl 6

2 = (4-14)

where 6 and 6 are the retardances of the two elements and

i d6i i dBi i dh

i Y, = 7-TT-= 5"^ + Z--JT (4-15)

1 6

1 dT Bt dT h

1 dT

4-20
6 =142.5

6 = 52.5

S MgF2

Quartz

4-6. Design for a temperature-compensated quarterwave plate using quartz and mag- nesium fluoride. Each segment is assumed to be a compound zero-order waveplate.

1 d6

2

I dAn

2

I dh

2 Y

2 " J~2 ~dT

= An7 dT

+ h^ dt~

(4-16;

The desired results are

Y 2

1 2 Y 2 " *i

(4-17)

and

6 -1 ^

2 2 Y 2 " Y X (4-is;

For the two materials quartz and MgF the results are shown in Figure 4-6.

The production of such a device is made more difficult than might be expected by a greater than desired uncertainty in the numerical value of y for quartz and

because the retardance of a compound plate is significantly dependent on the angle

of incidence.

4-21
Electro-optic Crystals

A temperature compensation scheme for electro-optic crystals that is similar to

that used for waveplates can also be contemplated. Recall from above that the

induced retardance of an electro-optic of class 43m is given by

r = h. n 3ru1 h E = C E. (4-19)

A ^ eo

If we consider two different crystals in series but rotated about the direction of

propagation by 90 deg to each other, the net induced retardance is

r

n

= i-j - r

2 (4-20)

which must be non-zero. At the same time we would like

dr

i dr 2

= (4-21)

dT dT

where for each component

1 dr 3 dn 1 dr,+

1 1 dh (A „„. - — = - — + -=- + 7- -= = £. (4-22)

r dT n dT r 41 dT h dT

This leads to the requirement that

n

i ?2 c? __

e0

2 1 eo l

and the result that

(4-23)

I 2 r - C 2 [ 1] (4-24)

n eo2 S x

which is the effective electro-optic coefficient of the combined crystals.

This technique has not been attempted experimentally, yet, because more data are needed on possible crystals, but the concept seems promising.

4-22
PROGNOSIS FOR HIGH PRECISION VOLTAGE SENSORS

The two most critical elements in determining the precision of an electro-optic

sensor are the electro-optic crystal, itself, and the waveplate.

We have been able to show that for most purposes, the stability of a Fresnel-romb

quarterwave plate will be adequate and that when the use of that device is not

possible or adequate, temperature compensated birefringent waveplates should, in

principle, be still better.

Obtaining data on the properties of electro-optic materials has proven more difficult than expected at the beginning of this study. Nonetheless, we have been able

to show that, because of the temperature dependence of the refractive index and of

the dimensions of various promising crystals, the precision of a sensor of the

sort shown in Figure 3-1 can not be appreciably better that 1 percent over a 100°C

temperature range. On the other hand, informal reports of experimental work elsewhere suggest that a precision not much worse than that may be achieved.

To reach a precision of 0.1 percent over 100°C will clearly require some sort of

temperature compensation. The principles of a temperature compensated device have

been described above. The practicality of such a device will depend on further

understanding of the properties of promising materials.

Some work in this area has already occured [4-15]. In the crystal Bii2Ge02o it

has been shown that an internal temperature compensation can occur by balancing

the temperature dependence of the electro-optic effect with the temperature dependence of the optical activity present in this class 23 crystal.

REFERENCES

4-1. Amnon Yariv and Pochi Yeh. Optical waves in crystals . John Wiley, 1984.

4-2. Ivan P. Kami now. An introduction to electrooptic devices . Academic Press,

1974.

4-3. J. F. Nye. Physical properties of crystals . Oxford, 1960.

4-4. "Landolt-Bornstein, Aahlenwerte und Funktionen aus Naturwissenschaften und

Technik." Neue Serie, K.-H. Hellwege, Ed., Gruppe III: Bandll , Elastische, piezoelektrische, pyroelektrische, piezooptische, elektrooptische Konstanten un nichtlineare dielektrische Suszeptibilitaten von Kristallen . Springer Verlag, 1979.

4-5. M. Kanoi, et al. "Optical voltage and current measuring system for electric

power systems." IEEE Power Engineering Society Summer Meeting, Vancouver, BC

Canada, 1985.

4-23
4-6. G. A. Massey, D. C. Erickson, and R. A. Kadlec. "Electromagnetic field com- ponents: Their measurement using linear electrooptic and magnetooptic effects."

Appl. Opt. , 1975, vol. 14, p. 2712.

4-7. Handbook of optics , Optical Society of America/McGraw Hill, 1978.

4-8. P. D. Hale and G. W. Day. "The selection of linear retarders (waveplates)

for use in high precision electro-optic sensors and other polarimetric systems,"

to be published.

4-9. M. Born and E. Wolf. Principles of optics . Pergamon Press.

4-10. D. A. Holmes. "Exact theory of retardation plates." J. Opt. Soc. Amer. , 1964, vol. 5, p. 1115-1120.

4-11. See for example, E. Hecht and A. Zajac. Optics . Addison Wesley, 1980.

4-12. Product literature. Meadowlark Optics, 7460 East County Road, Longmont,

Colorado 80501.

4-13. The Polaroid Corp. Polarizing filters . Spectral photometric data.

4-14. U.S Patent No. 3529885.

4-15. T. Mitsui, K. Hosoe, H. Usami , and S. Miyamoto. "Development of fiberoptic voltage sensors and magnetic-field sensors." IEEE Power Engineering Society

Summer Meeting, Mexico City, Mexico, 1986.

4-24
Section 5

CRITICAL EVALUATION OF MAGNETO-OPTIC SENSOR TECHNOLOGY

FACTORS LIMITING THE PRECISION OF BULK MAGNETO-OPTIC SENSORS

The Verdet Constant of Bulk Materials and its Temperature Dependence

The magneto-optic properties of materials have not been studied or tabulated to

the same degree as have the electro-optic properties. One of the best compilations is in an unpublished report prepared by M. J. Weber of Lawrence Livermore

Laboratory and issued in 1981 (5-1 ). In it, data on 34 glass and crystalline

materials are reviewed. Of particular interest is rarely available data on the

spectral dependence of the Verdet constants of these materials. Other useful com- pilations can be obtained from the Schott Glass Company (5-2,5-3).

Of primary interest in this study is the variation of Verdet constant with temperature. Temperature coefficients in paramagnetic materials have been widely

studied and it is generally accepted (5-1 ) that the Verdet constant of these materials can be expressed as a function of temperature (for temperatures well above

absolute zero) as follows:

V(T) = V dia (T) + V par

/T, (5-1)

where V d i a is attributable to diamagnetic effects present in all materials, V par

is attributable to the presence of a paramagnetic ion, and T is absolute temperature. By convention in the definition of the Faraday effect V dia is positive and

V par is normally negative. When fairly large densities of paramagnetic ions are

present V« a ^ becomes the dominate parameter yielding a negative Verdet constant

that varies inversely with absolute temperature, i.e., of the order of 0.3 percent/^ near room temperature. This large coefficient is unacceptable for high

precision sensors and leads generally to the use of materials that show only a diamagnetic effect. Unfortunately, the temperature dependence of V dia for most

materials is unknown, beyond the fact that it is small compared to that of paramagnetic processes and can often be ignored (5-4).

5-1
\lery recently, some reports of the variation with temperature of the Verdet con- stant of a few diamagnetic materials have appeared in the literature. These are listed in Table 5-1.

Table 5-1

TEMPERATURE DEPENDENCE OF THE VERDET CONSTANT

FOR SEVERAL MATERIALS

Material 1 dV

V dT

x(um) Ref.

ZnSe 2.5 x 10"1* 0.87 a

ZnSe <1.4 x 10" 1* 0.82 b

Bii2Si020 1.5 x 10 _!t 0.87 a

Bi i2Ge02o <2.8 x 10"^ 0.85 b

SF6 glass <0.9 x 10"-4 0.87 b

a T. Mitsui, K. Hosoe, H. Usami , S. Miyamoto. Development of Fiber-optic Voltage

Sensors and Magnetic Field Sensors. IEEE Power Engineering Society Summer Meeting, Mexico City, Mexico (1986).

b 0. Kamada, et al . Matsushita Electric, Moriguchi, Osaka 570, Japan, private com- munication.

To supplement these data, we have, during this study, constructed a measurement

system to measure the Verdet constant of various bulk materials versus temperature. A diagram of that system is shown in Figure 5-1. The system is based on a large electro-magnet with a field region of about 15 cm long by 10 cm diameter,

capable of producing a magnetic flux density of about 0.5 T. A small nonmagnetic

oven, capable of heating a sample as long as 10 cm is located in the field region,

Light from a laser makes two passes through holes in the pole pieces of the magnet. Its rotation as a function of magnetic field is determined for about 10

field values and 5 to 10 temperatures between room temperature and 120°C. Figure

5-2 shows an example of rotation versus field data for a particular material and

temperature. Figure 5-3 shows an example of Verdet constant versus temperature

data for a particular glass.

5-2
P c

Sample

In oven )

BS

S-D P D Magnet

5-1 Measurement system for determining dV/dT. C—Chopper, P—Polarizer,

M--Mirror, BS--Beam Splitter, D--Detector. Light makes two passes through the

sample, doubling the rotation.

120

oD

o 80

o

40 -

/

Bdl (T cm)

5-2 Rotation versus magnetic field for a sample of SF-57 glass at 25°C. Sample

was approximately 10 cm long.

5-3
12.1

Eo—

.

01 •o

oo

>

11.8 45 63 81

Temperature, C

5-3 Verdet constant versus temperature for a sample of SF-57 glass. Error bars

represent a one standard deviation uncertainty in the slope of curves of the form

shown in Figure 5-2.

To date, we have focused on two glasses, a lead silicate (flint) glass known com- mercially as SF-57 and fused silica in a grade known commercially as Suprasil.

Our best evaluation of the temperature coefficients of these materials to date are given in Table 5-2. These data suggest that, all other problems being solved, a precision no better than +1 to 2 percent over a 100°C temperature range should be

possible with a sensor design similar to those shown in Figures 3-11 and 3-13.

Other materials are being studied to determine if smaller values of dV/dT can be

found.

One may consider ways to predict the value of dV/dT for various diamagnetic materials from other, more readily available information. The Becquerel equation,

derived in the early part of this century using classical physics (i.e., without

quantum theory) is useful in predicting the Verdet constant of various materials

(5-1 ,5-5) It is given in SI units by

e\\i dn_

2mc dx (5-2)

5-4
Table 5-2

TEMPERATURE DEPENDENCE OF THE VERDET CONSTANT FOR TWO GLASSES

Material

SF57

SiO„

1 dV

V dT

(10

-4,

2.8

2.2

x(ym)

0.633

0.633

where e is the electronic charge, X is the wavelength, m the effective electron

mass, c the speed of light, and dn/dx is the dispersion of the refractive index.

Predictions based on the Becquerel equation are usually somewhat too large, but can be made to agree if the predicted value is multiplied by a factor, sometimes

known as the magneto-optic anomaly, and which is nearly constant for a given class

of materials. The magneto-optic anomaly typically takes values between 0.6 and

0.9 for glasses.

One might expect, from Eq. 5-1, that the temperature dependence of the dispersion

of the refractive index would be a good predictor of the temperature dependence of

the Verdet constant. The dispersion at different wavelengths and temperatures is

often available in glass catalogs. We have used these to compute dV/dT for

several materials. The predictions are found to be of the same order of magnitude

as our measurements, but further work is required before final conclusions can be

drawn.

Stress-Optic Effects in Bulk Materials

Because the presence of linear birefringence adversely affects the Faraday effect

and because stress in a material, either residual stress arising during fabrication or externally applied, can cause linear birefringence, it is desirable to

choose materials for sensors that have a small stress-optic effect.

In isotropic materials such as glass, the stress-optic effect is much more easily

described than in crystals. The birefringence induced by applying a uniform pressure P transverse to the direction of propagation (Figure 5-4) is given by

5-5
An = CP (5-3)

where An is the difference in refractive index between the components of transmitted light parallel to and perpendicular to the applied stress, C is the stressoptic coefficient, normally in units of TPa" 1 (1 terapascal is equal to 10 12 N/m2

and is the same as the historical unit called a Brewster), and P is the applied

pressure in Pa.

Table 5-3 gives representative values of the stress-optic coefficient for several common glasses. The values range over approximately two orders of magnitude with

fused silica having one of the largest values and SF-57 one of the lowest. SF-57

is in fact a good approximation of the so-called Pockels glass ( 5-6 ) which

resulted from the observation that within the lead silicate glass family it was possible to prepare glasses with either positive or negative stress-optic

coefficients and that therefore it might be possible to prepare a glass with zero stress-optic coefficient. Because it also has a relatively high Verdet constant,

it therefore becomes one of the leading candidates for bulk Faraday current

sensors.

