Dual-mode single-crystal photoelastic modulator andpossible applications

Rok Petkovšek,1,* Ferdinand Bammer,2 Dieter Schuöcker,2 and Janez Možina1

1Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva 6, SI-1000 Ljubljana, Slovenia2Institute for Forming and High Power Laser Technology, Vienna University of Technology, Franz Grillstrasse 1,

Arsenal Objekt 207, A-1030 Vienna, Austria

*Corresponding author: rok.petkovsek@fs.uni-lj.si

Received 30 July 2008; revised 4 November 2008; accepted 4 November 2008;posted 5 November 2008 (Doc. ID 99192); published 3 December 2008

A new type of acousto-optic device based on a LiTaO3 crystal is presented. A harmonic voltage with aproper frequency applied to the piezoelectric LiTaO3 crystal generates mechanical oscillations in thematerial. Due to photoelasticity, an artificial modulated birefringence is induced by this oscillation.By using a properly adjusted polarizer and analyzer, the transmission of trough-going polarized lightcan be modulated. By simultaneous excitation of two modes, an advanced optical response can beachieved. For the applications presented here, the first shear eigenmode must have exactly three timesthe frequency of the first longitudinal eigenmode. © 2008 Optical Society of America

OCIS codes: 230.4110, 140.3540.

1. Introduction

Most common acousto-optic modulators apply bulkacoustic waves possessing wavelengths that aresmall in comparison with the crystal. Acoustic wavesinduce small changes in the refractive index of amedium and form gratings that deflect the incominglight. On the other hand, the photoelastic modulatorspresented in this paper are based on the resonance ofmechanical oscillations, and therefore the acousticwavelength directly relates to the physical dimen-sions and geometry of the crystal. Further, acousto-optic modulators directly modulate beam intensityby deflecting part of the beam from its originaldirection. The photoelastic modulators control thedirection of polarization of the incoming light.A photoelastic modulator can be built of a piezo-

electric transducer and a piece of glass (e.g., SiO2,CaF2, ZnSe) [1,2]. Both pieces must first be tunedto the same longitudinal resonance frequency andthen glued together. Consequently, when the trans-ducer is electrically excited on this frequency, the

whole assembly starts to oscillate with high ampli-tude in a longitudinal mode. Now, due to the photo-elastic effect, a birefringence is induced in the initialisotropic glass such that it acts as a wave plate withtemporally varying retardation. By adjusting the re-tardation amplitude and using one or two polarizers,such an element can be used as a light modulator. Anobvious disadvantage of the above described schemeis the need for precise adjustment of the frequenciesof both pieces.

To overcome the problems related to the precisetuning, one single crystal can be used for the samepurpose [3,4]. In this case, a modulated birefringenceis induced in the electrically excited element itself.For this type of modulator, the crystal class 3m, towhich the well-known materials LiNbO3 and LiTaO3belong, can be used [5,6]. The materials do not haveoptical activity and can be transversely excited(Fig. 1). In fact, a crystal orientation similar to thatin a LiNbO3 Pockels cell can be used. The importantdifference is that the crystal dimensions are chosensuch that a pure longitudinal oscillation is possible.

In this research, we prefer LiTaO3, which has alower natural birefringence than LiNbO3. Thismakes optical adjustment easier (Fig. 1), since rays

0003-6935/09/070C86-06$15.00/0© 2009 Optical Society of America

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that deviate from the optical axis suffer a smaller un-wanted influence on their polarization.In this paper we present a further modification of

the single crystal photoelastic modulator (SCPEM),namely, the dual mode SCPEM (DMSCPEM). Thisimplies the simultaneous use of two fundamentaleigenmodes: the first longitudinal and the first shearmode.For the applications considered here, it is neces-

sary that the ratio between the frequencies of thetwo modes is exactly 1 to 3. Thus an advanced opticalresponse can be obtained with a faster switchingfrom closed to open states. There are several possibleapplications of the SCPEM: ellipsometric devices, op-tical time multiplexing [7], pulse picking, and laserQswitching [4].

