Tunable frequency shift of photorefractive oscillators
Shmuel Sternklar, Shimon Weiss, and Baruch Fischer
Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
Received October 24, 1985; accepted December 26, 1985
We report on an experimental study of the self-frequency detuning in wave mixing oscillators with the photorefrac-tive barium titanate crystal. We show its dependence on a dc electric field on the crystal, optical phases in theoscillator cavity, and light intensity in the crystal. This resolves many aspects of previously observed andunexplained self-frequency detuning effects with similar oscillators and indicates the existence of an internalelectric field in the mixing crystal.
Wave mixing oscillators with photorefractive crystalshave been shown to display self-frequency shifts of theoscillating beams. Recent reports of self-frequencyscanningl,2 with a passive phase-conjugate mirror(PPCM) coupled to a dye-laser cavity have led to somespeculations concerning the mechanism that causesthis nondegenerate oscillation. Self-frequency de-tuning has also been observed in the double phase-conjugate resonator.3
We have developed a theory of self-frequency de-tuning in these oscillators.4-6 Here we present experi-mental results that resolve many aspects of self-fre-quency detuning, which we show is easily controllableby external means.
Two four-wave mixing configurations were studied:the semilinear PPCM [Fig. 1(a)] and the ring PPCM[Fig. 1(b)]. The ring PPCM is especially interesting,since it has been shown5 to have similar detuningproperties to those of the two-interaction-region (2IR)PPCM used in frequency-scanning experiments. Atheoretical study5 has revealed that the ring and semi-linear configurations differ fundamentally in their de-tuning characteristics because of their differentboundary conditions. In the semilinear PPCM, thedetuning has a wide region of an approximately lineardependence on dc electric field along the grating wavevector, expressed by 5
Tfr = -OEo, (1)
Tr = atC - Eo, (2)
where a = (MIM + 1) (sinh yol/yol). M is the ring'sintensity transmittance, yo is the coupling constant forthe wave mixing with zero detuning and electric field,and 1 is the effective crystal width. i is the nonrecip-rocal optical phase in the ring (-7r < 0 < ir). The 2IRPPCM is essentially a ring PPCM with a double phaseconjugator7 in the feedback loop, which does not ofitself contribute a nonreciprocal phase to the ring.5Therefore it will be governed by a similar detunitigdependence on t and E04,.
Since the semilinear PPCM is free of any opticalphase dependence in its detuning property, it was apreferred starting point for our experiments. A bareBaTiO3 crystal was held with pressure between twothin metal electrode plates and connected to a dc volt-
D
where 7 ,3 = Ep/Ed(Ed + Ep) and EOp2 << Ed(Ed + Ep).Here 5 is the frequency detuning as shown in Fig. 1,and r is the time response of the crystal. Ep =epd/elf,kg and Ed = kBT kg/e, where Pd is the density oftraps in the material, kB is Boltzmann's constant, T istemperature, and kg is the grating wave number. E4,and E0o, are the dielectric constant and the effective dcelectric field, respectively, along the grating wave vec-tor kg. In this device, vanishing boundary conditionsfor two of the beams implies no detuning dependenceon the beams' phases. Therefore for E0 ,s = 0, 6 = 0also, and the oscillation is degenerate.
For the ring and 2IR PPCM's, frequency detuningcan occur even for a zero electric field. Any nonrecip-rocal optical phase between the counterpropagatingbeams in the ring is accompanied by frequency detun-ing of oscillating beams 3 and 1 with respect to beams 2and 4 by an amount 5. In the nearly linear detuningregion 5,6
(a)
<7"' M
( b)Fig. 1. (a) Semilinear PPCM with external mirror MI.The BaTiO3 crystal is held with pressure between two elec-trodes and connected to a dc voltage supply. A portion ofoutput beam 3 is combined with the reference beam on thedetector D. (b) Ring PPCM.