Source Properties: Spectral Stability

With regard to source requirements, magneto-optic devices differ from electrooptic devices only in the spectral dependence of the Verdet constant. The Verdet

constant is dispersive, as suggested by the above stated Becquerel equation, and

may be modeled with varying degrees of accuracy by any of the traditional material

dispersion formulas. A relatively simple and often used formula is (5-1 )

V < A

> = xTTTT {5 "4)

where K is a constant and x t is a wavelength, typically in the ultra-violet portion of the spectrum. Experimental data fitted to this equation yield values for

the two parameters. One may differentiate Eq. 5-1 with respect to wavelength,

yielding

T

= uf~T2-y

dx - (5 " 5)

5-6
PCPa]

5-4 Configuration for studying the stress-optic effect in isotropic materials.

such as glass. A uniform pressure is applied normal to the direction of

propagation resulting in a change of refractive index both for light polarized

parallel to the direction of the pressure and perpendicular to it. The difference

in these refractive indices under applied stress is the induced birefringence.

Table 5-3

VALUES OF THE STRESS-OPTIC COEFFICIENT FOR

SEVERAL COMMON GLASSES

Glass CCTPa -1

) Ref,

BK-7 2.74 a SF-6 0.63 a SF-57 0.03 a SF-59 -1.46 a Si02 -3.36 b 7070 -4.6 b 8363 1.1 b

d 0ptical Glass, Schott Optical Glass, Inc., York Ave., Duryea, PA 18642,

bAmerican Institute of Physics Handbook, McGraw Hill, 1972.

5-7
A reasonable first approximation for wavelengths substantially greater than x t is

or

dV

= l!dX (5 . 7)

V X

The bandgap of a semiconductor material shifts with temperature by an amount that

depends on the specific material but which is of the order of 10""V°C. This suggests that sources for high precision MO sensors must be temperature stabilized to

about 0.1°C to achieve a precision of 10" 3

, a not particularly difficult requirement. It has not been possible during this study to evaluate the possibility of

long term shifts in the operating wavelength of semiconductor devices. To our knowledge no such effects have been reported.

Other Components

The other components found in magneto-optic sensors—polarizers, lenses, detectors, etc. --have basically the same performance requirements in a magneto-optic

sensor as in an electro-optic sensor. The reader is therefore referred to Section 4 for information on those parameters.

FACTORS LIMITING THE PRECISION OF OPTICAL FIBER MAGNETO-OPTIC DEVICES

Relevant Properties of Optical Fiber

Essentially all efforts to produce a magneto-optic sensor in which the Faraday

effect in an optical fiber is utilized have involved single mode fibers of the same basic type as those used for communications. These consist primarily of

fused silica, with various dopants incorporated to achieve the required guidance

and propagation characteristics. The only attempt that we are aware of to measure

carefully the Verdet constant of various fibers were undertaken in our laboratory

prior to the beginning of this study. A measurement system, shown schematically

in Figure 5-5, was constructed and several different types of fiber were measured.

Differences between the Verdet constants of the fibers and pure fused silica of

several percent were found but as yet no correlation between the known compositions and guidance characrteri sties of the fibers and the variations in Verdet

constants have been found. Because silica and the other dopants commonly used in

fiber are all diamagnetic we expect the temperature dependence of the Verdet

5-8
Verdet Constant Measurement System

}fe=§H

Dither Coil

Polarized Laser Polarizer Solenoid

DVM

Polarize

Detector

anzer

OSC

Lock in

Constant

Current Supply

5-5 Measurement system for determining the Verdet constant of optical fiber. It is based on a 1-m long solenoid having approximately 3000 turns and operated at 30 A. Polarizers are oriented manually to determine rotation, the identification

of a null being facilitated by the use of a dither coil and a lock-in amplifier.

Shape(form) birefringence

cladding

y axis = fast axis

increases with a/b, An

5-6 Geometry of form birefringence in an optical fiber. The fast axis is the

minor axis of the ellipse. The magnitude of the birefringence increases with the

ellipticity and with the difference in refractive index between the core and

cladding.

5-9
constant to be similar to that of bulk diamagnetic materials. We also expect, and

have observed with the apparatus in Figure 5-5, variations of the Verdet constant

with wavelength that are consistent with the properties of the bulk materials. The

major fundamental difference in using fiber rather than bulk materials is that the

waveguiding propagation characteristics of the fiber can have a very significant

effect on the polarization state of light propagating through it. This, in turn,

complicates the simple picture of the Faraday effect presented previously, and in severe cases effectively quenches the Faraday entirely. A complete picture of the

polarization properties of optical fiber would be too extensive to present here

( 5-7 ). However, because of the importance of these considerations in sensor

design, the basic considerations are discussed below. The basic concept is that a so-called single mode fiber, that is one that supports only a single spatial mode,

in fact supports a pair of orthogonal polarization states, which in general have

slightly different phase velocities. It is therefore, more precisely, a two mode

fiber. The reason is a lack of perfect circular symmetry, geometric or otherwise,

in the fiber either as it was manufactured or because of externally applied perturbations. If the core of a fiber is slightly elliptical (Figure 5-6) it will

exhibit what is known as "form birefringence." Form birefringence is a difference

between the phase velocities of light polarized parallel to the minor axis of the

ellipse and that polarized parallel to the major axis. The minor axis is the

"fast axis." The degree of ellipticity and the difference in refractive index

between the core and cladding determine the amount of birefringence present.

Fibers in which the circular geometric symmetry is imperfect also exhibit "stress

birefringence." This is a result of the fact that the various layers of the fiber

structure have different thermal expansion characteristics and thereby cause an inherent radial stress. Through the stress-optic effect, additional birefringence

appears, having the same axes as the form birefringence, and the two add algebraically. It is possible, through careful design and manufacturing techniques, to

produce a fiber in which the form and stress birefringence is very low (^S.)*

However, even these fibers dre subject to birefringence induced by external

effects (5-9 ), the most important of which is bending. Bending introduces asymmetrical stress into the fiber that causes birefringence of magnitude

K. 2 ^b

= y- £r rad/ m ( 5 ~ 8 )

where K

b is a (slightly wavelength dependent) constant equal to about 0.85, X is

wavelength, r is the fiber radius, and R is the bend radius (Figure 5-7). The

fast axis is in the plane of the bend. If the fiber is bent under tension, as for

5-10
Bend-Induced Linear Birefringence

Ap=7.7 x 10 7

r 2 /R 2 deg/m

AJ$ = 4.8 x 10 8

r 2 /R deg/turn

633 nm

400r

m 200 o

a.<

r s 62.5 tim

R. cm

5-7 Geometry of bend-induced birefringence in single mode fiber and a numerical

illustration for 125 ym diameter fiber at a wavelength of 633 nm.

example by winding it tightly around a coil former, there is an additional component to the bend birefringence, sometimes called "tension coiled birefringence"

that takes the form

K. A3

tc —tc r

- e rad/m,

A K Z (5-9)

where K

tc is another (slightly wavelength dependent) constant equal to about 3.1

and e z is the longitudinal strain. As might be expected, transverse stress also

induces linear birefringence in a fiber. The magnitude is given by

K

f

Af3 p

* \r rad/m (5-10)

where f is a line force (units of newtons/meter) and K_ is approximately 3 x 10 11 .

Experience suggests that all of these effects are significant in determining the

stability of a fiber current sensor. Tension coiled birefringence and transverse

stress can be largely avoided through proper mechanical design. Bend

5-11
birefringence is more difficult to avoid. To determine the magnitude of the

problem, one must compute the transfer function of a fiber sensor under various

conditions.

The method of computation ( 5-10 ) is to use Jones calculus, a matrix technique of

describing the changes in polarization state of light as it passes through anisotropic materials. The equation relating the polarization state at the output of a fiber current sensor to that at the input is as follows:

E (z) xVz)

<J>z . A8 . d>z 2F . *z

C0S ^-J 7~ sin r T sin 2-

|L 5 in^ cos-^+j^sin^

<P C c. CD C

E (0)

Ey

(0)

(5-11)

where

(W

• AS- (f)2 + (F)2 ;

E x and E y are the components of the optical electric field in and perpendicular to

the coil, A8 is the linear birefringence per unit length of fiber, and F is the

induced Faraday rotation per unit length.

Utilizing Eqs. 3-3 and 5-10 it is then straightforward to compute the transfer

function for various coil configurations and polarizer orientations. Figure 5-8

shows the result for two sensor designs, the coils having different diameters and

number of turns and the polarizer configuration being that of Figure 3-7. In each

case the transfer function is distorted for relatively low currents but approaches

the ideal when the current becomes sufficiently large.

One technique for minimizing the effect of linear birefringence is to twist the

fiber (5-11 ). Twisting introduces a torsional stress that, again through the

stress-optic effect, causes a rotation of the plane of polarization in addition to

the Faraday effect. In terms of the transfer function, it can be seen in Figure

5-9 that the effect is to shift the distorted portion of the transfer function

away from the origin. For coils with diameters of about 10 cm or greater, it is

usually possible to introduce enough twist to cause the slope at the origin to be

effectively equal to that which would be measured without linear birefringence.

The problem is that the twist-induced rotation is temperature dependent, which means that the origin (i.e., the parameter 
 in Eq. 2-2) shifts with temperature.

5-12
R(I)

-_ 1.0

R(I)

-^ 1.0

-1.0 JL *w*

5-8 Transfer functions for two fiber current sensor configurations showing the

effect of bend birefringence. Dotted curves assume no birefringence; solid

include only bend birefringence, (a) 1 cm diameter coil, 1 turn; (b) 10 cm diameter coil, 10 turns. Both cases: 125 ym diameter fiber, wavelength 633 nm.

5-13
" (I) T 1.0

I, MA

R(I)

5-9 Transfer functions for the two coils of Figure 5-8, but with twisted fiber,

(a) Twist rate 40 turns/meter; (b) twist rate 10 turns/meter. All other

parameters same as Figure 5-8.

5-14
laser

high birefringence fiber

detectors

fiber

polarizer conductor

polarization

splitter

low or circularly

birefringent fiber

5-10 Possible configuration of an all-fiber current sensor.

An alternative technique is to relieve the bend induced birefringence by annealing

( 5-12 ). In this case the fiber is formed into the desired sensor configuration

and then heated to temperatures of up to 800°C. After slow cooling, the birefringence of the coil is found to be greatly reduced. To date, coils as small

as 3 cm diameter with as many as 20 turns have been annealed in our laboratory

with reductions in birefringence by more than two orders of magnitude.

It is difficult to make general statements about the magnitude of linear birefringence that can be tolerated in a high precision current sensor. In relatively

low precision sensors, a linear birefringence of roughly 50 deg, total, can generally be accepted without appreciable decrease in response. If the total birefringence is stable with temperature, it may be possible to accept nearly as much

in high precision devices.

Another aspect of the problem with linear birefringence in fiber current sensors

is that stress resulting from vibration or acoustic disturbances introduces noise

into the sensor output. Mechanical design thus becomes critical in isolating the

fiber from these perturbations.

5-15
Other Fiber Components

The optical fiber current sensor shown diagramatically in Figure 3-12 suggests

that bulk polarization components might be used in conjunction with the fiber. In fact, one of the greatest long term attractions of a fiber current sensor is the

possibility of producing an all-fiber system. Such a system is indicated in Fig- ure 5-10. All of the components required have been demonstrated in research

laboratories and most are available commercially.

Several types of fiber polarizers have been demonstrated experimentally (5-13 ).

Of these, a design based on differential attenuation in a fiber with high linear

birefringence is the only one available commercially. The requirements placed on the polarizer in this case are relatively mild and should be met acceptably by

existing devices.

Polarization maintaining fiber (5-7 ) is used in the leads to the sensor coil.

This is fiber designed to have a ^ery high linear birefringence by deliberately

avoiding cylindrical symmetry. If the birefringence is \/ery large compared to any

externally caused effects, linearly polarized light propagating along one of the

axes of birefringence will remain linearly polarized. Polarization maintaining

fiber is manufactured by several companies and is readily available.

Polarizing couplers are a more difficult problem. While demonstrations of principle have been achieved no practical devices are available ( 5-14 ). Two alternatives exist. One is to use a normal, nonpolarizing coupler and two fiber polarizers. This has the disadvantage of wasting half of the optical power and is subject to possible problems with changes in the coupling ratio with temperature.

The other is to detect only one polarization, thereby obtaining a transfer function of the form shown in Figure 2-1. The disadvantages of this approach were discussed in Section 2.

Source and Detector Considerations

A semiconductor laser would likely be used in an all-fiber current sensor to take

advantage of the improved coupling between source and fiber. The higher coherence

is not expected to be a problem, with the exception that optical feedback from the

system into the source must be avoided to minimize amplitude noise. Otherwise,

the same source and detector requirements apply as in the case of the other

configurations.

5-16
Temperature Compensation Techniques

In principle, a temperature compensated current sensor is more difficult to con- ceive that a temperature compensated field sensor because the current sensor is

basically a distributed sensor, integrating the magnetic field around the conductor. Two possible approaches can be considered, however.

One possibility is to investigate new materials or material combinations in which

dV/dT would be very small. Recent work in that direction [5-15] using mixtures of

Yttrium Iron Garnet (YIG) and Terbium Iron Garnet (TbIG) which have temperature

dependences of opposite signs. Preliminary data indicate that the Verdet constant

of the resulting mixture, (Yi_ x Tb x ) 3 Fe 5 12 , varies with temperature by much less

than 1 percent over the temperature range from 300 to 415°C when x = 0.19. This

material is ferromagnetic and exhibits saturation which makes it less than ideal

for sensors, but it may be possible to extend the technique to other materials.

