CA1274010A - Thermally compensated reference interferometer and method - Google Patents

Abstract

THERMALLY COMPENSATED REFERENCE
INTERFEROMETER AND METHOD
ABSTRACT OF THE DISCLOSURE
A first birefringent material is positioned to receive an optical output from an optical source. A second birefringent material is positioned to receivethe signal transmitted through the first birefringent material. The birefringence of the first birefringent material is modulated to produce a modulation in the phase difference between two polarizations propagated between the birefringent materials. A detector forms an electrical signal indicative of the phase shift produced by the first and second birefringent materials between a pair of orthogonal polarizations in the optical signal received by the first birefringent material. This phase shift is opposite to phase shifts caused by changes in thesource wavelength. A feedback signal indicative of the base shift caused by thecrystals is fed back to the optical source to stabilize its frequency. The system produces a temperature-independent phase shift between the two polarizations by apparatus of proper selection of the lengths of the crystals in the optical path.

Description

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THERMALLY C:ONIPENSATED RFERENCE

BACKGROUND OF THE INVENTIC)N
This invention relates generally to apparatus and methods for controlling the frequency of light sutput from an optical signal source. This invention is particularly related to apparatus and methods for controlling th~ frequenoy of optical signals output from coherent light sources. Still more particularly thisinv~ntion r~!ates to apparatus and methods for controlling tha frequency output ~rom an optical signal source us~d in a fiber optic rotation sensing system to stabilize the scale factor that relates the Sagnac phase shif~ to the rotation rats.
A fiber optic ring inter~erometer typically comprises a loop of fiber optic material having counter-propagating light waves therein. After traversin~ the loop, the count6r-propagating waves are combined so that they constructively or clestnJctively interfere to form an optical output signaL The intensity of th~ optical output signal variss as a function of the type and amount of interference, which is clependent upon the relative phase of th~ counter-propagating waves.
Fiber optic ring interferometers ara particularly use~ul for sensing rotations. Rotation of the loop creates relati~e phase difference between the counter-propagating waves, in accordanoe with the Sagnac effeot, with the amount af phasa difference being a ~unction of the an~ular velocity of the loop.The optical output signal producad by th~ interference of the counter-propagating waves vanes in int~nsity as a function of the rotation rate of the loop. Rotation s~nsing is accomplished by deteoting the optical output signal and prQoessing the optical output signal to determins the rotation rate.
In ord~r to be suitable for inertial navigation appliea~ions, a rotation sensor must have a very wide dynamic range. The rotation sensor must be oapable of detec~in~ rotation rates as low as 0.01 degrees pcr hour and as high as 1,000 degrees per second. The ratio of the upper limit lower limits to be rneasured is approxima~ely 109.
The developmang and practical implementation of rotation sensing systems using optica! signals requira stability in the optical pulsas input to the optical fibers. Optical sensing systems may usa semiconductor diode lasers or superluminescent diodes as light sources. Broadband semiconductor light sources hava baen used in fiber optic rotation sensors to reduee noise ansing ~rom backscattering in the fiber and for reducing errors caused by the optical .
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Kerr effect. For a high precision fiber optic rotation sensor th~ wav~l~ngth of the light source rnust bc stabili~ed since the scale factor of the s~nsor dcp~nds upon th~ source wavel~ngth. A navigation grade rotation sensor rcquires wavelength stability of about one part in 1 o6.
All solid stat~ cohersnt li~ht sourees include two polished parallel faccs that ar~ parpendicular to tha plane of a junction of th~ p-type and n type s~miconductors. The combination of ~lectrons injected from th~ n-region into the p-region with holes, or positive charge carriers, in the p-region causes th~emission of coherent light. The emitted light reflacts back and forth across thercgion betwe~n the polished sur~aces and is consequently amplified on each pass through the jun~ion.
The wavelength of ths light amitted from a solid state coh~rent light source varies as h~nctions of th~ operating temperature and the inj~ction curr~nt applied. Effactive US6 of coherent light sources in an optical rotation sensor 1~ r~quires an Ol~tpl~t of known wavelength.
Superlumines::~nt diodes used as light sources in fib~r optic rotation s~nsors typically have fractional lin~widths of about 10,000 ppm. They aiso have operating lifetimes of about 100 hours and provide about sao ~lW or l~ss optical powar into an optical fiber. SLD's have linewidth to frequency stabilityratios of about 10,000 and r~quire ralatively high injection currents that typically exceed 100 mA. The short oparating lifetim~ and exc~ssive linswidths mak~s ~;LD's unacceptabla tor fiber optic rotation sensors, which shouid operat~
r~liably for thousands of hours without sourc~ r~placement.
Som~ familiarity with polanzation of light and propagation of ii~ht within a guiding strudure will facilitate an understanding of the present invention. It is well-known that a light wave may be repres~nted by a time-varying electromagnetic field comprising orthogonal alectric and magn~tic field vectors having a frequency ~qual to the frequency of the light wave. An electromagnetic wave propasating through a ~uiding structur~ can be described by a s~ of normal modes. ~h~ normal modes are the pcrmissible distributions o~ tho electric and magnetic fields within the guiding structurc, for example, a fiber optic waYeguide. The field distributions ar~ directly related to the, distribution of energy within the structure. The normal modes are g~nerally represented by rnathematicai functions that d~seribe the field compononts in the wave in terms of the frequency and spatial distribution in the guiding structure. The specific , -.~ Z~4 functions that describe the normal modes of a wave~uide depend upon th~
~eomatry of the waveguide. For an optical fiber, where the guided wave is confined to a structure having a circular cross section of fixed dimensions, only ~ields havin~ certain ~requencies and spatial distrib~ltions will propagate without 5 sever~ attenuation. The waves having field components that propagate with low attenuation are called normal modes. A single mode fiber will propagate only one spatial distribution of ener~y, that is, one normal mod~, for a signal of a given frequency.
In describing the normal modes, it is oonv0nient to refer to the direction of 10 the electric and magnetic fields relative to the direction of propagation of the wav~. Th~ dir~ction of the electrio field vector in an el~etromagn~tic wave is the polarization of the wave. If only the alectrie fleld Yector is perpendicular to the direc~ion of propagation, which is usually called the optic a~tis, then the wave is a transverse electric (TE) mod~. If cnly the magn~ic field vector is p~rpendieular15 to to th~ optic axis, the wave is a transverse ma~netic (TM) mode. If both the el0ctric and magnetic field v~ors are perpendicular to ~he optic axis, then the wave is a transverse electromagnetic (TEM) mode.
None of the norrnal modes require a definite direction of the field cornponents. In a TE mode, for example, the electric field may be in any 2û ~irection that is perpendicular to thc optic axis. In generai, a wave will have random polarization in which there is a uniform distribution of electric field vcctors pointing in all dirsotiens permissible for a ~iven mcde. If all the electric fi~ld vectors in a wave point in only a particular direction, the wave is linsarly polarized. If the e!ectric field eonsists of two orlhogonal electric field components 25 o~ equal magnitude and a phas~ difference of 90, the slectric field is circularly polarized, because the n~t electric field is a vector that rotates around th~
propagation direction at an angular velocity equal to th~ frequency of the wave.If thc two linear polarizations are unequal or have a phase difference other than 90, the wave has elliptical polarization. In general, any arbitrary polarization 30 can be ~presented by the sum of two orthogonal linear polarizations, two oppositely dir~ctsd circular polariza~ions or two counter rotating elliptical polarizations that have orthogonal major axes.
An optical flb3r comprises a central core and a surrounding cladding. The relFractiva index of the cladding is greater than that olF the cors. The diameter of 35 the core is so small that light guided by the core impinges upon the core-. . ~

