Analytic-numerical approach to non-linear problems in dielectric waveguides

摘要

A combined analytic-numerical approach is presented for investigations of electromagnetic signal propagation in dielectric waveguides containing a non-linear medium. The approach is based on the resolvent method for the Volterra integral equation describing an electromagnetic process. The proposed algorithm uses the exact expression for the solution to the integral equation for the electromagnetic field in the planar waveguide with time jump changing of the medium properties. In the case of a non-linear dielectric as the waveguide core the continuous change of the medium parameters is replaced by jump changes of the latter. This is the only approximation made in the algorithm. The resolvents that are constructed give the exact solution on each jump step. The results from some example numerical calculations are presented. References: 27