We show numerically that the existing photocurrent anisotropy strongly a ects the form of initially circular beam after self-focusing in photorefractive crystals. We estimate the ellipticity of the output beam in strontium barium niobate and barium titanate and compare it with existing experimental data.Single beam self-focusing in photorefractive materials has attracted a lot of attention. Of special interest is the so called soliton regime, in which the di raction is compensated by the nonlinearity, and the beam width is preserved with propagation [1]. A typical arrangement for self-focusing observation is depicted schematically in gure 1. Ferroelectrics are the materials of choice because of their high electro-optical coe cients. In this case the external electric eld is normally applied along the c-axis. The existing theory states that if the input beam is circular and additional illumination is used (the 2D screening soliton), the steady state response of the refractive index is not local and the soliton-type solution cannot have circular symmetry [2,3]. The primary reason for this is that the 2D beam distorts current lines, the y-component of the electric eld appears, and the x-component su ers complicated changes ( gure 1, see also gure 1 of [2]). For the e ective lens induced by Gaussian intensity distribution, the ratio of focal strengths in the direction of the applied eld and perpendicular to it is 3:1 [2]. Thus, it is expected that self-focusing in photorefractives is highly anisotropic.Experiments con rm this conjecture for barium titanate where the output intensity distribution is elliptic with an approximately 3:1 ratio between widths [4]. Experiments with strontium barium niobate (SBN) demonstrate, in some cases, close to circular output [5]. Here we discuss the possibility of resolving this contradiction by taking into account the photoconductivity anisotropy of ferroelectrics. This factor is quite pronounced. For barium titanate, the ratio between conductivities in c-axis and a-axis directions is 1 : 14 ¥ 20 [6][7][8]. For SBN, this ratio is approximately 3:1 [7], i.e. in this crystal the conductivity is greater along the c-axis, whereas in barium titanate it is greater along the a-axis. However, in earlier studies the conductivity was always considered isotropic.It is easy to understand that the SBN-type ratio favours more circular output than the isotropic conductivity case. If the conductivity along the c-axis is much greater than along the a-axis, the current lines are nearly parallel to the c-axis, and Journal of Modern Optics
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