The second possibility is to define carefully and maintain the geometry of the sensor so that the sensing material need not be homogeneous. The optical path

could then consist of several segments of two or more materials that have opposite

signs of dV/dT. Such a device would not, in principle, be immune to stray fields

from nearby conductors, but both that problem and the need to maintain the geometry can be addressed by increasing the number of segments. A greater question is

whether diamagnetic materials can be found that have a negative dV/dT. If not it

may be necessary to use paramagnetic materials which would limit the temperature

range over which the balancing could be maintained.

Prognosis for High Precision Current Sensors

Eventually, most magneto-optic current sensors will be of the all-fiber type. The

advantages include reduced size, greater flexibility, better sensitivity,

avoidance of alignment problems, etc. and are significant. The technology is

progressing steadily. It has already reached the stage where fiber current sensors are the preferred technology for certain types of applications, including

pulsed current measurements and other situations where precision requirements are

not severe. However, it is not yet possible to design, from readily available

components, a sensor that will meet high precision requirements. With further,

foreseeable progress in controlling the polarization properties of fiber it should

be readily possible to achieve a sensor with a precision of around

5-17
2 percent over a temperature range of 100°C. This would be limited by the temperature coefficient of the Verdet constant in fused silica. Progress beyond that

will require significant study of fiber materials.

For now and probably for the next few years high precision devices can be achieved

more easily with bulk components than with fibers. Enough is now known about

design principles to produce sensors that have a precision limited by the temperature dependence of the Verdet constant. A good choice of material for this purpose is the SF-57 glass, for reasons given previously. It is inexpensive and

readily formed into desired component shapes. Based on measurements reported

here, the calibration of such a device would remain constant to within about ±1

percent. Temperature compensation schemes must be employed to provide a sensor

with a better precision. These are feasible, but more difficult than for electric

field/voltage sensors.

5-18
References

5-1. M. J. Weber. Faraday Rotator Materials . Lawrence Livermore Laboratory,

June 1982.

5-2. Optical Glass . Schott Optical Glass Inc., Duryea, PA 18642.

5-3. "Faraday effect in optical glasses, The wavelength dependence of the Verdet

constant." Technical Information number 17, Schott Gleswerke, Mainz, F. R. Germany.

5-4. Herbert Piller. "Faraday Rotation," Ch. 3 in Semiconductors and Semimetal^, Vol. 8, R. K. Willardson and A. C. Beer, Eds. Academic Press.

5-5. A. Sommerfeld. Optics . New York: Academic Press, 1964, Chapter III, Section 20.

5-6. G. W. Morey. Properties of Glass . Reinhold Co., 1938.

5-7. S. C. Rashleigh. "Origins and control of polarization effects in singlemode fibers." IE EE J. Lightwave Tech ., 1983, vol. LT-1, p. 312-331.

5-8. D. N. Payne, A. J. Barlow, and J. -J. Ramskov Hansen. "Development of lowand high-birefringence optical fibres." IEEE J. Quantum Electron ., 1982,

vol. QE-18, p. 477-488.

5-9. G. W. Day. "Birefringence measurements in single mode optical fiber."

Proc. SPIE 425 , 1983.

5-10. G. W. Day, L. R. Veeser, G. I. Chandler, R. W. Cernosek. "Progress in the

design of optical fiber sensors for the measurement of pulsed electric cur- rents." Proc. Workshop on Meas. of Elect. Quant, in Pulse Power Systems,

1986, Gaithersburg, MD.

5-11. S. C. Rashleigh and R. Ulrich. "Magneto-optic current sensing with birefringent fibers." Appl. Phys. Lett ., 1979, vol. 34, p. 768-770.

5-12. G. W, Day and S. M. Etzel . "Annealing of bend-induced birefringence in

fiber current sensors." Techni c al Digest , 11th European Conference on Optical Communications/5th Internatio"haT~Conference on Integrated Optical

and Optical Communications ., 1986, Venice.

5-13. See, for example: L. Li, et al. "Low cost metal/glass fibre polarisers

produced in continuous lengths." Proceedings, 4th International Conference

on Optical Fiber Sensors, 1986, Tokyo. K. Bohm, et aK "Simple metal

cl added fibre pofarizerT" Ibid. M. P. Varnham, et al . "Coiled birefringent-fibre polarisers." Electron Lett ., 1984.

5-14. I. Yokohama, K. Okamoto, and J. Noda. "Fibre-optic polarizing beam splitter employing birefringent-fibre coupler." Electron. Lett ., 1985, vol. 21,

p. 415-416.

5-15. 0. Kamada, Y. Tsujimoto, and Y. Hayashi . "Fiber-optical current sensors using mixed rare-earth iron garnet crystals." Proceedings, 3rd Sensor

Symposium , (sponsored by IEE, Japan) Tsukuba, 1983.

5-19

Section 6

SUGGESTED APPROACHES TO THE DEVELOPMENT OF

HIGH PRECISION OPTICAL CURRENT AND VOLTAGE SENSORS

During the course of this study it has become apparent that if high precision

optical current and voltage sensors are to be developed and introduced into power

systems, the process will be evolutionary. In this section we suggest and discuss

three areas where increased emphasis would accelerate progress toward these goals.

1. The engineering and field testing of moderate precision current

and voltage sensors specifically for power system configurations.

Based on our own work and on discussions with a number of manufacturers, we believe that it is possible to produce both current and voltage sensors that offer

many of the advantages of optical sensors—high bandwidth (including dc), freedom

from interference, small size, safe operation, modest cost, etc. --and moderate

precision (roughly ±1 percent over a 100°C temperature range) using technology

that has already been demonstrated in the laboratory or early prototypes. Such

devices, fully suitable for use in the field, have not yet been produced but could

be provided fairly quickly by several potential vendors, both domestic and

foreign. Some technical issues remain to be resolved and would form the basis for

final design and testing. These include

o Basic engineering design—configuration, placement,

structure, insulation, etc.

o Transient temperature stability

o Vibration sensitivity

o Interface to existing instrumentation

2. The development of passive temperature compensation techniques

for both voltage and current sensors.

If optical current and voltage sensors are to achieve a precision of the order of

0.1 percent over a temperature range of 100°C or greater, it is now clear that

some form of temperature compensation must be used. Passive techniques—those in

which the different properties of materials and components are exploited, rather

6-1
than measurement and adjustment or temperature control --are to be preferred for

their simplicity and therefore cost. In this document we have proposed several

such passive temperature compensation schemes. These need to be investigated further, including

© Accumulation of more data on the temperature coefficients

of the linear electro-optic effect and the Faraday effect

o Laboratory demonstration of a temperature compensated

electro-optic device

© Further analysis of schemes for temperature compensation

in magneto-optic devices

3. Research and development on special fibers, fiber components,

and planar waveguide electro-optic components.

We believe that, eventually, optical current sensors will be all-fiber devices and

that the only non-fiber component in a voltage sensor will be an electro-optic

crystal which will appear as a guided wave component. Such sensors will offer

significant advantages in configuration, size, and cost. Optimism that they can

be produced is based on recent rapid advances in the understanding and control of

the polarization properties of fiber, the development of several new fiber types,

and progress in planar waveguide technology. Three main areas of attack are suggested, as follows:

o Development and refinement of fiber components—circularly

birefringent fibers, fiber polarizers, fiber couplers, and

polarization splitters

© Investigation of the stability of such devices

© Fabrication and study of planar electro-optic modulators

in 43 m crystals

6-2
Section 7

SUMMARY

We began this study and this report with the central question, "What precision can

be achieved with an electro-optic voltage sensor or a magneto-optic current sensor?" We have pursued the answer in numerous ways—through an investigation of

the basic properties of materials and components, both as reported in the

literature and new data generated in our laboratory, through attempts to

demonstrate the feasibility of overcoming certain limitations in the properties of

components, through analysis of some fundamental limitations, through the proposal

of new or refined designs, and through discussions with numerous other

investigators.

We conclude that ease of obtaining high precision (in a power systems context) is

not included among the many advantages of using optical sensors for measurement of

electromagnetic quantities. The principal difficulty is with the necessity of

designing sensors that will maintain their calibration over extremely broad temperature ranges (at least 100°C) without the possibility of temperature stabilization. We find, specifically, that using relatively standard approaches and an appropriate definition of precision, a precision not better than about +1 percent

can be expected. Achieving that level will require wise choices of materials,

components, and design, but we have been able to offer numerous suggestions in

this regard.

Judgments about the commercial viability of such devices should perhaps be left to

those more expert in that subject than we. We should remember, however, that

worst case situations are encountered infrequently, and therefore represent pessimistic assessments of performance in real applications. We also suspect that the

other advantages of optical sensors may in some applications be dominant considerations. Safety is one example.

We are very optimistic about improving the precision of optical sensors by a desired order of magnitude or more, principally by investigating passive temperature compensation techniques. We have examined several of these analytically, and

7-1
suggest that they be further investigated. Other approaches, including temperature compensation by measurement and adjustment, could be considered, but were not

discussed here. We are also optimistic about the development of all-fiber or nearly all -fiber sensors that could provide very simple, low cost measurements,

even if the highest precision is not achieved, and have suggested further work in

that area.

7-2
Appendix A

NOISE ANALYSIS FOR ELECTRO-OPTIC OR MAGNETO-OPTIC SENSORS

To examine the limitations imposed by noise on the precision of a sensor we assume

that the sensor configuration is such that there are two detectors, one providing

a transfer function of the form

R(x) = A sin 2 (x/x + u/4)

and the other

R(x) = A sin 2

( x/x - -rr/4)

yielding a difference

R(x) = A sin(2x/x )

as indicated in Section 2.

We assume that each detector is followed by a transimpedance amplifier with a feedback resistor Rf. Such an amplifier is depicted in Figure 4-5. Assuming

further that laser noise and amplifier noise are or can be made negligible, shot

noise associated with the average detector current and Johnson noise associated

with the feedback resistor remain as the fundamental noise sources.

The equivalent input noise current of each detector is given by

i* = [ttT/R, 2e. av

]

where k is Boltzmann's constant, T is absolute temperature, e is the electronic

charge, and I av

is the average detector current (which produces an output from the

detector of A/2). The change in detector current, per unit of the measurand, is

2I av /xo« The noise equivalent measurand (NEM), that is the value of the measurand

that produces a signal equal to the noise, is given for each detector by

A-l
1/2

NEM = [4kT/R

f

+ 2eI av :TV[2I av /xo3.

Using two detectors as described increases the noise current by a factor of 2^2

(assuming uncorrected noise processes) and increases the signal by a factor of 2,

thereby reducing the NEM by a factor of 2

1 / 2 and yielding

1/2 NEM --= [2kT/R

f + el av

] wt

/[21 av

/x ]

Recalling that for a current sensor 1/xo = uoVN and for &n electric field sensor

l/x n = Ceo/2, we can now plot both the noise equivalent current (NEI) or the noise

equivalent electric field (NEE) as a function of the value of the feedback

resistor and the average detector current. Figure A-l shows such a plot for a single turn current sensor using the Verdet constant of fused silica for an electric field sensor using the appropriate value of Ceo

for a bismuth germanate

crystal that is five times longer than its thickness, both assuming a wavelength

of 633 nm.

100 2000

<

e

3

>3w

o2

0.001 0.01 0.1 Average Detector Current, mA

A-l. Noise equivalent current for a single turn current sensor of fused silica

and noise equivalent voltage for a bismuth germanate voltage sensor with a length

to thickness ratio of 5, both operated at a wavelength of 633 nm, as a function of

amplifier feedback resistor size and average detector current.

A-2
Appendix B

OPTICAL DESIGN FOR BULK SENSORS

As shown in Appendix A, a major factor in determining the signal to noise performance of a sensor is the average detector current, which is assumed to be proportional to the average optical power incident on the detector. Particularly when

bulk components are incorporated into a sensor, maximizing the power at the detector require several trade-offs in optical design. In this appendix we examine

some of the choices that must be made.

The problem can be divided into two parts. One is maximizing the power launched

from a source into the input fiber. The other is maximizing the transfer of power

from one fiber, through a series of bulk components, and back into another fiber.

Here we consider the case of a sensor using an LED source with multimode fiber.

MAXIMIZING LAUNCHED POWER

If maximizing the launched power were the only consideration, one would choose a large area (and therefore high power) LED, a fiber with an equally large core and

as large a numerical aperture as possible. Assuming that there is no mismatch in area and that the LED is centered very near the end of the fiber, the coupling

efficiency will depend on the radiation properties of the LED, the numerical

aperature of the fiber and its refractive index profile.

The radiation pattern of an LED is normally symmetric about the axis of propagation, with an angular distribution given, to a useful approximation, by

I = I (COS a)"

1 (B-l)

where I and Io represent irradiance (units of power/area), a is angle with respect

to the axis, and m (m > 1) is a parameter governing the angular width of the pattern. The case m = 1 corresponds to what is commonly known as a Lambert i an source. The index profile of a multimode fiber is usefully approximated by the

form

B-l
n(r)

ni [l -2A(^) g

] 1/2

r < a

njl - 2a]

1/2

r > a

(B-2)

and

A =

(nf - n

2 )/2n 2

where n(r) is the refractive index as a function of radius, nx is the refractive

index at the center of the core, and n2 is the refractive index of the cladding,

and g is a parameter governing the shape of the profile. The case of g

= « corre- sponds to what is known as a step index fiber. Most fibers described as graded

index fibers have g « 2.