2. Principle of Single- and Dual-Mode Operation of aSCPEM

In the case of a SCPEM, because of electrical excita-tion and the photoelastic effect, an additional artifi-cial modulated birefringence is induced [5,6]. Themodulator therefore acts as a wave plate with tem-porally varying retardation. Hence the polarizationof light will be modulated.We consider an example when a maximum ampli-

tude of induced oscillation corresponds exactly to ahalf-wave retardation (λ=2) while an incident polar-ization is inclined 45° to the direction of the longitu-dinal oscillation (axis x). In general, this will causeelliptically polarized light. Because of the changing

retardation, the eccentricity (the ratio between theminor and the major axis) of the ellipse that repre-sents the polarization state is varied, too. At the mo-ment when retardation is λ=4, the ellipse correspondsto a circle, so that circular polarized light is obtained.Furthermore, when retardation reaches its maxi-mum (λ=2 in this case) the ellipse is transformed toa line rotated by 90° with respect to the initial polar-ization. The output light is then linearly polarizedwith its polarization perpendicular to the polariza-tion of the incident light (Fig. 1).

Figure 1 shows how the orientations of the crystalaxes have to be chosen. The given directions x, y, zcorrespond to the crystallographic axes of the crystal,and the crystal is cut along these axes. The electrodesare placed on the y facets (the y axis is normal to thefacets).

The first and most important eigenmode that canbe excited by these electrodes is a longitudinal oscil-lation in the x direction with the frequency f 1, whichis determined by the x dimension of the crystal. Twofurther significant resonance peaks correspond to alongitudinal oscillation in the y direction and to a yzshear oscillation. Below we describe the possible useof these two additional oscillations for simultaneousoperation with two or three eigenmodes. Here “long-itudinal” refers to the parallelism between the mo-tion of the crystal particles and the direction ofpropagation of the corresponding acoustic wave.On the other hand, it does not mean parallelism tothe applied electrical field.

Figure 2 shows typical resonance curves for cur-rent and deformation, which are common to all piezo-electric resonators. It can be seen that outside therange of resonance the crystal acts electrically as acapacitor, i.e., the phase shift between the resultingcurrent and the driving voltage is 90°. At resonance,the current and deformation demonstrate a strongmaximum, while at the slightly higher frequencyof antiresonance, the current amplitude is extremelysmall (zero in the case of a lossless device). Thedeformation amplitude at resonance in the standingwave regime is usually 2 or 3 orders of magnitudehigher than the static deformation. The important

Fig. 1. SCPEM made of a 3m crystal

Fig. 2. Behavior of a piezoelectric crystal at resonance with frequency f 1 as can be obtained from theory. Amplitude and phase (inreference to the excitation voltage) of deformation (left) and current (right).

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advantage is now that, for half-wave retardation, theamplitude of the driving voltage is of the order of10V, i.e., 2 orders of magnitude lower than thatfor typical electro-optic devices.The resonance behavior of the SCPEM leads to a

very limited frequency range that is determined bythe bandwidth of the resonance curve, which isusually below 0.1% of the resonance frequency.When the electrodes are placed on its y facets, the

crystal offers many further eigenmodes and corre-sponding eigenfrequencies [3]. One important eigen-mode is the first yz shear mode. In this case themotion appears in the yz plane, and its frequencyis governed by the y and z dimensions of the crystal.The smaller of these, which in our case happens to bethe z dimension, has more influence. In addition tothis, one can also excite a longitudinal oscillationin the y direction, the frequency of which is deter-mined by the y dimension of the crystal. All three ei-genmodes affect the birefringence of the crystal insimilar ways, as we describe in more detail laterfor the case of the x longitudinal mode. The frequen-cies of these three eigenmodes (x and y longitudinaland yz shear) can be tuned nearly independentlyfrom each other by adjusting the x, y, and z dimen-sions of the crystal. It is therefore possible to fabri-cate the crystal such that the frequencies aremultiples of one another. With proper excitation theeffect of these eigenmodes can be superposed to ap-proximate certain desired output waveforms. We de-scribe this in detail for the superposition of the first xlongitudinal eigenmode with the yz shear mode,which shows the effect in a slightly stronger fashionthan the y longitudinal eigenmode. It is important tonote that the frequencies of higher-order x longitudi-nal eigenmodes are not exact multiples of f 1.When in resonance, the yz shear eigenmode shows