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74Q ao cladding interface at angles less than the critical an~le for total internalreflection.
The boundary between the core and cladding is a di01~ctric interface at which certain well-known boundary conditions on the field components must be 5 satisfied. For example1 th0 component of the electric fieid parallel to the interface must be continuous. A single mode optical fiber propagates electNmagnatic energy having an slectric field component perpendicular to thc coro-cladding interface. Since the fiber core has an index of refraction great~rthan that of the claddin~ and light impinges upon the interface at angles great~r 10 than or squal to the critical angle, assentially all of th~ electnc field r~mains in ~he core by intemal r~fl0ction at the interface. To satisfy both the continuity and intsrnal reflection requirements, the radial slectric field component in the cladding must ba a rapidly decaying exponen~ial function. An ~xponentially decaying electric field is usua!ly called the "evanesc~nt field."
The veloci~y of an optical signal depsnds upon th~ index of refraction of the medium through which the light propagates. C:ertain materials have differ~ntrefractiv~ indices for different poiarizations. A material that has two refractive indices is said to be birefringent. The polarization of the signal propagatingalong a single modc optical fiber is sometimes referred to as a mode. A
20 standard single mode optical fiber rnay be regarded as a two mode fiber because it will propagate ~wo waves of the same frequenoy and spatial distribution that have two different polarizations. Two different polarization compon~nts of the sams normal mode can propagate through a birefringent material unchanged except for a Yelocity difference between the two 25 polarizations.
There are a number of birefringent rnaterials. For exampl~, depending on thair s~ructure and orientation to the ligh~ propagating ~hrough it, c~rtain crystals aro circularly birefringent; and other crystals are linearly birefringent. Othertypes of crystals, such as quartz, can have both oircuiar birefringence and linear 30 birefringence.
Stabilization of the scale factor is critical to the p~rform~nce of a high accuraoy fiber optic gyroscope. The scale factor, which relates the angular rotation rate of the sensor to the Sagnac phase shi~t, is sensitive to changes in the langth of the fiber and to variations on the operation wavelen~th of the 35 source. In superluminasc~nt diodes (SLDs), variations in the emission . - . ,.
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wavelength are caused by thermal fluctuations in the active re~ion caused by changes in the ambient temperature and in the interaction curr~nt. Typically, th~
temperature dependence of the SLD emission wavelength is about 0.2 namnmeters per C. To obtain the required wavelength stability by tharmal apparatus alone would r~quins the tamperature of the SLD to be helcl constant toa few millidegreas. The need for such stringant temporature stability can be obviatsd by using a refer~nce interferometer to continuously monitor the emission spectrum of the SLD. In this scheme, changes in tho emission spectrum generate an error signal which is processed and fed back to the diode to hold the wavelength constant.
Lasers, with their long coherencQ length, are readily stabilized by using a temp~rature stabilized scanning Fabry-Perot intefferometer to lock the cavity length. HoweYer, tho larg~ spectral bandwidth of the SLD precludes the use of optical spectrum analyzers to monitor the emission waYelength of the dioda.
Th~ mirrors of a Fabry-Perot interferomotQr to analyze the typical 10 nm emission bandwiclth of an SLD would have ~o b~ spaced approximately 1 ,um apart, which is impractical.
Previously propos~d methods for stabilizing th~ SLD wavelength use either an in-line technique in which the dispersion of the fiber is used ~o monitor the SLD wavelength or a break out methocl in which the SLD emission is monitored ind~pendantly. In the first method, a Bragg cell is rcquired to ~enerate the largc frequenoy shifts needed to confldently utilize fiber dispersion.
Such bulk optic components placed in line with the sensor would introduce alignment problems whioh could become more pronounced with temperature cycling.
A practical wavel@ngth stabilization scheme must taka into account the volume budget of the gyro and should be capable of being packaged within the gyro housing. This constraint limits the volume of the wavalength stabili~ation device to a maximum of a few cubic centimeters.

A devic0 according to the invention for controlling th~ frequenoy of an optical signal output from an optical signal soure~ comprises a first birefringent material positionsd to receive an optical signal output from tho optical source sa that the si~nal propagates thsrethrough; appara~us for modulating the birefringence of ~he first birefringent mat~rial; a second birafringent material ., ~ ' , i2'741t?~

positioned to receive the si~nal output from th~ first birefringent rnaterial;
detector apparatus for forming an electrical signal indicative of the phase shift produced by the first and second birefringent materials batween a pair of or~hogonal polarizations in the optical signal received by the first birefringent material; and apparatus for processing the electrical signal for adjusting the frequency of the optical signal output from the signal source.
Th~ device according to the invention for controlling the frequsncy of an optical signal output from an optical signal source may fur!h0r comprise a firstpolarization beamsplitter positioned between the optical source and the first birefringent material; and a ~econd polarization bcamsplittcr positionad betweenfhe dete~or apparatus and the second birefringent material.
The first polarization baamsplit~er preferably has a polarization axis ariented a~ 45 to the principal axes of the first birefringent material and th0second pola~ization beamsplitter preferably has a polarization axis oriented at 45 to the pnncipal a~tes of the second birafringent materlal.
The modulating apparatus in the device according to ths invention for oontrolling the frequency of an cptical si~nal output from an optical signal source preferably comprises an oscillator electrically coupled to the first birefringent material, the first bir~frin~ent material being electrooptically active so that signals ~O from the oscillator change at least one of the rafractive indices of the first birefnn~ent ma~erial. The modulating apparatus prefarably further includes a mixer connected both to tho oscillator and to the d~tecting apparatus to receivesi~nals therefrom; and an amplifier conn~ctsd to th~ mixor to raceive the mix~d oscillator and detector siynals.
The d~vice according to th~ invention for controlling th~ frequency of an optical signal output from an optical signal source includes apparatus for producing a temperature-independent phase shift between the two polarizaticns that are input to the first birefringent material and output from the second birefringent material. The apparatus for producing a temperature-independent phase shift includes a first length L1 of the first birefringent rnatenal and a second length L2 of the second bir~frin~ent material such that L1/L2 = K~B2/K1 B1, where Bl and B2 represent the birefringence of the first and second birefringent rnaterials, respectively and Kl - (1/B1) dB1/dT + 11/4) dL1/dT, and 12'~

