Flat Silicon Gradient Index Lens with Deep Reactive-Ion-etched 3-Layer Anti-Reflection Structure for Millimeter and Submillimeter Wavelengths

We present the design, fabrication, and characterization of a 100 mmdiameter, flat, gradient-index (GRIN) lens fabricated with high-resistivitysilicon, combined with a three-layer anti-reflection (AR) structure optimizedfor 160-355 GHz. Multi-depth, deep reactive-ion etching (DRIE) enablespatterning of silicon wafers with sub-wavelength structures (posts or holes) tolocally change the effective refractive index and thus create anti-reflectionlayers and a radial index gradient. The structures are non-resonant and, forsufficiently long wavelengths, achromatic. Hexagonal holes varying in size withdistance from the optical axis create a parabolic index profile decreasing from3.15 at the center of the lens to 1.87 at the edge. The AR structure consistsof square holes and cross-shaped posts. We have fabricated a lens consisting ofa stack of five 525 μm thick GRIN wafers and one AR wafer on each face. Wehave characterized the lens over the frequency range 220-330 GHz, obtainingbehavior consistent with Gaussian optics down to -14 dB and transmittancebetween 75