1. Introduction

Beamscanning antenna systems are becoming increasingly prominent in millimeter-wave (MMW) communications applications. Current 5G MMW standards require beamforming capability at base stations and small-medium cells [1]. Similarly, space-based internet ground stations must track low earth orbit (LEO) satellites in mega constellations over a wide field of view [2,3]. Given that 5G user cells and space internet ground stations are becoming increasingly widespread, the associated beamforming systems need to be economical with low power consumption.

Phased array systems — exhibiting excellent beam-scan performance and scan-loss exponents as low as $1.0$ [4,5] — are the classical solution for these applications. However, the requisite millimeter-wave beamforming electronics and antennas tend to make phased array solutions expensive and power-inefficient [5,6]. Beamscanning gradient index (GRIN) lens systems offer a lower-cost, lower-power alternative to phased array scanning systems [7–10]. Modern switched beam GRIN lens systems demonstrate high aperture efficiency with comparably low cost and simple construction due to advances in 3D printing and PCB processes [7,10–16]. While phased array systems still demonstrate superior beamscanning [4–6,17,18], it is expected that GRIN lens beamscan systems will be sufficient for many emerging MMW applications.

However, beamscanning GRIN systems still face practical limitations. GRIN lens systems with high beamscan capability typically employ Luneburg lens designs with curved focal/feed surfaces: feeds are placed along a spherical edge and individually oriented toward the lens center [10,19]. This arrangement maximizes the collimation quality and minimizes spillover radiation but may be mechanically impractical and not amenable to feeds fabricated in planar processes. Furthermore, the associated lenses are typically bulky and undesirable from a profile standpoint.

An alternative configuration comprises a flattened aperture lens with feeds arrayed uniformly along a flat surface. This configuration is mechanically simpler, lower-profile, and is more amenable to standard planar fabrication methods. However, for such an arrangement to be viable, the lens system must overcome two significant performance limitations: (1) collimation error due to displacement from the Petzval surface and (2) spillover loss from offset feeds. A survey of recent flat lenses [12,13,15,20] investigated with flat feed surfaces reveals scan loss exponents — referring to the exponent in the $\textrm {cos}^{n}(\theta )$ expression approximating gain reduction vs. scan angle — ranging from $4$ to $7$ (see Sec.3.2). A flat feed surface definitionally displaces some feeds from the Petzval surface. The affected feeds generate greater phase error in the aperture field distribution, resulting in beam-broadening, reduced gain and increased coma lobes in the farfield. To compensate for this effect, the lens could be optimized for a maximally flat Petzval surface. However, regardless of the lens design employed, the scan loss will eventually be dominated by spillover losses associated with far offset feeds. For example, a vertically oriented feed that is offset to the very edge of the lens cannot achieve a spillover efficiency $\eta _s$ above $50\%$ and will contribute $2$-$3\,$dB of scan loss. This effect is exacerbated with greater feed offsets, further degrading beam quality at high scan angles.

One method of addressing this challenge is to change the physical geometry of the feed antennas on a per-feed basis. For example, in a horn-fed lens system, the individual rectangular waveguide sections could be elongated and the horns tilted — in this way the beam ports could lie along a flat focal surface but the horns themselves could conform to the petzval surface. This approach would entail costly machining procedures and does not have a clear analog to other feeding schemes like patch antennas where the radiating apertures and phase centers are ideally on a flat surface. Furthermore, this method would be especially challenging from an integration perspective if other beamforming electronics were involved.

Other techniques have been proposed in the literature that utilize different components to improve beam performance [21–24]. In [22] and [23] they use embedded GRIN components inside of the feed to realize broadband and high directivity performance. However, this design is only valid for broadside operation and cannot even achieve beam-scan because of the lens embedding. In [24] a beam scanning system employs a metallic ground within the space between feeds and a metasurface lens antenna to decrease the spillover loss. However, this design cannot take into account the phase of the interfering reflected fields so for this approach, the trade off between phase collimation and spillover loss can be significant. In [21], a two-stage quasi-optical focusing system is built to improve beam scan performance for imaging systems at THz (e.g. 350 GHz). The first stage is a parabolic reflector and the second consists of an array of dielectric lenses to reduce scan loss. The feed array lenses vary in terms of geometry or position relative to the associated feed antennas depending on location in the array. Due to the high operating frequency, the lenses are fabricated using homogeneous silicon with an elliptical surface and a low permittivity anti-reflection coating; this arrangement contributes to higher reflection loss with significant design constraints compared to GRIN media. The result is a scan loss of 1 dB at 17.5$^{\circ }$ which corresponds to a high scan loss exponent of $n=4.85$.

