Fiber-optic polarization and phasemodulator utilizing transparent piezofilmwith indium tin oxide electrodes

V. S. Sudarshanam and S. B. Desu

Ahighly efficient optical polarization and phase modulator formed by the placement of a thin transparentpiezofilm with indium tin oxide electrodes directly in the path of the output from an optical fiber ispresented. Various configurations that differ in the clamping conditions, utilization of epoxy, and opticalarrangement are presented. For a film thickness of 63.9 µm, a linear phase-shifting coefficient of 0.131rad@voltage peak 1Vp2 at 2 kHz and of 0.508 rad@Vp at 7.4 kHz is demonstrated. An intrinsicbirefringence of 0.0328 between the directions along the stretch and its perpendicular in the plane of thefilm has been measured. The polarization modulation coefficient was determined to be 0.323 rad@Vp at8.423 kHz, corresponding to a half-wave voltage of 8.353 Vp. Applications of the device involvingconcurrent spatiotemporal polarization and phase modulation are indicated.Key words: Phase modulator, polarization modulator, fiber-optic devices, transparent piezofilms,

optical interferometry, signal processing, transmission ellipsometry.

1. Introduction

Optical phase and polarization modulators1–4 form anintegral part of fiber-optic interferometric sensorsystems for phase calibration and for the implementa-tion or testing of several detection schemes thatextract the signal of interest from the ambient opti-cal, electronic, and mechanical noise. Such modula-tors can be of the bulk-optic kind, and they have beenutilized extensively in a variety of holographic, bulk-optic, and fiber-optic interferometers. In compari-son with the emphasis in holographic and bulk-opticinterferometers, the emphasis in fiber-optic sensorsystems has been on compactness, low insertionlosses, low drive voltages, and flexibility of design.Thus, in preference to the use of bulk-optic compo-nents, in-line, all-fiber phase and polarization modu-lators have been devised over the last decade whereinthe light remains guided within the fiber in theinteraction region of the modulator. For example,such an interaction is commonly achieved by bondingthe fiber onto a piezoelectric lead zirconate titanate

The authors are with the Department of Materials Science andEngineering, Virginia Polytechnic Institute and State University,Blacksburg, Virginia 24061-0237.Received 6 December 1993; revised manuscript received 11 May

1994.0003-6935@95@071177-13$06.00@0.

r 1995 Optical Society of America.

cylinder or a thin strip of polyvinylidene fluoride1PVDF2 film.1–4 Modulators in which bonding isbrought about by the use of an adhesive or epoxy as amedium for transfer of strain from the strictiveelement to the fiber have been shown3,4 to exhibit alarge nonlinearity of response and reduced straintransfer efficiency resulting in a low value for thephase-shifting coefficient 1PSC2 and the dynamic range.The reduction in the strain transfer efficiency occursbecause of the different elastic parameters of thematerials forming the fiber, the piezofilm, and theepoxy. These limitations become pronounced whenlonger fiber lengths are used to increase the integralphase and polarization modulation, because longerfiber lengths imply a larger volume of epoxy used.Further, multiple passes of the fiber over the interac-tion region become necessary if a long fiber is used,thus leading to the requirement that the device bedesigned to be compact. This, however, is not pos-sible in configurations that utilize a single flat strip ofthe strictive element.4Whereas in suchmodulators time-dependentmodu-

lation alone has been considered and has been neces-sary, several applications exist that require concur-rent spatial modulation5 along with temporalmodulation. This paper presents a fiber-optic phaseand polarization modulator utilizing a thin piezoelec-tric PVDF film with optically transparent electrodesmade of indium tin oxide 1ITO2. The piezofilm is

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placed directly in the path of the fiber output as in abulk-optic modulator configuration, with the differ-ence that the interaction length 1the optical thicknessof the film2 is far smaller than that of the single-crystal modulators. The device performance charac-terization and demonstration of reliability for theseveral different configurations reported herein indi-cate the utility of directly depositing the film and theelectrodes on the end face of a fiber, thus combiningthe advantages of the fiber geometry and the longitu-dinal modulator configuration. Compared with sev-eral meters of fiber interaction length used in existingfiber modulator configurations, a single thin film of,64 µm is shown to provide the same order ofmagnitude of the PSC. The modulator was testedwith a combined Mach–Zehnder–Fabry–Perot inter-ferometric configuration for measuring the phaseshift, and a typical transmission ellipsometric arrange-ment for themeasurement of polarizationmodulation.In contrast to in-line all-fiber polarization modula-tors, the utility of the PVDF film for polarizationmodulation has several advantages, such as 1a2 easyidentification of fast and slow axes that are perma-nently fixed and do not change with time and externaldisturbances as in the optical fiber, 1b2 a high value ofintrinsic birefringence, and 1c2 a large modulationdepth for a given applied voltage with a shorterinteraction length.The experimental arrangement and signal detec-

tion schemes are described in Section 2, followed bythe experimental results for both phase and polariza-tionmodulation in Section 3. The experimentalmea-surement of the piezofilm birefringence and thicknessas well as the origin of polarization modulation in anelectrically driven PVDF film are also discussed inSection 3. From the experimental results obtained,the utility of the device for applications in opticalsystems of the holographic, bulk-optic, and fiber-optickinds is indicated in Section 4, followed by the conclu-sion in Section 5.

2. Experimental Arrangement and Signal Detection

Wemeasured the transmission spectrum of the PVDFpiezofilm6 along with the ITO electrodes by using anultraviolet–visible–near-infrared scanning spectropho-tometer 1Shimadzu UV-3101PC2; the spectrum isshown in Fig. 1. As we see from Fig. 1, for theparticular sample of the piezofilm used, the transmit-tance at 633 nm was 71.77%, whereas that at the IRwavelengths of 1300 and 1550 nm were 89.81% and88.71%, respectively. However, for convenience, thesource utilized was a He–Ne laser operating at 633nm. The plot in Fig. 1 shows a distinct fringe patternof appreciable modulation depth, especially in theregions of higher wavelengths. The utility of thisfringe pattern for the estimation of the thickness ofthe film is discussed in Subsection 3.B.

