A Mathematically Rigorous Cutoff Analysis of Parabolic Cylindrical Waveguides

Abstract

We present a rigorous study of a planar waveguide which, under the influence of unintentional or deliberate effects, takes the form of a parabolic cylindrical waveguide. Extending our earlier study on this problem, where some physically plausible assumptions were made, we now develop the characteristics and the cutoff condition equations for such a waveguide under mathematically rigorous conditions. It is found that results again show a bunching tendency of modal cutoff confirming the validity of our earlier results. Mode-bunching is thus found to be a fundamental characteristic of parabolically bent slab waveguides.