A Fast Procedure to Accurately Determine Leaky Modes in Multilayered Planar Dielectric Substrates

Leaky modes of multilayered substrates play an important role in efficient numerical electromagnetic solvers. In this paper, the location of the propagation constants of the transverse electric and transverse magnetic leaky modes are determined in an efficient way for multilayered substrates with commensurable layer thicknesses. It is shown that, for all practical applications, accurate quasi-static approximations for high mode orders can be derived rapidly by finding the roots of an analytically obtained polynomial. Furthermore, simple closed-form expressions are derived for some particular cases. Starting from these estimates, only a few additional Newton steps are required for a very precise determination of the propagation constants. The proposed method is validated by means of several illustrative numerical examples.