Coordinate-independent dyadic formulation of the dispersion relation for bianisotropic media

This paper presents a coordinate-independent dyadic formulation of the dispersion relation for general bianisotropic media. The dispersion equation is expanded with the aid of dyadic operators including double-dot, double-cross and dot-cross or cross-dot products. From the dispersion relation, the Booker quartic equation is derived in a form well-suited for studying multilayered structures. Several deductions are made in conjunction with the bianisotropic media satisfying reciprocity and losslessness conditions. In particular, for reciprocal bianisotropic media, the dispersion equation is biquadratic in wave vector while for lossless bianisotropic media, all dispersion coefficients are of real values. As an application example, the dispersion equation for gyrotropic bianisotropic media is considered in detail.