992 OPTICS LETTERS / Vol. 29, No. 9 / May 1, 2004

Ultrahigh-gain bulk solid-state stimulated Brillouin scatteringphase-conjugation material

Mark A. Dubinskii and Larry D. Merkle

U.S. Army Research Laboratory, AMSRD-ARL-SE-EO, 2800 Powder Mill Road, Adelphi, Maryland 20783

Received November 20, 2003

We report what is believed to be the first observation of phase conjugation by stimulated Brillouin scattering(SBS) in TeO2 single crystal. The observed very low threshold for phase-conjugate mirror (PCM) formation,high PCM ref lectivities in this initial experiment, and commercial availability of material hold promise for ahost of practical applications in the near future. The resultant steady-state gain parameter, �100 cm�GW,is to our knowledge the largest ever reported for any SBS material.

OCIS codes: 190.5040, 160.4330.

There has long been interest in high-average-powerlasers with near-diffraction-limited beam quality forboth military and industrial applications. In recentyears, technological developments plus considerationsof compactness, ruggedness, and power source haveturned this attention increasingly to solid-state lasersystems. Because the scaling up of solid-state lasersexacerbates thermal distortions, double-pass amplif i-cation with phase conjugation for beam quality im-provement represents a promising approach to scaling.For Q-switched lasers, stimulated Brillouin scattering(SBS) is a particularly attractive method for phase con-jugation, as it requires only one beam (that is, no loopformation is required) and relatively simple alignmentof the SBS medium with the beam.

To date the best-performing SBS media have beenliquids and gases. Solid SBS media are far morerugged but typically have lower SBS gain and longerBrillouin phonon lifetimes than liquids. Two of thebest solid-state media to date have been fused silicaand deuterated L-arginine phosphate (dLAP).1 Fusedsilica has only a modest SBS gain parameter but isreadily available in fiber, in which a long interactionlength can ameliorate that limitation, provided thatthe pulse energies to be used are not sufficient to dam-age the material when they are focused into the fibercore. The advantages of dLAP are its particularlylarge gain coefficient and its lower absorption at Ndand Yb laser wavelengths than that of nondeuteratedLAP.1,2 However, it is hygroscopic, and its absorptionnear 1 mm is still not negligible and thus is an issuefor high average powers.

Here we report promising SBS results with a ma-terial familiar to the acousto-optics community, TeO2,but for which SBS was not previously reported to ourknowledge. We have observed remarkably low SBSthresholds at 1064 nm, substantially better than re-ported for dLAP (Ref. 2) and comparable to those forliquid SBS media.

The condition for backward SBS threshold is gen-erally taken to be gIL � M , where g is the SBS gaincoeff icient, I is the incident beam intensity, L is theinteraction length, and M is a numerical factor suchthat exp�M� is sufficient to amplify noise photons atthe Brillouin-shifted frequency to a measurable level.

M is generally taken to be �30, although it variessomewhat, depending on beam focusing.3,4 In thesteady-state regime g is1

gsteady � 4p2n7p2t�cvrl2, (1)

where n is the refractive index, p is the elasto-opticcoefficient, t is the lifetime of the acoustic phonon thatis active in the SBS process, v is the acoustic phonon’sspeed, r is the material density, and l is the laserwavelength in vacuum. If laser pulse duration tp isnot suff iciently longer than t, the transient gain is lessthan the steady-state gain by a factor derivable fromRef. 3 as

gtran�gsteady � �8tp�Mt���1 1 2tp�Mt�2,

tp�t , M�2 . (2)

Thus, promising solids for SBS are those with largerefractive index, large elasto-optic coefficient, low den-sity, and low sound speed. If sufficiently long pulsesare used, long phonon lifetime also increases the gain,but for Q-switched lasers the transient regime gener-ally applies, for which the decrease in gain coeff icientmakes t far less important. It is mainly the largeelasto-optic coefficient and low density of dLAP thatmake it favorable for SBS.

TeO2 is nonhygroscopic and is well known as anacousto-optical material, such that all its parametersfor the SBS steady-state gain coeff icient are readilyavailable, except for t [largest p � p13 � 0.340,v � 4200 m�s, r � 6.00 g�cm3, no � 2.2005, andne � 2.3431 (Refs. 5–7)]. Its very large n and p areparticularly favorable, and its acoustic phonon speedis relatively low. Only its high density is unfavorable.Indeed, these parameters indicate that its gsteady�tshould be two or three times as large as that ofdLAP. It is for this reason that we selected TeO2 forstudy.

The TeO2 sample was obtained commercially andwas 4.0 cm long in the beam propagation direction and1.0 cm in each lateral dimension. The long axis wasparallel to the crystalline c axis, to enable the largestelasto-optic coefficient to be used.6 Efforts were made

May 1, 2004 / Vol. 29, No. 9 / OPTICS LETTERS 993

to f ind relatively low surface scatter regions for theexperiments, as the surfaces exhibit numerousscratches (poor polishing quality).

