General Analytical Coupled-mode Solution of Multiwaveguide Systems

Standard Coupled-Mode Theory (Standard CMT) is a well-known approach for analysis of coupling and propagation of guided modes in multiwaveguide systems. In order to analyze propagation of EM fields these systems, Standard CMT solves 1st order differential matrix equation (Standard CMT equation). Analytical solution for this equation currently exists only for the multiwaveguide systems with dielectric function, homogeneous along the optical axis (z-axis). Coupled-mode analysis of the devices, whose dielectric function varies along the optical axis (e.g. photonic components with integrated optical gratings) till now, is only available with numerical techniques. In this work, we propose the general Analytical solution for Standard CMT equation, including the case of dielectric function, inhomogeneous in the z-direction. This solution represents an effective analytical tool for fast and accurate analysis, design and optimization of a variety of photonic components, whose principles of operation are based on the variation of their dielectric function along the optical axis.