A. Phase-Shift Measurement through Interferometry

A hybrid fiber-optic Mach–Zehnder interferometerwas formed from a fused-fiber directional coupler and

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a beam splitter, as shown in Fig. 2. The output of theMach–Zehnder interferometer was accessed by detec-tor D1. The modulator consisting of the piezofilmand the mounting arrangement is hereafter referredto as the IPM, standing for ITO-coated PVDF 1phasepolarization2 modulator. The IPM was placed at theend of the signal fiber as shown in Fig. 2. Thereflections from the electrode surfaces of the piezofilmwould reach detector D2 through the signal fiber andthe directional coupler. Thus, an extrinsic fiber-optic Fabry–Perot interferometer7 is formed at thepiezofilm concurrently with the Mach–Zehnder inter-ferometer. The reflection from the end face of thereference fiber would also reach detector D2, and onrecombination with the reflections from the IPMsurfaces, form the output of a Michelson interferome-ter that is sensitive to path differences between thesignal and the reference fibers. To eliminate thiseffect, we terminated the reference fiber in index-matching liquid.8 The output from the Fabry–Perotinterferometer 1FPI2 at D2 would be more robustagainst random phase drifts than that from theMach–Zehnder interferometer 1MZI2 seen at D1.

Fig. 1. Transmission spectrum of the PVDF film with the ITOelectrodes as measured by the ultraviolet–visible–near-infraredscanning spectrophotometer. The vertical axis is marked on theleft-hand side in dimensionless units of transmittance, whereas theright-hand side is in terms of corresponding percentage of transmis-sion.

Fig. 2. CombinedMZI–FPI configuration for the measurement ofdynamic phase shift.

This is because the two backreflected beams arisingfrom the ITO surfaces travel the same distance withinthe signal fiber before reaching D2, resulting in leadinsensitivity to phase drifts by common path rejec-tion.To overcome the effect of random phase drifts on the

MZI, which is sensitive all along the path from thedirectional coupler to the beam splitter, we enclosedthe whole setup within a box that cut off air currents.The combined MZI–FPI configuration utilized herepermitted the direct verification of whether the inten-sity modulation seen at D1 and D2 was truly causedby the phase shift induced as a result of the straingenerated at the piezofilm. The phase shift as mea-sured at D2 should be twice that as measured at D1,because the reflected signal-modulated beam in thedirection of D2 traverses the piezofilm twice, whereasthe transmitted signal-modulated beam in the direc-tion of D1 transverses the piezofilm once. The trans-mission FPI output in the direction of D1 was ne-glected because experiments showed that the signalarising from this was far too small in relation to thatfrom the transmission MZI output. This is reason-able because the output from the fiber diverges as itcrosses the piezofilm,which onmultiple-beam interfer-ence in different directions results in an averagedtime-dependent intensity within the collection cone ofthe detector. It is also well known that the FPI has apoor contrast in the transmission mode in comparisonwith that in the reflection mode. It should be noted9that a special fringe pattern was obtained and uti-lized at D1, whereas the output at D2 is a zero-orderfringe that has no spatial modulation.The outputs from photodetectors D1 and D2 were

amplified and fed into a digital oscilloscope thatperformed a fast Fourier transform 1FFT2 to provide afrequency spectrum of the photovoltage. Alterna-tively, the time-domain output recorded by the digitaloscilloscope can be imported into a computer that canthen perform the filtering, FFT, and the calculationsfor the phase shift. For the purpose of determiningthe frequency response or the linearity of responsewhen the phase shift induced is not more than 0.3 rad1which can be estimated by observing and studyingthe peaks in the frequency spectrum2, it would sufficeto plot the photovoltage, V1 f 2, at the fundamentalfrequency as a function of the input frequency or thevoltage applied to the piezofilm. As no feedback forstabilization was applied to the interferometer, themaximum value of V1 f 2 over a prolonged period oftime was measured for each input voltage or eachinput frequency. Over such an extended period oftime, the random phase drift would scan the wholerange of 0 to 2p rad and attain a value of p@2 severaltimes, which corresponds to the maximum value forV1 f 2. Under the approximation that the value of theBessel function of the first order is proportional to itsargument, the plot of V1 f 2 as a function of the inputvoltage would determine the linearity of response at achosen frequency, whereas the plot of V1 f 2 as a

function of frequency would determine the frequencyresponse of the modulator.When the phase shift induced is appreciable as seen

from the surfacing of the higher harmonics in thefrequency spectrum, the J1 . . . J4 method2 can beimplemented to measure the phase shift directly.The J1 . . . J4 method utilizes the photovoltage ampli-tudes at the fundamental frequency 3V1 f 24 and thenext three harmonics 3namely, V12f 2, V13f 2, and V14f 24through the Bessel recurrence relation to provide alinear, direct, and self-consistent readout of the dy-namic phase shift in a homodyne interferometerwithout the need for feedback or phase biasing at thequadrature point, source stabilization, and fringevisibility control.

B. Detection of Polarization Modulation

Inserting polarization-sensitive optical elements andmodifying the arrangement shown in Fig. 2 wouldpermit the concurrent detection of polarization modu-lation and phase modulation. Thus, for a set ofexperiments that involved such concurrent detection,the FPI mode for interferometric phase detection andthe transmission polarimetric mode for polarizationdetection were utilized as shown in Fig. 31a2. Theoutput of the reference fiber terminated in index-matching liquid was not used, unlike in Fig. 2, andthe beam splitter was removed so that theMZI outputwas absent. In a different set of experiments, thefiber directional coupler was not utilized and a typicaltransmission ellipsometric arrangement consisting ofa serial placement of a half-wave plate, the IPM, anoptional quarter-wave plate, and an analyzer was setup as shown in Fig. 31b2. This was done to study thebehavior of the film when not attached to the fiberconnector. Whereas some of the experiments wereperformed with a compensator, others were not; thechoice depended on the achievement of maximumsensitivity of detection for a given input signal powerand linearity of operation for a chosen amplifier gain.

Fig. 3. 1a2 Extrinsic FPI and polarimetric mode of concurrentdetection of phase and polarization modulation. 1b2 The transmis-sion ellipsometric arrangement in the PSCAmode.

