Analysis of wave propagation in optical waveguide arrays using a rigorous transmission-line formulation

In this article, a rigorous, semi-analytical method for the analysis of propagation of TM waves in an infinite array of one-dimensional waveguides is proposed. In the proposed method, a number of current filaments are used to excite one of the waveguide modes. The spatial distribution of current is chosen to accurately model the excitation of the fundamental modes. To evaluate the response of the waveguide array when only a single waveguide is excited, the corresponding current distribution and its spatially shifted versions are linearly combined to constitute a set of pseudo-periodic current sheets whose superposition yields the required current distribution for the excitation of the fundamental mode in a single waveguide. Using a matrix formulation, we demonstrate how the response of structure to pseudo-periodic functions can be derived from the analysis of an equivalent network of ideal coupled transmission lines (TLs). As shown, this method can be simply generalized for study of lossy and/or anisotropic waveguide arrays.