The Algorithms For Non-Homogeneous Waveguide Equation Based On DtN Maps

Generally, the government equation for guided wave with inside lightsource is non-homogeneous Helmholtz equation. Two new computationalmethod for non-homogeneous Helmholtz equation for periodic waveguide,named M and P algorithm, are constructed, based on Dirichlet-to-Neumann(DtN) maps in this paper. The two methods can greatly reduce the requirementof internal memory and the amount of computation compared with thetraditional algorithms. In the M algorithm, only a DtN operator M needs to becalculated on one period and then the solution of the equation can be derivedrecursively. The main characteristic of the P algorithm is to transfer theboundary value problem of the differential equation into an initial valueproblem. It greatly simplifies the calculation. For periodic waveguide, alsoonly a state transition operator P needs to be calculated on one period and thenthe solution can be derived recursively. The developed algorithms provideefficient methods for waveguide problems with inside light source.