High-accuracy analytical solver for guided and unguided complex modes of optical waveguides

A highly accurate and primarily analytical solver for the vector modes of dielectric optical waveguides is developed based on the mode matching method. The method starts with the analytical solutions for the entire family of guided and un-guided complex modes of the corresponding 1D slab waveguides that make up the 2D channel waveguide. Subsequently, the standard mode matching method is applied to the solution of the full vectorial modes with high accuracy. Not only the guided modes, but also the un-guided higher-order complex modes may be obtained with accuracy not readily attainable with the traditional numerical methods such as the finite difference method. The mode effective indices are governed by a transcendental equation and may be solved by a complex root searching algorithm such as the particle swarm optimization method. The expressions of the modal fields are all analytical global functions without need for numerical discretization and free of round-off errors. It is expected that the modal solutions derived from this believed to be new method will be highly accurate and much more versatile for analysis and optimization due to its analytical nature. It may provide powerful and useful basis for the propagation problems for non-uniform optical waveguides by way of the mode matching method and/or the coupled-mode theory.