Self!focusing and !defocusing of light in two!wave mixing is investigated experimentally for BaTiO 2 and BSO[ Ampli_cation and self!focusing of a probe beam are measured as functions of the frequency shift between probe and pump beam[ The self!focusing in two!wave mixing in BSO is anisotropic\ whereas it is isotropic in BaTiO 2 [ Consequences of gain saturation for the measurement of self!focusing in BaTiO 2 are discussed[ Þ 0888 Elsevier Science Ltd[ All rights reserved[ Self!focusing in two!wave mixing was _rst suggested in the description of photorefractive res! onators ð0Ł[ Nonlinear transverse pattern formation in a photorefractive resonator requires at least coupling between transverse modes by means of the two!wave coupling nonlinearity[ In lowest order approximation\ the real and imaginary parts of the two!wave coupling nonlinearity correspond to gain saturation and self!focusing[ Thus\ in this approximation\ self!focusing is one means to couple transverse modes in a photorefractive oscillator ð1\ 2Ł[ In a strongly nonlinear case\ the nonlinearity can even make the system independent of boundaries\ in which case modes are no longer excited[ In this case\ shocks\ domains of tilted waves and cross!rolls can be observed ð3Ł[ One phenomenon in which the two!wave mixingÐself!focusing could be of importance is the spatial modulational instability in photorefractive crystals ð4Ð8Ł[ It appears as moving stripe! patterns in the near _eld of a drift!type photorefractive material[ These stripes could be regarded as 0D!solitary waves stabilized by two!wave mixingÐself!focusing[ Another phenomenon is light emission from optical lattices ð09Ł[ From its analogy with two wave!mixing\ one would suggest that here also\ self!focusing might play a role[ Self!focusing in two!wave mixing was _rst experimentally demonstrated in BSO ð00Ł\ a drift! type photorefractive material[ In the work reported here\ self!focusing and defocusing\ is dem! onstrated for the _rst time in the di}usion!type material BaTiO 2 [ We compare the strength of this self!focusing in BaTiO 2 with self!focusing in two!wave mixing in BSO and with values estimated from material constants[ In particular\ the anisotropy of the self!focusing is investigated for BSO[ Consequences of saturation of the gain are shown in the measurements of self!focusing in BaTiO 2 [
In two!wave mixing\ two coherent _elds induce a refractive index grating by means of the linear electro!optic e}ect[ If one of these beams "pump# is di}racted into the direction of the other beam "signal# by a su.cient phase shift between the refractive index grating and the light