Using Eqs. B-l and B-2 one can compute the coupling efficiency, n, and find for

m = 1

n = (g-*-zXNA)2

1/2 where NA is the numerical aperture of the fiber [NA = (nf - n

2

.) ' ].

of a step index fiber the functional dependence on m is given by

(B-3)

In the case

n = (H1-KNA) : (B-4)

COUPLING BETWEEN FIBERS

The components of a bulk sensor usually represent an optical system that is relatively long compared to its transverse dimensions. One option is to place the end

of the input fiber in the focal plane of a lens thereby collimating the light

through the sensor components (Figure B-l). The beam passing through the sensor

is smallest at the collimating lens and diverges with a half angle given by

n = a/f (B-5)

where a is the radius of the fiber core and f is the focal length of the lens.

This assumes that the refractive index of the sensor is 1, though it is of course

B-2
fiber

B-l Illustration of optical coupling from one multimode fiber, through a series

of sensor components, and back into an identical multimode fiber. In this case the light is collimated through the sensor. Dotted lines show acceptance cone of

output fiber.

fiber

B-2 Same as B-l, except that the output end of the input fiber is imaged at a point somewhat greater than midway between the lenses. This results in a greater

collection efficiency into the output fiber.

B-3
higher, and overstates the divergence accordingly. To avoid aperturing in the sensor or in the refocusing lens, it is therefore desirable to use an input fiber

with as small a core as possible and a lens with as long a focal length as possible. The first of these considerations conflicts with the conditions for maximizing launched power. The second, coupled with the use of large numerical aperture fiber, may require a large diameter lens and result in a beam size that is

unacceptably large, even where, at the lens, it is smallest.

An alternative and probably superior choice is to image the output of the input

fiber somewhere in the middle of the sensor (Figure B-2). The image represents

the minimum beam size, which can, in principle, be controlled through the choice

of input lens and fiber location. The actual design may be fairly difficult when

several components with different refractive indices are involved. In any case,

this approach also works best when the input fiber has a small core and small

numerical aperture.

The main point of this discussion therefore, is that optimizing the power

delivered to the detector may not be best achieved by maximizing the light

launched into the input fiber, but will in general involve an optimization of the

input fiber type and a fairly detailed design of the optical system that transmits

light from the input fiber, through the sensor, and back into the output fiber.

Reference

B-l A. H. Cherin, An Introduction to Optical Fibers . McGraw Hill, 1983.

B-4
Appendix C

PROPERTIES OF SELECTED ELECTRO-OPTIC CRYSTALS OF POINT GROUP 43m

In section 3 of this report, it was suggested that crystals of crystal class 43m

were the most suitable for electro-optic voltage sensors. In this appendix the

relevant properties of five materials having that crystal symmetry are tabulated. Numbers in parentheses are wavelengths in nanometers.

Material: Bismuth Germanate, Bi

lt Ge

3 12 Nominal transparent range (nm) 400 to 5000

Refractive index, n 2.0975 (633) [a]

Normalized temperature derivative of 2. (633) [b]

refractive index, (dn/dT)/n, (10

-5 /K),

at room temperature

Thermal expansion coefficient, (dh/dT)/h, 1. [b]

(10" 6 /K), at room temperature

n

3 ^

(pm/V) 8.8 (T) (631) [a]

Verdet constant, V (deg/cm-T) 16.5 (633) [c]

Relative dielectric constant, e NA

References:

a D. P. Bortfeld and H. Meier. "Refractive indices and electro-optic coefficients

of the eulitities Bi\Ge3 12 and Bi l+ Si 3 12

." J. Appl . Phys. , 1972, vol. 43, p. 5110-5111.

"G. W. Day, D. Conrad, K. S. Lee, and P. D. Hale. "Optical, electro-optical, and

stress-optical properties of bismuth germanate, Bi' 4 Ge

3 12

," unpublished.

CM. J. Weber. "Faraday Rotator Materials." Lawrence Livermore Laboratory Report,

1982.

C-l
Material: Zinc Sulfide, ZnS

Nominal transparent range, nm 500 to 14000

Refractive index, n 2.3450 (650) [a]

2.3062 (850) [a]

2.2721 (1500) [a]

Normalized temperature derivative of 2.3 (650) [a]

refractive index, (dn/dT)/n, (10" 5 /K), 2.1 (850) [a]

at room temperature 1.9 (1500) [a]

Thermal expansion coefficient, (dh/dT)/h, 6.8 [b]

(10" 6 /K), at room temperature

n3r 41 (pm/V) 28.1 (633) [c]

Verdet constant, V (deg/cm-T) NA

Relative dielectric constant, e r 8.3 to 9.0 [a]

References:

a H. H. Li. "Refractive index of ZnS, ZnSe, and ZnTe and its wavelength and temperature derivatives." J. Phys. Chem Ref. Data , 1984, vol. 13, p. 103-150.

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

materials characterization." Final technical report, Nat. Bur. Stand. (U.S).

Tech. Note 993, 1979.

c "Landolt-Boernstein, Zahlenwerte und Funktionen aus Naturwissenschaften und Technik," Neue Serie, K.-H. Hellwege, Ed., Gruppe III: Band 11, El astische, piezoelektrische, pyroelektrische, piezooptische, elektrooptische Konstanten und nichtlineare dielektrische Suszeptibilitaten von Kristallen . Springer-Verlag, 1979.

C-2
Material: Zinc Selenide, ZnSe

Nominal transparent range, nm 500 to 22000

Refractive index, n 2.5810 (650) [a]

2.5124 (850) [a]

2.4570 (1500) [a]

Normalized temperature derivative of 3.9 (650) [a]

refractive index, (dn/dT)/n (10" 5 /K), 3.1 (850) [a]

at room temperature 2.7 (1500) [a]

Thermal expansion coefficient, (dh/dT)/h, 7.3 [b]

(10" 6 /K), at room temperature

n

3 r

ltl (pm/V) 34.3 (632) [c]

Verdet constant, V (deg/cm-T) 67.6 (633) [d]

Relative dielectric constant, e p 7.6 to 9.6 [a]

References:

a H. H. Li. "Refractive index of ZnS, ZnSe, and ZnTe and its wavelength and temperature derivatives." J. Phys. Chem. Ref. Data , 1984, vol. 13, p. 103-150.

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

materials characterization." Final technical report, Nat. Bur. Stand. (U.S).

Tech. Note 993, 1979.

c "Landolt-Boernstein, Zahlenwerte und Funktionen aus Naturwissenschaften und Technik." Neue Serie, K.-H. Hellwege, Ed., Gruppe III:Band 11, Elastische, piezoe lektrische, pyroelektrische, piezooptische, elektrooptische Konstanten und nichtlineare dielektrische Suszeptibilitaten von Kristallen . Springer-Verlag, 1979.

^M. J. Weber. "Faraday Rotator Materials." Lawrence Livermore Laboratory Report,

1982.

C-3
Material: Gallium Arsenide, GaAs

Nominal transparent range, nm

Refractive index, n

Normalized temperature derivative of

refractive index, (dn/dT)/n, (10" 5 /K),

at room temperature

Thermal expansion coefficient, (dh/dT)/h.

(10" 6 /K), at room temperature

n\j (pm/V)

Verdet constant, V (deg/cm-T)

Relative dielectric constant, e r

1000 to 17000

3.50 (1020) [a]

3.347 (1900) [a]

3.313 (3000) [a]

1.7 (>5000) [b]

5.7 [c]

61. (T) (1150) [a]

44. (T) (3390) [a]

NA

12.3 to 13.2 [d]

References:

a "Landolt-Boernstein, Zahlenwerte und Funktionen aus Naturwissenschaften und Technik." Neue Serie, K.-H. Hellwege, Ed., Gruppe III: Band 11, Elastische, piezoelek - trische, pyroelektrische, piezooptische, elektrooptische Konstanten und nichtlineare dielektrische Suszeptibilitaten von Kristallen . Springer-Verlag, 1979.

^Yet-ful Tsay, Bernard Bendow, and Shashanka S. Mitra. "Theory of the temperature

derivative of the refractive index in transparent crystals." Phys. Rev. B , 1973,

vol. 8, p. 2688-2696.

c William L. Wolfe. "Properties of Optical Materials." In Handbook of Optics , Optical Society of America/McGraw Hill, 1978.

d Amnon Yariv and Pochi Yeh. Optical Waves in Crystals . John Wiley, 1984.

C-4
Material: Gallium Phosphide GaP

Nominal transparent range, nm 500 to 13000

Refractive index, n 3.36 (640) [a]

3.24 (850) [a]

3.07 (1400) [a]

Normalized temperature derivative of 1.3 (????) [b]

refractive index, (dn/dT)/n, (10 _5 /K),

at room temperature

Thermal expansion coefficient, (dh/dT)/h, 5.3 [c]

(10~ 6 /K), at room temperature

n

3 r^j (pm/V) 33. (T) (550. ..1300) [a]

Verdet constant, V (deg/cm-T) NA

Relative dielectric constant, e r

10. [d]

References:

a "Landolt-Boernstein, Zahlenwerte und Funktionen aus Naturwissenschaften und Technik." Neue Serie, K.-H. Hellwege, Ed., Gruppe III :Band 11, Elastische, piezoelektrische, pyroelektrische, piezooptische, elektrooptische Konstanten und nichtlineare dielektrische Suszeptibi litaten von Kristallen . Springer-Verlag, 1979.

b Yet-ful Tsay, Bernard Bendow, and Shashanka S. Mitra. "Theory of the temperature

derivative of the refractive index in transparent crystals." Phys. Rev. B , 1973,

vol. 8, p. 2688-2696.

c William L. Wolfe. "Properties of Optical Materials." In Handbook of Optics , Optical Society of America/McGraw Hill, 1978.

dAmnon Yariv and Pochi Yeh. Optical Waves in Crystals . John Wiley, 1984.

C-5

Appendix D

PROPERTIES OF SELECTED DIAMAGNETIC GLASSES

In this section we summarize the properties of several glasses that have been used

as the magneto-optic material in electric current sensors. Because it is difficult to specify glasses other than by commercial designation, those designations

are provided in addition to the general glass type. This should not be construed

as a recommendation or an implication that similar products from another supplier

might not be equally or more suitable for the purpose. Numbers in parentheses are wavelengths in nanometers.

Material: Dense flint glass, Schott SF-57

Composition (compound/wt. %)

Nominal transparent range (nm)

Refractive index, n

Stress-optic coefficient (pm/N)

Verdet constant, V (deg/cm-T)

Temperature coefficient of the

Verdet constant, (dV/dT)/V

Density (g/cm3

)

Thermal expansion coefficient, (dh/dT)/h,

(10" 6 /K), at room temperature

NA

430 to 2400

1.81184 (633) [a]

1.82045 (852) [a]

1.83957 (1060) [a]

0.03 (589) [a]

11.5 (633) [b]

3.8 (1060) [b]

5.51 [a]

8.3 [a]

References:

a 0ptical Glass, Schott Optical Glass, Inc., York Avenue, Duryea, PA 18642.

bM. J. Weber. "Faraday Rotator Materials." Lawrence Livermore Laboratory Report,

1982.

C M. Deeter, T. Milner, G. W. Day. "The temperature dependence of the Verdet con- stant in diamagnetic glasses," unpublished.

D-l
Material: Flint glass, Schott SF-6

Composition (compound/wt. %)

Nominal transparent range (nm)

Refractive index, n

Stress-optic coefficient (pm/N)

Verdet constant, V (deg/cm-T)

Temperature coefficient of the

Verdet constant, (dV/dT)/V

Density (g/cm3

)

Thermal expansion coefficient, (dh/dT)/h,

(10~ 6 /K), at room temperature

SiO,

K9 PBO

400 to 2400

1.77381 (633) [a]

1.78159 (852) [a]

1.65106 (1060) [a]

0.63 (589) [a]

10.3 (633) [b]

3.5 (1060) [b]

5.18 [a]

8.1 [a]

27.35

1.50

71.15

References:

a 0ptical Glass, Schott Optical Glass, Inc., York Avenue, Duryea, PA 18642.

^M. J. Weber. "Faraday Rotator Materials." Lawrence Livermore Laboratory Report,

1982.

CM. Deeter, T. Milner, G. W. Day. "The temperature dependence of the Verdet con- stant in diamagnetic glasses," unpublished.

D-2
Material: Fused silica, Si0

2 Nominal transparent range (nm)

Refractive index, n 1.4567 (644) [a]

1.4525 (852) [a]

1.4462 (1362) [a]

Stress-optic coefficient (pm/N)

Verdet constant, V (deg/cm-T)

Temperature coefficient of the

Verdet constant, (dV/dT)/V

Density (g/cm3

)

Thermal expansion coefficient, (dh/dT)/h,

(10" 6 /K), at room temperature

References:

a American Institute of Physics Handbook . McGraw Hill, 1972

bj. D. 0. McFadden and G. W. Day, unpublished.

