Nonlocal Optical Spatial Soliton with a Non-parabolic Symmetry and Real-valued Convolution Response Kernel

Abstract

Based on the picture of nonlinear and non-parabolic symmetry response, i.e., Δn2(I) ≈ ρ(a0+a1x-a2x2), we propose a model for the transversal beam intensity distribution of the nonlocal spatial soliton. In this model, as a convolution response with non-parabolic symmetry, Δn2(I) ≈ ρ(b0+b1f-b2f2 with b2/b1 > 0 is assumed. Furthermore, instead of the wave function ψ, the high-order nonlinear equation for the beam intensity distribution f has been derived and the bell-shaped soliton solution with the envelope form has been obtained. The results demonstrate that, since the existence of the terms of non-parabolic response, the nonlocal spatial soliton has the bistable state solution. If the frequency shift of wave number β satisfies 0 < 4(β - ρb0/μ) < 3η0/8α, the bistable state soliton solution is stable against perturbation. It should be emphasized that the soliton solution arising from a parabolic-symmetry response kernel is trivial. The sufficient condition for the existence of bistable state soliton solution b2/b1 > 0 has been demonstrated.