This work was supported in part by the National Science Foundation under grant no. ECS-9014481.
Gaussian beams, Optical wave guides -- Mathematics, Electromagnetic waves
To a good approximation, the electromagnetic-propagation characteristics of graded-index waveguides can be written in terms of polynomial-Gaussian modes. For uniform quadratic-index waveguides the behavior of these modes is well known. However, there are sometimes practical reasons for using tapered waveguides, but detailed propagation solutions are known for only a few specific taper functions. The parabolic taper is perhaps the most important special case, and the solution-generating techniques that we generalize are used to obtain analytic solutions for this case.
Anthony A. Tovar and Lee W. Casperson, "Beam propagation in parabolically tapered graded-index waveguides," Appl. Opt. 33, 7733-7739 (1994).