On a General Theory of Anomalies and Energy Absorption by Diffraction Gratings and Their Relation with Surface Waves

Anomalous absorption in TM polarization light by echelle gratings

Echelle grating plays an essential role in spectral analysis due to its broadband blaze, high dispersion, and high resolution; however, its absorption properties have received no attention. In this paper, we investigate the effect of parameters including incident wavelength, incident angle, and blaze angle on the absorption properties of the Al echelle grating. Based on calculations by the boundary integral equation method, we observe that the Al grating with a large blaze angle has an absorption enhancement effect on TM-polarized waves, and its intensity increases as the incident angle approaches the pseudo-Brewster angle (maximum absorption over 87%). In particular, this absorption enhancement effect is present in the wideband and somewhat generalizable to other metallic materials. In addition, the potential physical mechanisms underlying the absorption enhancement of the echelle grating are analyzed in detail through the electric field distribution. The resonance between the grating anomaly and the pseudo-Brewster effect results in the appearance of surface plasmon polariton and strong absorption. These findings will bring new understanding to the study of echelle gratings in case of high energy loss when the light incidents with a high angle for high resolution and will also show potential applications in electromagnetic stealth, photothermal conversion, and photodetection.

Propagating-order scattering matrix of conically mounted and crossed gratings

A systematic and formal study of the global and elemental properties of the propagating-order scattering matrix of conically mounted and crossed gratings is presented. The most general formulation of the scattering matrix is established. Expressions of the global properties (reciprocity and unitarity) of the scattering matrix (S matrix) in the general form previously not available in the literature are presented in the main text, and their full mathematical derivations are given in two appendices. The distinctive contribution of this work is an exposition of the elemental properties of the S matrix. The elemental S tensor and the elemental S matrix, the latter being the linear-space representation of the former, for a pair of an incident plane wave and a diffracted order are defined and studied. The key results of the exposition are two sum rules of diffraction efficiencies and a dot-product-free, vectorial reciprocity theorem.

Guided-mode resonant subwavelength gratings: effects of finite beams and finite gratings

The effects of finite beams and finite gratings on the performance of guided-mode resonant subwavelength gratings are characterized by using the rigorous boundary element method. The gratings are strongly modulated, have a finite number of periods, and are illuminated by normally incident Gaussian beams. Quantitative results are presented for silicon-on-sapphire resonant gratings and gallium arsenide-aluminum arsenide resonant gratings.

Unusual splitting behavior of the dispersion of surface polaritons in gratings of different symmetry, amplitude, and profile

The splitting behavior of the dispersion relation of plasmonic surface polaritons (surface plasmons) in silver gratings in the region of vanishing lateral momentum is investigated. The reflectivity of light was measured as a function of the amplitude and the shape of the grating. Although for nonsinusoidal gratings a splitting into low- and high-frequency branches of the dispersion relation is found, for sinusoidal gratings a splitting in lateral momentum is found. These phenomena are also found numerically by the use of a transfer matrix method.