<title>Means to find nonlinear modal fields using the finite difference beam propagation method</title>

Abstract

ABSTRACT A method to construct modal fields for an arbitrary one- or two-dimensional intensity depen-dent refractive index structure is described. An arbitrary starting field is propagated alonga complex axis using the slowly varying envelope approximation (SVEA) for the Finite Dif-ference Beam Propagation Method (FDBPM). By suitably choosing the complex value ofthe propagation step, one mode is maximally increased in amplitude. The applicability ofthe method is discussed and illustrated by a one-dimensional cross section test example withKerr-type nonlinearity. 1 INTRODUCTION In the last few years, a number of papers have appeared discussing the propagation ofwaves in nonlinear media showing third-order nonlinear effects of the intensity depen-dent refractive index. Special interest has been given to analytical 1—5 and numerical 6,7 methods for finding solutions in multilayer slab waveguides, the nonlinearity beingof Kerr-type in most papers, e.g. in ref. 1-5.For linear structures, a number of methods have been developed to find modal fieldsolutions for an arbitrary refractive index profile. Two-dimensional transfer matrixmethods can be used for two-dimensional structures 811,