Perturbation Analysis with Approximate Integration for Propagation Mode in Two-Dimensional Two-Slab Waveguides

On the basis of perturbation expansion from a gapless system, we calculate the propagation constant and propagation mode wave function in two-dimensional two-slab waveguides with a core gap small enough that there is only one propagation mode. We also perform calculations without the approximation for comparison. Our result shows that first-order perturbation contains the first-order Taylor expansion of (core gap)/(core width), and when the integration of the perturbation is suitably approximated, the result of the first-order perturbation is the same as that of the first-order Taylor expansion of (core gap)/(core width).