Mathematical physics of propagating modes in planar waveguides

Abstract

In this paper, we present a detailed physical analysis of the formation of the propagation transverse modes in planar dielectric waveguides using a mathematical-physics approach. We demonstrate physically that, at the wavelength scale, the pure stationary mode inside planar waveguide is described by the cosine function. Meanwhile, the sine function arises from the interference of waves that superpose with a relative phase shift e-ip, yielding a quasi-stationary periodic mode.