much higher current amplitude than the first x long-itudinal eigenmode. It influences polarization (retar-dation) in the same way (as the x longitudinaleigenmode), but quantitatively the effect is smallerby a factor of ∼3 . The frequency is governed mainlyby the z dimension of the crystal. We used a crystalwith specially tuned dimensions 21 mm × 7:4mm ×5mm in x, y, and z directions such that the frequencyof the shear mode f 3 ¼ 381kHz is exactly three timesthe frequency of the longitudinal mode f 1 ¼ 127kHz.Therefore we had to adjust the x dimension of thecrystal by polishing such that j3f 1 − f 3j < Δf∼f 1=1000, where Δf is the FWHM bandwidth ofthe x longitudinal resonance. This gives the possibi-lity of exciting both eigenmodes simultaneously in acoherent way. The driving circuit fixes the higher ex-citation frequency with a phase-locked loop to themechanical resonance frequency f 3 and additionallygenerates a second driving harmonic with frequencyf 3=3, which is also applied to the crystal electrodes.The amplitudes of both harmonic waveforms and thephase difference can be adjusted independently.With properly adjusted phase and amplitude for

the excitation of the two eigenmodes, sharp trans-

mission peaks can be achieved when a 45° polarizer(parallel to the input polarization) is placed behindthe crystal as sketched in Fig. 1. To explain this ef-fect, we need to define the retardation:

δ ¼ L ðn1 − n2Þ ¼ LΔn; ð1Þwhere L is the optical interaction length (the z di-mension of the crystal) and n1, n2 are the temporallyvarying refractive indices for x- and y-polarized light.These can be calculated via the time-dependentstrains ϵ1…ϵ6 and the photoelastic coefficients p11…

p66 [5,6]. For x- and y longitudinal and yz shear os-cillation modes Δn ¼ n1 − n2 is described by

Δn ¼ no3

2

�ðpE

12 − pE11Þðϵ1 − ϵ2Þ − 2pE

14ϵ4�: ð2Þ

The upper E in p11E, p12

E, p14E means that the elec-

tric field is held constant during the measurement ofthese coefficients [5,6]. The electro-optic contributionto birefringence is neglected here.

For the crystal class 3m the strains ϵ1, ϵ2, ϵ4 (¼yzstrain) are coupled to one another. In the case of xoscillation ϵ1 will give the main contribution toΔn, and in the case of yz shear oscillation the mainpart will come from ϵ4.

3. Experimental Results and Discussion

A. Light Modulation with a DMSCPEM

Crystal deformation, and hence the crystal strain, isdirectly proportional to the driving voltage UðtÞ. Ascan be seen from Eq. (2), Δn depends linearly on thestrain. The dependence of the retardation δ on Δn islinear, too; hence δ is directly proportional to the driv-ing voltage UðtÞ. Therefore a harmonic excitation atthe resonance frequency f 1 will generate a harmonicretardation:

δ ¼ A × sinω1t; ð3Þwith ω1 ¼ 2πf 1, and A is the amplitude of the retar-dation. In fact, for the first longitudinal eigenmode δis directly proportional to the motion of the x facet inthe x direction. The amplitude and phase of this mo-tion is shown in Fig. 2.

If incident light with wavelength λ is linearly po-larized at 45° and a polarizer oriented at the sameangle is placed behind the SCPEM, Fig. 1, the trans-mission T of such a setup can be calculated as [8]

TðδÞ ¼ cos2�πλ δ

�: ð4Þ

If Eq. (3) is inserted into Eq. (4) with A ¼ 0:5 λ, atime-dependent transmission as shown in Fig. 3 isachieved (solid curve). Now when the third harmo-nics are included, the following time dependence ofthe retardation can be achieved (ω3 ¼ 2πf 3):

