Reflection of light by a hyperbolic metamaterial layer in a case of propagation of special inhomogeneous waves in it

The boundary problem of reflection of electromagnetic waves by a hyperbolic metamaterial layer under conditions of total reflection from the boundary with this layer in the absence of birefringence has been solved. In this case, so-called “special inhomogeneous electromagnetic waves” may propagate in the layer. Analytical expressions are obtained for the vector amplitudes of the waves reflected by the layer and transmitted through it and for the special inhomogeneous electromagnetic waves propagating in this layer. These expressions allows calculating the energy characteristics of reflected and transmitted light for an optically uniaxial metamaterial.