Diffraction by a grating made of a uniaxial dielectric-magnetic medium exhibiting negative refraction

Diffraction of linearly polarized plane electromagnetic waves at the periodically corrugated boundary of vacuum and a linear, homogeneous, uniaxial, dielectric-magnetic medium is formulated as a boundary-value problem and solved using the Rayleigh method. The focus is on situations where the diffracted fields maintain the same polarization state as the s- or p-polarized incident plane wave. Attention is paid to two classes of diffracting media: those with negative definite permittivity and permeability tensors, and those with indefinite permittivity and permeability tensors. For the situations investigated, whereas the dispersion equations in the diffracting medium turn out to be elliptic for the first class of diffracting media, they are hyperbolic for the second class. Examples are reported with the first class of diffracting media of instances when the grating acts either as a positively refracting interface or as a negatively refracting interface. For the second class of diffracting media, hyperbolic dispersion equations imply the possibility of an infinite number of refraction channels.