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The compensator, typically a quarter-wave plate atthe wavelength of operation, was placed after theIPM, conforming to the PSCA 1polarizer–sample–compensator–analyzer2 arrangement.10 As a polar-ized laser was used, a half-wave plate was included torotate the angle of polarization of the beam incidentupon the IPM.The phase difference between the ordinary ray and

the extraordinary ray on traversing the IPM and thecompensator can be expressed as11

f 5 12pL@l21ne 2 no2 1 Dfc 1 Dfr 1 Dfs, 112

where L is the thickness of the piezofilm, l is thewavelength of the light, ne and no are the refractiveindices of the extraordinary and ordinary rays, respec-tively, Dfc is the phase change on traversal throughthe compensator,Dfr is the random phase drift causedby ambient air currents and temperature fluctua-tions, and Dfs is the phase shift induced by the signalapplied to the piezofilm. The contribution of theintrinsic static birefringence of the piezofilm at a fixedtemperature is expressed by the first term on theright-hand side of Eq. 112. Neglecting optical loss ontransmission through several elements, and on adjust-ing the compensator for a 50% transmission in theabsence of the modulating voltage,11 one can expressthe time-dependent intensity at the output of theanalyzer as2

I 5 1I0@22A1 2 cos DfR3J01m2 1 2 on51

`

J2n1m2cos12nvt241 sin DfR52 o

n51

`

J2n211m2sin312n 2 12vt46B 122

where I0 is the average intensity of the light incidentupon the detector, Jn’s are the Bessel functions of thefirst kind and order n, m is the depth of polarizationmodulation, and v is the angular frequency of thesignal.The phase term caused by static birefringence in

Eq. 112 has been lumped with the phase terms causedby the compensator and the random drifts to form atotal phase term, DfR, in Eq. 122. It must be pointedout that although Eq. 122 bears a close resemblance tothe expression for the instantaneous intensity in aninterferometer, the intensity modulation can be ob-served only if polarization-sensitive elements arepresent. The physical mechanism by which the po-larization modulation represented by depth m isbrought about is discussed in Subsection 3. E. Incomparison with the interferometric arrangement,the effect of random phase drifts in the polarimetricarrangement is relatively smaller. However, the ex-istence of a slow drift far less than that generallyobserved in the MZI setup was observed even afterenclosure within a box that cut air currents off. It ispossible that this slow drift arose from the tempera-ture dependence of the film birefringence, as thePVDF material is known to be a highly sensitive

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pyroelectric detector. It must be pointed out that thetemperature of the piezofilm was not controlled byany feedback mechanism, as is commonly done11 forsingle-crystal modulators. Under the assumptionthat the value of modulation depth m is small, theoutput voltage at the fundamental frequency wouldbe proportional tom when the condition DfR 5 p@2 isfulfilled, thus facilitating the measurement of boththe linearity of response and the frequency response.However, the value of m cannot be determined fromthe amplitude at the fundamental frequency aloneunless the exact instantaneous values of the intensity,visibility, and phase drift are known.The close resemblance of Eq. 122 to the instanta-

neous intensity of an interferometric system sug-gested the possibility of utilizing the J1 . . . J4 method2for the direct, linear measurement of the polarizationmodulation depth, m. This is the first time that theJ1 . . . J4 method has been applied to such detection ofpolarization modulation, the applications hithertohaving been to the measurement of the dynamicphase shift in an interferometer. The measurementof m through the J1 . . . J4 method directly led to thedetermination of the half-wave voltage, Vp, at whichthe polarization modulation depth reaches a value ofp rad. As any kind of bonding was observed toconstrain the piezofilm and reduce the PSC, thefree-standing piezofilm configuration of the IPM wasmost suitable for generating a polarization modula-tion large enough to be detected by the J1 . . . J4method. The structural design and optical arrange-ment of this and other configurations of the IPM aredescribed below.

C. Structural Arrangement of the IPM

Several configurations of the IPM that differed in theclamping conditions, the utilization of epoxy, and theinterferometric arrangement were studied and char-acterized for the device performance. The clampingconditions and the optical arrangement for testingthese IPM elements are summarized in Table 1. Forconvenience of reference, the acronym IPM for thefour IPM elements is followed by a letter A, B, C, or Dto distinguish between the individual elements.Figure 4 shows the geometry of the arrangement forthe IPM elements for coupling light in general fromthe fiber output or directly from the laser source to thepiezofilm. The cross-sectional view of the IPM isshown in Fig. 41a2, whereas the direct end-face view isshown in Fig. 41b2. The piezofilm with wire leadsattached at its edges was sandwiched with the use ofan epoxy between two identical circular metal wash-ers with the dimensions indicated in Fig. 41b2. Thepurpose of using a metal washer was to have theboundary clamping conditions well defined in geom-etry and stresses. It has been reported3,4 that thefrequency response and PSC of the piezofilm-basedmodulators are sensitive to the mechanical forcesacting on them because of the wire lead attachmentsand holding forces at their boundary with the mount-ing arrangement. The use of a circularmetal washer

Table 1. Clamping Conditions and Optical Arrangement for Testing Different IPM Elements

Element Clamping Conditions Coupling Arrangements Optical ConfigurationQuarter-WavePlate Used

IPMA Circular washer on both sides of thepiezofilm

Fiber ST connector butt-coupled or jux-taposed to piezofilm

MZI–FPI; polarimetric No

IPMB Circular washer on both sides of thepiezofilm

Fiber ST connector epoxied to piezo-film

FPI; polarimetric No

IPMC Circular washer on only one side of thepiezofilm

No fiber used; direct laser beam Polarimetric Yes

IPMD Rectangular film freely supported on aglass slide

No fiber used; direct laser beam Polarimetric Yes

led to a repeatable characterization of the modulatorperformance.After the epoxy dried, the inner metal washer was

