  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.
