Improved Bidirectional-Mode Expansion Propagation Algorithm Based on Fourier Series

In this paper, an improved version of a 2-D bidirectional eigenmode expansion propagation algorithm based on Fourier series expansion for modeling optical field distribution in waveguide devices is presented. The algorithm is very simple, numerically robust, and inherently reciprocal. It does not require root searching in the complex plane. Proper truncation rules are used to ensure good convergence properties for TM-polarized waves. Perfectly matched layers as absorbing boundary conditions can be implemented in a very simple way using complex coordinate stretching. The approach represents a transition between purely modal and Fourier expansion methods for modeling guided-wave photonic structures.