epoxied to a larger rubber ring, and this wholearrangement was mounted on a rotary stage. Thefiber in the signal arm was terminated in an ST 1aGTE trademark2 connector and polished to achieve asmooth and flat end face. In the case of interferomet-ric phase measurements for IPMA, the ST connectormounted on a micropositioner was butt-coupled to thepiezofilm, forming a small depression in the film fromapplied stress. In the detection of polarizationmodu-lation, the ST connector was juxtaposed to the piezo-film without any physical contact. The difference inthe arrangement permitted the study of the frequencyresponse in the loaded and unloaded conditions.IPMA was tested in both the combined MZI–FPI andthe polarimetric configurations. IPMB differed fromIPMA in that the ST connector was directly bonded tothe piezofilm with an optically transparent epoxy.This was done to study the loading effect of the epoxyin practical conditions, in which an arbitrary distancebetween the fiber output and the piezofilmmay not bedesirable, necessitating a well-defined, repeatablecontact. A photograph of IPMB is shown in Fig. 5,with electrical contact between the wire leads and thepiezofilm being established through thin, flexible,copper foil backed by a thick paper. IPMB wastested in the FPI and polarimetric configurationssimultaneously, thus providing an instantaneous com-parison of the intensity modulation arising from theinterferometric and polarimetric outputs. IPMChada metal washer on only the inner side of the film, noton the outer side, with the mounting on the rotarystage the same as in the case of IPMA. The beamfrom the laser source was used directly as shown inFig. 31b2, with only the polarization modulation hav-ing been of interest. The optical fiber was not usedfor transmission as in IPMB, because once the piezo-film is epoxied to the fiber ST connector at a particularangle, the IPM should not be rotated to align its fastand slow axes to a different angle. This limitationcan be overcome if a polarization-preserving fiber isused that is insensitive to twists and bends.The fiber used in our experiments was a circular

core single-mode fiber whose birefringence was depen-dent on external twists and bends. IMPD consisted

of a piezofilm cut in a rectangular shape with a tailleading to the wire leads for electrical contact, asshown in Fig. 41c2. The film was not bonded at anypoint, thus eliminating any stresses from the support-ing thick 11-mm2 glass slide. As the natural residualcurvature of the piezofilm was directed toward theglass slide, the film was freely supported in a stableposition by the holding forces at the tail section. Thepurpose of testing this IMPD was to generate apolarization modulation that was strong enough thatthe J1 . . . J4 method could be utilized for measuringmand thereby the half-wave voltage, Vp. IPMD wastested with the beam from the laser source beingdirectly incident upon the piezofilm without the use ofan optical fiber. It should be emphasized that thesize of the piezofilm forming the IPM need not exceedthe dimensions of the fiber itself or the spot size of thelaser beam itself. This enhances the significance ofthe possibility of depositing the electrodes and thePVDF film directly on the fiber itself. Although sucha fabrication would involve sophistication, the devicewould be compact and compatible with standardfiber-optic components currently used in the industry.However, in the research reported here, the piezofilmwas prefabricated, requiring the use of a larger areaof the piezofilm because of practical considerations forlaboratory purposes.

3. Results and Discussion

A. Interferometric Phase Detection

The induced phase shift measured by the J1 . . . J4method as a function of the input voltage applied toIPMA in the FPI mode at 2 kHz is shown in Fig. 6.The least-squares fit to the plot shown in Fig. 6 wasdetermined to be f 5 20.0004 voltage peak squared1Vp22 1 0.131 Vp1 0.0008 rad, indicating a linear PSCof 0.131 rad@Vp at 2 kHz. Figure 7 shows thefrequency response measured in the FPI mode forIMPA. The output voltage amplitude at the funda-mental frequency of the signal was normalized withrespect to the input voltage applied, and it wasplotted as a function of the frequency of the signal.This normalization overcame the inherent change ofthe output voltage of the function generator itself as afunction of the frequency. The normalized outputexhibits a resonance peak at a frequency of 7.5 kHz.In comparison with the flat strip fiber-on-PVDF film

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Fig. 4. General mounting arrangement for the elements IPMA,IPMB, and IPMC: 1a2 cross-sectional view, 1b2 direct end-faceview. 1c2Geometry of IPMD.

1182 APPLIED OPTICS @ Vol. 34, No. 7 @ 1 March 1995

1FPF2 modulator,3 which shows a resonance in theregion of 3–4 kHz, this presents a better suitability tofiber-sensor applications wherein a higher frequencyof operation is generally preferred to overcome low-frequency 1@f noise. That the phase shift as mea-sured by the reflection FPI mode at D2 must be twicethat measured by the transmission MZI mode at D1was confirmed by the combined MZI–FPI configura-tion for IPMA.Figure 8a shows the FFT frequency spectrum of

the output of the MZI mode, whereas that of the FPImode is shown in Fig. 8b. The phase shifts at 2 kHzfor these two modes as measured by the J1 . . . J4method were 0.97 and 1.923 rad, respectively. Thiswas further confirmed at the resonance frequency of7.4 kHz as shown for the MZI and FPI modes in Figs.8c and 8d, respectively. The phase shifts measuredat 7.4 kHz from these plots were 1.67 and 3.23 rad foran input voltage of 6.57 Vp. Thus, the fact that thephase shift originated from the integrated straingenerated in the piezofilm and not from any out-of-plane body displacement of the piezofilm in thedirection of the light beam is confirmed.

Fig. 5. Photograph of the direct end-face view of IPMB with theST connector epoxied to the piezofilm at the center of the circularwasher.

Fig. 6. Phase shift measured by the J1 . . . J4 method as a functionof the input voltage applied to IPMAat 2 kHz.

Further, as the resonance frequency is reached thePSC becomes larger, with the result that the PSC at7.4 kHz was 0.508 rad@Vp. The PSC of 1.77 rad@Vpfor the flat strip FPF modulator2,3 reported earlierwas obtained through the utilization of 1 m of interac-tion length of the fiber. In comparison with thislength, the interaction length in the IPM is thethickness of the piezofilm itself, only 63.9 µm, asmeasurements reported in the next subsection show.Comparing these values, we see that the performanceof the IPM direct modulation arrangement is farsuperior to that of the flat strip FPF modulator.Also, a single piezofilm has been used here, whereas astack of films bonded together with an opticallytransparent epoxy can be used to multiply the phaseshift produced. For this purpose, it would also beworthwhile to deposit a multilayer element consisting

Fig. 7. Frequency response of IPMA measured in the FPI mode.Note that the curves connecting the data points are only forindication and are not the best-fit curves.

