A multiport representation of the step junction of two circular dielectric waveguides

A multiport representation of the step junction of two circular dielectric waveguides of different size is given. 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 function. Applying the mode matching technique, a multiport representation of the step junction is derived. Numerical examples arc given where the results are tested for the conservation of power. Also the numerical results are compared with those from Marcuse's approximate methods.