TE Waves
A general form for the TE wave inside the substrate is
where the function f(k,z) satisfies the Schrodinger-type equation
and k and v(z) are given by
As z approaches positive infinity, f approaches eikz. This is the Jost solution denoted by f+(k,z).
Starting from a discrete set of k values it is possible to generate corresponding functions v(z;k) and associated Jost solutions f(k,z); that is, it is possible to "design" a graded-index film. This method has been applied to the design of graded-index waveguides.
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