Inhomogeneous electromagnetic plane waves in crystals (Q1819605)

The paper presents a thorough investigation of the propagation of inhomogeneous electromagnetic time-harmonic plane waves in nonabsorbing electrically anisotropic bodies. This is carried out in terms of the somewhat unusual ''bivectors'' (complex vectors) of Hamilton and Gibbs. The introduction of these representations allows one to interpret many results concerning the polarization of waves in isotropic, uniaxial and biaxial crystals in terms of the properties of ellipses and their degenerate forms associated with bivectors. The case of inhomogeneous circularly polarized waves receives special attention. The inhomogeneity of the considerd waves comes from boundary or initial conditions (as is the case for surface waves). Although bivectors are already met in other fields of mathematical physics (e.g., the Bel-Petrov classification of Einsteinian space-time manifolds in general relativity), their introduction in the field of crystal optics is also welcome but will necessitate some effort from the reader.