A note on hybrid waves in plane layered waveguiding structures

Background. The paper focuses on the problem of propagation of a hybrid electromagnetic wave in a plane layer filled with anisotropic dielectric. Such kind of problems attracts attention due to the mathematical aspects of the theory as well as the importance in microelectronics and photonics. Materials and methods. Classical methods of ordinary differential equations. Results. A linear two-parameter eigenvalue problem arising in the theory of guided electromagnetic waves is considered. The field configuration is adjusted with the symmetry of a plane layered waveguide. The guided wave is characterised by a pair of coupled propagation constants. The dispersion equation, which determines the coupled propagation constants, is derived. The equivalency between the original waveguiding problem and the dispersion equation is proved. Conclusions. The paper suggests a novel concept of a hybrid electromagnetic wave in a plane layered structure. The hybrid wave is the most general field configuration, which can exist in a plane waveguide. This concept generalises well known types of polarised guided waves (TE and TM waves).