Modified Smooth Transition Method for Determination of Complex Modes in Multilayer Waveguide Structures

The smooth transition method for determination of complex leaky modes in multilayer waveguides is revisited. The mapping between the mode solutions of the initial close waveguide and that of the final open waveguide is discussed and established. It is suggested that a more suitable initial guess should be the real guided modes and the imaginary evanescent modes in a close waveguide with perfect reflecting boundary conditions. Further, the artificial boundary should be positioned right at the two farthest interfaces of the multilayer stacks adjacent to the outer cladding layers. The accuracy, efficiency, and robustness of the new algorithm are validated through calculating the leaky modes in a multilayer waveguide structure and three-layer slab waveguide structures.