Modal analysis of a dielectric waveguide with planar guiding-nonguiding boundaries with a flare in the direction of propagation

Abstract

We make an analytical study of the modal characteristic equation of a slab waveguide with a flare bounded by two planes. We choose cylindrical polar coordinates (ρ, φ, z), and assume that the two bounding planes are extended infinitely in the z-direction, and are represented by φ = φ1 and φ = φ2 so that φ2 - φ1 is very small. The field in the z-direction is assumed to be uniform, and we consider propagation along the p-direction. Using the weak guidance approximation, the characteristic equation is obtained. Numerical computations show that only one global mode can be sustained in such a structure for the model v = 0, corresponding to the coordinate φ. There is an attenuation in this supported mode, and this is because of the flare. © 1998 John Wiley & Sons, Inc.