Abstract
A multiport representation of the step junction of two circular dielectric waveguides of different size and its application to the stepwise approximation of a tapered dielectric waveguide are presented. Continuous spectral modes of the circular dielectric waveguide are discretized at a terminal plane by means of expressing their mode amplitudes in the form of infinite series of orthonormal Gaussian Laguerre functions. Applying the standard mode matching technique at the terminal plane, a rigorous multiport representation of the step junction of two circular dielectric waveguides is derived. Using the multiport representation, a stepwise approximate solution is given for the tapered dielectric waveguide. Numerical examples are given where the results are tested for the conservation of power. Also the numerical results are compared with those from Marcuse’s approximate methods.
