Measurements of a Prototype 20 GHz Metamaterial Flat Lens Cassandra Whitton 1 , Christopher Groppi 2 , Philip Mauskopf 3 , and Paul Goldsmith 4 Abstract— In this paper, we present measurements of a prototype metamaterial flat lens. Flat, lenses with short focal lengths are of particular interest due to their potential use in quasi-optical observing in space-based cubesat applications. Our metamaterial flat lens was manufactured by using 11 layers of RO3003 circuit board laminate with etched sub-wavelength- sized copper patterning. The copper patterning is designed in such a way as to maximize the transmittance of the lens while applying the correct phase shift across the lens plane to give the lens its focusing properties. The lens was measured by scanning a receiver horn through one axis of the image plane of a transmitting horn. This measurement demonstrated that the waist of the focused gaussian beam is 30% wider than ideal. It is suspected that this non-ideality is caused by phase error in the design process, though simulations would be necessary to confirm this. Further measurements will be useful to fully characterize the lens’s focal properties and determine how much loss it incurs. I. I NTRODUCTION CubeSats may be an attractive prospective for those wish- ing to perform terahertz observations, due to the high atmo- spheric attenuation at these frequencies which makes ground- based observing difficult or impossible [6], and due to the often-prohibitive costs of other mission types which are able to observe from above the atmosphere. However, CubeSat missions come with their own set of design challenges, which particularly includes requirements for low weight and small form factor [2]. In particular, we would like to advocate for the use of metamaterial lenses as primary observing apertures in such systems, due to a number of advantages which help ameliorate CubeSats’ particular challenges. Metamaterials, which involve the structured embedding of metal elements within dielectric substrates, and metamaterial lenses in particular, have recently seen much advancement and development into the millimeter wavelength regime [3], [4]. The lenses which have been created so far are both thin and lightweight compared to a conventional lens of equivalent f -number, freeing up weight budget and making it easier to place and stow the lens, if a deployable design is Submitted for review 25 June 2019. This work was supported in part by the JPL SURP program. RO3003 material used in this work was provided gratis by Rogers Corporation. 1 Cassandra Whitton is with the School of Earth and Space Explo- ration, Arizona State University, Tempe, AZ 85287, USA (e-mail: cassan- dra.whitton@gmail.com) 2 Christopher Groppi is with the School of Earth and Space Ex- ploration, Arizona State University, Tempe, AZ 85287, USA (e-mail: cgroppi@asu.edu) 3 Philip Mauskopf is with the School of Earth and Space Explo- ration, Arizona State University, Tempe, AZ 85287, USA (e-mail: philip.mauskopf@asu.edu) 4 Paul Goldsmith is with the Jet Propulsion Laboratory, Pasadena, CA 91109, USA (e-mail: paul.f.goldsmith@jpl.nasa.gov) necessary or desirable. Furthermore, these design techniques by Ref. [4] ensure that no anti-reflection coating is necessary to minimize reflection losses. Finally, such lenses have been found to theoretically have less than half a dB of loss, which is significantly better than that of a Fresnel zone plate lens, which, while flat and light, can exhibit on the order of 3 to 4dB or more of loss [5]. Here we have created and tested a metamaterial flat lens which operates at 20 GHz. The lens we present here is intended to act as a low-frequency prototype to test our design procedure. A successful design procedure should allow us to experiment with more expensive high-frequency designs, operating at 600 GHz or even above 1 THz. II. LENS DESIGN The lens is designed in a narrow bandwidth around 20 GHz, and is designed in such a way as to transform an incoming plane wave to a gaussian beam. This phase trans- formation is given by Refs. [4] and [1] as φ(r)= - πr 2 λR (1) where λ is the operational wavelength, r is the distance on the lens plane from the lens center, R is the radius of curvature of the phase front, given by R(f )= f +  πw 2 0 λ  2 f (2) and w 0 is the waist of the focused beam at the focal plane. The focal length of the lens is given by f . In the case of our lens, the diameter of the active area is 254 mm, and the focal length is 105 mm, making our lens an f/0.41 lens. These parameters in combination give the phase transformation shown in the top plot of Fig. 1. Given this phase transformation, we subdivide the surface of the lens vertically and horizontally into pixels, each of square dimensions λ/10, which is, in this case, about 1.50 mm. Each of these pixels is assigned a single phase transformation based on the above equations. In our case, each pixel has 10 metal layers, with 10 copper squares of metal, stacked on top of each other and separated by 11 surrounding dielectric layers. The dimensions of each square may be picked freely. Then, using techniques as described in Ref. [4], each pixel is optimized to give the desired phase transformation and maximum transmittance. These optimiza- tions work by automatically tweaking the dimensions of each metal square until the desired conditions for that pixel are met. Because each pixel is treated independently from each other pixel, this is relatively computationally simple, as it 119