Large imaging arrays of detectors at millimeter and submillimeter wavelengths have applications that include measurements of the faint polarization signal in the Cosmic Microwave Background (CMB), and submillimeter astrophysics. We are developing planar lenslet arrays for millimeter-wavelength imaging using metamaterials microlithically fabricated using silicon wafers. This metamaterial technology has many potential advantages compared to conventional hemispherical lenslet arrays, including high precision and homogeneity, planar integrated anti-reflection layers, and a coefficient of thermal expansion matched to the silicon detector wafer. Here we describe the design process for a gradient-index (GRIN) metamaterial lenslet using metal-mesh patterned on silicon and a combination of metal-mesh and etched-hole metamaterial anti-reflection layers. We optimize the design using a bulk-material model to rapidly simulate and iterate on the lenslet design. We fabricated prototype GRIN metamaterial lenslet array and mounted it on a Polarbear/Simons Array 90/150~GHz band transition edge sensor (TES) bolometer detector array with sinuous planar antennas. Beam measurements of a prototype lenslet array agree reasonably well with the model simulations. We plan to further optimize the design and combine it with a broadband anti-reflection coating to achieve operation over 70--350~GHz bandwidth.
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