Abstract
By the use of the Rayleigh method we have calculated the angular dependence of the reflectivity and the efficiencies of several other diffracted orders when the periodically corrugated surface of an isotropic elastic medium is illuminated by a volume acoustic wave of shear horizontal polarization. These dependencies display the signatures of Rayleigh and Wood anomalies, usually associated with the diffraction of light from a metallic grating. The Rayleigh anomalies occur at angles of incidence at which a diffracted order appears or disappears; the Wood anomalies here are caused by the excitation of the shear horizontal surface acoustic waves supported by the periodically corrugated surface of an isotropic elastic medium. The dispersion curves of these waves in both the nonradiative and radiative regions of the frequency-wavenumber plane are calculated, and used in predicting the angles of incidence at which the Wood anomalies are expected to occur.
Highlights
In his measurements of the angular and wavelength dependencies of light diffracted from various metallic gratings, Wood [1, 2] noted ‘anomalies’ in the data he obtained when the wave vector of the incident beam was in the plane perpendicular to their grooves, and its magnetic vector was parallel to the grooves, i.e. in p polarization
We have shown that when a perfectly conducting lamellar grating is illuminated from vacuum by p-polarized light whose plane of incidence is perpendicular to the grooves of the grating, the angular dependencies of the diffraction efficiencies display Rayleigh and Wood anomalies
The positions of the Wood anomalies occur at the angles associated with the excitation of the surface electromagnetic waves supported by the periodically corrugated surface, as predicted by Fano [7] in his study of these anomalies in diffraction from a metallic grating
Summary
In his measurements of the angular and wavelength dependencies of light diffracted from various metallic gratings, Wood [1, 2] noted ‘anomalies’ in the data he obtained when the wave vector of the incident beam was in the plane perpendicular to their grooves, and its magnetic vector was parallel to the grooves, i.e. in p polarization. That the existence of p-polarized surface electromagnetic waves on periodically corrugated perfectly conducting surfaces is known, it seemed of interest to calculate their dispersion curves together with the angular dependencies of the diffraction efficiencies in the diffraction of p-polarized light from such gratings. The goal of these calculations is a demonstration that these surface electromagnetic waves give rise to Wood anomalies in the same way that surface plasmon polaritons give rise to Wood anomalies in the diffraction of p-polarized light from metallic gratings. In doing so we will use a modal approach analogous to the one employed by Lopez-Rios et al [21] to study the reflectivity of a lamellar metallic grating (see [22] and [23])
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