K2 - (1/B2) dB~/dT ~ (l/L2) dL~/dT, with T repres~nting the temp~ratur~
of the fir~t and s~cond birefring0nt mat~rials.
The method of th~ invention for controlling the frequ~ncy of an optical signal output from an opUcal signal source comprises th~ steps of positioning a first birefringent material to reo~ive an optical signal output from îhe opticalsourc~ so that the signal propagates therethrough; modulating th0 birefringencs of the first bir~tringent material; positioning a second birefringent mat~rial to receive the signal output from the first birefring~nt material; forming an el~ctrieal signal indicatiYe of tha phas~ shift produced by the first and s~cond birefringen~
materials between a pair of or~hogonal polarizations in the optical signal rec~ivcd by the flrst bir~fring~nt mat~rial; and processing the elsc:trical signal for adjusting the frequ~ncy of the opticai signal output from th~ signal source.
The method of the invention may further comprise th~ steps of placin~ a flrst polarization beamsplitter b~tween the optical sour~e and the fir~t bir0fring~nt material; and placing a second polarization b~amsplitter betwe~n the detector apparatus and th~ second birefringent mat~rial. Th~ method of the invention may further comprise the steps of arranging the first poJarization beamspiitter to have a polarization axis orient~d at 45 to the principal axes of the first birefringent material and arranging the second polarization beamsplitt~r to havea polarization axis orient~d at 45 to the principal axes of the seoond bi~fringent material.
The method of the invention may furth~r comprise th~ step of forming tha modulating apparatus ~o compr!se an oscillator electrically coupled to the firstbirefringent material, th~ first birafring0nt material being al~ctrooptically active so that signals from the oscillator change at Isast one of the refractive indices of the lirst bir~fringent mat~rial. Tha step of forming the rnodulating apparatus may further include the steps of connccting a mixer both to the oscillator and to the dctecting apparatus to receive signals therefrom; and amplifying the mixed oscillator and detsctor signals.
The method of the invention further comprises the step of producing a temperature-independent phase shift between the two polarizations that are input to th~ first bir~fringent mat~riai and output from th~ s~cond bir~fring0ntmaterial. Th~ step of producing a temperature-independent phase shift includes formin~ the first bir0fringent material to have a first length Ll and forming the seoond birefringent rnaterial to have second len~th L2 such that L1/L2 O

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K~B2/K1B1 wher~ B1 and B2 rspresent the birefring~nc~ of the fir~t and second birefringent materials, respectively and K1 = (1/B~)dB1/dT + (1/4)dL1/dT,and K2 - (l/B2) dB2/dT ~ (1/L2) dL2/dT, with T representing the temperature.
The invention also includes a fiber optic rotation s~nsing system compr~s~s an optical source; a first optical fiber for rec~iving light from the optical sourc~; a second optical fib~r having a s~nsing coil formed therein; optical coupling ~pparatus for coupling light b~twe~n the first and sacond optical fibers;
and appar~us for controiling th~ frequancy of an optical signal output from an optical signal source, cornprising a first birefringent material positioned to recaive an optic~l signal output from the optical source so that the signal propagates therethrough; apparatus for modulating the birsfnng~nce of th~ first birefringent material; a second bir~fringent material position~d to r~ceive the si~nal output from the first birsfring~nt material; det~ctor apparatus for forming an el~ctr~Gal si~nal indicative of the phase shift produc~d by the first and second birefringent materials betwaen a pair of orthogonal polarizations in the op~icalsi~nal received by the first birefring~nt material; and apparatus for processing the electrical si~nal for adjusting the frequency of the optical signal output from the signal sourcs.
The fiber optic rotation sensing system according to the invention fu~her includes apparatus for produoill~ a temperaturs-ind~p0ndent phas~ shift between the two polarizaVons that are input to the first birefringent material and output from th~ second birefnn~ent material. The apparatus for prodlJcing a t~mperature-ind~pendent phase shift preferably includes a first length L1 of thefirst birefringent material and a second length L2 of the second birefringent material such that L1/L~ - K2B2/K1B1, where E~1 and B2 represant the birefringence of the first and sacond birefringent materials, respectively and K1 = (1/B1~ dB11clT + (1/Lj) dL1/dT, and K2 - (1/B2) dB2/dT + (1/L2) dL2/dT, with T representing the ternperature of the first and second birefringent materials.
The method of the invention for measuring rotations comprises the steps of producing a light bsam with an optical source; receiving light from the optical source with a first optical fibar; forming a sensing coil in a second opticai fiber;
coupling light be~ween the first and second optical fibers so that the sensing coil guides a pair of counterpropagating waves; and oontrolling the frequency of an optical signal output from the optical signal source, comprising the steps of positioning a first birefringcnt material to receive an optical signal output from the optical source so that the signa! propagates therethrough; modulating the birefnngence of the first birefringent material; positioning a second birefringent mater~al to receive the signal output from the first birefringent material; forming an electrical signal indicativs of the phase shift produced by the first and sscond birefrin3ent materials between a pair of orthogonal polarizations in the opticalsignal raceiv0d by the first birefringent material; and processing the eleotrical signal for adjusting the freqwency of tha optical signal output from the signal 1 0 source.
The method of the invention for sensirlg rotations further comprises the step of producing a temperature-indapendent phase shift betw~en the two polarizations that are input to the first birefringent material and output from the sacond birofrin~erlt material. The step of producing a temperatura-indepandent phase shif~ includes ~orming the first birafringent material to have a first length L1 and ferming the second birefringent matarial to have second length L2 such that L1/ 2 = K2B2/K1B1 where B1 and B2 represent the birefringence of the first and ~econd birefringent materials, respactively and K1 ~ 1) d~ T + (114) dLl/dT, and K2 = (~/B2) dB2/dT ~ ~1/L2) dL2/dT, with T reprssenting th~ temperature.
BRIEF DESCRiPTlON OF THE DRAWINGS
Figure 1 illustrat~s a th~rmaily compensated reference interferometer according to the invsntion;
Figur~ 2 schematically iJlustrates orientation of crystals in the thermally compensated referenoe interferometer of Figure 1 rela~iva to tha polarization of~he inoident light;
Figure 3 graphically iiiustrates th0 spectrum of a typical superiuminescent diode used as an optical source in a fiber optio gyroscope;
Figure 4 graphically illustrates the visibility of the interference pattern producsd by the thermally compensated referenee interferometer of Figure 1 as a function of the optical path diffarence in the interferometer;
Figure 5 graphically illustrates the output of the thermally compensated reference in~erferometer of Figure 1;

