Mismatch of TE and TM modes in multilayer dielectric and metal–dielectric heterostructures

Abstract

A theoretical investigation is made of the mismatch between orthogonal modes (i.e., the relative difference between the refractive indices of guided TE and TM modes characterized by the same frequency and transverse index) propagating in four- and five-layer planar waveguides. An approximate expression is obtained for the mismatch between orthogonal modes in a five-layer planar waveguide characterized by relatively small discontinuities of the permittivity at the interfaces between the media and by relatively thick intermediate layers. It is shown that when an outer metal layer is deposited on a three-layer dielectric planar waveguide, the direction of change in the mismatch between orthogonal modes depends on the sign of the difference between the refraction indices of a guided TM mode in a three-layer waveguide and a surface plasmon traveling along the interface between the metal and an intermediate layer. If this difference between the refractive indices is positive, then matching of orthogonal modes is possible. The presence of a dielectric outer layer which is optically less dense than the intermediate one increases the mismatch between orthogonal modes. Subject to the assumptions made, the conclusions reached apply also to heterolasers with limited-thickness emitters.