Weakly guiding waveguides

Abstract

In Chapter 11 we discussed the fundamental properties of modes on optical waveguides. The vector fields of these modes are solutions of Maxwell’s source-free equations or, equivalently, the homogeneous vector wave equations. However, we found in Chapter 12 that there are few known refractive-index profiles for which Maxwell’s equations lead to exact solutions for the modal fields. Of these the step-profile is probably the only one of practical interest. Even for this relatively simple profile the derivation of the vector modal fields on a fiber is cumbersome. The objective of this chapter is to lay the foundations of an approximation method [1,2], which capitalizes on the small variation in refractive-index profile of fibers used for long-distance communications, i.e. Δ ≪ 1, where Δ is the profile height parameter of Eq. (11-48). The simplicity of this approximation method is that it relies on solutions of the scalar wave equation, rather than on vector solutions of the vector wave equation.