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-~0-Figure 6 graphically illustrat~s th~ fractional phas~ shift per C as a function of the ratio of th~ lengths of the crystals includ~d in tha thermally compansated reference int~rferometer of Figure 1;
Figure 7 schematically illustrates a fiber optic gyroscope that may be used 5 with the thermally compensated reference interferom0t~r of Figure 1;
Figure 8 is a cross sectional vi~w of a fib~r optic directional coupler th~t may be included in the fiber optic gyroscop~ of Figure 7;
Figure 9 is a cross sactional view along line ~9 of Figur~ 8;
Figur0 10 is pian vi~w of a phas~ modulator that may be included in th~
10 fiber optic ~yroscop~ of Figure 7;
Figur0 11 is an end slevation view of the phase modulator of Figure 10;
and Figure 12 is a perspectivs view of the phase rnodulator of Figures 10 and 11.
1 ~ DESCRIPTION OF THE PREFERRED EMBODIMENT
Rsferring to Fiyure 1, a thermally comp~nsa~ed ref~rence interferometer 10 according to the invention includes a lens 12 that receives light from an optical fiber 14. Light is input to the fiber 14 by an optical source 15, shown in Figur~ 7. The lens 12 is mounted on a bassplate 16. The lens 12 focuses the O 1i~3ht onto a polarization beamsplitter 18, which is also mounted on the b~sepl~te 16. The polarization beamsplitter 18 is preferably a bulk optics device for polarizing an optical input at 45 to ~he optic a~(is. The opUc axis is conveniently deflned as a line collinear with the light beam input from the fiber 14.
Light transmit~ed straight through thc pol~riza~ion b~amsplitter 18 25 impinges upon a flrst crys~al 20 that is mounted to th~ baseplat~ ~6. Light transmitted through th~ crystal 20 impiriges upon a s~cond crystal 22 moun~ed on the baseplate 16 near the crystal 20. Although other materials may be used the crystal 20 is preferably formed of lithium niobate, and the crystal 22 is formed of lithium tantalats. Both of these crystais 20 and 22 are birefringent 30 electrooptically active materials.
Referring still to Figure 1, a pair of electric leads 24 and 25 are connected to the crystal 2û. Although several other pairs of orystals wouid satisfy the temperature stability raquirements of the reference interferometer 10, electro-optic crystals are preferred to provide a discriminant for phase-sensitive 35 datection. This discriminant is obtained by applying an alternating voltage from ~ ~ , . -~ , .,;

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an oscillator 3~ to the crystal 20 to modulate the phase of the optical wave transmitted therethrough.
Light transmitted through the crystal 22 is then input to a second poiarization bea,7nsplitter 30 mounted to the baseplate 16. The polarization 5 ~amsplitter 30 polanzes the input light along a line at 45 to the optic axis.Ligh~ transmitted straight through the polarization beamsplitter 30 then impinges upon a lens 32, which focuses the light onto a detector 34 that is also mount~d on the basepl~te 16. A pair of absorbers 36 and 38 receive the light rejected bythe polari~ers 18 and 30, respectively. These absorbers 36 and 38 prevent the 10 rejected light from having any effect on the si~nal input to tha detector 34.The baseplate 16 and all the components mounted thereon ar~ preferably ~nclosed in a hermetically sealed container 40.
For an optical beam polarized at 45 to ~he optic axis of ~he lithium niobate crystal 20 and lithiurn tantalate crys~al 22, the phase difference be~we~n the two 1~ orthogonally polarized components is Y = 27cSI~ (1 ) where ~ is the wavelen~th of the source. The optical pathiength difference, S, between the two polarizations propagating in tha crystals, is S = L~81-L2B2 (2) ~0 wher~ Ll, L2 and B1 . B2 are the len~ths and birefringences of crystals 20 and 22~
respectively. The birefringenc0 is the difference in refractive index for waves of different polarizations.
For a thermally insensitive r~ference interfsrometer, the temperature derivative of the phase difference, Y, must be zero. Since the c~stals 20 and 2225 are birefringent, propagation of th~ light through them causes a phase chang~be~ween the two polarization components. Differentiating Equation (1) with respect to t~mperatur~ and setting the result equal to zero gives L1/L2 = K2B2/KlB1 (3) where Kj = (1/Bj) dBj/dt ~ (1/Lj) d4/dt (4) is the sum of the normalized rate of change of birefringence with temperature and the thermal expansion co~fficient of each crystal .X~ 17 2.
The lengths of the crystals 20 and 22 in the reference interferometer 10 are subject to thr~ restriction imposed by the spectral bandwidth of the source.35 That is, for 9QOd ~ringe visibility in the interferometer 10 the optical path ~2'74010 -12~
diffarence betwe0n the two polarizations must be less than the coherenc~ length of the source, XCoh. This criterion sets an upper limit on the total length of the orystals 20 and 22 in the intarferometer 10. Using Equation (3) and the requircment that the op~ical pathlength difference be less than the coh~r~nce 5 length of the source, an uppsr limit on the absoluts lengths of the crystats 20 and 22 is obtained. For the crystal 20, the upper length limit is L1 C X~ oh/[B1 (1 -K1 /K2)~
Figure 3 illustrates the spectrum of a typical SLD. The SLO has a 57 ~m coherence length and a center wavalength of 820 nm. Tha ma~imum length of 10 the lithium niobate crystal 20 is therefor~ 635 ~lm. From tha length r~tio L1/L2 ~
1.0~2 as detennin~d from Equation (3), the maximum length of the lithium tantalate crystal 22 is 5~2 llrn. Thus, the maximum combined length of the two crystals 20 and 22 in the interferometer 10 is 1.217 mm.
Figure 5 illustrates th~ output of the int~rferometer 10 ~or light input from 15 an SLD as a fune~ion of the optical path difference. Figur~ 4 illustrates thevisibi~ity of the interfer~nce pattern as a function of optical path diff~renc0.Optimization of the signal to noise ratio to facilitats signal processing r3quir0s that ~he fringe visibility in the interFerometer 10 be elose to unity.
Therefor~, the interferometer 10 is designed to have an optical path difference of 20 8.2 llm and is fix~d on the tenth fringe from ~ero pathlength diffsrence. Making th~ optical path diff~rence betw~en the two o~hogonai polarizations an integral numbar of waYelengths ensures that th~ throughput of the second polarizer 30 is a maximum when it is aligned parallel to the polarizer 18. For the 8.2 ,um optical path difference the lengths of the two crystals 20 and 22 are 91 ~m and 84 ,um, 25 respectively. The r~quirem~nts of crystal thickness and tolerance, although not routine, ar~ within the capabilities of crystal vendors.
Figure 6 is a plot of the fraGtional phasa shift per C l(dy/dT)/Y~, as a ~unction of the ieng~h ratio L1/L~. For a 1% error in the length Yauos~ which corresponds to an error of ~0.5 llm in absolute lengths of the crystals 20 and 22, 30 the fractional phase shift per C in the interferometer 10 is 3.3 ppm/C. By controlling th~ crystal temperaturos to i0.5 C, the phas~ shift in the inteff~romet~r 10 can bs held to within 3 ppm, which is nsc~ssary for holding the wavelangth constant to the required 10 ppm.
Referring to Figur0 2, the electric field for a quasi-mono-chromatic light 35 wava, Ej, polariz~d parallel to e1 and incident on th~ birefringent crystal 20 is . .

