Theory of Dyakonov–Tamm surface waves featuring Dyakonov–Tamm–Voigt surface waves

The propagation of Dyakonov–Tamm (DT) surface waves guided by the planar interface of two nondissipative materials A and B was investigated theoretically and numerically, via the corresponding canonical boundary-value problem. Material A is a homogeneous uniaxial dielectric material whose optic axis lies at an angle χ relative to the interface plane.

Material B is an isotropic dielectric material that is periodically nonhomogeneous in the direction normal to the interface. The special case was considered in which the propagation matrix for material A is non-diagonalizable because the corresponding surface wave — named the Dyakonov–Tamm–Voigt (DTV) surface wave — has unusual localization characteristics.

The decay of the DTV surface wave is given by the product of a linear function and an exponential function of distance from the interface in material A; in contrast, the fields of conventional DT surface waves decay only exponentially with distance from the interface. Numerical studies revealed that multiple DT surface waves can exist for a fixed propagation direction in the interface plane, depending upon the constitutive parameters of materials A and B.

When regarded as functions of the angle of propagation in the interface plane, the multiple DT surface-wave solutions can be organized as continuous branches. A larger number of DT solution branches exist when the degree of anisotropy of material A is greater. If χ=0°, a solitary DTV solution exists for a unique propagation direction on a DT solution branch and should be regarded as the manifestation of an exceptional point.

No DTV solutions exist if χ>0°. As the degree of nonhomogeneity of material B decreases, the number of DT solution branches decreases. For most propagation directions in the interface plane, no solutions exist in the limiting case wherein the degree of nonhomogeneity approaches zero; but one solution persists provided that the direction of propagation falls within the angular existence domain of the corresponding Dyakonov surface wave.