Homogeneous layer models for high-spatial-frequency dielectric surface-relief gratings: conical diffraction and antireflection designs

Abstract

The validity of various homogeneous layer models for high-spatial-frequency rectangular-groove (binary) dielectric surface-relief gratings is examined for both nonconical and conical diffraction. In each model the grating is described by a slab of uniaxial material with its optic axis parallel to the grating vector. The ordinary and principal extraordinary indices of the slab depend on the grating filling factor, the substrate and cover refractive indices, and the ratio of the wavelength to the grating period. These indices can be determined by solving two transcendental equations. Higher-order indices are defined as the exact solution to these equations. Second-order indices (second-order dependence on the wavelengthto- period ratio) and first-order indices (no dependence on the wavelength-to-period ratio) are defined by approximate solutions to these equations. Layer models using higher-order and second-order indices are shown to be accurate for high-spatial-frequency gratings, even at wavelength-to-period ratios near the onset of higher-order propagating diffracted waves. These models are used to design example antireflecting gratings on silicon substrates, including designs for conical incidence. All designs are evaluated and optimized by exact rigorous coupled-wave analysis.