In this paper, we address accurate computation of complex propagation constants and field distributions of different modes, in general, lossless and lossy optical dielectric waveguides. Using the vector finite-element formulation of the beam propagation method combined with the imaginary distance propagation technique, sequence of both the guided and leaky modes can be accurately calculated. To show the versatility and numerical precision of the proposed technique,we compute the modes of three different three-dimensional (3-D) waveguide structures and compare the results against those of other, different, vector formulations. Further, we present the design of a higher order mode filtering device, based on a 3-D leaky mode optical waveguide.
S. S. A. Obayya, B. M. Azizur Rahman, Kenneth T. V. Grattan, and H. A. El-Mikati, "Full Vectorial Finite-Element-Based Imaginary Distance Beam Propagation Solution of Complex Modes in Optical Waveguides," J. Lightwave Technol. 20, 1054- (2002)