The presence of hole-electron competition in photorefractive materials has ... R + Io. S with Io. R and Io. S being the incident irradiances for the pump and signal ...
Resonance peaks for holes and electrons in photorefractive space-charge waves
Ivan de Oliveira and Jaime Frejlich Laboratorio de O ptica - IFGW - UNICAMP Abstract
The resonance peak characteristic for both the electron- and the hole-photoactive centers in a Bi12 TiO20 photorefractive crystal were detected in a nearly degenerate two-wave mixing experiment under applied electric eld. The general features in this experiment were analyzed using a simpli ed mathematical model describing the e ect of hole-electron competition upon running holograms.
1 Introduction Nearly degenerated two-wave mixing in a photorefractive material produces a volume hologram that, in steady state, moves synchronously with the pattern of light along the hologram vector direction K~ with a velocity v that depends on the frequency detuning Kv between the interfering beams [1]. The strength of the resulting moving hologram, as measured by its di raction eciency , strongly depends on Kv. A resonance value for does exist and depends on the nature of the charge-carriers and the photoactive centers involved in the recording process as well as on other experimental parameters like applied electric eld, spatial frequency, etc. The presence of hole-electron competition in photorefractive materials has been reported by several researchers [2] as well as the resonance peaks corresponding to electron-photoactive, particularly for fast materials like sillenites [3] (Bi12 TiO20 (BTO), Bi12 SiO20 (BSO) and Bi12 GeO20 (BGO)). Although the existence of similar resonance peaks for hole-photoactive centers have been theoretically predicted [4], as far as we know, it has never been experimentally reported before. In this work we report an experiment where the resonance peaks for electrons and holes are clearly detected in a BTO sample that is known to have a comparatively large concentration of hole-photoactive centers. In order to analyze these results we use a simpli ed theoretical model that shows the way holephotoactive centers may a ect the behavior of running holograms and also that minoritary holes may be easily detected thanks to their resonant behavior. We shall neglect birefringence and optical activity (as we are concerned with a rather thin sample) but will take self-di raction into consideration. The e ect of bulk optical absorption, that produces a variation of the material response time along the crystal thickness [5, 6], will not be considered for the sake of simplicity. Not considering bulk absorption will certainly a ect size, position and other informations about the electron and hole peaks, however it will not prevent us to identify the presence of these peaks and their general features. Even for this simpli ed model the number of independent material parameters is too much large to allow a quantitative analysis.
2 Theory Running holograms can be obtained by means of a moving (with velocity v) pattern of interference fringes of light such as [1]
I = I0 + I20 (m exp[i(Kx ; t)] + m exp[;i(Kx ; t)]);
(1)
where m is the visibility of the incident pattern of light on the crystal, K is the spatial frequency of the pattern of fringes and I0 is the average irradiance. The movement of the fringes is produced by slightly detuning one of the two beams in the two-wave mixing setup where the detuning is = Kv. An important parameter in the study of volume holograms in photorefractive crystals is the di raction
eciency that determines the amount of incident light that is di racted by the hologram. For a simple one-center model electron-arising running hologram the di raction eciency is 2 d=2) ; cos( d=2) ; = 1 2+ 2 cosh(; ; 2 e ;d=2 + e;d=2 3 re ;4n3re 0 that is characteristics of electrons. However another (much thinner) peak clerarly appears for Kv < 0 in the gure 2B that, according to the theory, should be associated with the hole-photoactive centers. The graphics 2A exhibits much larger data dispersion, in agreement with what has been published elsewhere [7]. Data dispersion makes dicult to identify any hole-arising peak for Kv < 0 or any other particular feature in gure 2A.
4 Conclusions This work reports the unequivocally experimental detection of charge-wave resonance peaks both for electron photoactive centers and for hole centers in a photorefractive Bi12 TiO20 crystal. The sensible reduction of data dispersion in the negative two-wave mixture amplitude gain setup is the important experimental
Figure 2: Di raction eciency measured (spots) as a function of Kv for a Bi12 TiO20 crystal, (BTO-02), using the 514.5nm wavelength with K = 4:87m;1, Eo 7:3 KV/cm. For (A) positive gain for electrons and for (B) negative gain. The continuous curves are the experimental data averages. fact that allows the detection of the hole-arising resonance peak in this work. The interpretation of these experimental data is facilitated by a theoretical, although simpli ed, simulation of running holograms in the presence hole-electron competition.
5 Acknowledgements We are grateful to PAFESP and CNPq for the nancial support to this work.
References [1] S. Stepanov, P. Petrov, Photorefractive Materials and Their Applications I, volume 61, chapter 9, pp. 263{289, P. Gunter and J.-P. Huignard, Springer-Verlag, Berlin, Heidelberg (1988). [2] F. P. Strohkendl, J. M. C. Jonathan, R. W. Hellwarth, Hole-electron competition in photorefractive gratings, Opt. Lett. 11, 312{314 (1986). [3] E. Shamonina, K. H. Ringhofer, P. M. Garcia, A. A. Freschi, J. Frejlich, \Shape-asymmetry of the di raction eciency in Bi12 TiO20 crystals: the simultaneous in uence of absorption and higher harmonics", Opt. Commun. 141, 132{136 (1997). [4] I. Aubrecht, H.C. Ellin, A. Grunnet-Jepsen, L. Solymar, \Space-charge eld in photorefractive materials enhanced by moving fringes: comparison of hole-electron transport models", J. Opt. Soc. Am. B. 12, 1918{1923 (1995). [5] Ivan de Oliveira, Jaime Frejlich, \Dielectric relaxation time measurement in absorbing photorefractive materials.", Opt. Commun. 178, 251{255 (2000). [6] Ivan de Oliveira, Jaime Frejlich, \Photorefractive running holograms for materials characterization", J. Opt. Soc. Am. B 18, to be published (2000). [7] Ivan de Oliveira, Jaime Frejlich, \Gain and stability in photorefractive two-wave mixing.", submitted (2000).
