Fourier decomposition of the transverse field for analyzing optical waveguides using beam propagation method

Abstract

Analytical solutions of the wave equation exist only for a few waveguide structures. Direct numeric solution of the wave equation is possible for many structures, although this usually involves iteration to find the approximate eigenvalue. This paper studies the modes of structures, otherwise not amenable to analytic or approximate solution, by integrating Fourier decomposition of the transverse field with the Beam propagation method (BPM). Numerical simulations of special structures such as waveguides with bends or reflective mirrors, split Y-couplers and coupled adjacent waveguides have been carried out. We also examine the operation of a coupled waveguide and apply its theory to calculate its performance to compare it with simulation.