NUMERICAL-SOLUTION METHOD OF NONLINEAR GUIDED MODES WITH A FINITE-DIFFERENCE COMPLEX AXIS BEAM-PROPAGATION METHOD

A method to construct modal fields for an arbitrary one- or two-dimens ional intensity dependent refractive index structure is described, An arbitrary starting field is propagated along an imaginary axis using t he Finite Difference Beam Propagation Method (FDBPM) based upon the Sl owly Varying Envelope Approximation (SVEA). First the modes are found for the linear part of the refractive index structure, By suitably cho osing the complex value of the propagation step, one mode is maximally increased in amplitude, After the nonlinearity has been put on, two m ethods are applied to find the modes for the nonlinear structure. One method is the same as the method used for the linear part, in the othe r method the propagation step is left unchanged, The applicability of the method is discussed and illustrated by a calculation on a waveguid e with one-dimensional cross section having Kerr-type nonlinearity.