Antireflection surface structure: dielectric layer(s) over a high spatial-frequency surface-relief grating on a lossy substrate

Abstract

With proper design, a dielectric (or lossy) overcoated high spatial-frequency rectangular-groove grating on a lossy substrate can exhibit zero reflectivity. A procedure for designing these structures based on impedance matching and the effective index of the grating in the long wavelength limit is presented. The needed filling factor and groove depth of the grating to produce antireflection behavior are calculated for a given complex index of refraction of the substrate and index and thickness of the coating layer. The analysis is applicable to any wavelength and angle of incidence and for either TE or TM polarization. It is shown that multiple zero-reflectivity solutions occur. Necessary and sufficient conditions for zero-reflectivity solutions are derived in the appropriate parameter space. The analysis is also extended to multiple dielectric (or lossy) overlayers. Since the treatment is based on the equivalence of the grating to a lossy layer in the long wavelength limit, the treatment also includes as an intermediate step the design of a dielectric (or lossy) overcoated homogeneous lossy layer on a lossy substrate. The designs of zero-reflectivity gold gratings overcoated by a single dielectric layer are presented for wavelengths in the 0.44–12.0-μm range. The sensitivity of these resulting structures to changes in the angle of incidence, the coating thickness, the coating index, the filling factor, and the groove depth are presented. Furthermore, the design of dielectric overcoated gold gratings that are simultaneously antireflecting for both TE and TM polarizations is presented.