Semi-guided Gaussian beams

<jats:p>Several recent proposals in integrated photonics concern components that operate on so-called semi-guided waves. Given a dielectric multilayer slab structure, these are wave solutions that propagate along the slab with the functional dependence of ordinary harmonic plane waves, but with modal confinement in the direction perpendicular to the slab plane. While the in-plane unbounded waves are valid as a theoretical construct, practical devices will have to work with laterally confined optical fields. To that end we consider Gaussian superpositions of semi-guided waves, for a range of in-plane propagation angles, here named “semi-guided Gaussian beams.” This paper collects a series of relations that characterize these wave bundles, with emphasis on their divergence. The expressions resemble standard results for optical Gaussian beams, with modifications originating from the 1-D guiding and 1-D bundling. Examples for a high-contrast silicon-on-insulator slab at a typical telecom wavelength are discussed.</jats:p>