Flat Silicon Gradient Index Lens With Deep Reactive-Ion-Etched Three-Layer Antireflection Structure for Millimeter and Submillimeter Wavelengths

In this article, we present the design, fabrication, and characterization of a 100 mm diameter, flat, gradient-index (GRIN) lens fabricated with high-resistivity silicon, combined with a three-layer antireflection (AR) structure optimized for 160–355 GHz. Multidepth, deep reactive-ion etching enables patterning of silicon wafers with subwavelength structures (posts or holes) to locally change the effective refractive index and, thus, create AR layers and a radial index gradient. The structures are nonresonant and, for sufficiently long wavelengths, achromatic. Hexagonal holes varying in size with distance from the optical axis create a parabolic index profile decreasing from 3.15 at the center of the lens to 1.87 at the edge. The AR structure consists of square holes and cross-shaped posts. We have fabricated a lens consisting of a stack of five 525 μm thick GRIN wafers and one AR wafer on each face. We have characterized the lens over the frequency range 220–330 GHz, obtaining behavior consistent with Gaussian optics down to −14 dB and transmittance of 99<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula>3%.