Graded-index Planar Waveguides

Graded-index Planar Waveguides

The waveguide structures that we have examined up to now had a step-index profile,
with three well-defined regions (cover, film and substrate) of constant refractive
indices. These structures are obtained by any of the deposition techniques summarised
in Chapter 1. When the waveguide fabrication is performed by a local index increase
on a substrate material, by means of diffusion techniques, for instance, the refractive
index of the waveguide shows in general a graded index profile in depth, expressed
as n = n(x). In this case the structure is called a graded-index waveguide. Usually
the maximum index increase is located at the substrate surface, slowly decreasing in
depth, until the refractive index reaches the substrate value, the typical depth being of
the order of a few microns (Figure 3.24).
There are several methods that can be used to calculate the effective refractive
index of the modes in waveguide structures with graded index profiles. Here we will
describe two methods which are widely used and provide excellent results, namely,
the multi-layer approximation and the ray approximation method. For both, we will
discuss advantages and disadvantages, and the best choice for a given problem. We
will also describe a method for reconstruction index profiles, given a discrete set of
measured modal indices.