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:~2~g~
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Ej(x,t) = e1 Eo cos (Kx~ t) (6) where K - 2~ is th~ wave number, ~ is tha angular frequency of tha wave in radians per second, and x and t re the is displacernent and tim~ coordinatcs, respectively. The optic axes of the two crystals 20 and 22 ar0 align~d parallel to 5 each other and a~ 45 to the polarization of th~ incident wav~. Th~ wave exiting tho crystal ~2 and directed to the l~ns 32 includes two ortho~onal components shifted in phasa with resp~ct to eaeh other. The field distributions for the ordinary and the extraordinary polarizations are Eo - E cos (Kol L1 ~ Ko2L2 - c~t) (7) 1 0 and E~ = E cos (~1 Ll ~ ko2L2 - ~t) (8) respectivcly. L1 and L2 are the lengths of the crystats 20 and 2~, resp~ctiv~iy, and ko and ke are th~ wave numbers of th~ ordinary and extraor~inary wav~s in tha crystals. The polarization bearnsplittar 30 is oriented 1~ so tha~ the polarization of the transmitted wav~ is parall~l to e1. Tim~-av~raged transmittacl and reflected powar are respectively given by Pt = Po[1 ~V cos(Y)]/2 (9) and Pr- Po[1-\lcos(Y)]/2. (10) Po is the square of the ficld amplitude, Eo. For a broad bandwidth sour~e ~;uch as an SLD1 tha cosine functions in Equations (9~ and (10~ are multiplied by th~ fring~ visibility function, V. For an SLl:) with a 10 nm spectrai bandwidth ~he visibility function monotonically decraases from a maximum value of one at zero optical path difference to zero at appr~ximately 60 ,um a.e shown in Figure 4. The design of the interferomster 10 maximizes the transmitted power, Pt, from Equation (9), and makes the reflected power, Pr~ vanishingly small by makin~ thaoptical path differ~nc~ of the interferom0ter an intagral number of wavelengths.For an SLD with a center wavelen~th ef 8~0 nm as shown in Figure 3, the intafferometer 10 has an opticai path diff~renc~ of 8.~ ~lm.
A discriminant for phase-serlsitivo detection of the wavelength shifts in the SLD is obtained by elactro-optically modulating the phase retardation in the lithium niobate crystal 20. This crystai 20 is x-axis cut, and ~lectrode 100 is bonded to an X-2 fac~t as shown in Figu~ 1. Anoth~r electrod~ (not shown) similar to th~ slectrod~ 100 is mounted to th~ other x-z facet.ln this configuration, LISI~ iS mad~ of th0 large r42 electro-optic coefficient to reduc~ the voltage (?~

r~quired to achieva th~ desired phase shift in the crystal 20. Using accepted values for nO - 2.25g8, r42 (32x10-12) mN, and r~2 (~.8 x 1û12), the scal0 factor forth~ 91 ,um long lithium niobate crystal 20 is 0.1 rad mN.
To minimize the appli~d voltage, the optical beam inside the interferometer 10 is soft-focused to a beam raclius cf 18 ~,lm with a Rayleigh rangs of 1.0 mm, which is approximat~ly ~ times the interf~rom~t0r i~n~th. This rela~ively large Rayleigh range ensures a n~ar ,olanar wavelength ov~r the 175 ~Lm long interferometer. The crystals 20 and 22 are cut to a 250 Jlm square cross-section in the y-z plane, which is large enough to accommodate the focused optical beam without any appreciable diffraction effects. With this 250 ~m separation between the electrodes on the x-z facets of the lithium niobate crystal, the scala factor is 0.44 milliradian per volt.
The phase differenca of the two polarizations optica! wave in the interferometer oan be varied by applying an electric field to the electro-optic crystal ~0. A sinusoidal electric field ~f amplitude Ey and angular frequency c~will modulate the phase difference and provide a discriminant for phase sensitive detection.
From Equation (9) the power transmitt~d through th~ polarization beamsplitter 30 is P~ - PO[~ ~ V cos(Y ~ Z cos c~t)~
where Y, given by Equation (1), is the phase retardation in the interferometer 10 in the absence of the clectric fieid applied to the crystal 20, and Z is the electrically induced phass retardation.
Since by design Y is an integral multiple of 27~, the phase of the optical