CM. Deeter, T. Milner, G. W. Day. "The temperature dependence of the Verdet con- stant in diamagnetic glasses," unpublished.

"Handbook of Optics . Optical Society of America/McGraw Hill, 1978.

3.36i (633) [a]

2.1

1.2

(633)

(850)

D>]

[b]

[c]

2.20 [d]

8.3 [d]

D-3
Material: Borosilicate Crown glass, Schott BK-7

Composition, (compound/wt. %)

Nominal transparent range (nm)

Refractive index, n

Stress-optic coefficient (pm/N)

Verdet constant, V (deg/cm-T)

Temperature coefficient of the

Verdet constant, (dV/dT)/V

Density (g/crn 3

)

Thermal expansion coefficient, (dh/dT)/h,

(10" 6 /K), at room temperature

SiO ? B

2 Na 2 K

? CaO

BaO

A1

2 3 330 to 2300

1.51509 (633) [a]

1.50981 (852) [a]

1.50669 (1060) [a]

2.74 (589) [a]

2.3 (633) [b]

1.0 (1060) [b]

2.51 [a]

7.1 [a]

69.58

9.91

8.44

8.37

0.07

2.54

0.04

References:

a 0ptical Glass . Schott Optical Glass, Inc., York Avenue, Duryea, PA 18642.

"M. J. Weber. "Faraday Rotator Materials." Lawrence Livermore Laboratory Report,

1982.

CM. Deeter, T. Milner, G. W. Day. "The temperature dependence of the Verdet con- stant in diamagnetic glasses," unpublished.

D-4
Appendix E

THE CHARACTERIZATION OF WAVEPLATES

In order to measure small changes in retardance of various types of waveplates,

the measurement system shown in Figure E-l was developed. It uses a quartzhalogen incandescent source with a temperature stabilized interference filter,

usually placed near the detector, to define the wavelength of measurement. A prism polarizer at the input to the waveplate is adjusted to transmit light polarized at 45° to the axes of the waveplate. A prism polarizer at the output rotates

about its axis at a rate of about 200 Hz yielding a signal at the detector of the

form

I = I (l + cosS si nut) (E-l)

where 6 is the retardance of the device.

Thus by measuring the ac and dc components of the detector output we can obtain

cos 6.

The system is obviously most sensitive when 5 « tt/2 so that it is ideal for the

characterization of quarter-wave plates. The resolution in that case, depending

on the wavelength of measurement, can be as good as 0.1 mrad. For the measurement

of waveplates with retardances other than tt/2 rad, it is possible to use a Babinet-Soleil compensator in series with the waveplate to achieve a net retardance of tt/2.

For measuring the temperature dependence of various waveplates, the devices to be

tested are placed on a small optical mirror mount inside a specially built oven.

The oven has no windows, nor are there any other optical components between the

two polarizers. The temperature inside the oven near the waveplate can be maintained to within about 0.1°C over a range from 15 to 100°C.

E-l
The system operates under the control of a desk-top computer which adjusts the oven heater, measures the temperature, the dc output of the detector, and the out- put of the lock-in amplifier, computes the birefringence, and plots the results.

Figure E-2 shows examples of the data obtained for a quartz waveplate and a poly- mer waveplate.

incandescent

lamp

polarizer

temperature

controlled region

waveplate n

interference

filter

rotating

polarizer

computer —

detector

lockin amplifier

DVM

E-l Measurement system for the determination of the temperature coefficient of

the retardance of various waveplates.

E-2
1.210 - o

2

•

u

c

CD D>-ce 1.200 -

1.190

1.580

o

a;o

c

CO

a.

1.575

1.570 -

E-2 Retardance versus temperature for a mica quarter wave plate (a) and an acromatic polymer waveplate (b).

E-3

APPENDIX F

BIREFRINGENCE MEASUREMENTS IN SINGLE MODE OPTICAL FIBER

(Proc. SPIE, Vol. 425, 1983)

F-l
Birefringence measurements in single mode optical fiber

G. W. Day

Electromagnetic Technology Division, National Bureau of Standards

325 Broadway, Boulder, Colorado 80303

Abstract

Because their cores are not perfectly circular or because of stress, inherent to the

structure or externally applied, practical single mode fibers are birefringent . These

sources of birefringence are reviewed briefly. A simple model for the fiber consists of a combination of one linearly birefringent element and one circularly birefringent element.

Depending on the magnitude of the birefringence, different techniques of evaluating the

parameters of the model may be suitable. Several methods appropriate for low and high birefringence fiber are described and some of their advantages and disadvantages outlined.

In an idealized single mode optical fiber, in Which none of the structural or optical

parameters varies with the azimuthal coordinate, all polarization states within the fundamental mode are degenerate; that is, neither the phase nor group velocity depends on polarization. In practice, however, -this degeneracy is usually lifted by non-circularity of the core, by inherent stress in the guiding structure, or by stress resulting from bending,

pressure, or twisting. Light entering the fiber with an arbitrary polarization state will

then be resolved into a pair of orthogonal polarization states that propagate with different

velocities. As a phase shift develops between them, the state of polarization will vary

periodically along the fiber. The orthogonal states may be linear, circular, or in general

elliptical, depending on the specific mechanisms involved.

Birefringence i6 a measure of the difference in phase velocity between the two states and

is precisely expressed as the difference between their effective refractive indices:

B - fin - —AB 2u

where AB is the difference between the two propagation constants. Alternatively, birefringence ie sometimes taken to be synonymous with AS and is expressed in radians (or degrees)/

unit length. Primarily for linear birefringence, a useful related quantity is the beat

length (L) defined as the distance of propagation necessary for a phase shift of 2* radians

to develop between the orthogonal states:

2ir X P

=

AB * B

For circular birefringence, it is more common to specify the rotation per unit length (n) of

linearly polarized light that occurs in such a medium:

a - AB • , /2 . circular

For some purposes, it will be necessary to use fiber with extremely low values of birefringence. In certain types of fiber sensor sytems, for example, magnetic field sensors based on the Faraday effect, the measured response to an external stimulus is a change in

polarization. Birefringence in such devices may alter or even quench the desired effect;

furthermore, it may render the device unstable as the birefringence changes with other ex- ternal parameters. Also differences in phase velocity with polarization generally imply

differences in group velocity that result in a form of signal distortion known as polarization mode distortion. Under certain circumstances, polarization mode distortion could

represent a significant contribution to the total bandwidth limitation of a single mode

fiber

.

In other cases it will be helpful to use fiber designed to have extremely high values of

inherent birefringence. Externally induced birefringence is then K.

x-dh less significant and

light entering the fiber with a properly chosen input polarization will maintain that

polarization over long propagation distances. Applications for high birefringence fiber

include interf erometric sensors and heterodyne communications systems. In each of these

cases, random variations in polarization at the fiber output would represent a major source

of noise. As a further enhancement of this type of fiber, it has recently been shown 1 that

F-2
the attenuation as well as the propagation constants of the two polarization states can be

dramatically different, leading to a truly single polarization fiber.

Before examining methods for characterizing these fibers it will be useful to review the

factors that contribute to fiber birefringence. Further detail can be found in a recent

paper on the development of high and low birefringence fibers. 2

If the cross section of the fiber is taken to be an ellipse, light linearly polarized

with its electric field parallel to the minor axis has a higher phase velocity (smaller propagation constant) than the orthogonal linear polarization.* The magnitude of this linear

birefringence increases with the ellipticity and with the refractive index difference (An)

between the core and the cladding. This dependence on An means that fiber desinged to have

a very low birefringence will typically have a low An and thu6 a relatively large core. Similarly, high birefringence elliptical fiber designs usually involve large values of An and very small core dimensions. The birefringence also depends on the normalized frequency

(V) of the fiber, reaching a maximum at a V-value slightly less than the cut-off of the

second mode

Variations in the thermal expansion coefficient of fused 6ilica with dopant and dopant

concentration inevitably result in stress which alters the refractive index through the

stre6s-optic (photoelastic) effect. *• In a perfectly axiaAly symmetric structure this stress would be radially directed and axially symmetric and would not therefore lead to birefringence. However, if the core is slightly elliptical the effect of stress will be anisotropic

and will add algebraically to the linear birefringence resulting from ellipticity alone. To

achieve low birefringence fiber one chooses dopants and structures that minimize differences

in thermal expansion coefficients. 5 To achieve high birefringence fiber one may choose

dopants that enhance these effects and may, as well, use other techniques to increase the

azimuthal dependence of the stress. 6

The direction of the axes of ellipticity or of the stress induced birefringence may well

vary along the fiber, even in a straight, unperturbed fiber; this will modify the apparent

macroscopic birefringence. It is, in fact, possible to eliminate effectively the intrinsic

linear birefringence by fabricating the fiber in such a way that the axes of birefringence

rotate with a pitch much greater than the intrinsic beat length (spun fiber). 7 In such a fiber the observed birefringence is almost entirely the result of externally applied stress. Bending introduces linear birefringence with the fa6t axis in the plane of the bend,

having a magnitude

r

2 0.85 r2 ^ -0.14por i^ • -j— £7 rad/m

where r is the radius is the radiu6 of the fiber, R is the radius of the bend, and X is the

wavelength in meters. 8 Furthermore, if the fiber is under longitudinal tension when bent,

it incurs an additional ("tension-coiled") birefringence 9 having the same fast axis as bend

birefringence and given by «..~r 3 .1 r , . B_ - 0.49 - or AB. „ —— - e rad/m

tc R tc X R z where ez

is the relative fiber elongation. A one-dimensional compressive force applied to a fiber normal to its axis produces a linear birefringence with the fast axis parallel to the

applied force, 10 given by

_l l

. „ , A-i, f 3.0 x 10 f .. B - 4.8 x 10 1Z - or A6 - rad/m

P r p X r where f is the applied force per unit length in newtons/m and r is in meters.

TwiBting of a fiber causes a rotation of the axes of any linear birefringence that may be

present; furthermore, it produces torsional stresses that give rise to circular birefringence. The net result of twisting depends on the rate of twi6t relative to the linear birefringence present. 11 If the linear birefringence is negligible the stress produces a rotation of

where g is a constant (• 0.073 for silica) and i is the twist rate. At the other extreme,

if the linear birefringence i6 very large, the torsional stress i6 of little consequence,

but rotation of the axes produces a rotation equal to the twist rate,

0-5-

Intermediate cases require more complex descriptions.

F-3
fiber

model

Figure 1. A simple model for the birefringence of an optical fiber consists of a linearly

birefringent element of retardance R and orientation plus a circularly birefringent element (rotator) with rotation fi.

An arbitrary fiber, exhibiting (potentially

along its length could, in principle, be descr

ferential optical retarders with varying retar

ferential optical rotators (circular retarders

evolution of the polarization state along such

nately, in many cases the microscopic characte

than its macroscopic or end-to-end characteris

it is important to know the polarization state

fringence fibars where a single effect (or a s

) all of the above effects at various points

ibed by a model consisting of a series of difdation and orientation, interspersed with dif-

) of varying strength. A prediction of the

a fiber would be very difficult. Forturistics of the fiber are much less important

tics. Furthermore, many of those cases where

as a function of length involve high bi re- mall number of effects) predominates.

For end-to-end characterization it i6 possible to use a very simple model, for it can be

shown in general that any system composed solely of linear retarders and rotators can be

represented by a single retarder with an appropriate orientation and a single rotator. 12 The parameters of this model are the orientation of the retarder relative to an external

coordinate system ($), the value of the retardance (R) , and the value of the rotation (n)

(fig. 1). This simple characterization is most suitable for moderate to low birefringence

fibers where specimens shorter than one beat length can be evaluated.

The model has at least one pair of orthogonal linear input polarization states for which

the output state i6 also linear. These correspond to the axes of the retarder and are some- times called principal axes. Less obviously, there is also a pair of generally elliptical

input 6tates that appear unaltered at the output and are generally called eigenstates. The

existence of principal axes and eigenstates does not necessarily imply, however, that light

launched into one of those states will not pass through other intermediate states during

propagation.

m=^-

unDOlarized polarizer

source specimen polarizer detector

Figure 2. A basic system for birefringence measurements.

F-4
Step 1

»+!}•• 45°

Step 2

Input Output

Figure 3. The first step in determining the parameters of the model is to rotate the input

and output polarizers until a linear-input —linear-output condition is obtained.

This gives 41 and n. The second step i6 to launch linearly polarized light at 45* to the axes of the retarder element. This gives an elliptically polarized output

from which R can be obtained.

The simplest apparatus for determining 4, R, and n is shown in figure 2. It consists of an unpolarized (or perhaps circularly polarized) light source, two low birefringence lenses

(usually microscope objectives), two high quality polarizers, and a photodetector . With a specimen in place the polarizers are rotated iteratively until a null in the transmission

occurs. In this linear-input-linear-output condition, the orientation of the input polarizer corresponds to one of the principal axes at orientation *, and the output polarizer

orientation corresponds to f + fi + 90* (output polarizer parallel to y' in fig. 3).

