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Sonehara et al. Vol. 24, No. 5 /May 2007/J. Opt. Soc. Am. B 1193

Frequency-modulated stimulated Brillouinspectroscopy in crystals

Toshiaki Sonehara, Yusaku Konno, Hitomi Kaminaga, and Seishiro Saikan

Department of Physics, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan

Seigo Ohno

Terahertz-wave Research Program, RIKEN, 519-1399 Aoba, Aramaki, Aoba-ku, Sendai 980-0845, Japan

Received October 27, 2006; revised January 17, 2007; accepted January 22, 2007;posted January 29, 2007 (Doc. ID 76471); published April 17, 2007

We have developed a Brillouin spectrometer based on frequency modulation (FM) spectroscopy in order to en-hance the detection sensitivity and to detect separately the real and imaginary parts of the Brillouin spectrum.With this spectrometer, we have measured Brillouin spectra at room temperature in a variety of single crystalsincluding SiO2, CaF2, LiNbO3, deuterated L-arginine phosphate, PbMoO4, TeO2, langatate�La3Ta0.5Ga5.3Al0.2O14�, and KRS-5. To determine the Brillouin linewidth and shift from the observed FM spec-trum, we have derived a spectral formula for the FM-stimulated Brillouin spectrum by taking into accountseveral contributions from both electrostrictive and absorptive Brillouin scattering and polarization ellipticityof pump or probe waves. This formula reproduces the observed FM Brillouin spectra quite well. © 2007 Op-tical Society of America

OCIS codes: 290.5900, 160.1050.

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. INTRODUCTIONecently we have developed a high-precision stimulatedrillouin spectrometer.1 Compared with previously devel-ped stimulated Brillouin spectrometers,2–4 a higher fre-uency resolution reaching 20 kHz has been achievedith the use of stable lasers [monolithic isolated single-ode end-pumped ring laser (MISER)-type Nd:YAG la-

ers] for the pump and probe waves and a real-time fre-uency monitor. The frequency monitor has been achievedhrough the measurement of the beat frequency betweenhe two lasers by using a microwave frequency counter.he real-time frequency monitor enables repetitive aver-ging of data while maintaining high spectral resolution.n that spectrometer, the pump wave was mechanicallyhopped for the lock-in detection, that is, the amplitudeodulation was employed for the signal processing. How-

ver, it has been well known that the frequency modula-ion (FM) spectroscopy5 is a particularly useful techniqueor the improvement of the signal detection sensitivity,nd also for the separate detections of real and imaginaryarts of stimulated light-scattering spectrum. Therefore,e tried to improve the stimulated Brillouin spectrometery adopting FM spectroscopy. With this FM Brillouinpectrometer we have measured the Brillouin spectrumn a variety of crystals including TeO2, deuterated-arginine phosphate (d-LAP) and LAP that have previ-usly been employed as crystalline materials for a Bril-ouin phase conjugator, but whose phonon lifetime, i.e.,he Brillouin linewidth, has not been measured so far.6–8

ccurate measurement of the phonon lifetime is neces-ary to estimate the gain factor of stimulated Brillouincattering. From the large number of FM Brillouin mea-urements, we have noticed that almost all crystals ex-

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ibit more or less a spectral distortion or a spectral asym-etry, in particular, at low temperature. To accurately

etermine the Brillouin linewidth and shift from the ob-erved FM spectrum, we derive a spectral formula for theM-stimulated Brillouin spectrum by taking into accounteveral contributions from electrostrictive, absorptiverillouin scattering9 and polarization ellipticity of pumpnd probe waves.10

