Field decomposition for analysis of hyperbolic media

Abstract

A field decomposition of Maxwell's equations for uniaxial hyperbolic media based on the 2D Helmholtz theorem is provided. This decomposition is particularly useful since it produces TE and TM field sets that are orthogonal and allows for identification of two independent scalar potential formulations. It is shown that these formulations provide substantial mathematical simplification, enhanced physical insight, ease of boundary condition enforcement and a trivial field recovery process. An example involving a parallel-plate waveguide filled with hyperbolic media is given to demonstrate the functionality and practicality of the decomposition.