2~ throughput is modulated about a maximum. Wavel~ngth shifts in the emission spectrum of ths SLD ars d~tected as a signal at the fundamental of the modulation frequency b3.
When the sourca stabilization system 10 shown in Figures 1 and 7 is activated, ~he phas~ shift, F, induced by the crystals 20 and 22 opposes the phasa shift errors, y, induced by the drift in the smission wavelength of the SLD.
The transmitted power, Pt, is then Pt = Po[1 + V cos(y - F ~ Z cos ~ot)~. (12) Expanding Equation ~11 ) givos a Bessel functicn senes Pt = Po ~ Po[Jo(Z)cos(y-F) + J1 (Z)sin(c~t)sin(y-F) ~ J2(Z)cos(c~t)cos(y--F) ~ . . . (13) The ~ervo system process all information in the sp~ctral vicinity of cl) and ignor~s all other t~rms. Tha eff~ctive input signal to ~he s~rvo system from Equation (12) is Pt(0ff) = POJ1(~)sin(c~t)sin(y-F) (1~
Referring again to Figures 1 and 7, an output signal of frequency c~ from the oscillator 31 is input to a mixer 33, which also receives the elaetrical signal from the photodetector 34. The effective input signal given by Equation (14) is mixed with the local oscillator signal ot frequency c~ from the oscillator 31. The output of th~ mixer 33 is than low pass filtered and amplifiHd by the amplifier 3~.
The output of the amplifier 3~ is the feedback signal which is used to stabilizethe ~mission wavel~ng~h of the SLD, and is givan by FB = POa sin(y-F), (15) where ~ reprssents the elec~ronic ~ain of the amplifier 351 which connected betwe~n ~he int~fferometer 10 and the source 1~. The si~nal FB is input to the optical seurce 15 to control the frequsncy of the emitted light signal.
In a solid state light source, the signal FB controls the injection current. Th~frequency stabilization apparatus of the invention may be used with gtas discharge lasers (not shown), in which case the signal FB controls the length ofthe r~sonant cavity in which the discharge occurs~
The obj~ct of the f~sdback signal is to produce a phase shift, F, which cancels the phase shift y. When, as in all servo systems, the ability of the fesdback phas~ shiît to ~rack the phase shift, y, induc~d by changQs in the souree wavelength is dctermined by the loo,u gain of the amplifier 35. Th~ loop gain for the servo systern d~scrib~d is praf~rably larg~ enough (>100) so that y-F is always less than 0.1 radians. In this case, the sin (y~) term in Equation (14~
can be approximat~d by (y F) with negligibl~ arror. The servo system thus op~rates over a linear ran~e, and parameters that provide the waveleng~h stabilization are:
Po = 1 0 llW
G O loop gain (in radians~ = 200 or gre~ter BW = loop bandwidth = 100 Hz Y = loop bandwidth = 100 Hz Z - peak phase modulation amplitude - 0.1 radians d = servo systom damping ratio ~ 0.5 .
., .

.2'7~

Under th~ above op~rating conditions the wav~length stabilization systsm 10 maintains a source wavelength stability of better than 10 ppm~
Referring to Figur~ 7, the fiber optic rotation sensor 41 comprises a sensing loop 42 formed in the fiber 106. The optical signal from the source 15 5 propagates in the fiber 14 to an optical coupler 43, which divides the light between the fiber 14 and the fiber 106. The signal in the fiber 106 propagat~s to an optical coupler 44 that divides th~ light to procluce li~ht waves that propagate counterclockwise (CCW) and clockwis0 (CW) through the loop. After traversin~
the loop 42, the waves then imping~ upon the optical coupler 44. The optical 10 coupler 44 then combines portions of the waYes so that a superposition of ~he C:W and CCW waves propagates back through the fiber 106 to the optical coupler 43, which directs a portion of the combined waves to a Sagnac detector 45, which may be any suitable photodiode.
Th~ output of ths Sagnac detector 45 is an electncal signai indicative of 15 th~ rotation rate of the sensin~ loop about its sensing axis, which may ~e a line p0rpendicular to the plane of the loop 42. The wava traveling around the loop 42 in the direction of rotation will have a longer transit time in th~ loop 42 than the wave traveling opposite to the direction of rotation. This differcnce in transit tirne is detocted as a phass shift in the waves. Tha amount of phase shift is a ?0 function of the rotation rats ancl the waval~ngth of the light input to the sensing loop 42. Th~ scal~ factor relates thQ rotation rate to the parameters of the sensing system.
The electrical output of tha Sa~nac detector 45 is input to a summing amplifier 46 tha~ also receives signals from an oscillator 47. Th~ oscillator 4725 drives a phase modulator 48 ~hat is formed to adjust the phass of light in the sansing loop 42. The output of the summing amplifier 46 is input to a second amplifier 49 that produces a controi signal that is input to an oscillator 37. The oscillator 37 is pr~ferably a sawtooth wave generator. The sawtooth wave cirivesa serrodyne phase modulator 53 that adjusts the phase of th~ light in the loop 30 42.
The summing amplifier 46, oscillator 47, phase modulator ~8, amplifi~r ~9, oscilla~or 39 and phase modulator 53 comprise a phase nulling servo loop 51. In order to providc a wider clynamic range, the servo loop adjusts the light in the sensing loop 42 to null the phase differences caused by rotations of the ~: , ..
,: , ' ' ':

sensin~ loop. The rotation rate is d~termined by measuring th~ amount of phas~
moelulation by the phase modulator 53 to null the rotation induc~d phasa shil~.
A fiber optic directional coupler suitable for use in single mode applications as the coupler 43 of Figure 7 is described in ths Maroh 29, 1980 5 issue of Electronics L~tters, Vol. 28, No. 28. pp. 260 261 and in lJ.S. Patent4,493,528 issued January 1 S, 1985 to Shaw et aL That patent is assigned to the Board of Trustees of the Lcland Stanford Junior University.
As iilustrated in Figures 8 and 9, the coupl~r 43 includes the optical fibers 14 and 106 of Figure 7 mounted in a pair of substrates 50 and S2, respectively.
1 0 The fiber 14 is moun~ed in a curved groovs 54 formed in an opticaliy fl~ ~urface 58 of th~ substrate 5û. Sirnilarly~ the fiber 106 is mounted in a curved groov~ 56 formod in an optically flat surfac~ 60 of the substrat~ 52. The substrate 50 andfib0r 14 mounted ther~in comprise a coupler half 621 and the substrate 52 and ~b~r 106 mounted ther~in Gompr~se a couplar half 64.
The curv~d grooves 54 and 56 each have a radius of curvature that is large compared to the diameters of the ~ibers 14 and 106, which are ordinar~ly substantially identical. The widths of the grooves 54 and 56 ars slightly larger~han the fiber diam~ters to permit the fibers 14 and 106 to conform to th~ pathsde~ined by Ihe bottom walls of the grooves 54 and ~6, r~spectiv~ly. The depths ?0 of the grooves 54 and 56 vary from a minimum at the ~nter of ~he substrates 5û
and 52, respectivety, to a maximum a~ the ~dges of th~ substrat~s 50 and 52.
The variation in groove depth permits the aptical fibers 14 and 106, when mounted in the grooves 54 and 56, rsspectively, to gradually conv~rg~ toward the centers and diverge toward the sdg~s of the substrates 50 and 52, 25 respectively. The yradual curvature ~f th~ fibers 14 and 106 prevents the occurr~nce of sharp bends or other abrupt chan~ss in dir~ction of the fibers 14 and 106 to avoid power loss through mode perturbation. The grooves 54 and 56 may be rsctangular in cross section; however, other cross sectional configura~ions such as U-shaped or V-shaped may bs us~d in forming the 30 coupler 43.
Referring still to Figures 8 and 9, at the centers of the substrates 50 and 52, the d~pths of the grooves ~4 and 56 are less than the diamaters of the fibers 14 and 106. At the ~dges of th~ substrat~s 50 and 52, the dspths of the grooves ~4 and 56 ar~ preferably at least as great as the fiber diameters. Fiber optic 35 material is removed from each of the fibers 14 and 106 by any suitable method, . ~

