A simple approach to mode analysis for parabolic waveguides

A simple method of mode analysis for parabolic waveguides, based on one-dimensional analytic continuation, is presented. The method gives essentially exact values for parabolic cylinder functions; i.e., the relative error in the computed result is on the order of the machine round-off. When supplemented with a Newton-Poisson shooting method and simple homotopy techniques, this continuation method can be used to find the transverse electric and transverse magnetic mode eigenvalues, and associated separation constants, for arbitrary parabolic domains. These methods are also used to compute a power-handling efficiency factor for a range of parabolic regions