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