Anisotropy, nonlocality, and space-charge field displacement in (2 + 1)-dimensional self-trapping in biased photorefractive crystals

The complete basic equations for $\left(2+1\right)$-dimensional self-trapped beam propagation in photorefractive media are numerically solved, with the anisotropic nonlocal response, diffusion, and space-charge-field displacement effects taken into account. Initial Gaussian beams show elliptical beam shapes, self-deflection, and long-lived oscillations after propagation. The critical parameters that determine the possible damping of the transients are discussed.