Fig. 8. FFT of the output of a, the MZI and b, the FPI for phaseshift at 2 kHz, and c, the MZI and d, the FPI for phase shift at theresonance frequency of 7.4 kHz. The vertical axis in each of theseplots indicates the photovoltage, whereas the horizontal axisindicates the frequency.

of alternate films of PVDF and ITO to avoid the use ofepoxy.

B. Piezofilm Birefringence and Thickness Measurement

For the study and understanding of the polarizationmodulation in the presence of an applied electric field,it is necessary to know 1a2 the intrinsic static birefrin-gence of the piezofilm in the absence of the electricfield, 1b2 the thickness of the piezofilm for characteriz-ing the PSC and the depth of polarizationmodulation,and 1c2 the directions of the fast and slow axes of thefilm for achieving proper orientation of the film withthe other optical elements. The polarizationeigenaxes of the piezofilm can be determined throughthe use of the transmission ellipsometric arrange-ment shown in Fig. 31b2 without the quarter-waveplate. The half-wave plate and the analyzer arerotated alternately until the intensity seen at thedetector on transmission through the piezofilm isminimum. Thus, one would find two mutually per-pendicular directions of the piezofilm for which theminimum intensity occurs. The piezofilm as pro-vided by the manufacturer would show visible macro-scopic straight lines on the film surface as a result ofthe uniaxial stretching necessary to make the poly-mer filmpiezoelectric.12–14 The eigenaxes of the piezo-film are thus seen to occur naturally in the directionsalong the stretch and perpendicular to it. In prac-tice, the straight-line stretchmarks generate a scatter-ing pattern, which is a thin straight band again whenan uncollimated beam of small diameter is useddirectly from the laser. This thin band of scatteredlight, seen in both the forward and backward direc-tions of propagation, would be perpendicular to thestretch direction and is used for quick alignment ofthe piezofilm.We measured the optical birefringence of the piezo-

film by using the automated Metricon 2010 prismcoupler. The principle of operation of the prismcoupler15 closely resembled that of anAbbe refractom-eter. The piezofilm of refractive index nwas broughtin close contact with the base of a prism of refractiveindex np. The light from a He–Ne laser operating at633 nm was incident upon the base of the prism,making an angle, u, with the normal to the prism baseat the point of incidence. This beam would be totallyreflected into the prism when the critical angle, uc, isreached, where

uc 5 sin211n@np2. 132

The critical angle is directly measured by the observa-tion of the output of a photodetector that accesses thereflected beam coming out of the prism. The detectoroutput drops abruptly as u becomes less than uc whenlight begins to travel into the film. With the value ofnp known, refractive index n of the film can bedetermined from Eq. 132. For a thick film as is thecase here, an approximation is made that the angle ofthe first film mode equals the critical angle. Theerror in themeasured index caused by this approxima-tion is typically less than 0.004 for a film thickness of

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3 µm, less than 0.001 at 5 µm, and less than 0.0003 at10 µm.When the laser emits polarized light, TE incidence

1electric field vibrating transverse to the plane ofincidence2 and TM incidence 1electric field parallel tothe plane of incidence2 can be used to determine therefractive indices in the plane of the film and perpen-dicular to it, respectively. In the plane of the film,under TE incidence, one can find the refractive indi-ces in the directions of the fast and slow axes byrotating the film appropriately. As we mentionedabove, the eigenaxes of the piezofilm are along andperpendicular to the stretch marks. Figure 9 showsthe output of the detector for the determination ofthe index along the stretchmarks, under TE incidence.By locating the angle at which the knee in theintensity occurs and by using Eq. 132, we determinedthe refractive index to be 1.4452 along the stretchmarks. Rotating the piezofilm in its plane by 90°and repeating the measurement led to the determina-tion of the index perpendicular to the stretch marks of1.4124. For the determination of the index in thedirection perpendicular to the plane of the film, TMincidence was used, leading to a value of 1.4112.Thus a birefringence of 0.034 was measured betweenthe directions of the stretch and the perpendicular tothe plane of the film, whereas a birefringence of0.0328 was measured between the directions of thestretch and its perpendicular both in the plane of thefilm. These values were repeatable as observed in aself-consistency check involving several trials. Thesevalues are also in close agreement with those reportedearlier16 for bare PVDF film with no electrodes on it.The necessity for the exact measurements in thisstudy arose because our purpose was to characterizethe piezofilm with the ITO electrodes present aswould be used in our device, and because the piezofilm was obtained from a manufacturer different fromthat for the earlier reports. It must be noted that

Fig. 9. Variation of the totally reflected intensity seen by thedetector in the prism coupler as a function of the angle of incidenceof the laser beam. The numbers on the horizontal axis correspondto discrete steps in angle, with 20 steps 5 1° and the referencedirection of 0° being along the perpendicular to the prism incidentface. This plot is for TE incidence along the direction of thestretch marks on the piezofilm.

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the ITO layers have a high value of refractive index17of approximately 1.9 1 i0.025. However, as we cansee on comparing the measurements of this study andthat of Ref. 16, the ITO layers did not influence theobtained index values appreciably because the thick-ness of the ITO was far smaller in relation to that ofthe PVDF layer.It is possible to utilize the transmission spectrum of

a weakly absorbing thin film to measure its refractiveindex and thickness, as reported in Ref. 18. Such amethod considers the envelopes of the maxima andminima of transmittance as continuous functions ofthe wavelength. The method would be accurate onlyif the transmittance values of themaxima andminimaare largely different for the wavelength of interest,and if the variation with wavelength of the refractiveindex and absorption coefficient is small. As seenfrom Fig. 1, both of these conditions were not fulfilledin the short-wavelength region in which the He–Nelaser 1633-nm2 light used in our experiments lay.However, an estimate of the thickness, namely 62 µm,was obtained from the long-wavelength region inwhich sharp fringes are seen under the assumptionthat the refractive index is constant over a period oftwo maxima. To overcome this limitation of themethod to our present study, we utilized a variableangle monochromatic fringe observation method.19This method utilizes the interference maxima andminima in the light reflected from the film surfaces asthe angle of incidence of the light is varied. Becausea single wavelength is used, which in our experimentswas 633 nm, the measurement does not requireknowledge of the refractive index as a function of thewavelength except that at the single chosen wave-length. The values of the refractive indices alreadymeasured at 633 nm by the critical angle method thuswere used to determine the thickness accurately.Figure 10 shows the maxima and the minima for thePVDF film with the ITO electrodes. The expressionfor the thickness, d, of the film is given by19

d 5 DNl@32µ1cos r2 2 cos r124, 142

Fig. 10. Variation of the surface-reflected intensity seen by thedetector in the variable angle monochromatic fringe observationarrangement as a function of the angle of incidence of the laserbeam. The numbers on the horizontal axis indicate discrete stepsin angle, with 40 steps 5 1°.

where l is the wavelength, µ is the refractive indexof the film, rj is the angle of refraction at that fringefor which the angle of incidence is ij and sin rj 51sin ij2@µ, and DN is the number of fringes observedbetween i1 and i2. Using this expression in an aver-aged form,19 we determined the thickness of thepiezofilm used in the IPM to be 63.93 16 1.742 µm.

