Microwave Journal

Online Spotlight: A Gradient Index Lens to Enable 180-Degree Field-of-View in a Phased Array System

March 13, 2022

New demands in novel communications and radar systems require the adoption of active antenna systems to take them to new generations. High atmospheric attenuation along with higher degrees of channel fading conditions prevalent in upper microwave and mmWave frequencies have driven system designers across the industry to develop steerable, active systems, like phased array antennas. While existing phased array antenna systems may be suitable for their intended purpose, the addition of a synthetic gradient index (GRIN) lens, enabled by new dielectric 3D-printing techniques, simplifies the phased array system to increase steering performance and overcome the wide-angle limitations of flat panel phased array antennas.


For many high frequency RF applications, a fixed antenna array or an omnidirectional antenna is not sufficient to cover all required directions while providing sufficient radiated power to overcome atmospheric attenuation and high levels of channel fading. This has driven system designers to seek steerable systems to concentrate the signal for a specific target or user.1

While mechanically steerable antennas were developed to address this challenge for certain applications, they are less desirable for others due to limited steering speed for spatial multiplexing and limited reliability, since many consist of motors and other moving parts that are susceptible to wear.2

With recent advancements in flat panel electronically steered antennas, many high frequency applications can use antenna arrays that are electronically controlled by manipulating the signal feeds to individual antenna elements within a larger array. These are commonly manufactured using PCB fabrication processes that integrate the antenna arrays (e.g., patch antennas) with a feed network that connects them to other front-end components.

One way of achieving beam steering in these antenna arrays is to switch on and off certain elements; another way is to control the relative phase and amplitude of the signals to/from groups of array elements, or to/from each individual element. With a large enough antenna array and an electronic control and feed system, beam steering antenna arrays are designed to direct the main radiating lobe of the antenna array anywhere up to a maximum beam angle, rapidly steering the beam and even creating multiple lobes that are independently steered.3

The main disadvantage of flat panel electronically steered systems is the available effective aperture versus steering angle. This fundamentally limits the steering angle. Typically, for a flat panel phased array, the theoretical gain achievable at a given steering angle is a function of cos(θ), where θ is the target angle and θ = 0 degrees is the boresight direction.4 One possibility to overcome this limitation while preserving the many advantages of an electronically steered system is to supplement the system with a GRIN dielectric lens. A theoretical phased array lens system is imagined here.


A phased array antenna system operating from 37 to 40 GHz is designed in Ansys HFSS for supplementing with a field-of-view enhancing GRIN lens. Assumptions are made to achieve a proof-of-concept and to ease the computational resources required to arrive at a useful design. A 16 x 4 element array is designed with rectangular patches at λ/2 spacing; and, for each individual patch, continuous phase and amplitude control is assumed. The array produces 23 to 24 dBi gain at boresight within the 37 to 40 GHz band with all elements excited (see Figure 1).

Figure 1

Figure 1 Simulated antenna pattern of the 16 x 4 element phased array without a lens and with uniform weighting.

A volume of 50 x 35 x 130 mm (height x depth x width) is chosen above the phased array as the potential area for a dielectric lens (see Figure 2). To efficiently iterate designs, an optimization technique is selected that maximizes performance for a given input figure-of-merit. In addition, to ease the computational load for optimization, the lens area is segmented into approximately 5 mm cubeseach representing a specific dielectric constant within the overall structure. The optimizing variables, include: 1) the Dk of each cube constrained between 1 and 3.6 in 0.2 increments and 2) the phase and amplitude settings for each element to achieve maximum directivity at  ±90 degrees in azimuth, effectively achieving a 180-degree field-of-view in the simulated electronically steered, phased array antenna system.

Figure 2

Figure 2 Lens design area above phased array antenna.


The design includes three distinct high dielectric constant areas with graded lower dielectric constant areas (see Figure 3).

Figure 3

Figure 3 Isotropic view of GRIN lens system cut in half along symmetry plane.

Antenna patterns of the simulated system steering from 0 to +90 degrees in 3-degree increments are shown in Figure 4. Each set of patterns for a given target steering angle in the overlaid chart has a unique phase and amplitude profile for the radiating elements. Since the lens is symmetrical, similar performance is expected from 0 to -90 degrees. The drop in directivity from boresight to 90 degrees is approximately 2 dBi, while flat panel phased arrays, alone, typically drop around 3 dBi from boresight to 60 degrees.

