Second-Order Perturbative Analysis with Approximated Integration for Propagation Mode in Two-Dimensional Two-Slab Waveguides

We calculated propagation constants of supermodes for two-dimensional two-slab waveguides, with small core gap, using secondorder perturbation expansion from gapless slab waveguide system, and compared our results with the existing works. In the perturbation calculation, we used trapezoidal method to calculate the integral over the transverse direction in space and obtained second-order expansion of (core gap)/(core width) for propagation constants. Our result can explain the qualitative relationship between the propagation constants and the gap distance in the neighbor of (core gap)/(core width) being zero. key words: propagation constants of supermodes, second-order perturbation, two-slab waveguides, Maxwell’s equation, Schrödinger’s equation