Abstract

We report experimental results on self-focusing and self-defocusing of light in two-wavemixing. The complex coupling coefficient for two-wave-mixing and the corresponding first-order (linear) susceptibility were derived in as in Weiss and Fischer.¹ In an analogous way we define the nonlinear (third-order) susceptibility,² which is self-focusing. Such self-focusing in two-wave-mixing was also predicted for a photorefractive oscillator in Staliunas et al.³ Amplification and self-focusing were measured as functions of the frequency shift between signal and pump beam in two-wavemixing in BSO² and BaTiO₃ (Fig. 1). The frequency dependence of the self-focusing is found to have a dispersion shape as is plausible from the analogy of the photorefractive and the laser amplification. In a drift-type material, the self-focusing in two-wave-mixing has to be distinguished from photorefractive self-focusing.⁴ This is possible because two-wave-mixing self-focusing requires coherent fields, while photorefractive self-focusing does not. In diffusion-type material, photorefractive self-focusing is absent. The nonlinear susceptibility for two-wave-mixing is determined not only by the material constants of the photorefractive medium but also by the parameters of the two-wave-mixing process, especially the frequency shift between signal and pump beam. In general, in-drift-type material self-focusing by two-wave-mixing is observed simultaneously with the photorefractive self-focusing. In this case the photorefrative self-focusing causes to first order a frequency shift between the two-wave-mixing gain line and the self- focusing profile. This shift is absent for pure two-wave-mixing self-focusing. We were able to observe pure two-wave-mixing self-focusing by using pump/signal ratios above 10, at which value the photorefrative self-focusing is suppressed. The self-focusing in two-wavemixing in diffusion-type material (BaTiO₃) is isotropic in the transverse plane, whereas in the case of drift-type material (BSO) we found that the amount of self-focusing in two-wavemixing is larger by a factor of about three along the direction of the external field than along the direction perpendicular to the external field. This anisotropy can be explained by pump depletion in BSO. Consequences of gain saturation for the measurements of self-focusing in BaTiO₃ are discussed. In general two-wave-mixing self-focusing can be changed to defocusing by a change of frequency shift between signal and pump beam and by a change of orientation of the crystal. The self-focusing investigated here plays an important role in the dynamics of photorefractive oscillators.⁵

© 1998 Optical Society of America