. EXPERIMENTAL SETUP FOR THEREQUENCY MODULATION BRILLOUINPECTROMETERhe experimental setup for the FM-stimulated Brillouinpectroscopy is shown in Fig. 1. MISER-type Nd:YAG la-ers (Innolight M500 and M200) were employed as theump and probe laser sources, respectively. The MISER-ype laser is known to be very stable because the opticalavity consists of a tiny monolithic laser element. Theseasers have a lasing wavelength of 1.06 �m, a spectralinewidth of 1 kHz/100 ms, and a tunable frequencyange of 30 GHz. To increase the interaction length in thetimulated Brillouin measurement, we adopted a trulyounterpropagating configuration for the two beams. Inhat case, the two optical isolators had to be installed inront of lasers in order to prevent the optical feedbackrom another laser. The pump and probe beams whose in-ensities are �240 and 80 mW, respectively, were looselyocused into the sample using a pair of lenses with the fo-al length of 30 cm. The beam diameter at the minimumeam spot was �100 �m. Since the confocal parameter inhe present case is �3 cm, which is longer than theample length of 1 cm, the beams in the sample can bereated approximately as plane waves.

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1194 J. Opt. Soc. Am. B/Vol. 24, No. 5 /May 2007 Sonehara et al.

The frequency difference between the pump and probeeams was monitored as a light beat frequency by using aicrowave frequency counter (Advantest R5373). The

ighest frequency that can be measured by this counter is7 GHz. As shown in Fig. 1, parts of the two beams werepatially overlapped and then injected into a single-modeptical fiber simultaneously. The fiber was connected to aigh-speed photodetector (New Focus 1414), and the out-ut signal was fed into the frequency counter after beingmplified by 18 dB by using an amplifier (New Focus422). The use of the frequency counter enabled repetitiveveraging of data while maintaining high spectral resolu-ion. The sign of the frequency difference, which denotesither the Stokes or the anti-Stokes side of the spectruman be determined from the increase and decrease of theeat frequency during the frequency sweep of the pumpaser.

The probe wave is phase modulated electro-optically atrequency 80 MHz and the pump wave is mechanicallyhopped at 800 Hz. The transmitted probe light is de-ected by a photodiode, and then the signal is amplifiedModel 315, Sonoma Instrument Company) and dividednto two equal signals. Each signal is fed into the rf portf a double balanced mixer (DBM). By using a digital syn-hesizer (AD9854/PCB Analog Devices) and an amplifierMHW1345, Free-Scale), we prepared an 80 MHz sineave oscillator that was used for both the electro-opticalodulator and the local oscillator for the DBM. To detect

eparately the real and imaginary parts of the Brillouinpectrum, the output signal from the 80 MHz oscillator ised into a variable phase shifter (Model T072-1377A,hamway) that has two outputs with different phasehifts of 0° and 90°. Each output from the phase shifter isonnected to the local oscillator (LO) port of the DBM. Fi-ally, the internal frequency (IF) output of the DBM is fed

nto a lock-in amplifier synchronized with the mechanicalhopper. Thus we can detect simultaneously the real andmaginary parts of the Brillouin spectrum. Following theork of Bjorklund,5 we derive the spectral formula for FMrillouin spectroscopy.

ig. 1. (Color online) Experimental setup for FM-stimulatedrillouin spectroscopy. F.P. denotes confocal Fabry–Perot. Thelectro-optical modulator (E.O.M) is driven at 80 MHz. Mirrors

1 and M2 have a reflectivity of 98% and 50%, respectively, athe wavelength of 1.06 �m. Other mirrors have a reflectivity of00%.

. FREQUENCY MODULATED BRILLOUINPECTRUMhe field of the phase-modulated probe wave is written as

E2�t� = E exp�i�2t + im sin��mt��

= E exp�i�2t� �n=−�

�

Jn�m�exp�in�mt�, �1�

here �2 and E are the frequency and the amplitude ofncident probe wave, m is the modulation index, �m is thehase modulation frequency, and Jn�m� is the nth-orderessel function. Since the modulation index m is low, we

onsider only five Fourier components of the resultingmplitude:

