Dynamics of incoherent bright and dark self-trapped beams and their coherence properties in photorefractive crystals

Abstract

Using the coherent density approach, we study the propagation dynamics of incoherent bright and dark beams in biased photorefractive crystals. We show that, under appropriate initial conditions, bright as well as darklike incoherent quasi-solitons can be established in this material system. Our numerical simulations demonstrate that the coherence properties of these beams can be significantly affected by the self-trapping process.

Self-trapping and stabilization of doubly-charged optical vortices in two-dimensional photonic lattices

“…invariant during propagation. Here, to better simulate the real experimental situation, we take into account the nonlinear propagation of the partially coherent lattice beam by using the so-called coherent density approach [45,51,52]. In other words, we let the lattice beam propagate nonlinearly rather than have a constant linear lattice as assumed in most prior numerical work.…”

“…is the angular power spectrum of the partially coherent field, x and y are the angles at which each component, respectively, propagates with respect to the z axis, 0 is a constant related to the spatial coherence length [45], and È(x, y) ¼ È 0 [cos(x/Ã) þ cos(y/Ã)]/2 determines the intensity distribution of the lattice-inducing beam with È 0 being the peak intensity and à being the lattice spacing. The nonlinear constants L ¼ 0:5k 0 n 3 o r 13 E 0 and V ¼ 0:5k 0 n 3 e r 33 E 0 are determined by the electro-optic coefficients in the SBN:60 crystal as well as the bias field E 0 .…”

“…k 0 ¼ 2/ is the free-space wave-vector, and n o and n e are the refractive indices for ordinarily-polarized and extraordinarily-polarized light, respectively. For the isotropic model, the normalized nonlinear refractive index change Dn(I ) is simply determined by À(1 þ I ) À1 , as a saturable photorefractive nonlinearity [26,30,45]. For the anisotropic model, however, the refractive index change Dn(I ) has to be calculated from the gradient of the electrostatic potential U (i.e.…”

“…Interferometric techniques are employed to examine the phase distribution of the output vortex beam. In order to better understand the evolution of the vortex field through the nonlinear periodic medium, numerical simulations are performed using two different models with both isotropic [26,30,45] and anisotropic [46][47][48] nonlinearities. With the isotropic model, we show that nonlinear self-trapping of the DCV leads to formation of a rotating 'quasi-vortex' soliton while the topological charge flips periodically from m ¼ 2 to m ¼ À2 through a quadrupole-like transition state.…”

Interactions of incoherent localized beams in a photorefractive medium

“…The progress was facilitated by the appearance of new methods for the treatment of incoherent localized beams in PR media: the coherent density method [4,5,9,14], the selfconsistent multimode method [2,7,8,11,13,15,18,19], and the mutual coherence function method [6,12]. They were developed independently to describe exactly such sorts of solitary waves in theory; however, it was soon demonstrated that these three seemingly different theoretical methods are equivalent to each other in inertial nonlinear media [21].…”