Terahertz Optics: Widefield terahertz lens is made via additive manufacturing

A non-spherically symmetric terahertz lens keeps the wide field of view of the Luneburg lens while allowing for a flat image surface.

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Refractive lenses for imaging with terahertz radiation can be made of Teflon, stacked metal plates, or even paper. In addition, metamaterial optics are being developed for terahertz imaging (one reason being that because of the long wavelengths of terahertz radiation, metamaterial optics are far easier to experiment with in the terahertz than, say, infrared or visible spectral regions).

When its structure is varied as a function of position within an optic, a metamaterial can serve as the basis for a gradient-index (GRIN) lens. Because terahertz metamaterials have unit cell sizes on the order of 100 μm in size, they are relatively easy to fabricate precisely. Therefore, very interesting types of GRIN lenses can be made. For example, the Luneburg lens is a well-known GRIN lens design that takes the shape of a sphere and can image objects at infinite conjugates onto an image surface coincident with the surface of the Luneburg lens, with no aberrations. Because the Luneburg lens itself is spherically symmetric, the lens has a 360° field of view (although adding an imaging-detection surface restricts to field of view of less than that).

One big flaw of the Luneburg lens stems from its spherical symmetry: the image surface itself is a sphere, eliminating easy use of the lens with common imagers, including terahertz imagers. Taking the design as a starting point, researchers at Northwestern University (Evanston, IL) and Oklahoma State University (Stillwater, OK) developed a non-spherically symmetric terahertz lens that keeps the wide field of view of the Luneburg lens while allowing for a flat image surface (see figure).1 The lens is made of polymer via an additive-manufacturing technique called projection microstereolithography (PμSL).

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A Luneberg lens is spherically symmetric, with a refractive index that is highest at its center (top left; shown as a variation in color). The lens images a plane wave incident from one direction onto the opposite surface of the lens, resulting in a spherical imaging surface (top center and right). A modified version has been transformed so that its refractive-index distribution is no longer spherically symmetric (bottom left). The result is a flat imaging surface (bottom center and right).

Excellent imaging over 0.4 to 0.6 THz

In shape, the lens resembles a light bulb with its bottom cut off, with the flat bottom being the image plane. Calculations produced a quasiconformal transformation of the Luneburg lens that reconfigured the spherical image surface to the flat one, with the limits of the transformation leading to a maximum angular imaging range for the lens of ±41.4°. The refractive index within the lens varies from 0.451 to 1.719 as a function of position (metamaterials can have a refractive index of less than 1, and even less than 0 in some cases).

The PμSL system, which used a programmable liquid-crystal-on-silicon (LCoS) display chip as the mask, had a pixel size at the fabrication plane of about 7 × 7 μm and a fabrication area of about 1 × 0.75 cm. Vertical stepping precision was 0.5 μm using a stage made by Aerotech (Boxford, MA). The refractive index of each 82.5 μm unit cell was adjusted by varying the volume-fill ratio of polymer to air within the cell. To make a 4.27-mm-thick lens, 100 layers were fabricated, resulting in more than 120,000 defect-free unit cells. The lens' imaging performance was determined by using a fiber-based, angular-resolved terahertz time-domain spectroscopy (THz-TDS) technique in which a laser-micromachined metallic mask contained an object such as a single 200 μm slit or double 200 μm slits with an edge-to-edge distance of 300 μm (to determine lens resolution).

Simulation and experiment agreed: the double slit was easily resolved over a spectral range of 0.4–0.6 THz. In comparison, a terahertz spherical lens made of a uniform dielectric with a refractive index of 1.64 could not resolve the double slit at frequencies below 0.5 THz. The use of the PμSL technique should enable the conception and fabrication of new types of terahertz optical elements.


1. F. Zhou et al., Adv. Opt. Mater. (2016); doi:10.1002/adom.201600033.

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