E2�t� = E exp�i�2t��J−2e−2i�mt + J−1e−i�mt + J0 + J1ei�mt

+ J2e2i�mt�. �2�

hen the frequency difference �=�1−�2 between pump�1� and probe waves ��2� is near at resonance with Bril-ouin frequency �B, the amplitude and phase of the probeave vary during passing through the sample due to the

timulated Brillouin gain or loss. If the magnitude of therillouin gain or loss is sufficiently low, the probe wave2�t� after being transmitted through the sample can beritten as

E2�t� = E��1 + iX−2�J−2ei��2−2�m�t + �1 + iX−1�J−1ei��2−�m�t

+ �1 + iX0�J0ei�2t + �1 + iX1�J1ei��2+�m�t

+ �1 + iX2�J2ei��2+2�m�t�, �3�

here Xn is the response function of Brillouin scattering9

or the probe frequency �2+n�m and the pump frequency1, and is given by

Xn��� =�e + i�a

�B2 − �� − n�m�2 + i�� − n�m��

= ��e2 + �a

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ith

�2 = arctan��a/�e�,

�n��� =1

�B2 − �� − n�m�2 + i�� − n�m��

= �n� − i�n� ,

here �e and �a are, respectively, the electrostrictive andbsorptive coupling constants and � denotes the FWHMf Lorentzian spectrum. Equation (4) has been derivedonsidering the coupling between mass density and ther-al expansion due to optical absorption.9 Equation (4)

an be simplified for the Stokes component as

XnS��� =

�e + i�a

2�B��B − �� − n�m� + i�/2�. �5�

When the signal is absent, i.e., Xn=0, the photodetectorurrent that is proportional to E2�t�E2

*�t� has no Fourieromponent at �m because of the phase cancellation. Thiss the most important characteristic of the FMpectroscopy,5 i.e., extremely low background noise for the

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Sonehara et al. Vol. 24, No. 5 /May 2007/J. Opt. Soc. Am. B 1195

requency component of �m. Any interaction with theample that disturbs the amplitudes or phases of the side-ands and the carrier of the probe wave leads to a detect-ble modulation of the current. The current modulationan be detected in a phase-sensitive manner by using aBM to demodulate the detector current. Thus the realnd imaginary parts of the Brillouin spectrum are ob-ained with the correct adjustment of the phase �1 of theocal oscillator of �ei��mt+�1�+c.c.�. The dc output from theF port in the DBM gives the FM Brillouin spectrum, andhe FM spectrum is calculated under a condition that theroducts such as XnXm

* are much smaller than a single Xn:

I1��� � 2�E�2J1ei��1−�/2���J0�X−1 + X1* − X0 − X0

*�

+ J2�X−2 + X2* − X1 − X−1

* �� + c.c., �6�

here the relations J−1=−J1 and J−2=J2 have been used.ow let us see the electrostrictive FM Brillouin spectrumore in detail. By decomposing �n into �n� – i�n� and setting

a=0, Eq. (6) can be written as

I2��� � 2�E�2J1ei�1�J2�2� − iJ2�2� + �J0 + J2��1� − i�J0 − J2��1�

+ i2J0�0� − �J0 + J2��−1� − i�J0 − J2��−1� − J2�−2�

− iJ2�−2� � + c.c. �7�

herefore the real and imaginary parts of the Brillouinpectrum can be obtained separately by taking either 90°r 0° for the value of the phase �1. Figure 2 indicates �1ependence of the FM Brillouin spectrum calculated fromq. (7). In this calculation, J2 was set to zero for simplic-

ty. It should be noted that the signal at the frequency �B,orresponding to the real part of the Brillouin spectrumith �1= /2, is twice as large as those at the frequenciesB±�m. Therefore higher sensitivity is expected for theeasurement using the real part of the FM Brillouin

pectrum although stimulated Brillouin spectroscopy hassually been performed by measuring the imaginary partf the Brillouin spectrum.2–4

The spectral shape observed in the spontaneous Bril-ouin scattering is usually a symmetric Lorentzian. How-

ig. 2. (Color online) �1 dependence of FM spectrum for elec-rostrictive Brillouin scattering with �2=0 in Eq. (8). The ab-cissa 1 and the frequency interval 0.15 correspond to the Bril-ouin frequency shift �B and the modulation frequency �m,espectively. � is set to 0.01. (a) �1= /2, (b) �1= /3, (c) �1 /6, (d) � =0.