Obtaining the retardance R is only slightly more difficult. The input polarizer is first

rotated by exactly 45* so that the field components parallel to each of the principal axes

are identical. Under these circumstances the output state will be an ellipse with its major

or minor axis rotated by 4 + fl + 45* from the positive x axis. The electric field components in the x' and y' direction are equal but differ in phase by R:

Ee

.R

X

2 Ee

.R - 1!

A standard polarimetric method for determining R is to measure the power transmitted by a polarizer parallel to each axis of the ellipse (Ix

h and ly») • With some simple mathematics

one find6,

x /2" y 2

= E

2

., y

/2

1 E

•2

X

/2 y

2E 2 cos 2-

.R .R E

2 X 2 _1 2.2 —(-e + e ) 2E 2 sin 2 -

F-5
and

I - I ., x y

i „ ; i „ - cos R - x' y All three parameters in the model are thus determined, but subject to several ambiguities. Neither R nor can be distinguished from values related by ±n2* radians. Furthermore, it was not determined whether the principal axis at the input angle 4 was a fast or slow axis, which is equivalent to noting that the sign of R cannot be determined from the

symmetric cosine function, or that values of n related by ±n* radians are indistinguishable.

Finally, since the cosine function is dual valued within any one period, values of R are indistinguishable from those of 2r - R radians.

When these ambiguities cannot be resolved through a priori estimates of some of the

values they may often by distinguished by multiple cutback methods. In this case the parameters $, R, and n are determined for a successively shortened fiber and a uniform length

dependence is assumed. This cut-back technique is widely applicable except that as a practical matter it becomes difficult when the birefringence is extremely high.

Alternatively, R may be determined from the output polarization ellipse (step 2, fig. 3)

using a calibrated Babinet-Soleil compensator, a device that can be adjusted for any retardance. The compensator is placed between the fiber and the output polarizer and is oriented

with its fast or slow axis parallel to x' . The output polarizer is oriented parallel to

y" . When the compensator is adjusted for a null in the detected signal the birefringence

added to the system by the compensator is equal in magnitude and opposite in sign to R. (Equivalently, and sometimes more conveniently, the compensator may be placed at the input

with its axes parallel to the principal axes.)

Compared to the first approach, the use of the compensator has several advantages. The

measurement is generally simpler to perform. It yields much less ambiguous results; only

the in2ir ambiguities remain and the cut-back technique is therefore more easily employed.

And finally, the compensator technique does not depend on source or coupling stability since

only nulls and not relative power levels are required. A disadvantage is that the compensator used must be of high quality and carefully calibrated.

A third possibility for obtaining R from the output polarization ellipse is to place a quarter wave plate just before the output polarizer with its fast axis parallel to x"

.

Under these circumstances, the elliptical state is converted to a linear state at an angle

with respect to the positive x axis of $ + £5 + 45° + •=. Ambiguities other than ±n2r do not appear

.

It i6 easier to use the quarter-wave plate than a compensator, and this approach has been

used to develop an automated measurement system. ^ However, a single Babinet-Soleil compensator can be calibrated and used at any wavelength of interest while separate quarter wave plates mu6t be used for each wavelength.

Various types of polarization modulators have been used in systems similar to that outlined above to study crystals and other anistropic media. Generally the motivation for this

approach is greater sensitivity, especially for low values of birefringence. One such technique that has been successfully applied to fiber characterization is the use of a photoelastic modulator. 15 A suitable device is a block of fused silica to which a piezoelectric

transducer has been attached in such a way as to provide a uniaxial stress normal to the

direction of propagation. The result is a linearly birefringence element, the retardance of

which may be modulated at rates of several tens of kilohertz. A convenient method of using

the modulator is to attach it directly to the output polarizer so that the two elements

rotate together with a fixed relative orientation of 45°. The detected signal in general

contains harmonics of the frequency at which the modulator is driven. It may be shown that

Wj « sin R sin 2(8! - )

and W 2 « [cos 2(6! - *.) sin (28 2 - 2C1) + cos R sin 2(6i - *) cos (26 2 - 2£J)]

where W is the magnitude of the modulation component at the drive frequency, W is the cor- responding value at twice the drive frequency, 8. is the angle of the input polarizer and 8

2 is the angle of the modulator axis, with respect to the x axis.

The procedure then simply consists of nulling the W component by adjusting the input

polarizer (W does not depend on the orientation of the modulator-output polarizer combination) and then nulling the W 2 component to obtain 0. To determine R one rotates the input

F-6
polarizer by 45° (8. - +45*). Then W « sin R and W « cos R from which R can be determined, again only with the ±n2» ambiguity.

In certain cases, it may be desirable or necessary to evaluate unambiguously the evolution of polarization 6tates along a fiber without changing its length. Examples include in

situ measurements of low birefringence fiber where external stress may be significant and

the characterization of very high birefringence fiber where cut-back techniques are impractical . One approach in these cases is another class of modulation techniques in which the birefringence of the fiber itself i6 modulated at a point along its length and the corresponding

change in polarization state at the output is determined. The essential basis for this

approach is that in a system consisting of linearly and circularly birefringent elements the

change in output state resulting from a local change in polarization state depends only on local parameters and not on the properties of the system preceding or following the point of

modulation. Modulators inducing either linear birefringence or circular birefringence in the fiber have been used for this purpose. 15 ' 16

Circular birefringence may be introduced into a fiber by using a small electromagnet that

provides a field parallel to the fiber axis. 16 The magnitude of the resulting change in

polarization (Faraday effect) depends on the polarization state at the point of modulation.

It is most effective when the polarization state is linear and is zero for a circular polarization. Therefore, by moving the magnet along the fiber one may, for example, directly

determine the beat length as twice the distance separating points of maximum modulation.

This technique is easy to employ and extremely useful for high birefringence fiber, though

for extremely short beat lengths (L_ < 1 mm) it may be difficult to design a magnet to give

sufficient spatial resolution.

A linear birefringence may be introduced into a fiber either by applying a large electric

field normal to the axis (Kerr effect) 16 or by applying a tranverse stress 16 as described

above. The beat length can be obtained, again by longitudinal translation of the modulation. Furthermore, since the azimuth of the induced birefringence can be varied it is possible to deduce the exact polarization state at the point of modulation.

Another technique that is widely used for nondestructive determiniations of the beat

length is the observation of the length dependence of Rayleigh scattering normal to the

axiB. 18 If linearly polarized light is launched into the fiber at 45* to the principal axes

and if the scattered light is viewed at the same azimuth, a series of bright and dark bands

will appear along the length of the fiber. This results from the fact that the angular

dependence of Rayleigh (dipole) scattering passes through a null along the dipole axis and a maximum normal to the dipole axis. Bright regions appear where the direction of observation

is normal to the local plane of polarization, recurring with a periodicity equal to a beat

length. This method is best suited to the evaluation of moderately high birefringence

fibers (L^ ~ a few millimeters) in the visible region of the spectrum where the scattering

is relatively large and the light and dark bands are easily seen. Rayleigh scattering can also be used to determine the beat length using a modified form

of optical time domain ref lectometry (OTDR) known as polarization OTDR, or POTDR. 19 If a polarized probe pulse is used the backscattered light will show a time dependent polarization state that depends on the polarization state of the probe pulse at the point of scattering. The temporal periodicity observed in the backscattered light can therefore be

directly related to the beat length. 20 A lack of sufficiently short pulses and pulse

broadening within the fiber generally limit this technique to the measurement of fairly long

beat lengths.

A final possiblity for studying the properties of high birefringence fibers nondestructively involves observing changes in the output state as the wavelength is scanned. For a length of fiber 1 the total phase difference (retardance) between the orthogonal states is 2w

R - ABt 5 kBl = — Bt.

For a frequency change Ak the corresponding change in retardance, AR, is

M . £li££! Ak - l[B + k g] Ak. dk dk

Assuming a fixed input state, the output state varies periodically with wavelength, the

period corresponding to AR 2*.

F-7
If the dispersion of the birefringence (dB/dk) were negligibly small or known, it would

be possible to measure unambiguously the fiber birefringence in this way. Unfortunately,

dB/dk is generally not negligible. 2^ Furthermore, it depends in a complicated way on the

mechanisms producing the birefringence and so is not readily predictable. One may thus

reliably determine only the the relative change in birefringence with wavelength in this

way

.

22

Such a relative measurement does allow a prediction of the polarization mode distortion, 22 since the difference in group delays of the two states is given by

I d( AB) At

g c dk

In high birefringence fibers this expression provides a good estimate of the pulse spreading

that is measured on long fiber lengths. In low birefringence fiber the above expression

usually overestimates substantially the observed pulse spreading. This is because in low

birefringence fibers significant coupling between the orthogonal states serves to equalize

the propagation times.

Acknowledgment

The author is greatly indebted to members of the Optical Communications Research Group at the University of Southampton, especially Dr. A. J. Barlow, for numerous fruitful discussions on this subject. Research at JffiS on the polarization characteristics of optical fiber

is supported in part by the Department of Defense, Calibration Coordination Group.

References

1. J. R. Simpson, F. M. Sears, J. B. MacChesney, R. H. Stolen, W. Pleibel, and R. E. Howard, "Single polarization fiber," Digest, OFC 83, New Orleans.

M. P. Varnham, D. N. Payne, R. D. Birch, and E. J. Tarbox, "Single polarization

operation of highly birefringent optical fiber," Electron. Lett. , Vol. 18, pp. 246-247.

1983.

2. D. N. Payne, A. J. Barlow, and J. J. Ramskov-Hansen, "Development of low and high

birefringence optical fiber," IEEE J. Quantum Electron. , Vol. QE-18, pp. 477-488. 1982.

3. R. B. Dyott, J. R. Cozens, and D. G. Morris, "Preservation of polarization in optical fiber waveguides with elliptical cores," Electron. Lett.

,

Vol. 15, pp. 380-382. 1979.

J. D. Love, R. A. Sammut, and A. W. Snyder, "Birefringence in elliptically deformed

optical fibers," Electron. Lett. , Vol. 15, pp. 615-616. 1979.

4. A. J. Barlow and D. N. Payne, "The stress optical effect in optical fibers," IEEE J. Quantum Electron. , Vol. QE-19, pp. 834-839. 1983.

5. S. R. Norman, D. N. Payne, M. J. Adams, and A. M. Smith, "Fabrication of single mode

optical fibers with extremely low polarization birefringence," Electron. Lett , Vol. 15, pp. 309-311. 1979.

6. T. Okoshi and K. Oyamada, "Single polarization single mode optical fiber with

refractive index pits on both sides of core," Electron. Lett. , Vol. 16, pp. 712-713. 1980.

T. Hosaka, K. Okamoto, Y. Mika, Y. Sasaki , and T. Edahiro, "Low loss single polarization fibers with asymmetrical strain birefringence," Electron. Lett. , Vol. 17, pp. 530-

531. 1981.

R. D. Birch, D. N. Payne, and M. P. Varnham, "Fabrication of polarization maintaining fibers using gas-phase etching," Electron. Lett. , Vol. 18, pp. 1036-1038. 1982.

T. Katsuyama, H. Matsumura, and T. Suganuma, "Los loss single polarization fibers,"

Electron. Lett. , Vol. 17, pp. 473-474. 1981.

T. Al J~. Barlow, D. N. Payne, M. R. Hadley, and R. J. Mansfield, "Production of single

mode fibers with negligible intrinsic birefringence and polarization mode dispersion,"

Electron. Lett. , Vol. 17, pp. 725-725. 1981.

8~. R~. Ulrich, S. C. Rashleigh, and W. Eickhoff, "Bending induced birefringence in

single mode fibers, " Opt. Lett. , Vol. 5, pp. 273-275. 1980.

9. S. C. Rashleigh and R. Ulrich, "High birefringence in tension coiled single mode

fibers, " Opt. Lett. , Vol. 5, pp. 354-356. 1980.

10. J. Sakai and T. Kimura, "Birefringence and polarization characteristics of single

mode optical fibers under elastic deformations," IEEE J. Quantum Electron. , Vol. QE-17, pp. 1041-1051. 1981.

A. M. Smith, "Single mode fiber pressure sensitivity," Electron. Lett. , Vol. 16, pp. 773-774. 1980.

11. R. Ulrich and A. Simon, "Polarization optics of twisted single mode fibers," Appl

.

Opt

.

, Vol. 18, pp. 2241-2251. 1979.

T2 . F. P. Kapron, N. F. Borrelli, and D. B. Keck, "Birefringence in dielectric optical

waveguide," IEEE J. Quantum Electron. , Vol. QE-8, pp. 222-225. 1972.

13. R. C. Jones, "A new calculus for the treatment of optical systems," J. Opt. Soc

.

Am. , Vol. 31, pp. 388-493. 1941.

F-8
14. A. M. Smith, "Automated birefringence measurement system," J. Phys. E: Sci

Instrum. , Vol. 21, pp. 927-930. 1979.

15A. J. Barlow and D. N. Payne, "Measurement of fiber polarization properties using a photo-elastic modulator," Technical Digest, Symp. Opt. Fiber Meas. 82, Boulder, CO. 16. A. Simon and R. Ulrich, "Evolution of polarization along single mode fiber," Appl

Phys. Lett. , Vol. 31, pp. 517-520. 1977.

17. N. Chinone and R. Ulrich, "Elasto-optic polarization measurements in optical fiber,"

Opt. Lett. , Vol. 6, pp. 16-18. 1981.