C. Polarization Modulation Measurement

IPMA was tested in the polarimetric mode afterblocking the output from the reference fiber as seen inFig. 2 and inserting a half-wave plate and analyzer asshown in Fig. 31a2. The ST connector was movedaway from the piezofilm as mentioned earlier. Aninput voltage at the frequency of 8.4 kHz was given toIPMA. Figure 11 shows the output of IPMA as seenat the detector as the analyzer is rotated for anarbitrary angle of the incident polarization. Such anintensity modulation was as expected, showing thatthe signal seen at 8.4 kHz was due to polarizationmodulation. A similar type of intensity variationwas recorded as the half-wave plate was rotated andis also shown in Fig. 11. As we expected, the periodfor the half-wave plate rotation was half that for theanalyzer rotation. One could use these plots forchoosing the angles of the half-wave plate and theanalyzer such that the modulation depth is optimizedfor a given relative angle of the IPM element.Whereas the intensity modulation seen in Fig. 11arose from polarization modulation, concurrent phasemodulation could also lead to intensity modulation ifreflection-based interference effects exist.To evaluate this effect, we recorded the instanta-

neous intensity at the detector 1which had an effectiveaperature of 1 cm22 as the analyzer was brought inplace and subsequently removed. As we see fromFig. 12, the detector output showed a signal at 8.4kHz in the presence of the analyzer between the start

Fig. 11. Output of IPMA as seen by the detector when theanalyzer is rotated 1*2 for an arbitrary angle of the half-wave plate,and the angle of the half-wave plate is rotated 132 for an arbitraryangle of the analyzer. Note that the curves connecting the datapoints are only for indication.

1st2 and the stop 1sp2 points. This signal died down toa negligible level in the absence of the analyzer,demonstrating that the intensity modulation seen isindeed entirely due to polarization modulation and isnot due to any reflection-based interference effects.The frequency response of IPMA as measured by thedetection of polarization modulation is shown in Fig.13 in terms of the ratio of the output voltage to theinput voltage. It is seen that the significant reso-nance peak is shifted to 8.4 kHz as compared withthat of 7.4 kHz, as shown in Fig. 7. This change inthe resonance frequency between the loaded andunloaded conditions of the piezofilm was as expected.Figure 14 shows the variation of the output voltage atthe fundamental frequency of 8.4 kHz as a function ofthe input voltage. The least-squares fit to this plotwas determined to be 1Vo 5 0.001 Vp2 1 0.644Vp 1 0.1762, showing that the linearity of polariza-tion modulation was excellent However, a direct

Fig. 12. Instantaneous output of IPMA when the analyzer isinserted 1st2 and subsequently removed 1sp2.

Fig. 13. Frequency response of IPMA 1upper curve2 and IPMC1lower curve2 as measured by the detection of polarization modula-tion. Note that the curves connecting the data points are only forindication.

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measurement of modulation depth m was not pos-sible because no higher harmonics were present,indicating a very small value form.IPMB was tested in the extrinsic FPI mode and the

polarimetric mode simultaneously with the experi-mental arrangement shown in Fig. 31a2. The linear-ity of response for IPMB in terms of the outputvoltage as a function of the input voltage at afrequency of 6 kHz is shown for both the FPI andpolarimetric modes in Fig. 15. The least-squares fitto these plots were 1Vo 5 20.041 Vp2 1 2.702Vp 1 0.5442 and 1Vo 5 20.069Vp2 1 8.292 Vp 10.2662, respectively. In comparison with the resultsfor IPMA, a higher ratio of the nonlinearity coefficientto the linearity coefficient is seen for IPMB for asimilar range of input voltage. This is in agreementwith the reports3,4 for the earlier piezofilm modula-tors, in which it was shown that the epoxy leads to alarge nonlinearity in the response.

Fig. 14. Linearity of response of IPMA with the input voltage at8.4 kHz.

Fig. 15. Linearity of response of IPMB in the FPI mode 1*2 and thepolarimetric mode 1s2 simultaneously measured with the inputvoltage at 6 kHz.

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The frequency response of IPMB in both the extrin-sic FPI and polarimetric modes is shown in Fig. 16 foran input voltage of 10.3 Vp. The two plots shown inFig. 16 are similar in behavior, with two significantresonance peaks seen to occur in both the plots atfrequencies of 5.95 and 7.8 kHz. This agreement isas expected, for the frequency-response behavior isbased on the physical parameters and conditions ofthe device and not on the mode of detection. Itshould be pointed out that the detection of phasemodulation utilizes the phase difference between thereference and signal arms or paths of the interferome-ter, whereas the detection of polarization modulationutilizes the phase difference between the orthogonalpolarizations. Thus these two modes of detectionwould exhibit modulation characteristics that arequalitatively similar. However, the intensity modu-lation as seen with the polarimetric mode is stronglydependent on both the angle of the analyzer and thehalf-wave plate as shown in Fig. 17, whereas the FPIoutput is, as expected, relatively constant with theangle of the analyzer compared with that of thehalf-wave plate. This is because of the residualpolarization sensitivity of the directional coupler,which comes into play in the interferometric modewhen the half-wave plate is rotated but not when theanalyzer is rotated.IPMC was tested in the PSCA mode as shown in