δ ¼ A1 sinω3

3tþ A1

3sin ω3t with A1 ¼ λ

24π : ð5Þ

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This contains the first two terms of the Fourierseries of the periodic extension of the functionδsquare ¼ fλ=2 for 0 < ω3t=3 < π and − λ=2 forπ < ω3t=3 < 2πg, i.e. the function δsquare oscillates be-tween −λ=2 andþλ=2. This desired temporal retarda-tion δsquare would, according to Eq. (4), yield zerotransmission most of the time, with infinite shorttransmission peaks at the jumping points (polaritychange). At least in theory it would be straightfor-ward to excite the corresponding fifth-harmonic fre-quency if the y longitudinal eigenmode is used toachieve even sharper transmission peaks. The useof a fourth eigenmode to generate the seventh har-monic is not possible, though, since the crystal offersonly three physical dimensions that can be used toadjust the resonance frequencies, and therefore onlythree eigenmodes can be superposed. The retarda-tion described by Eq. (5) requires the following driv-ing voltage:

UðtÞ ¼ U1 sin�ω3

3tþ γ

�: ð6Þ

The phase shift γ depends on the frequency mis-match j3f 1 − f 3j. If the latter is zero, γ is 180°, sinceΔn has opposite signs for the two eigenmodes. Sinceour electronics oscillate exactly on the resonance fre-quency f 3 of the shear mode, the voltage amplitudeU3 has a fixed minimum value of the order of 8V toachieve the necessary retardation amplitude [¼A1=3,Eq. (5)] for λ ¼ 633nm, which is rather large, sincethe optical response of this eigenmode is weak incomparison with the x longitudinal mode. U1 de-pends again on the frequency mismatch. It takesits minimum value of ∼3:5V to achieve half-wave re-tardation for λ ¼ 633nm when the mismatch is zero.Experimentally U1 and γ are simply adjusted untilthe transmission TðtÞ in Fig. 4 is achieved, accordingto Eq. (5).The corresponding time-dependent transmission

curve is shown in Fig. 4 (solid curve). Clearly the

transmission peaks are much sharper than in thecase shown in Fig. 3. This is due to the much fastertransition through zero retardation with thisexcitation scheme. Only zero retardation allows fulltransmission.

An experimental verification can be seen in Fig. 5.It was taken with a He–Ne laser at λHN ¼ 633nm.The current response shows clearly that the lowerfrequency with low amplitude is superposed by athree-times higher frequency signal with higher am-plitude. The driving voltage had the parametersU1 ¼ 3:5V, U3 ¼ 8V, and γ ¼ 180°. The phase shiftand the low amplitude of the first harmonic provesthat the frequencies were adjusted very well. Thelower graph is the transmission curve taken witha photodiode. It shows a very satisfying coincidencewith the graph in Fig. 4 (solid curve). The uppergraph in Fig. 5 is the current flowing through thecrystal. As is shown in Fig. 2, the current amplitudeexperiences a significant peak for the resonance fre-quency. It should be noted that the crystal is a goodelectrical isolator; hence this current is caused onlyby the dielectric displacement of the crystal. Themeasurement of this current is important, since itgives us reliable information on the status of the re-sonance. The phase shift between current and vol-tage is zero in resonance (Fig. 2). The frequency ofthe transmission peaks is 254kHz, which is twicethe mechanical frequency f 1 ¼ 127kHz, since theSCPEM takes its undeformed shape, which corre-sponds to full transmission, twice every period.

Because of the relatively narrow resonance curve itis essential to build an electronic feedback loop thatlocks the frequency of the driving circuit to the me-chanical frequency of the crystal. Such a circuit, ofcourse, increases the complexity of the system. How-ever, once such a circuit has been built, it is relativelyeasy to apply further harmonic waveforms. In the fol-lowing subsection it will be shown that this effortleads to much better results when this modulatoris used inside a laser cavity for Q switching.

Fig. 3. Typical time-dependent retardation (dashed curve) andresulting transmission of a SCPEM polarizer configuration (solidcurve) as obtained by inserting Eq. (3) into Eq. (4).

Fig. 4. Adding a third harmonic to the retardation: typical time-dependent retardation (dashed curve) and resulting transmissionof a SCPEM polarizer configuration (solid curve) as obtained byinserting Eq. (5) into Eq. (4).