18. A. Papp and H. Harms, "Polarization optics of index gradient optical waveguide

fibers," Appl. Opt. , Vol. 14, pp. 2406-2411. 1975.

I. P. Kaminow, "Polarization in optical fibers," IEEE J. Quantum Electron. , Vol. QE17, pp. 15-32. 1981.

19. A. J. Rogers, "Polarization optical time domain ref lectometry, " Electron . Lett

, Vol. 16, pp. 489-490. 1980.

20. M. Nakazawa, T. Horiguchi, H. Tokuda, and N. Uchida, "Polarization beat length meas- urement in a single mode optical fiber by backward Rayleigh scattering," Electron. Lett

, Vol. 17, pp. 513-515. 1981.

B. Y. Kim and S. S. Choi, "Backscattering measurement of bending induced birefringence in single mode fibers," Electron. Lett. , Vol. 17, pp. 193-194. 1981.

21. S. C. Rashleigh, "Measurement of fiber birefringence by wavelength scanning: effect

of dispersion," Opt. Lett

, Vol. 8, pp. 336-338. 1983.

S. C. Rashleigh, "Wavelength dependence of birefringence in highly birefringent

fibers," Opt. Lett. , Vol. 7, pp. 294-296. 1982.

22. S. C. Rashleigh, "Polarization mode dispersion in single mode fibers," Opt . Lett

, Vol. 3, pp. 60-62. 1978.

F-9

APPENDIX G

PROGRESS IN THE DESIGN OF OPTICAL FIBER SENSORS FOR

THE MEASUREMENT OF PULSED ELECTRIC CURRENTS

(Proc. Workshop on Measurement of

Electrical Quantities in Pulse Power Systems,

March 1986, Gaithersburg, MD)

G-l
PROGRESS IN THE DESIGN OF OPTICAL FIBER SENSORS

FOR THE MEASUREMENT OF PULSED ELECTRIC CURRENTS

G. W. Day National Bureau of Standards

Boulder, CO 80303

L. R. Veeser and G. I, Chandler

Los Alamos National Laboratory

Los Alamos, NM 87545

R. W. Cernosek

Sandia National Laboratory

Albuquerque, NM 87185

ABSTRACT

The state of the art sors for pulsed electric

the more useful configura

pared. Transfer function

illustrate the effect of twisting on the character

technique of annealing be described and its present

analysis of the ultimate

current is given, suggest

magnitude improvement sho

in the design of fiber sen- currents is reviewed. Some of tions are described and coms are computed and used to linear birefringence and istics of the sensors. The nd-induced birefringence is capabilities indicated. An limits to noise equivalent

ing that several orders of

uld be obtainable.

INTRODUCTION

The measurement of pulsed electric currents must

often be performed 1n the presence of substantial elec- tromagnetic interference, making the use of conventional sensors difficult. Optical sensing techniques

can effectively eliminate this Interference.

In this paper we describe recent progress in the design of current sensors based on the Faraday effect

in single-mode optical fiber. These sensors are being

used successfully in several measurement systems at Los Alamos and Sandia National Laboratories where the pulse

amplitudes range from about 100 A to 50 MA with durations as short as 1 ys. We anticipate that fiber current sensors can be used in a much broader range of applications, including those that require several orders of magnitude improvement in minimum detectable

current.

BASIC SENSOR DESIGNS

The Faraday effect 1s a magnetically induced rotation of the plane of polarization of linearly polarized

light (i.e., an induced circular birefringence), given

by

e = v / 8 . <5z (i)

where e is the rotation, V is a material parameter

knosn as the Verdet constant, B = uH is the magnetic

flux density, and z is the direction of propagation.

In an optical fiber current sensor [1,2,3], one or more

loops of single-mode optical fiber surround the electrical conductor. Then, since M dz (2)

about any closed path around a conductor carrying a current I, the plane of polarization of light propagating in the fiber is rotated by an amount

6 iVNI, (3)

Polarizer m>

Single mode liber-*'

Polarizer Conductor

1. Schematic of an optical fiber current sensor. Linearly polarized light passing through one or more turns of fiber surrounding the conductor is rotated in proportion to the current. A polarizer

at the output allows the rotation to be detected as

a change in transmittance.

where N 1s the number of turns of fiber around the con- ductor. For a single turn of fused silica fiber

(u r

u ) the ratio of rotation to current is approximately 265 deg/MA at a wavelength of 633 nm.

To measure this rotation the fiber is usually

placed between polarizers and the transmitted light

monitored with a high-speed photodiode (Fig. 1). The transmittance of the sensor as a function of current depends on the relative orientation of the polarizers.

For two important cases, namely crossed polarizers and polarizers at 45 deg to each other, the transfer func- tions are given by (Fig. 2)

R(l) *\ (1 cos 2u n VNI)

and

respectively.

R(I) --g (1 t sin 2u VNI).

RCI)

(4)

(5)

2. Computed transfer functions for the sensor shown in F1g. 1 for the case of polarizers aligned for minimum transmittance at zero current (a) and for polarizers oriented for a transmittance of 0.5 at zero current, i.e., the output polarizer at 45 deg

to the minimum transmittance orientation (b).

G-2
When the currents to be measured are small, it is generally preferrable to use the latter case (Eq. (5)) to take advantage of the greater sensitivity. A fur- ther, two fold, increase in sensitivity can be obtained

by using a polarizing beamsplitter at the output,

detecting both the +45 and -45 deg components, and taking the difference electronically. From Eq. (5), the transfer function then becomes

R(I) = sin 2u VNI. (6)

ipiAn/\^^

10

S e e•

£ 4 a

2 -

_L

-300 -250 -200 150 -100 -SO

lime, ps

(a)

J_ J_ 8

time, ps

12 16

3. Raw data from a sensor similar to that shown in Fig. 1. The current was produced by a capacitor

bank discharged into a low-impedance load and approximates a damped sinusoid with a peak ampli- tude of about 2.4 MA.

When the currents to be measured are large, the multivalued nature of this transfer function may be a problem. Often, however, the general shape of the waveform

is known in advance so that ambiguities can be resolved

by inspection. Examples of such cases are illustrated

in Figs. 3 and 4. Figure 3 shows raw data from an experiment in which a capacitor bank was discharged

Into a very low impedance load. With the prior knowl- edge that the current waveform should approximate a damped sinusoid, it is easy to recognize the peak of the first half cycle at about 5.5 gs and the first zero-crossing at about 11.5 us. Figure 4 shows some processed data from a two-stage, explosively driven

flux compression generator. The current was Initiated

by capacitive discharge yielding a peak current of about 1 MA. After one stage of flux compression the peak current increased to about 10 MA (Fig. 4a) and after the second stage to more than 50 MA (F1g. 4b). 6ood agreement between the optical sensors and conventional sensors (Rogowski coils) also used 1n this experiment was observed except that the Rogowski coils

1n the second stage failed slightly earlier than the optical sensor.

When the general shape of the current waveform is not known in advance or when the data are processed

automatically, a two polarization detection scheme can

be used to resolve ambiguities [4]. Figure 5 shows such a system. The output of the fiber is split with a polarization-independent beamsplitter, allowing the detection of two separate polarization components. One polarizer/detector combination is oriented for minimum

transmittance at zero current and therefore provides a cosinusoidal transfer function of the form of Eq. (4). The other polarizer/detector combination 1s oriented

for a transmittance of 0.5 (I.e., at 45 deg to the first) and provides a sinusoidal transfer function of the form of Eq. (5). By examining the sign of the sine

and cosine signals the rotation can be determined unam- biguously within the range -90 < 8 < +90. Furthermore,

if the signals are sampled at least once within each

90 deg of rotation, multiple rotations can be identified [4].

4.

100

Processed data from a two stage high-explosivedriven flux compression generator. The upper curve

Is the current measured at the output of the first stage; the lower curve 1s the current at the output

of the second stage. Time zero is the firing of the second stage. Points are from the optical sensor; solid lines are from a Rogowski coil. [After L. R. Veeser, et al. Proc. SPIE 506, San Diego, CA, 1984.]

Detector Beam

Splitter

Detector

A two-polarization detection scheme that provides

both sinusoidal and cosinusoidal transfer functions

and therefore allows resolution of ambiguities

resulting from the multivalued transfer function.

A sensor configuration that avoi polarizers entirely is the Sagnac int shown in Fig. 6. As in an optical fi coupler divides the Input light into counter-propagating waves in a fiber coupler, like a beamsplitter In an 1n introduces a 90 deg phase shift betwe beams. Therefore, if the field acts propagating waves reciprocally, the t bining at the output port cancel and returned to the input port. Any nonr

in the coil, specifically those produ

ds the use of erferometer [5] ber gyroscope, a equal amplitude,

coil. The terferometer

en its two output

on the counterwo components corn- all the power is eciprocal effects

ced by rotation

G-3
EFFECT OF LINEAR BIREFRINGENCE IN THE FIBER

OUT

Single mode fiber

6. Schematic of a Sagnac interferometer used as a current sensor. No polarizers are required. The transfer function, which is identical to that shown

in Fig. 2a, is independent of the input polarization state.

about

ent ef For th can be polari

by res states result

polari

a coil

the coil axis,

fects, cause po

e case of Farad obtained eithe

zation state of olving the inpu

and considerin

, somewhat surp zation state, a placed between

a magnetic fi wer to appear

ay rotation,

r by consider

the countert state into

g the induced risingly, is nd is identic crossed pola

eld, or

at the the tran

ing the propagat

orthogon

phase s independ

al to th rizers (

time dependoutput port, sfer function

change in ing beams or

al circular

hifts. The

ent of input

at found for

Eq. (4)).

In all of the configurations described above, the induced rotation or circular birefringence is converted

to a change in transmittance. In some cases it may be desirable to observe the induced birefringence directly. This can be done using a rotating linear input

polarization state [6,7,8].

A rotating linear polarization state is equivalent

to orthogonal circular polarization states shifted in (optical) frequency by the rotation rate. The induced circular birefringence produced by the magnetic field

can therefore be observed as a change in phase of the rotating linear polarization.

High rotation rates are most easily produced by

starting with frequency shifted, orthogonally linearly

polarized beams which can be produced by Zeeman splitting of a gas laser [7] or acousto-optic modulation

[8]. When passed through a quarter wave plate the desired rotating linear polarization is produced

(Fig. 7). Changes 1n the phase of the rotation can be observed by detecting the input and output signals

through linear polarizers and using standard phase measurement electronics.

The sensor characteristics described in the pre- ceeding section can be achieved only when, in the absence of applied fields, the propagation characteristics of the fiber are independent of polarization

state. This is not, in general, a good assumption.

Indeed, the primary difficulty with fiber current sensors is that linear birefringence in the fiber, resulting from inherent geometrical imperfections and stress

or induced by applied stress, can seriously distort the transfer function.

Inherent linear birefringence can be effectively

eliminated using certain manufacturing techniques.

Birefringence resulting from applied stress, particularly from bending, remains a problem. Bend-induced

linear birefringence can be predicted analytically [9] and is highly reproducable [10]. It is given by

AB = <

x rVR 2

, (7)

where r is the fiber radius, R is the bend radius, and

K. is a parameter equal to about 7.7 x 10 7 deg/m for silica fibers at a wavelength of 633 nm.

Faraday rotation in a linearly birefringent medium

such as a fiber coil can be modeled using Jones calculus. The relationship between the input and output

polarization states is given by [11]

x

v

'

E (2)

2F . *z r

cos sln f

|i -j M lin £ E (0)

x

v

'

E (0)

(8)

where E„ and E^ are complex electric-field amplitudes,

AB is the birefringence per unit length, F is the Faraday rotation per unit length, and

(!)

2 .

C|£)S in 7 (9)

Inspection of Eqs. (8) and (9) indicates that when

F << AB the matrix in Eq. (8) approaches that of a pure linear retarder, indicating that the rotation is effec- tively quenched. When F << AB the matrix approaches

that of a pure rotation (circularly birefringent) ele- ment.

Mil K0>

MtV

Q

<OOi9 O

phe»e meter

Schematic of a sensor using a rotating input

polarization. Two input signals, differing in optical frequency by AX and having orthogonal

linear polarizations, are passed through a quarter

wave plate to yield the required input state.

A particular advantage of this technique is that

it can be used to raise the detection frequency above

the range where laser noise dominates. Also, since most phase meters provide both sine and cosine outputs,

ambiguities arising from the multivalued transfer func- tion are more easily resolved than with the two- detector method described above.

This behavior can be observed in the computed transfer functions shown in Fig. 8. Figure 8a shows the transfer function of a sensor consisting of a single 3 cm diameter turn of 125 ym diameter fiber between crossed polarizers and operated at 633 nm. The bend-induced birefringence is approximately 127 deg,

leading to significant distortion in the amplitude of the transfer function for rotations less than about 180 deg (about 0.7 MA). Figure 8b shows the transfer function for a 10 turn, 10 cm coil of the same fiber,

in which the total birefringence is about 382 deg. In this case, both the amplitude and the periodicity of the transfer function show significant distortion.