age-supply source. We set up a semilinear PPCM, asshown in Fig. 1(a). Light from the 488-nm line of anargon-ion laser without an 6talon was focused with abeam spot diameter of approximately 1. mm in thecrystal. The angle 4' in the crystal between the pumpbeam 4 and oscillation beams 1 and 2 was about 70,and so - 74° between kg and the c axis of the crystal. Aportion of phase-conjugate beam 3 and a referencebeam were combined on detector D. The appliedvoltage formed an electric field in the crystal in therange I EA] < 1.3 kV/cm. Note that EA., = EA sin so isthe component of EA along the grating wave vector.There exists the possibility, however, that the actualvoltage drop across the interaction region in the crys-tal was somewhat different from this value because ofa nonuniform voltage in the crystal. Photoconductiv-ity in the interaction region, in particular, would con-tribute to this nonuniformity. A strong backgroundirradiation on the crystal, however, did not change ourresults. In all our experiments, the applied electricfield was perpendicular to the crystal's c axis. Thishas important implications for our experimental re-sults and is discussed below.
A sample of typical plots of the measured detuningdependence on an electric field is shown in Fig. 2(a) forslightly varying crystal orientation or input powerdensity. The intensity of the oscillation did notchange appreciably for different EA; thus Io was ap-proximately constant. For the plot marked with cir-cles, the input power density was 15 mW/mm 2 . Forthis run, we noticed instabilities in the detuning forcertain values of EA, especially at +0.6 kV/cm. Forthe other graphs, the power density was 25 mW/mm2.No instabilities were noticed in these runs. Invari-ably, we observed small positive detuning for a zeroapplied field, which decreased to zero in the region EA= Ei - 0.2 kV/cm. These graphs indicate that aninternal electric field EIN exists within the crystal andhas a component EINq, = -Ei, along kg, where Ei4, = Eisin lo 0.19 kV/cm. This field may be due to the bulkphotovoltaic effect that causes an electric field to formalong the c axis (or the z coordinate). We can estimatethis internal photovoltaic field EIN = zEi4jcos so = zEitan ,o 0.7z kV/6m. The actual electric field may bedifferent, as explained earlier. The lack of data pointsaround zero detuning (EA Ei) reflects the small6(EA) sensitivity in this region and a poorly definedpoint of absolute zero detuning in some graphs. Onereason for this may be the presence of a set of gratingwave vectors, for a set of oscillation angles between thecrystal and the external spherical mirror. The com-ponents of the internal field EINZ along these differentgrating wave vectors cannot be canceled out simulta-neously by the externally applied field EAX. In thisregard, an applied field parallel to the c axis and theinternal field, so that EA = EAZ, should be more effi-cient because it would cancel out the vectorial internalfield.
Turning to the ring PPCM, we measured 6(EA) forthis device with the setup shown in Fig. 1(b). Theinput power density was 25 mW/mm 2 , so - 74°, and 4- 7°. Typical plots are shown in Fig. 2(b) for slightlyvarying crystal or external ring orientations. The dif-ference between these plots and those for the semilin-
ear PPCM is striking: here the 6(EA) dependenceshifts vertically along the detuning axis, with bothpositive and negative detuning observed for a zeroapplied field. This is easily explainable through theaOu term in detuning expression (2) for the ring PPCM.A nonreciprocal phase t may be due to incomplete
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March 1986 / Vol. 11, No. 3 / OPTICS LETTERS 167
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I [2]Fig. 3. Experimental data of detuning versus optical powerdensity in the crystal for the semilinear PPCM with zeroapplied field. The data with the triangles were taken withthe crystal used in the other experiments in this paper, andthe squares with another BaTiO3 crystal.
phase conjugation, which would result in differentcomplex amplitude transmissivities for the counter-propagating beams in the ring. In general, we ob-served that optimization of the oscillation throughcareful alignment resulted in a smaller detuning.This suggests a possible method for determining thedegree of phase conjugation with this phase-conjugatemirror. Another factor may be the presence of reflec-tion gratings in the crystal. These gratings might giverise to a dependence also on reciprocal phases and therings' optical-path-dependent phase. These gratingswere absent in our experiments since the beams' co-herence length was smaller than the ring path. In the2IR PPCM, however, the small internal ring is condu-cive to the formation of reflection gratings.