1

ver, in the stimulated Brillouin scattering, we have oftenbserved unsymmetrical spectra. Several reasons are con-idered for the asymmetry.

If there is an absorptive contribution to Brillouin scat-ering, the spectrum will be unsymmetrical. By substitut-ng Eq. (4) into Eq. (6), we obtain the FM Brillouin spec-rum, which takes the absorptive effect into account:

I3��� = 2�E�2��e2 + �a

2J1ei��1−�/2�� �J0cos �2��−1 + �1* − �0

− �0*� + i sin �2��−1 − �1

* − �0 + �0*� + J2cos �2��−2

+ �2* − �1 − �−1

* � + i sin �2��−2 − �2* − �1 + �−1

* �� + c.c.

�8�

The terms with a factor of cos �2 correspond to the elec-rostrictive effect, and the terms with a factor of sin �2orrespond to the absorptive effect. Figure 3 shows �1 de-endence of the FM spectrum for absorptive Brillouincattering calculated according to Eq. (8) with fixed val-es of �2= /2 and J2=0. Therefore, when �2 takes aalue between 0 and /2, the FM Brillouin spectrum be-omes unsymmetrical. Furthermore, as was demon-trated in “Brillouin-induced Kerr-effect spectroscopy,”9

hen the pump or probe waves have elliptical polariza-ion, an additive phase shift has to be included in �2 ofq. (4).10 The change of polarization from linear to ellip-

ical polarization might occur when the sample is a bire-ringent crystal or the sample has a strain induced opticalnisotropy, and the reflectivity or the transmissivity of op-ical elements such as mirrors is strongly polarization de-endent.

. EXPERIMENTAL RESULTS ANDISCUSSIONSy using the present FM Brillouin spectrometer, we haveo far measured Brillouin spectra in a variety of crystalsncluding TeO2, PbMoO4, SiO2, LiNbO3, LAP, and d-LAP.he sample length is usually from 4 to 10 mm. Typical ex-mples of the FM Brillouin spectra measured at roomemperature are shown in Figs. 4–8. In each figure, thepper and lower half denotes, respectively, the imaginary

ig. 3. (Color online) �1 dependence of FM spectrum for absorp-ive Brillouin scattering with �2= /2 in Eq. (8). The abscissa 1nd the frequency interval 0.15 correspond to the Brillouin fre-uency shift �B and the modulation frequency �m, respectively. �s set to 0.01. (a) �1= /2, (b) �1= /3, (c) �1= /6, (d) �1=0.

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1196 J. Opt. Soc. Am. B/Vol. 24, No. 5 /May 2007 Sonehara et al.

nd real parts of the FM Brillouin spectrum. The solidurves are numerical fittings according to Eq. (8). Fromhese fittings, we can determine the Brillouin linewidthnd shift. Figure 4 is the Brillouin spectrum of transversecoustic mode in LiNbO3 along the [100] direction at roomemperature.11 The longitudinal mode could not be mea-ured because the frequency of the longitudinal acousticode in LiNbO3 is beyond the measurable frequency

7 GHz of this spectrometer. The extremely narrow line-idth of 2 MHz is consistent with the result of ultrasonicttenuation measurement,12 which previously reportedhat LiNbO3 is one of low acoustic-loss materials.