Fig. 31b2 with the use of the quarter-wave plate. Theanalyzer was crossed with respect to the direction ofpolarization at the exit of the half-wave plate. Theeigenaxes of IPMCwere aligned at 45° to the analyzerand the incident polarization. As we mentionedabove, the quarter-wave plate was then rotated toallow 50% transmission in the absence of the appliedvoltage. Figure 13 shows the frequency response ofIPMC as obtained from polarization modulation.A strong resonance peak at 9.72 kHz was observedwith other appreciable peaks occurring at higherfrequencies. Figure 18 shows the linearity of re-

Fig. 16. Frequency response of IPMB in the FPI 1*2mode and thepolarimetric mode 1s2 for an input voltage of 10.3 Vp. Note thatthe curves connecting the data points are only for indication.

sponse for IPMC at the chosen frequencies of 9.912,11.914, 12.5, and 17.334 kHz. This study of thelinearity response at the chosen frequencies wasundertaken to compare the effect of resonance on thelinear behavior of the piezofilm. In contrast to theflat strip FPF modulators3,4 that showed an appre-ciable nonlinearity at resonance, IPMA and IPMCwhen not in a loaded configuration showed negligiblenonlinearity even at the resonance frequencies. Acomparison of the least-squares fit to these plots,shown in Fig. 18, demonstrated that the averagevalue of the ratio of the nonlinearity coefficient to thelinearity coefficient for all these plots was at least fourtimes smaller than that for IPMB, which is anepoxied configuration.

Fig. 17. Output of the FPI and the polarimetric modes for IPMBwith the input voltage at 6 kHz as the analyzer is rotated 1*2 andthe half-wave plate is rotated 1s2.

Fig. 18. Linearity of response of IPMC at the frequencies, kilo-hertz of 9.912 1*2, 11.914 1s2, 12.500 132, and 17.334 112. The legendsummarizing the least-squares fit to the plots shows the values ofthe frequency, the nonlinear and linear coefficients, and theintercept.

The freely supported piezofilm used in IPMD gener-ated significant polarizationmodulation so thatmodu-lation depth m could be measured by the J1 . . . J4method. IPMD was tested in the PSCA mode asshown in Fig. 31b2. The same procedure of alignmentas for IMPC was followed. Figure 19 shows thefrequency response of IPMD in the polarimetric modeas measured by the J1 . . . J4 method. The depth ofpolarization modulation measured in radians wasnormalized with respect to the input voltage becausethe difference in the value of the phase shift for agiven voltage between the resonance frequencies andothers was large. The phase shift measured bythe J1 . . . J4 method at 8.423 kHz is shown in Fig. 20as a function of the input voltage applied to thepiezofilm. From the least-squares fit to this plot,shown in Fig. 20, the linear polarization modulationcoefficient was found to be 0.323 rad@Vp. The half-wave voltage, Vp, at this frequency of 8.423 kHz 1taking

Fig. 19. Frequency response of IPMD in the polarimetric modemeasured by the J1 . . . J4 method.

Fig. 20. Depth of polarization modulation for IPMD measured bythe J1 . . . J4 method as a function of the input voltage at 8.423 kHz.

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into account the linear and nonlinear coefficients ofthe best fit2was determined to be 8.353 V 1peak2.

D. Frequency Response: Implications for Design

The behavior of the frequency response and thelinearity of response for the four IPM elements seenfrom the above results for measurements in both theinterferometric and polarimetricmodes can be summa-rized thus: 1a2 the most significant resonance peakfor the circularly clamped configuration in the ab-sence of loading by the fiber ST connector occurs inthe range of approximately 8.6 to 9.7 kHz; 1b2when theST connector is either butt coupled to form a depres-sion on the piezofilm or is epoxied at the center of thepiezofilm, the resonance peak shifts to a lower fre-quency, in the range of approximately 5.9 to 7.5 kHz,whereas 1c2 the freely supported IPMD shows a de-crease in the modulation depth with increasing fre-quency after the resonance frequency, the circularlyclamped configurations, IPMA, and IPMC in theabsence of the ST connector 1see Fig. 132 show a highermodulation depth at frequencies above the resonancepeak as compared with those below the resonancepeak; and 1d2 the inclusion of an epoxy as in IPMBresults in higher nonlinearity of response. In com-parison with the frequency response of the other IPMelements, the response of IPMD exhibits severalsignificant peaks in the range of approximately 2.6 to10.5 kHz.Thuswe can see that the circularly clamped configu-

ration selectively enhances the response at only cer-tain frequencies out of this range, the selected frequen-cies being dependent on the clamping conditions andthe utilization of epoxy. The determination of theexact resonance frequencies from elasticity theory ofvibrations for individual elements was not possiblebecause the exact mechanical forces at the boundaryof the elements could not be determined. The dimen-sions of the circular metal washer were 6 mm for theinner diameter and 1 cm for the outer diameter. Inall the circularly clamped configurations, the film wasbonded over the area between the inner and outercircumference. The resonance frequency for similarsample mounting in a circularly clamped configura-tion and similar dimensions of the metal ring, althougharising from the different physical phenomenon of photo-thermal bending, has been reported20 to be approxi-mately 7 kHz. The observed frequency response behav-ior also is an indicator of the physical mechanism thatgenerates polarization modulation in the IPM ele-ments, as explained in the following subsection.

E. Origin of Modulation in the IPM

The quantitative experimental results presented abovewere preceded by qualitative studies of the FFT of thephotovoltage for the elements IPMA, IPMB, andIPMC as the input voltage was increased from 0 to amaximum of approximately 16 Vp permitted by thefunction generator. The FFT showed a peak at onlythe fundamental frequency of the applied voltage,with no peak at the second-harmonic frequency, for

