Reflected energy flux anomaly under grazing incidence: the Brewster angle analogy

Abstract

The paper presents thorough theoretical and numerical analysis of the anomalies accompanying light diffraction on periodical structures (gratings). We have developed appropriate theoretical approach allowing to consider strong anomalous effects. Obtained results are presented in the form of analytical expressions for the quntities of interest, both diffracted field amplitudes and the outgoing waves energy fluxes. It is proved existence of the fluxes extrema at the specific grazing angle of incidenceб or wavelength. Namely, the specular reflection can be suppressed even for rather shallow gratings up to approximately total suppression.This effect is accompanied by essential energy redistribution between all outgoing waves depending on the grating profile. It is of essence that the energy maxima exist in all nonspecular diffraction orders at the same point (angle, wavelength) as the minimal specular reflectivity. For small period gratings, such that there do not exist other outgoing waves except the specular one, the reflectance minimum is attended by approximately total absorption of the incident radiation. Thus, we show that the grazing anomaly (GA) can be accompanied by redirection of the incident wave energy into nonspecular diffraction channels and into absorption. The results are applicable in the wide spectral region, from visible and near-infrared to terahertz and high-frequency regions for metals and semiconductors with high permittivity. The anomaly considered is well expressed for high electromagnetic contrast of the adjacent media, say, air and metal or semiconductor. Then the high contrast is due to the high value of the metal/semiconductor dielectric permittivity  ,  1 , and the anomaly corresponds to incidence of TM polarized wave. It is shown that the grazing anomaly (GA) is of rather general type and can take place if other than the specular diffraction order experiencies grazing propagation also. This property follows from the results obtained by strict application of the optical reciprocity theorem to the geometry under consideration. The specific case of harmonic relief grating is discussed in detail. It is demomstrated existence of the characteristic inclination, cr a , of the relief inclinatuion for the grating period comparable with the incident radiation wavelength, 1 cr a  , where  stays for the surface impedance,  1  . The condition cr a a , or greater, corresponds to highly expressed GA. The theoretical results are illustrated by numerical applications to gratings on Cu\vacuum (air) interface in THz region. The results obtained can be simply transferred to the TE polarized waves. For this we have to consider the adjacent media with high contrast magnetic properties, i.e., high value of the magnetic permeability  ,  1 . This case is of high interest for nowaday applications in nanophotonics and metamaterials development. As compared with other anomalies GA is attributed to the resonance-type behaviour of the energy flux, not wave amplitudes, the latter change monotonically within this anomaly contrary to the well known Rayleigh and resonance anomalies, where the wave amplitude experiences fast nonmonotonous dependence on the angle of incidence and wavelength.