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B. SCPEM as a Q Switch

From Eq. (4) it is clear that the effect of the retarda-tion on transmission scales with the wavelength.Further, if the modulator is used in a laser cavityin a double-pass configuration as sketched in Fig. 6,the retardation is doubled. If we have a measure-ment of the retardation δHN for a He–Ne laser(wavelength λHN ¼ 633nm), with a correspondingtransmission as shown in Fig. 5, the retardation toachieve the same transmission in, e.g., a Nd:YAGlaser cavity (wavelength λL ¼ 1064nm) is given by

δLðtÞ ¼ 2λHN

λLδHNðtÞ: ð7Þ

If the transmission in the laser cavity should bethe same as in Fig. 5 for the He–Ne laser, the voltageamplitudes of the two driving harmonics need to bechanged by approximately a factor of λL=λHN=2 ¼0:84. A more precise calculation should consider dis-persion and the wavelength dependence of the photo-elastic coefficients.

A schematic diagram of the experimental setup isshown in Fig. 6. It is based on a Nd-doped D-shapeddouble-clad fiber (DCF). The concentration of Nd2O2is 1300mol ppm (where ppm is parts in 106). Thelength of the fiber is 5m, and the diameter of the ac-tive core and inner cladding is 13 and 400 μm, respec-tively. The corresponding numerical aperture is 0.13and 0.37. Pumping light with 808nm from a 5W la-ser diode is guided through a free-space coupler tothe fiber end that also acts as an output mirror(4% reflectance) of the laser cavity. The output laserlight is reflected by the wavelength-sensitive mirror2 and measured by a photodiode. On the other end ofthe fiber the emerging laser light is collimated andthen led through a polarizer and a DMSCPEM.Finally the light is reflected by a highly reflectiveinterference mirror 1 to travel again through theDMSCPEM and the polarizer back to the fiber.

Figure 7 shows one typical result of the measure-ments, namely, a 127kHz pulse sequence at an aver-age power of 50mW. The peak power is 1:5W, andthe pulse duration is 300ns.

Note that the repetition rate is only half of the fre-quency of the transmission peaks (Fig. 5), since be-cause of the low pumping level sufficient energy toemit a pulse is stored only every second transmissionpeak. It is important to note that, while the laser

Fig. 5. Measurement of the time-dependent transmission of aDMSCPEM (lower graph). The transmission peak frequency is254kHz. The upper graph shows the current flowing throughthe crystal.

Fig. 6. Setup of a fiber laser with a SCPEM Q switch. Two photo-detectors are used simultaneously to detect both the transmit-tance of the SCPEM and the output pulses of the laser.

Fig. 7. (a) 127kHz pulse sequence of the fiber-laser–DMSCPEM combination sketched in Fig. 6. (b) An output pulse for single-mode anddual-mode operations of the SCPEM Q switch.

C90 APPLIED OPTICS / Vol. 48, No. 7 / 1 March 2009

characteristics are changed dramatically, the aver-age power of the laser is hardly influenced by themodulator. An advantage of using dual-mode opera-tion can be seen from the right-hand graph in Fig. 7.To offer a good comparison, a pulse produced in aSCPEM Q-switched laser is shown for both single-mode and dual-mode operation. Owing to the muchfaster switching time in the case of dual-mode opera-tion, the width of the output laser pulse is approxi-mately 50% shorter.

4. Conclusion

A new type of single-crystal photoelastic modulator(SCPEM) that works simultaneously on two differenteigenmodes is presented. In general, such a modula-tor can be used for ellipsometry, optical time multi-plexing, pulse picking, and laser Q switching. Bysimultaneous excitation of two mechanical modes,the optical switching time can be significantly low-ered in comparison with single-mode operation. Thisis especially important for certain applications suchas pulse picking and laser Q switching. The maindeficiency of a SCPEM is its fixed modulation fre-quency. On the other hand, however, it is small,

cheap, and relatively easy to drive with supply vol-tages in the range of 10V.

The authors acknowledge the support of theAustrian Ministry for Traffic, Innovation andTechnology (BMVIT) for the project “Fiber lasers”of the Austrian Laser Working Society (ARGELAS).

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