1188 APPLIED OPTICS @ Vol. 34, No. 7 @ 1 March 1995

even the highest voltage applied at any frequency ofinterest below approximately 25 kHz. This showedthat the modulation arose from a linear relationshipin the electro-optic interaction. IPMD showed peaksat the higher harmonics of the fundamental fre-quency as the input voltage was increased. How-ever, the presence of the peak at the fundamentalfrequency, and its behavior as in an interferometer,established that these higher harmonics arise fromthe nonlinearity inherent in the relationship given inEq. 122, and not from a quadratic electro-optic effect.Generally, electro-optic coefficients are determined atzero strain as in a sample well clamped in all direc-tions. However, in a sample that is free to respond,the electro-optic coefficient, ri j, measured at zerostress 1freely supported2would differ from that at zerostrain, ri j8, according to the relation21

ri j 5 ri j8 1 ok51

6

pikdkj, 152

where pik is the strain-optic coefficient and dkj is thepiezoelectric constant of the material.The frequency response can then be interpreted as

arising from the variation in the amplitude of thepiezoelectric strain with frequency. At low frequen-cies, the sample is free to be strained and the value ofri j is obtained. At high frequencies, the strain isinhibited by the inertia of the sample, and thereforethe value of ri j8 is obtained. Thus from the frequencyresponse studies for the different IPM elements re-ported above, the physical mechanism by which thepolarization modulation is brought about in the IPMcan be modeled as an electro-piezo-optic effect ratherthan as purely an electro-optic effect. The half-waveretardation voltages in the longitudinal and trans-verse electro-optic configurations for a PVDF film ofthickness ,30 µm have been reported22 to be 5.6 3105 V and 1.5 3 106 1d@L2 V, respectively, where d@L isthe ratio between the interelectrode distance and theoptical path.As the voltages utilized here were extremely low

compared with these values, and because an electricfield greater than 50 MV@m is required to observeappreciable electro-optic hysteresis,23 it is reasonableto assume that the magnitude of the electro-opticeffect at low voltages as utilized here is very small.The goal in the design of the IPMwas to generate withthe use of the PVDF film a phase and polarizationmodulation that was large enough at low frequencieswithin the upper limit of ,25 kHz for suitability toexisting optical sensor systems. To this end, thepiezoelectric contribution serves to enhance the de-vice performance.

4. Applications

Recent interest in all-fiber devices has given rise tothe development of many generic modulators based17on the accession of the evanescent light emanatingfrom the guided mode in the core of a polished fiberhalf-block. With the use of an overlay whose optical

properties can be modulated by an electrical signal,the device can be used for intensity modulation.Such devices utilizing liquid crystals,17 for example,have been demonstrated to have low loss, high modu-lation depth, andmoderate drive voltages. The phaseand polarization modulation performance demon-strated here for the PVDF film with transparent ITOelectrodes indicates the high potential application ofPVDF to the all-fiber intensity modulator. Further,the birefringence properties of the PVDF film can beutilized for polarizing the guided light. If the birefrin-gent indices are chosen such that one is higher andthe other lower than the effective index of the fiber,the mode that sees the high index is not guided andthe orthogonal mode seeing the low index is guidedwithin the fiber. The fact that PVDF can be dopedwith the desired concentration of copolymers such astrifluoroethylene enhances its potential utility forsuch devices.The same principle of accessing the evanescent

light can also be utilized for the construction of afiber-optic switch with the PVDF layer sandwiched inbetween two polished fiber half-blocks. The utility ofthe PVDF film in the transmission mode to two-dimensional spatial phase modulation has been dem-onstrated.5 From the temporal performance of thePVDF film reported here, concurrent spatiotemporalmodulation assumes significance for holographic inter-ferometric systems that map the phase distributionover an extended surface. The IPM modulator canalso be configured to function in a feedback mode tostabilize the phase or polarization in the presence ofrandom drifts in optical sensors of the bulk-optic orfiber-optic kinds.

5. Conclusion

The PVDF-film-based phase and polarizationmodula-tor utilizing the optical properties of the film in thepresence of an applied electric field has been charac-terized for the linearity of response at chosen frequen-cies, the frequency response, the phase-shifting coeffi-cient, and the depth of polarization modulation.Through the use of the J1 . . . J4 method, a linearphase-shifting coefficient of 0.508 rad@Vp at 7.4 kHzfor the circularly clamped configuration and a polar-ization modulation depth of 0.326 rad@Vp at 8.4 kHzfor the freely supported configuration have beenmeasured. The device performance of the differentconfigurations of the IPM has demonstrated the ge-neric utility of the transparent PVDF film for achiev-ing a large dynamic range of phase and polarizationmodulation in a broad range of frequencies for use inoptical sensor systems. Specifically, there exists ahigh potential for the utility of the PVDF film inall-fiber intensity modulators.

This research was partially supported by the Ad-vanced Research Projects Agency through the Officeof Naval Research. V. S. Sudarshanam thanks D.Port of Atochem Sensors for providing the piezofilmand J. Jackson of Metricon for the measurement ofthe indices and thickness of the piezofilm.

References and Notes1. R. P. De Paula and E. L. Moore, ‘‘Review of all-fiber phase and

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2. V. S. Sudarshanam and K. Srinivasan, ‘‘Linear readout ofdynamic phase change in a fiber optic homodyne interferome-ter,’’ Opt. Lett. 14, 140–142 119892.

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4. V. S. Sudarshanam and R. O. Claus, ‘‘Frequency response andphase shift nonlinearity of a cylindrical PVDF film based fiberoptic phasemodulator,’’ J. Lightwave Technol11, 595–602 119932.

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9. V. S. Sudarshanam and S. V. Pappu, ‘‘Holographic optical elementbased single mode hybrid fiber optic interferometer for realizingzero order fringe,’’Fiber Integr. Opt.11, 71–83 119922.

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16. H. Ogura and K. Kase, ‘‘Evaluation of the Lorentz factor ofb-phase polyvinylidene fluoride crystals with the measuredrefractive index,’’ Ferroelectrics 110, 145–156 119902.

17. Z. K. Ioannidis, I. P. Giles, and C. Bowry, ‘‘All-fiber opticintensity modulators using liquid crystals,’’ Appl. Opt. 30,328–333 119912.

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19. W. A. Pliskin and E. E. Conrad, ‘‘Nondestructive determina-tion of thickness and refractive index of transparent films,’’IBM J. Res. Dev. 8, 43–51 119642.

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21. See, for example, R. O. B. Carpenter, ‘‘The electro-optic effectin uniaxial crystals of the dihydrogen phosphate type. III.Measurement of coefficients,’’ J. Opt. Soc. Am. 40, 225–229119502.

22. D. Broussoux and F. Micheron, ‘‘Electro-optic and elasto-opticeffects in polyvinylidene fluoride,’’ J. Appl. Phys. 51, 2020–2023 119802.

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