Three-dimensional beam propagation method based on the variable transformed Galerkin's method

摘要

A novel three-dimensional beam propagation method (BPM) based on the variable transformed Gaierkin's method is introduced for simulating optical field propagation in three-dimensional dielectric structures. The infinite Cartesian x-y plane is mapped into a unit square by a tangent-type function transformation. Consequently, the infinite region problem is converted into the finite region problem. Thus, the boundary truncation is eliminated and the calculation accuracy is promoted. The three-dimensional BPM basic equation is reduced to a set of first-order ordinary differential equations through sinusoidal basis function, which fits arbitrary cladding optical waveguide, then direct solution of the resulting equations by means of the Runge-Kutta method. In acrlition, the calculation is efficient due to the small matrix derived from the present technique. Both z-invariant and z-variant examples are considered to test both the accuracy and utility of this approach.