Rigorous determination of the modal spectrum for multilayered structures through a simple closed-form approach

In this work, novel closed-form expressions are shown and applied for a very efficient determination of the modal spectrum in arbitrary planar multilayered structures, useful in a variety of propagation and radiation problems. The speedy but rigorous determination of the number of surface waves and of the relevant cutoff frequencies is illustrated as a function of the physical parameters involved. The advantage of this formulation in terms of efficiency is validated by means of numerical comparisons with full-wave dispersive analyses based on the usual numerical solution of transcendental characteristic equations.