Simulation of Spatial Solitons in Photonic Crystal Fibers

Abstract

We consider the guidance problem, at a given frequency, in a triangular PCF which can have a nonlinear response in silica. That is, we solve the following nonlinear equation: [∇2 + k02(n02(x) + n22(x)|φ|2)]φ = β2φ where we search for electric field solutions with well‐defined constant polarization. The linear refractive index profile function n0(x) is one in the air‐holes and equals nsilica in silica, whereas the nonlinear index profile function n2(x) is different from zero only in silica. We approach this problem using a generalization of our modal method to describe linear propagation in PCF’s [1]. In our previous method, the linear differential equation for guided modes is transformed into an algebraic problem consisting in the diagonalization of a matrix representation of the differential operator. The nonlinear eigenvalue equation is formally identical to that found for a soliton solution in a modal approach to dispersion‐management systems [2]. By taking advantage of this fact, we use the same i...