Figures 5 and 6 are, respectively, the Brillouin spec-rum of longitudinal and transverse acoustic mode in a-LAP single crystal along the [100] direction. This crys-al has been reported to be a promising material for anpplication to phase conjugated Stimulated Brillouincattering (SBS) mirror because of the relatively highain of SBS.6,7 Since the d-LAP crystal belongs to theoint group 2 of triclinic crystal symmetry, both trans-erse and longitudinal acoustic modes are detectable in aonfiguration of backward scattering. Comparing Figs. 5nd 6, we notice that the transverse mode is significantlyarrow compared with the longitudinal mode. This mighte because the frequency of the transverse mode is almostalf the longitudinal mode, and the Brillouin linewidth isroportional to a square of the Brillouin frequency. Thisendency has also been observed in crystals of LiTaO3 andbMoO4.Figures 7 and 8 are the Brillouin spectra of longitudi-

al modes in PbMoO4 crystal along the [100] directionnd TeO2 crystal along the [110] direction, respectively.ince these crystals have a high optoacoustic figure of

ig. 4. (Color online) FM transverse Brillouin spectrum for the100] direction of LiNbO3. In Figs. 4–8, the upper and loweralves correspond, respectively, to the imaginary (Im) and realRe) parts of FM Brillouin spectrum.

erit,12 they have been utilized as crystals for thecousto-optical modulator. It has recently been pointedut that TeO2

8 and As40Se60 (glass)13 as well as d-LAP7

re also promising candidates for an application to thehase conjugate mirror due to the large Brillouin gain co-fficient. Among them, since the TeO2 crystal has a nar-ow Brillouin linewidth of �10 MHz, the acoustic phononifetime in this crystal is relatively long.

ig. 5. (Color online) FM longitudinal Brillouin spectrum alonghe [100] direction of d-LAP.

ig. 6. (Color online) FM transverse Brillouin spectrum alonghe [100] direction of d-LAP.

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Sonehara et al. Vol. 24, No. 5 /May 2007/J. Opt. Soc. Am. B 1197

The data for Brillouin linewidth (HWHM) and shift de-ermined in the present experiment are listed in Table 1.everal features of the Brillouin linewidth in crystals arenumerated as follows.

1. Crystals such as LiNbO3 and langatate, which havecomplex crystal structure, exhibit relatively narrow

rillouin linewidth.14

ig. 7. (Color online) FM longitudinal Brillouin spectrum alonghe [100] direction of PbMoO4.

ig. 8. (Color online) FM longitudinal Brillouin spectrum alonghe [110] direction of TeO .

2

2. As shown in the data of TeO2, the Brillouin line-idth varies greatly depending on the crystal orientation.3. The linewidth of transverse acoustic modes tends to

e narrower than that of longitudinal modes.4. There is no large difference of linewidth between

atural and synthetic quartz.

. CONCLUSIONSe improved the performance of the stimulated Brillouin

pectrometer by adopting frequency-modulation spectros-opy. With this spectrometer, we measured Brillouin spec-ra in a variety of single crystals. To determine the Bril-ouin linewidth and shift from the observed FM spectrum,e derived a spectral formula for the FM-stimulated Bril-

ouin spectrum by taking into account the contributionsrom electrostrictive, absorptive Brillouin scattering, andolarization ellipticity of the pump or probe waves. All ofhe observed FM Brillouin spectra were numerically re-roduced with this formula, and the Brillouin linewidthnd shift were determined accurately.

CKNOWLEDGMENTShe authors sincerely thank Kei Kamada, who belongs tonstitute of Multidisciplinary Research for Advanced Ma-erials in Tohoku University, for his kind supply of lan-atate crystal. This work was partially supported by theinistry of Education, Culture, Sports, Science and Tech-

ology through a 21st Century Center of Excellence pro-ram, “Exploring New Science by Bridging Particle-atter Hierarchy.”

