Application of the differential method to uniaxial gratings with an infinite number of refraction channels: Scalar case

The differential method (also called the C method) is applied to the diffraction of linearly polarized plane waves at a periodically corrugated boundary between vacuum and a linear, homogeneous, uniaxial, dielectric-magnetic medium characterized by hyperbolic dispersion equations. Numerical results for sinusoidal gratings are presented and compared with those obtained by means of the Rayleigh method, showing that both the differential method and the Rayleigh method can fail to give adequate results for gratings supporting an infinite number of refracted Floquet harmonics.