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~y~

such as lapping, to form oval-shaped in the fibers 14 and 106 that are coplanar with the confronting surfaces 58 and 60 of th~ substrates 50 and 52. The oval surfaces arc juxtapose~l in facing relationship to form an interaction region 66where the evanescent field of light propagated by each of th~ fibars 14 and 106 5 intaracts with the other fiber. Tha amount of fiber optic material rsmoved increas0s ~radually from zero near the edges of the substrates 50 and 52 to a maximum amount at th~ir ccnt~rs. As shown in Figures 8 and 9, the tapered removal of fiber optic matenal enables the fibars 14 and 106 to converge and diverge gradually, which is advantageous for avoiding backward reflection and 10 excessive loss of li~ht energy at the interaction region 66.
Light is transfarred between the fibers 14 and 106 by evanesoant fiald coupling at the interaction region 66. The optical fiber 14 comprises a central core B8 and a surrounding cladding 7û. The fiber 106 has a core 72 and a cladding 74 that ara substantiaily identical to the core 68 and cladding 70, 15 r~spectiv~ly. The core 68 has a refractive index that is greater ~han that of the cladding 70l and the diameter of the co~ 68 is such that light propagating within the core 68 internally reflects at the core-cladding interface. Most of the optical energy ~uided by the optical fiber 14 is confined to its core 68. How~ver, solution of the wave aquations for the fiber 68 and applying the well-known 20 boundary conditions shows that th~ energy distribution, although primarily in tha core 68, includas a portion that extsnds into the claddin~ and dacays expon0ntially as tha radius from the c~nter of tha fibar increases. The exponentially decaying portion of the energy distribution within tha fiber 68 isgenerally oalled the 0vanescent field. If the evanesc~nt fisld of th~ optical 25 energy initially propagated by th~ fiber 14 extends a s~lfficient distanc0 into th~
fiber 43, energy wiil coupl~ from the fiber 14 into the flber 106.
To ensure proper evanescent field coupling, the amount of ma~erial r~moved from the fibers 14 and 106 must be carefully cont~lled so that the spacirlg batween th~ cores of tha fibers 14 and 106 is within a predetermined 30 critical zone. The ~vanescent field extends a shor~ distance into the cladding and deor~ases rapidly in magnitude with distance outsid~ thc flber core. Thus, sufficient fiber optic mat~rial should b~ removad to permit overlap between the evanescent fieids of waves propagated by the two fibers 14 and 106. If too little material is removed, the cores will not be sufficiently close to permit the :. ;; : .
. ~.

7~

~van~sc~nt fields to cause the dasir~d interaction of tha guidad waves; and th~refore, insufficient coupling will result.
Removal of too much mat~rial alters th~ propa~ation charact~ristics of th~
fibers, resulting in loss of light encrgy from ths fibers due to mo~ p~rturbation.
However, when the spacing between the cores of the fibers 14 and 106 is within the critical zon~, each fib~r 14 and 106 rec~ives a significant portion of the evanescent fi~ld energy ~rom the other to achi~ve good coupling without significant energy loss. The critical zone includes the region in whioh the evanescent fields of the fibers 14 and 106 overlap sufficiently to provide ~ood evanescent field coupling with each core being within tha evan~scent field of light guided by tha other core. It is believed that for weakly guided mod~s, suoh as the 1 IE14 mode guided by ~ingle mod~ fibers, mod~ perturbation occurs when the fiber core is exposed. Therefore, the critical zone is the co~ spacing that causes the evanescent fields to overlap sufficiently to cause coupling without c~using substantial mode perturbation induced power loss.
The coupler 43 of Figure 7 includ~s four ports label~d 43A, 43B, 43C and 43D. IPorts 43A and 43B, whioh are on the l~ft and right sides, r~spectively, ofthe coupler 43 oorrespond to the fiber 14. The ports 43C and 43D similarly ~)rrespond to the fiber 106. For purposes of ~xplanation, it is assumed that an optical signal input is applied to port 43A through the fib~r 14. The signal pa~ses through th~ coupler 43 and is output at either one or bo~h of ports 43B or 43D depenciing upon the amount of coupling between lhe fiber~ 14 and 106.
The "coupling constant" is defined as the ratio of the coupled pow~r to the total output power. In th~ above ~xample~ th~ coupling constant is tho ratio of ~he pow~r outpu~ a~ por~ 43D divided by the sum of the power output at ~he ports 43Band 43D. This ~atio is sometim~s call~d the "coupling efficiency", which is typically Qxpressed as a percent. Therefore, when the term "coupling constant"
is used herein, it should be understood that the corresponding coupling efficiency is equal to the coupling constant times 100.
The coupl~r 43 may be tuned to adjust th~ coupling constant to any desired value between zero and 1.0 by offset~ing ~he confronting suffaces of thefib~rs 14 and 106 to oon~rol ~he dimensions of the region of overlap of the evanascent fields. Tuning may be accomplished by sliding the substrates 50 and 52 laterally or longitudinally relative to one another.

