Modal analysis of slab optical waveguides: Fresnel equations v.s. wave equations

We demonstrate both analytically and numerically that the modal analysis of optical slab waveguides based on the total internal reflection (TIR) method and the wave equation method are equivalent. The analytical method based on the TIR and Fresnel equations is also applied to the evanescently-pumped active waveguides where the cladding layers have optical gain, and the results are compared to the numerical simulations. This study establishes a direct connection between the field reflection and transmission coefficients given by the Fresnel equations to the mode solutions of the wave equation in waveguides.