Large-aperture wide-bandwidth antireflection-coated silicon lenses for millimeter wavelengths

The increasing scale of cryogenic detector arrays for sub-millimeter and millimeter wavelength astrophysics has led to the need for large aperture, high index of refraction, low loss, cryogenic refracting optics. Silicon with n = 3.4, low loss, and relatively high thermal conductivity is a nearly optimal material for these purposes, but requires an antireflection (AR) coating with broad bandwidth, low loss, low reflectance, and a matched coefficient of thermal expansion. We present an AR coating for curved silicon optics comprised of subwavelength features cut into the lens surface with a custom three axis silicon dicing saw. These features constitute a metamaterial that behaves as a simple dielectric coating. We have fabricated and coated silicon lenses as large as 33.4 cm in diameter with coatings optimized for use between 125-165 GHz. Our design reduces average reflections to a few tenths of a percent for angles of incidence up to 30 degrees with low cross-polarization. We describe the design, tolerance, manufacture, and measurements of these coatings and present measurements of the optical properties of silicon at millimeter wavelengths at cryogenic and room temperatures. This coating and lens fabrication approach is applicable from centimeter to sub-millimeter wavelengths and can be used to fabricate coatings with greater than octave bandwidth.