' . :
.:

Light that is cross-coupled from one of th~ fibers 14 and 1û6 to the oth~r undergoes a phase shift of 7~/2, but li~ht that passes straight through th~ coupler 43 without being cross-coupled is not shifted in phase. For ~xampl~, if th~
coupler ~ has a coupting constant of 0.5, and an optical signal is input to port5 43A, then tha outputs at ports 43B and 43D will be of equal magnitude; but theoutput at port 43D will b~ shifted in phase by ~/2 relative to the output at port 43B.
Referrin~ to Figur~s 10-12, the phase modulator 48 may oompris~ an optical waveguide 470 formed on a substrate 472 of an electrooptically activ~
10 material such as lithium niobats. A pair of ~l~ctrodes 474 and 476 are attach~d to the substrate 472 on epposits sid~s of the waveguide 470. The alectrodes 474 and 476 may be fcrm~d on the substratQ 472 by vapor deposition of aluminum. The optical waveguide 470 may be forrned in the substrate 472 by first depositing a strip of titanium on the substrate 480 and h~ating it to dnve the 15 titanium into the substrate 472. Tha resulting waveguide 470 has a generally semicircular cross section as shown in Figur~s 11 and 12. The fiber 106 rnust be cut to have two ends 1 06A and 1 06B that are butt ceupled to opposite sides of the optical wav~guid0 470 as shown in Figures 7 and 10.
Applioation of a voltage across the electrodes 474 and 476 ohanges the 2û refractive index of the optical waveguide 470 lay apparatus of th~ el~ctrooptio effect. The transit time of a light wave ~hrough the waveguide 470 is th~ product of the length of the waveguide and its refractiv~ index divided by tha spesd of light in vacuum. Chanying tha ref~active index of the optical waveguide 470 thuschanges ths transit time of an opticai signal through it. 5ecause of th~
25 sinusoidal naturs of the electromagnatic fields that cornprise ths light wave, the change in transit time is se~n as a chang~ in phase of th~ wav~.
Changes in the temperature of the optical signal sourca change the output wavelength. It is possible to control th~ wavelength output of the source1~ by controlling its temperature. The base plate 16 is preferably formed of a 30 material that exhibits the Peltier effect and the light source is mounted on the baseplate in thermal contact therewith. The phase ohange caused by the crystals 20 and 22 opposes the ohang~ in phase caused by temperature chan~es. Therefore using the feedback si~nal to control the thermoeleotric heat~r th~ feedback permits cuntrol of the source wavelength.

,, ~ . .

'' ' ' .

~Z74~1~

Although the invention is ciescrib~d with r~f~rcnc0 to an SLD, it may also be used to stabilize a sotid state laser. The long ceherenc~ langth of ~uch las~rs parmits tho crystals to ba larger than ths dimensions d~scribod h~roin for th~
short coh~r~nc~ l~ngth SLD~

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Claims (10)

-22-What is claimed is:

1. A device for controlling the frequency of an optical signal output from an optical signal source, charaeterisecl by:
a first birefringent mat~rial positioned to rec~ive an optical signal output from the optical sourca so that the signal propagates therethrough;
apparatus for modulating the birefringence of ths first birofring~nt material;
a second birefringent material positioned to rcc~ive the signal output from the flrst birefringent mat~rial;
detector apparahls for forming an electrieal signal indicativ~ of the phas~
shift produced by the first and second birefringent materials between a pair of orthogonal polarizations in the optical signal received by th~ first birefringent material; and apparatlJs ~or processing the electrieal signal for adjusting the frequency of th~ op~ical signal output from ~he si~nal source.

2. Th~ dsvic~ of claim 1, including.
a first polarization b~amsplitt~r positioned between the optical sourca and the first birefrin~ent material; and a second polarization beamsplitt~r position~d between the dstec~or apparatus and the s~cond birefring~nt mat~rial.

3. The devic~ of claim 2 wherein the modulating apparatus includes an oscillator electrically colJpled to the first birefrin~ent material, the first bir~fringent material being electroeptically ac~iv~ so that signals ~rom the oscillator chang~ at least one of the refractive indices of the flrst birefringent material;
a mixer conn~ctcd both to th~ oscillator and to the detecting apparahls to r~c~ivQ signals therefrom; and an amplifier connectsd to the mixer to receive the mixsd oscillator and detector signals.

4. The devic~ of claim 3, wherein th~ first polarization beamsplittar has a polarization axis ori~nted a~ 45° to the principal axes of th~ flrs~ birefringent material and the second polarization beamsplitter has a polarization axis oriented at 45° to the principal axes of the second birefrin~ent material.

5. The d~vice o~ claim 3, further including apparatus for producing a temperature-independent phase shift ~etween the two polanzations that are input to the first birefringent material and output from the second birefringentmaterial, wherein the apparatus for producing a temperature-independent phase shift includes a first length L1 of the first birefringent material and a second length L2 of the second birefringent material such that L1/L2 = K2B2/K1B1, where B1 andB2 represent the birefringence of the first and second birefringent materials, respectively and K1 = (1/B1) dB1/dT + (1/L1) dL1/dT, and K2 = (1/B2) dB2/dT + (1/L2) dL2/dT, with T representing the temperature of the first and sacond birefringent materials.

6. A method for controlling the frequency of an optical signal output from an optical signal source, characterised by the steps of:
positioning a first birefringent material to receive an optical signal output from the optical source so that the signal propagates therethrough;
modulating the birefringence of the first birefringent material;
positioning a second birefringent material to receive the signal output from the first birefringent material;
forming an electrical signal indicative of the phase shift produced by the first and second birefringent materials between a pair of orthogonal polarizations in the optical signal received by the first birefringent material; and processing the electrical signal for adjusting the frequency of the optical signal output from the signal source.

7. The method of claim 6, including the steps of:
placing a first polarization beamsplitter between the optical source and the first birefringent material; and placing a second polarization beamsplitter between the detector apparatus and the second birefringent material.

8. The method of claim 7, further including the steps of:
forming the modulating apparatus to comprise an oscillator electrically coupled to the first birefringent material, the first birefringent material being electrooptically active so that signals from the oscillator change at least one of the refractive indices of the first birefringent material;
connecting a mixer both to the oscillator and to the detecting apparatus to receive signals therefrom; and amplifying the mixed oscillator and detector signals.

9. The method of claim 8, further including the steps of arranging the first polarization beamsplitter to have a polarization axis oriented at 45° to the principal axis of the first birefringent material and arranging the second polarization beamsplitter to have a polarization axis oriented at 45° to the principal axes of the second birefringent material.

10. The method of claim 8, further including the step of producing a temperature-independent phase shift between the two polarizations that are input to the first birefringent material and output from the second birefringentmaterial, wherein the step of producing a temperature-independent phase shift includes forming the first birefringent material to have a first length L1 and forming the second birefringent material to have second length L2 such that L1/L2 = K2B2/K1B1 where B1 and B2 represent the birefringence of the first and second birefringent materials, respectively and K1 = (1/B1) dB1/dT + (1/Li) dL1/dT, and K2 = (1/B2) dB2/dT + (1/L2) dL2/dT, with T representing the temperature.