Flat Low-Loss Silicon Gradient Index Lens for Millimeter and Submillimeter Wavelengths

Abstract

We present the design, simulation, and planned fabrication process of a flat high resistivity silicon gradient index (GRIN) lens for millimeter and submillimeter wavelengths with very low absorption losses. The gradient index is created by subwavelength holes whose size increases with the radius of the lens. The effective refractive index created by the subwavelength holes is constant over a very wide bandwidth, allowing the fabrication of achromatic lenses up to submillimeter wavelengths. The designed GRIN lens was successfully simulated and shows an expected efficiency better than that of a classic silicon plano-concave spherical lens with approximately the same thickness and focal length. Deep reactive ion etching (DRIE) and wafer-bonding of several patterned wafers will be used to realise our first GRIN lens prototype.Many applications in astronomy from tens of GHz to THz frequencies, such as CMB polarization studies and Sunyaev-Zeldovich effect observations, would benefit from low loss and wide bandwidth optics. High resistivity silicon (HRSi) is an excellent material for optics within this frequency range because of its high refractive index (n Si = 3.42 1,2 ), achromaticity, lack of birefringence, low loss 3 , high thermal conductivity, and strength. Silicon's high index, however, presents a challenge for antireflection (AR) treatment, which our approach addresses. To develop wide bandwidth and low loss silicon optics, we are focusing on two key elements: 1) the fabrication of multilayer AR structures via multi-depth deep reactive ion etching (DRIE) and wafer-bonding; and 2) the assembly of gradient index (GRIN) optics, flat-faced to be consistent with AR treatment, by bonding multiple silicon wafers patterned with the desired radial index profile by DRIE. The fabrication of 1-layer 7,8,9,10,11 and 2layer 7,12 AR structures for THz frequencies has already been demonstrated, such as wafer bonding of unpatterned 13,14,15,7 and patterned 16 silicon wafers. Prior attempts to fabricate GRIN lenses for millimeter and submillimeter wavelengths, using silicon and DRIE 17,18,19 ,

Development of large terahertz heterodyne receiver arrays for future space observations

“…A Silicon Etched GRIN Lens allows a detector attached to the back side of it and more than 90% of the radiation to be transmitted from antenna to the lens. The gradient refractive index is achieved by etching holes with different diameters on a sub-wavelength pitch in a dielectric material such as Si by use of the deep reactive ion etching process [75,81,82]. Pisano et al simulated and fabricated a 19-pixel hexagonal lens array for the 90 and 150 GHz bands and the simulation shows losses (~ 20%) into the Si.…”