S. Saikan’s e-mail address is saikan@aser.phys.tohoku.ac.jp.

Table 1. Data for Brillouin Linewidth (HWHM)and Shift Determined in the Present Experimenta

SamplePropagation

Direction ModeShift(GHz)

HWHM(MHz

TeO2 [100] L 13.482 6.20[110] L 19.668 10.95[001] L 17.387 9.26

PbMoO4 [100] L 16.287 21.19[100] T 9.662 12.63

�cos 29° ,sin 29° ,0� L 18.958 28.74SiO2 [100] L 16.908 14.01

Natural quartz [010] L 17.411 15.15LiNbO3 [100] T 16.340 2.11

LAP L 12.297 13.64T 4.458 3.97

d-LAP [100] L 9.728 13.74[100] T 5.684 4.25

CaF2 L 17.170 6.10KRS-5 L 9.267 10.95

a3Ta0.5Ga5.3Al0.2O14 L 23.473 3.54

aExcitation wavelength is 1.06 �m. L and T denote longitudinal and transversecoustic modes, respectively.

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1198 J. Opt. Soc. Am. B/Vol. 24, No. 5 /May 2007 Sonehara et al.

EFERENCES AND NOTES1. S. Ohno, T. Sonehara, E. Tatsu, A. Koreeda, and S. Saikan,

“kHz stimulated Brillouin spectroscopy,” Rev. Sci. Instrum.77, 123104 (2006).

2. W. T. Grubbs and R. A. MacPhail, “High resolutionstimulated Brillouin gain spectrometer,” Rev. Sci. Instrum.65, 34–41 (1994).

3. G. W. Faris, L. E. Jusinski, and A. P. Hickman, “High-resolution stimulated Brillouin gain spectroscopy in glassesand crystals,” J. Opt. Soc. Am. B 10, 587–599 (1993).

4. G. W. Faris, M. Gerken, C. Jirauschek, D. Hogan, and Y.Chen, “High-spectral-resolution stimulatedRayleigh–Brillouin scattering at 1 �m,” Opt. Lett. 26,1894–1896 (2001).

5. G. C. Bjorklund, “Frequency-modulation spectroscopy—new method for measuring weak absorptions anddispersions,” Opt. Lett. 5, 15–17 (1980).

6. H. Yoshida, M. Nakatsuka, H. Fujita, T. Sasaki, and K.Yoshida, “High-energy operation of a stimulated Brillouinscattering mirror in an L-arginine phosphate monohydratecrystal,” Appl. Opt. 36, 7783–7787 (1997).

7. M. Yoshimura, Y. Mori, T. Sasaki, H. Yoshida, and M.

Nakatsuka, “Efficient stimulated Brillouin scattering in

the organic crystal deuterated L-arginine phosphatemonohydrate,” J. Opt. Soc. Am. B 15, 446–450 (1998).

8. M. A. Dubinskii and L. D. Merkle, “Ultrahigh-gain bulksolid-state stimulated Brillouin scattering phase-conjugation material,” Opt. Lett. 29, 992–994 (2004).

9. R. W. Boyd, Nonlinear Optics (Academic, 1992).0. T. Haga, M. Higuchi, K. Abe, and T. Shigenari, “Optical

heterodyned coherent Brillouin spectroscopy (OHD-BIKES)using continuous-wave (cw) dye lasers,” Jpn. J. Appl. Phys.,Part 1 28, 1199–1205 (1989).

1. This Brillouin scattering is always observed in the FMspectroscopy, because the phase modulator for the FMspectroscopy consists of LiNbO3 crystal with the crystalorientation of [100].

2. N. Uchida and N. Niizeki, “Acousto-optic deflectionmaterials and techniques,” Proc. IEEE 61, 1073–1092(1973).

3. K. Ogusu, H. Li, and M. Kitao, “Brillouin-gain coefficientsof chalcogenide glasses,” J. Opt. Soc. Am. B 21, 1302–1304(2004).

4. D. W. Oliver and G. A. Slack, “Ultrasonic attenuation ininsulator at room temperature,” J. Appl. Phys. 37,1542–1548 (1966).