On the propagation of Voigt waves in energetically active materials

If Voigt-wave propagation is possible in a dissipative anisotropic dielectric material characterised by the permittivity dyadic $\mathop{\varepsilon }\limits_{\raise{2pt}=}$, then it is also possible in the analogous energetically active material characterised by the permittivity dyadic $\mathop{\tilde{\varepsilon }}\limits_{\raise{2pt}=}$, where $\mathop{\tilde{\varepsilon }}\limits_{\raise{2pt}=}$ is the hermitian conjugate of $\mathop{\varepsilon }\limits_{\raise{2pt}=}$. This symmetry follows directly from a theoretical analysis of the necessary and sufficient conditions for Voigt-wave propagation in anisotropic materials. As a consequence of this symmetry, a porous dissipative material that exhibits Voigt-wave propagation can be used to construct a material that allows the propagation of Voigt waves with attendant linear gain in amplitude with propagation distance, by means of infiltration with an electrically or optically activated dye, for example. This phenomenon is captured by the Bruggeman formalism for homogenised composite materials based on isotropic dielectric component materials that are randomly distributed as oriented spheroidal particles.