Efficient marching solver for a class of three-dimensional optical waveguides

An efficient marching method of the wave propagation computation in the three-dimensional (3D) rectangular box is developed by solving the scalar Helmholtz equation with the weakly range-dependent refractive-index or wavenumber profile. The method is based on the application of the one-way formulation accompanied by a truncated technique that allows for the reduction of the number of eigenmodes and for quickly achieving reliable numerical results. The merits of the high accuracy and fast computation with a larger range step are shown to solve the equation. This treatment can be also applied to other complicated 3D waveguides.