SBS ref lectivity experiments were performed withan injection-seeded single-longitudinal-mode Contin-uum PL8000 Nd:YAG laser. Single-mode behavioris important for quantitative study of SBS materi-als because the multinanosecond phonon lifetimesof solids result in rather narrow gain bandwidths.One can vary the pulse duration by adjusting theQ-switch delay, but for durations beyond �18 nsinjection seeding eff iciency suffers and multiple modesgenerally appear, thus limiting the maximum pulseduration for these experiments. The beam qualitywas monitored frequently and was found to have adivergence �1.7 times diffraction limited. Polariza-tion coupling was used to separate the SBS returnfrom the incident beam, such that the light incidentupon the sample was circularly polarized. The beamwas focused into the sample with a lens of 18-cm focallength. Given the unfocused beam size, the refractiveindex and the beam quality of the laser, the Rayleighrange was �0.56 cm and thus the interaction lengthwas L � 1.12 cm. The sample was tilted by a fewdegrees to separate Fresnel ref lections by the un-coated surfaces from the phase-conjugate SBS returnsignal.

The observed SBS return signal is shown in Fig. 1 asa function of incident pulse energy. We corrected boththe incident and return energies for the front surface.Fresnel loss, thus approximating the behavior expectedfor antiref lection-coated samples. At lower energiesthan those displayed, the return energy was too smallto trigger the energy meters employed.

The most important feature of the data is the lowthreshold energy. Extrapolating the curves to zero re-f lectivity gives thresholds of 0.35, 0.38, and 0.42 mJfor pulse durations of 7.8, 12.5, and 18.0 ns, respec-tively. The estimated uncertainty in these values is0.01 mJ. The low SBS threshold energies for TeO2imply remarkably high gain.

Figure 1 also indicates substantial SBS ref lectivity,not yet fully saturated at the maximum incident energyshown. This maximum was limited by surface dam-age, which occurred at peak (on-axis) f luences near4.4 J�cm2. Better surface polishing and using longersamples can alleviate this problem.

It is possible to estimate the phonon lifetime and thesteady-state gain coefficient from the pulse-durationdependence of threshold by using Eq. (2) and thethreshold energies for two pulse durations. SinceFig. 1 shows that the pulse-duration dependence israther weak, we used only the shortest and longestdurations to infer g and t. We report the results fora threshold exponential multiplication factor valueof M � 28. The results are shown in Fig. 2. Theseveral points shown indicate the effect of varyingthe threshold energies by the estimated uncertaintyof 60.01 mJ. For comparison, the prediction ofEq. (1) is also shown for the parameter values fromRef. 5. The agreement with the parameters forM � 28 is excellent. For different values of M , g

varies approximately in proportion to M and t variesmore weakly, decreasing somewhat as M increases.

The resultant steady-state gain parameter value ofroughly 100 cm�GW is remarkably large, indeed largerthan that for any SBS material known to us. Table 1illustrates the exceptionally high TeO2 steady-stategain with respect to several known practical SBSmaterials. For comparison, the value reported byFaris et al.1 for the most favorable orientation ofdLAP is �30 cm�GW, and that for fused silica is only�2.9 cm�GW. With these results, Eq. (2) indicatestransient gain coefficients of roughly 25 cm�GW for7.8-ns pulses and 50 cm�GW for 18-ns pulses, alsomuch larger than those for dLAP with its rather longphonon lifetimes.

Because of the weak dependence of SBS thresholdon pulse duration, our estimates of phonon lifetimeand absolute gain parameter are quite approximate.However, the ratio gsteady�t is far less sensitive to

Fig. 1. TeO2 SBS ref lectivity data at 1064 nm for threepulse durations tp.

Fig. 2. Steady-state gain parameter and Brillouin phononmode lifetime. Points are inferred from experiments for7.8- and 18.0-ns pulse duration. The theoretical line refersto Eq. (1).

994 OPTICS LETTERS / Vol. 29, No. 9 / May 1, 2004

Table 1. Comparison of TeO2 SBS-RelatedParameters with Known

Practical Solid-State and Liquid SBS Materials

SBS gsteady-state Acoustic PhononMaterial �cm�GW� Lifetime (ns)

SolidsTeO2

a 100 6DLAPb 29.9 12.2KD�Pb 5.09 9.3Fused silicab 2.90 16.1

LiquidsCS2

c 130.0 5.2SnCl4d 11.2 1.75Fluorinerte 4.7 1.36aThis work.bRef. 1.cRef. 8.dRef. 9.eRef. 10.

uncertainties in t, and, as Eq. (2) shows, provides afirst-order correction for the reduced gain in the tran-sient regime. This ratio is thus a useful tool for com-parison of different SBS materials in the transientregime and for TeO2 is approximately six times as largeas for dLAP and �30 times as large as for fused silica.

TeO2 does not violate the usual pattern of solids’having longer Brillouin phonon lifetimes than liquids.Thus it will be necessary to pay close attention tophase-conjugate fidelity, particularly to the degree ofcorrection for high-spatial-frequency beam distortions.However, among solids TeO2 already appears particu-larly promising.

In summary, we have observed very low-thresholdSBS phase-conjugate return in single-crystal TeO2and have inferred a steady-state gain parameter anda gsteady�t ratio substantially larger than those of any

other solid yet reported, to our knowledge. The lowthreshold should make TeO2 an attractive alternativeto fragile liquid and gas cells for low-energy appli-cations. With better surface polishing and longersamples, it appears likely that the pulse energy andref lectivity will be increased further, making thismaterial highly attractive for higher-energy lasersas well.

Mark A. Dubinskii’s e-mail address is mdubinskiy@arl.army.mil.

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