Figure 4

Figure 4 Simulated antenna patterns for 30 beam steering states between 0 and +90 degrees, overlaid and shown at 37, 38.5 and 40 GHz for each state.

Manufacturing is accomplished relatively easily with a digital manufacturing process like 3D-printing. With a varying density lattice that has small enough features relative to the operating wavelength, the component behaves like one graded dielectric constant structure as designed in simulation. There is little change in manufacturing complexity with alterations in design, and many different iterations can be made and tested quickly. In combination with Rogers Corporation’s new RadixTM 3D-printable dielectric materials, designers can take advantage of the most scalable, high-resolution process to realize these components. A rendering of the lens design as a printable part is shown in Figure 5.

Figure 5

Figure 5 Rendering of the simulated phased array GRIN lens as a 3D printable component in nTopology software.

To verify that the complete flexibility of GRIN and 3D printing is required, simulations are done on an approximated version of the design, where the dielectric constant values are approximated into three “buckets” used within the overall structure versus an optimized design with a more graded transition. The designs and resulting antenna patterns are shown in Figures 6 and 7 respectively. The near continuous gradient is likely needed to maximize performance, and a process like 3D printing is one of the few processes that can produce it.

Figure 6

Figure 6 Optimized phased array lens design (green outline) versus an approximated design (orange outline).

Figure 7

Figure 7 Simulated antenna pattern of a target beam peak at +90 degrees for the optimized (green) and approximated design (orange).


To see how the high steering angles are achieved, a closer look at the antenna element amplitude and phase profile is needed. In addition to large phase shifting between adjacent elements, a significant amplitude tapering is implemented. Specifically, for the 90-degree steering case, the elements on the same side as the formed beam are not illuminated while the center and opposite elements are illuminated with a slight amplitude taper. A hybrid of switching and phase shifting helps achieve the steering performance in its current embodiment due to refraction within the lens mandated by the dielectric gradient. Notice that the effective aperture for this 90 degree beam is equal to the height of the lens. An illustration of these points can be seen in Figure 8. One drawback of the proposed solution is a reduced effective isotropic radiated power by using only a given portion of the flat array patches.

Figure 8

Figure 8 Antenna port layout (a) with relative element amplitudes to achieve 90-degree steering (b) and an illustration of the refraction effect within the dielectric lens (c). 


With new dielectric 3D printing manufacturing technology, exotic GRIN parts that enhance the figure-of-merits of any antenna system can be realized. The combination of this technology with new computational tools allows designers the flexibility to no longer be constrained to classical lens designs from literature, like the Luneburg Lens. In fact, many variations and alterations of the simulated system shown here could be designed and produced for different performance goals.

While traditional lens antenna designs often have their merits compared with phased array systems, as seen from this design, there are opportunities to use lenses synergistically with phased array antennas to enhance certain requirements such as gain over angle performance.


We thank Ben Wilmhoff and team at BluFlux for radiation pattern measurements and Stephen O’Connor at Rogers Corporation for material formulation. We also thank Shawn Williams, Karl Sprentall and Bob Daigle at Rogers Corporation for valuable discussions and feedback.


  1. B. Sadhu and L. Rexberg, 2019, Phased Arrays for 5G Millimeter-Wave Communications, G. Hueber and A. M. Niknejad (Eds.), Millimeter-Wave Circuits for 5G and Radar, pp. 243- 272, Cambridge University Press.
  2. B. Nevius and P. Freud, “Enabling Scalable + Affordable SATCOM Solutions,” SatMagazine, September 2020.
  3. M. Ascione, G. Bernardi, A. Buonanno, M. D'Urso, M. Felaco, M. G. Labate, G. Prisco and P. Vinetti, “Simultaneous Beams in Large Phased Radar Arrays,” IEEE International Symposium on Phased Array Systems and Technology, October 2013.
  4. “Phased Array Antennas,” Microwaves101, Web: www.microwaves101.com/encyclopedias/phased-array-antennas.