TWISTED FIBERS

One technique for overcoming induced linear bire- fringence is to twist the fiber. Twisting, like the Faraday effect, induces a rotation or circular bire- fringence in the fiber. The magnitude of the rotation

is given by

9 5. (10)

G-4
RCI) R(D

-2.0

RCI)

-0.2 -0.1

I. MA

R(I)

-0.2

(b)

<e> 1 lurn. 9 c« dia

(ft) 10 turns. 10 c» dia

With ancfrirtganca

Without biratrrnaanca

<•) 1 lurn. 3 cm dia . 60 lurnarraalar

(b) 10 lurnt. 10 ctn dia . 10 lurnarmol

With biiafrinoanca

Without biratrmgancs

126 um

k (13 nm

8. Computed transfer functions of fiber current sensors showing the effect of bend-induced linear birefringence in the fiber, (a) One turn, 3 cm

coil diameter, 125 pm fiber diameter, 633 nm operating wavelength, (b) 10 turns, 10 cm coil diameter, 125 ym fiber diameter, 633 nm operating

wavelength. The linear input polarization is aligned with one of the axes of birefringence.

Dotted curves show the transfer functions that would be observed if linear birefringence were not present.

where n Is the rotation per unit length, 5 is the twist

per unit length, and g' is a material parameter which

at a wavelength of 633 nm is equal to about 0.08. The twist-induced rotation may be added algebraically to

the magnetically-induced rotation in Eq. (8). This is illustrated in Fig. 9 which shows that the effect of twisting is, in essence, to bias the sensor away from

the distorted part of the transfer function. The extent to which the transfer function can be shifted

depends on the relative magnitude of the linear birefringence and twist-induced rotation per turn . Since

for a rotation p given twist per unit length the twist

per turn increases (linearly) with coil diameter and bend-induced birefringence per turn decreases (inversely) with the coil diameter, twisting becomes much more effective with larger coil diameters (Fig. 9b versus

Fig. 9a).

Many 125 urn silica fibers will withstand twists of between 40 and 50 turns/m; with care, some will reach 80 or 90 turns/m. For small coils this may not bias the transfer function sufficiently to measure dual polarity waveforms, though for single-polarity waveforms less bias is required (Fig. 9a).

Computed transfer functions of the same sensors illustrated in Fig. 7 showing the effect of twist- ing the fiber, (a) The 3 cm diameter coil using a twist rate of 50 turns per meter, (b) The 10 cm diameter coil using a twist rate of 10 turns per meter. Dotted curves assume no linear birefringence.

Another diff parameter g defin dependent so that

the bias in the t nique for elimina

fiber in opposite

drift in the twis

to be compensated

The effect of alt tion is to shift the origin. Thus

to measure small polarizers orient

a 10 turn, 10 cm without twisting

in Fig. 10.

The effect of twisting on a Sagnac current sensor

is qualitatively similar to the effect of alternate twisting in a polarimetric sensor. Specifically, the transfer function remains symmetric about zero current

and the distortion caused by linear birefringence

shifts away from the origin (Fig. 11). One of the most important properties of the Sagnac, its independence on Input polarization state, is retained, at least for the symmetric geometry considered nete.

iculty with twisting is that the

ed in Eq. (10) is slightly temperature

when large amounts of twist are used ransfer function may drift. One tech- ting this problem is to twist the directions about its center [2]; any t-induced rotation in one half tends

by an equal drift in the other half, ernate twisting on the transfer functhe distortion in both directions from

it 1s most useful in sensors designed currents and which therefore use

ed at 45 deg. The transfer function of diameter coil in that configuration,

and with alternate twisting is shown

G-5
-0.2

R(I)

<) um».»i»e

<*> tllirnililf t»iatad

10 t«»r»/mol«'

•Vitft birafriAeanca

Without girafringanca

r.oa. 4. antic IJ6 urn

10 twrnt, to CM dia

10. Computed transfer function showing the effect of alternate twisting. Coil is the same as 1n Figs. 8b and 9b except that the polarizers are oriented for a transmittance of 0.5 at zero current, (a) The fiber is not twisted, (b) The fiber

is twisted at a rate of 10 turns per meter about

Its center. Dotted curves assume no linear birefringence.

ANNEALING OF BEND-INDUCED BIREFRINGENCE

To produce multiple turn coils much smaller than

10 cm diameter, one must consider other techniques for minimizing the bend-induced birefringence. One technique that has been successful in reducing the bire- fringence of coils as small as 3 cm diameter is annealing at high temperatures [13].

With all coatings removed, fibers are placed into

a ceramic fixture (Fig. 12) that determines their ulti- mate configuration. By heating the coil to tempera- tures in the vicinity of 700°C, maintaining those tem- peratures for periods of several days, and cooling

slowly, the birefringence can be reduced by an order of magnitude or more. When cool, the fibers retain their

coiled form without confinement and can, if desired, be removed from the annealing fixture. They are strong

enough to be handled but could be encapsulated for further protection.

Most of the testing to date has been performed on coils with five and a half turns of fiber. These coils show the sensitivity that would be expected for coils without linear birefringence.

1.0 I MA — Wr.ir D"«tring#nce Fto*' di«m«i«r 1?5um

Without Gniotrinpor. c« £ 633 nm

1 turn, 3 cm 0>»

11. Computed transfer function for a Sagnac inter- ferometer configuration showing the effect of twisting. Coil is the same as in figures 8a and

9a. Twist rate is 50 turns per meter. Dotted curve assumes no linear birefringence.

12. Fixture used for annealing bend birefringence. The material Is machinable ceramic. The fiber lies in a 3 mm wide channel and makes several 3 cm diameter turns around a hole through which a conductor can be placed.

SIGNAL/NOISE ANALYSIS

It is widely believed that the relatively small Verdet constant of fiber limits the application of fiber current sensors to applications involving very large currents. Actually, if other noise sources can

be reduced to the point that shot noise in the detector

is the limiting factor, quite small currents can be measured.

Numerous parameters

mining the noise equivale

sensor. The signal level constant, the number of t power propagating in the detector and its load res normally set by fluctuati

(laser noise) in combinat

the detector load resista associated with the avera

must be considered in deternt current of a fiber current

1s determined by the Verdet

urns of fiber, the optical

fiber, the responsivity of the istance. The noise level is ons in the optical power

ion with the Johnson noise of nee and/or the shot noise

ge detector current.

G-6
o i Z J

0.001 0.01 0.1

Averts* Oatactor Current, »A

13. Computed noise equivalent current for a single-turn

sensor as a function of detector load resistance

and average detector current. Laser noise is assumed to be insignificant.

For a sensor based on a single turn of fiber, with

a beamsplitting polarizer and two detectors at the output as described above, the noise equivalent current

(NEI) can be computed as a function of average detector

current and detector load resistance. The transfer

function is assumed to be as given by Eq. (6). Laser noise and acoustic noise are assumed to be negligible.

The result is shown in Fig. 13.

For small load resistances and small average detector currents, the slope of the curves is unity.

Indicating a Johnson noise limitation. For larger load resistances and/or larger average currents, the slope

of the curves shifts to one half, indicating a shot noise limitation. At an average detector current of

1 mA the noise equivalent current ranges from 1 to

2 mA/Hz 1/2 for a broad range of load resistances.

An average detector current of 1 mA 1s probably a practical upper limit for such a sensor system. Other options for decreasing the NEI of a sensor based on this configuration are using more turns and using a fiber with a higher Verdet constant.

Increasing the number of turns of fiber to improve

the sensitivity is limited by the extent to which

linear birefringence can be controlled and to which a reduction in the response time of the sensor can be tolerated. Calculations similar to those presented above suggest that, using relatively large (e.g., 10 cm diam.) coils of twisted fiber, 1t may be practical to

use more than 100 turns. Such a device should provide

a NEI of the order of 10 U A/Hzi /2 . The transit time of

a 100 turn, 10 cm diameter coll is about 160 ns.

Several research groups are now exploring the pos- sibility of producing fibers with a higher Verdet constant [14,15,16,17]. Among the possibilities are fibers containing lead and various rare earth elements.

An examination of data for various commercial bulk glasses suggests an increase in the Verdet constant of

a factor of 10 to 20 might be achieved in this way. If so, It 1s reasonable to anticipate fiber current sensors with a NEI of the order of 1 U A/Hzi /2 .

and Sandia National Laboratories and the Bonneville

Power Administration, and also by the Empire State Electric Energy Research Corporation and the Electric

Power Research Institute through the Bonneville Power Administration. This paper represents U.S. Government

work and is therefore not subject to copyright.

REFERENCES

1. A. M. Smith, Polarization and magnetooptic properties of single-mode optical fiber, 17, 52-56

(1978).

2. S. C. Rashleigh and R. Ulrich, Magneto-optic cur- rent sensing with birefringent fibers, _34_. 768-770

(1979).

3. A. Papp and H. Harms, Magnetooptical current transformer. 1: Principles. Appl . Opt. 19 37 29- 3734 (1980).

4. W. F. Hemsing, VISAR: 2 1/2 minutes for data reduc- tion, Proc. SPIE 427, San Diego, 1983.

5. H. J. Arditty, Y. Bourbin, M. Mapuchon, and C. Puech, Current sensor using state-of-the-art fiber- optic interferometric techniques, Technical Digest, Third International Conference on Integrated Optics and Optical Fiber Communications, San Francisco,

1981.

6. D. L. Mitchell and R. F. Wallis, Interband Farday

Rotation in Germanium, Phys. Rev. 131, 1965-1971

(1963); E. D. Palik, The use of polarized infrared radiation 1n magneto-optical studies of semicon- ductors, Appl. Opt. 2. 527-539 (1963).

7. T. Yoshino and M. Nara, Some fiber-optic sensors using differential heterodyne method, Proc. 4th Sensor Symposium, 1984, Institute of Electrical Engineers of Japan.

8. G. I. Chandler, P. R. Forman, and F. C. Jahoda, Measurement of Faraday rotation in twisted optical

fiber using rotating polarization and analog phase

detection, Proc. SPIE, 566, San Diego, 1985.

9. R. Ulrich, S. C. RashleTgK", and W. Eickhoff, Bend- 1ng-1nduced birefringence in single-mode fibers,

Optics Lett., 5, 273-275 (1980).

10. G. W. Day, D. "N". Payne, A. J. Barlow, and J. J. Ramskov Hansen, Design and performance of tuned fiber coil Isolators, IEEE J. Lightwave Tech., LT-2 , 56-60 (1984).

U. W. J. Tabor, A. W. Anderson, and L. G. VanUitert, Visible and Infrared Faraday rotation and bire- fringence of single-crystal rare-earth orthoferrites, J. Appl. Phys., 41, 3018-3021 (1970).

12. R. Ulrich and A. Simon,-

Polarization optics of twisted single-mode fibers, Appl. Opt.,_l§, 2241- 2251 (1979).

13. G. W. Day and S. M. Etzel , Annealing of bend- Induced birefringence in fiber current sensors, Technical Digest, EC0C/I00C 1985, Venice.

14. P. Sanders, D. Krohn, and M. Maklad, Faraday rota- tor single-mode fiber, SPIE 566, 1985, August 1985,

San Diego.

15. K. Shiraishi, K. Nishino, and S. Kawakami, Tem- perature-insensitive fiber Faraday rotator, Appl.

Opt. 24, 1896-1897 (1985).

16. K. Shiraishi, S. Sugaya, and S. Kawakami, Fiber Faraday rotator, Appl. Opt. _23, 1103-1106 (1984.

17. S. Poole and D. N. Payne, Fabrication of optical fibers containing low levels of rare earth ions, Technical Digest, EC0C/I00C 1985, Venice.

ACKNOWLEDGMENTS

Research on optical fiber current sensors at the

National Bureau of Standards has been supported in part

by the U. S. Department of Energy through Los Alamos

G-7

•C U.S. GOVERNMENT PRINTING OFFICE 1987-7 7 5 316/ 65135
NBS-114A irev. 2-8Q

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET [See instructions)

1. PUBLICATION OR

REPORT NO. NBS/TN-1307

2. Performing Organ. Report No 3. Publication Date

March 1987

4. TITLE AND SUBTITLE

Limits to the Precision of Electro-Optic and Magneto-Optic Sensors

5. AUTHOR(S)

G.W. Day, P.D. Hale, M. Deeter, T.E. Milner, D. Conrad, S.M. Etzel

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions]

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State, ZIP)

Bonneville Power Administration (BPA) , Empire State Electric Energy Research Corp,

(ESEERCO) , and the Electric Power Research Institute (EPRI)

10. SUPPLEMENTARY NOTES

J Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

The principles of electro-optic and magneto-optic sensors suitable for use

in power system applications are reviewed with particular attention to the

properties of materials and componen ts that limit the precision of such

sensors. Data on a number of materials are collected and presented. For

high-precision electro-optic sensors, it is recommended that crystals of

point symmetry 43m be used. For high-precision magneto-optic sensors, a lead glass with a low stress-optic coefficient is recommended. Choices for

other components are also suggested. For both types of sensors, a precision

of roughly ±1 percent over a 100 °C temperature range should be attainable.

To achieve a precision better than that, it will be necessary to use temperature compensation techniques, several of which are proposed and discussed.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

current; electric power; electro-optic; fiber optic sensors; magneto-optic;

measurements; power systems

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