Modes of optical waveguides

TLDR

Waveguide modes are studied for structures with circular symmetry and for those with two preferred axes of symmetry, such as elliptical cores. The paper presents a simple method for determining modes in optical waveguides whose cladding refractive index differs only slightly from that of the core. The method is applicable to waveguides with arbitrary refractive index profiles, any number of propagating modes, and any cross‑section shape. The resulting modal fields and propagation constants reveal the waveguide’s polarization properties, and demonstrate that only a minute eccentricity is required to stabilize LP modes on an elliptical core while causing power coupling among circular modes.

Abstract

A simple method is presented for finding the modes on those optical waveguides with a cladding refractive index that differs only slightly from the refractive index of the core. The method applies to waveguides of arbitrary refractive index profile, arbitrary number of propagating modes, and arbitrary cross section. The resulting modal fields and their progagation constants display the polarization properties of the waveguide contained within the ∇ ∊ term of the vector wave equation. Examples include modes on waveguides with circular symmetry and waveguides with two preferred axes of symmetry, e.g., an elliptical core. Only a minute amount of eccentricity is necessary for the well-known LP modes to be stable on an elliptical core, while the circle modes couple power among themselves.