From Eq. (1) or (2) and recalling that the time con-stant is intensity (Io) dependent as7 r ; A/IO, we maywrite
0(E',, Io) (O/A)EoIo, (3)
where Eoq, = EA, + EIN,. This permits control of thedetuning by using Io. We checked this dependence onthe power density with two crystals and obtained theplots shown in Fig. 3. For this experiment, we usedthe semilinear PPCM configuration with zero appliedfield. The observed detuning dependence on Io wasnearly linear. The deviation in the slopes for differentcrystals is due to different values for EIN,P or i3, whichare strongly dependent on the particular wave mixingconfiguration within the crystal. EIN,, EP, Ed, and rare 4 and lp dependent through kg and E,.
We fitted all plots in Figs. 2 and 3 to straight linesand normalized the slopes 6 versus EA in Fig. 2 to Io =25 mW/mm2. This resulted in an average slope ofMM1/A = 0.46 (rad/sec)/(kV/cm) for both the semilinearand ring PPCM's, as expected. In Fig. 3, the slope 6
versus Io for the same crystal is #EIN, 2,/A = 0.005 (rad/sec)/mW/mm2. Assuming that Ep 5 kV/cm and Ed
1 kV/cm in our experiments gives fi 0.7 cm/kV forkg = 2ir/(1.5 gm), a dielectric constant along kg of e4,L e. sin2 sr - 4000 (e, >> e,), and Pd 5 X 10 1 6/cm 3 . Thisresults in A = 37 sec mW/mm 2 for the 6(EA) experi-ments and A = 26 sec mW/mm 2 for the 6(b) experi-ment (where we assume that EIN, = -0.19 kV/cm).This implies that r 1-1.5 sec in the 5(EA) experi-ments with Io = 25 mW/mm 2 .
The hypothesis that the internal electric field has abulk photovoltaic origin is supported by observed pho-tocurrents in BaTiO3.
8 ,9 An analysis 5 shows that itaffects the detuning by modulating the nonuniformspace charge field and by a uniform dc field that isformed. In an open circuit along the c axis, as is thecase in our experiment, the effect of the dc field almostcancels the overall detuning. Thus either some as-sumptions used in the derivation of the photovoltaiceffect on the coupling constant are incorrect or thecrystal is effectively partially short circuited internal-ly. The latter possibility has support from otherworks. 10
We have experimentally resolved many aspects ofself-frequency detuning. For the ring or 2IR PPCM,the combination of a nonreciprocal phase in the feed-back ring and an internal field are the sources of theself-detuning.11 The amount of detuning and its sign(positive or negative), and so the scanning rate anddirection when coupling to a dye-laser cavity, are de-pendent on the crystal orientation. This entersthrough the detuning dependence on -yo, i, the opticalphase 0, fi, and the component of the internal fieldalong kg. The semilinear PPCM, however, is not sen-sitive to optical phase in the oscillation path for itsdetuning and should therefore prove to be a moreuseful detuning device in certain applications. Theself-frequency detuning is easily controllable throughan applied dc electric field or the light intensity in thecrystal. This will permit external biasing of interfer-ometers such as the ring passive phase-conjugate gyro-scope4 and optical frequency and intensity control andmodulation.
References
1. W. B. Whitten and J. M. Ramsey, Opt. Lett. 9,44 (1984).2. F. J. Jahoda, R. G. Weber, and J. Feinberg, Opt. Lett. 9,
362 (1984); J. Feinberg and G. D. Bacher, Opt. Lett. 9,420 (1984).
3. M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. 0.White, and A. Yariv, Opt. Lett. 10, 353 (1985).
4. B. Fischer and S. Sternklar, Appl. Phys. Lett. 47, 1(1985).
5. B. Fischer, Opt. Lett. (to be published).6. S. Sternklar, S. Weiss, and B. Fischer, Appl. Opt. 24,
3121 (1985).7. M. Cronin-Golomb, B. Fischer, J. 0. White, and A.
Yariv, J. Quantum Electron. QE-20,12 (1984).8. A. G. Chynoweth, Phys. Rev. 102, 705 (1956).9. V. M. Fridkin, Appl. Phys. 13, 357 (1977).
10. P. Gtinter, Phys. Rep. 93,199 (1982).11. After this work was completed, other relevant work was
published. Our results and theory (see Refs. 4 and 5)differ from the approach taken by K. R. MacDonald andJ. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
