Frequency versus Wave Vector for a Diatomic Ionic Orthorhombic Biaxial Crystal

Theoretical expressions are presented for the frequency $\omega$ versus the wave vector $\overrightarrow{\mathrm{k}}$ resulting from the interaction between the electromagnetic field and an undamped vibrating diatomic ionic crystal with orthorhombic symmetry. The rigorous treatment using retarded electromagnetic fields shows that the resultant vibrations consist of a mixture of electromagnetic waves and mechanical lattice vibrations, as shown previously for cubic lattices in Huang's classic paper. Our treatment is applicable to biaxial crystals with orthorhombic symmetry. A systematic method for evaluating all cases is illustrated. It is noted that a theory for biaxial crystals with monoclinic and triclinic symmetries is complicated by the fact that the principal axes of physical properties are not simply oriented to the crystal axes.