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GRIN Lenses for Millimeter-wave Communications and Sensing

Current military and future commercial wireless communications systems are relying more and more on multi-antenna arrays (e.g., AESAs, MIMO, massive MIMO) to realize the benefits of spatial reuse, interference mitigation, and higher gain.

Traditionally, a beam-steering antenna array employs active microwave circuits (variable gain amplifiers and phase shifters or true time delay units) in each element (or sub-array) of the array to achieve beam steering and pattern/sidelobe control. These active components, in addition to requiring significant power, are large and expensive. Modern fully-digital phased arrays employ full bandwidth DAC/ADC data processors at each element (or sub-array) to form many beams from one aperture (up to the number of elements in the array) but this approach requires significant power and cost, especially as channel bandwidth increases (in the GHz) in future systems. One approach to realizing the flexibility of digital beamforming while lowering the power and cost is to use hybrid beamforming methods in which part of the beam is formed by a digital baseband and part is realized with traditional VGAs and phase shifters. This incremental approach to the problem of increasing data rates is only a stop-gap measure.

We are investigating new fully analog solutions to the problem of multi-beam, wideband, millimeter-wave antennas for both base stations and mobile devices. Modern fabrication methods such as 3D printing and microfabrication make it possible to easily fabricate gradient index lenses such as the Luneberg lens. This fabrication approach, combined with designs methods such as transformation optics (TO) and field-based ray tracing provide a means for designing flat, on-wafer gradient index (GRIN) lenses. Our fabrication methods span 10’s of GHz to 500 GHz and target both large area and compact lenses.

Lens Design

Lens designs typically target high aperture efficiency, wide scan angle, or compact size as the most important metric. We use several complementary design methods to span the space from initial concept, parametric studies, and final optimization with fidelity ranging from approximate ray tracing to full-wave electromagnetic simulation. The table below summarizes some of the pros and cons of various design methods. 

An example of one methond is the Transformation Optics (TO) method. The approach, shown below, follows a four-step process.

  1. An original lens design (upper left) such as the spherical Luneberg lens which is selected for its desirable qualities such as beam-scan, low sidelobe levels, and a match to free space.
  2. Next, a spatial transformation is defined which transforms the original bulky spherical lens into a more desirable geometry such as a flattened disc.
  3. The transformation optics then converts the spatial transformation into a material transformation which results in a new permittivity and permeability profile.
  4. Finally, we have a fully automated simulation loop which begins in Matlab or Python and automates Ansys HFSS to perform full-wave electromagnetic simulations of the design as well as optimization.

Our current research is on alternative lens designs which do not suffer from some of the issues associated with TO such as the need for anisotropic materials and are able to realize a wave impedance match to free space.


Once a permittivity profile is defined, we have two paths for fabrication of the resulting lens designs: silicon microfabrication in the Notre Dame Nanofabrication facility (https://www3.nd.edu/~ndnf/) which targets very high frequency designs from 50 to 500 GHz, and PCB-based drilling with third-party PCB fabrication partners which targets very large area apertures and covers bands below 50 GHz. The silicon microfabrication process is summarized in the figure below. A single layer of a lens is comprised of unit-cells which are contiguous polygons to afford the maximum range of permittivity from air (εr=1.0) to that of the host material, in this case, silicon (εr=11.8). Each unit-cell is sized to be much smaller than a guided wavelength at the maximum frequency of the lens to ensure the effective permittivity is refractive and wideband, not diffractive. The Bosch deep reactive ion etch process is used for etching the unit-cells. A complete lens is comprised of a stack of such wafers so that a full 3D GRIN can be realized: both in wafer and between wafers.

System Integration

The lenses can be combined with a wide variety of electronics below the lens depending upon the application

Another application of interest is in very low energy spectrum sensing and direction of arrival detection. Here we combine a GRIN lens with passive angular filtering with a compact filter bank (such as a cochlear filter) with a zero-bias diode energy detector. The result is a completely passive, zero-energy direction of arrival (DoA) spectrum sensor (except for the final readout which is effectively DC).  This configuration is useful to deployment of SWaP constrained platforms such as micro-UAVs.