Computation of Mode Propagation Constants and Cut-off Frequencies of Optical Planar Layers Using the Resonance Technique

By applying Fourier transformations to Maxwell's equations, we derive transmission-line equations representing the TE and TM modes of dielectric planar layers. The propagation constants of any mode can be found from the resonance condition of the T circuit representation of the transmission line. The cut-off frequency equivalent circuit is also derived, which is useful for the computation of the cut-off frequencies of the propagation modes. The method is developed for uniaxial materials and is applied to uniaxial planar layered structures of arbitrary refractive index. The inhomogeneous isotropic profiles are a special case in this analysis. Examples are given for comparison.