In contrast, GRIN media provides significant design freedom which can be brought to bear upon the considerable problem of scan loss in wideband lens antennas. In this work we propose to place small GRIN components on the apertures of the far offset feeds. These feed-corrective-lenslets or FCLs combine two functions as shown in Fig. 1: i) FCLs squint the radiation from the feed toward the center of the lens, recovering spillover losses into main beam gain; and ii) FCLs translate the phase center of the feed vertically up and toward the Petzval surface, improving the aperture phase distribution. The phase center translation also increases the feed’s effective focal angle — the angle between the propagation axis and the line from the lens bottom center-point to feed phase center — and corresponding beam angle.

 

Fig. 1. (a) Feed-correction lenslet (FCL) concept. FCLs improve spillover efficiency by squinting feed patterns toward the aperture lens and improve taper efficiency by shifting the feed phase center closer to the Petzval surface (thereby improving collimation). The depicted FCL patterns, translated feed phase center and aperture $\angle E$ are full-wave simulations of the prototype. Translated feed positions #1-#5 are also shown and the GRIN profile of FCL#5 is provided. (b) Near-field measurement setup for lens/FCL system. WR-62 Horn feed is placed at position $\#4$ with FCL$\#4$ attached via a small (non-interfering) piece of Kapton tape. The aperture lens is encased in an EPS foam radome and a WR-62 open ended waveguide (OEWG) nearfield probe is visible in the background.

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Section 2 discusses the design and optimization methodologies for the lens and FCLs. Section 3 discusses the fabrication, measurement and farfield results of the FCL prototypes. Section 3 also includes a comparison of the scan performance of the proposed system with the anticipated scan performance of state of the art GRIN flat lenses.

2. Design approach

2.1 Aperture lens design

The primary GRIN lens in the aperture of the system is referred to as the ‘aperture’ lens (Fig. 2(a)). The aperture lens design used in this work is $101.6\,$mm in diameter and is based on the wideband matched lens design principles in [11,25]. The lens is optimized according to [15] for aperture efficiency (averaged over scan angle and frequency) and Petzval surface flatness to maximize compatibility with a flat feed surface. It was found that a mild 2$^{\textrm {nd}}$ order polynomial curvature on the top and bottom surfaces of the lens enhanced the flatness of the Petzval surface. This curvature is constrained to $<25\%$ of the total lens depth to maintain a relatively flat profile. The aperture lens geometry and permittivity profile are shown in Fig. 2(a); the aperture lens permittivity varies from $\varepsilon _{min} = 1.5$ at the exterior to $\varepsilon _{max} = 7.1$ in the center.

 

Fig. 2. (a) Lens geometry and permittivity profile. (b), (c) and (d): permittivity profile and $18\,$GHz far-field radiation patterns for FCL$\#3$, FCL$\#4$, and FCL$\#5$ respectively. Simulated FCL patterns are shown in yellow and measured FCL patterns are shown in red. Horn radiation patterns are shown in black for reference.

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2.2 General FCL design principles

The FCL performs two primary functions for far-offset feeds: 1) re-direct spillover radiation into the lens and 2) improve phase collimation. The first of these functions is easy to conceptualize: by applying a linear phase gradient to the aperture of the FCL (much like the phase distribution of an off-broadside plane wave), the feed antenna’s beam can be squinted. Qualitatively, the FCL must then apply a monotonic phase delay to the feed’s aperture fields. In practice, this means that higher permittivity material must be placed on the squint-side of the aperture as shown in Fig. 1(a). However, given that such an approach would place high permittivity material directly in the aperture, some degree of impedance matching is required to prevent reflections. Single layer anti-reflective coatings can be used though in this manuscript we employ wideband impedance matching tapers (as per [11,25]) due to the wide bandwidth of the horn feed. This approach also allows for the use of wideband impedance matching unit-cells as described in [11]: given the phase distribution in the feed aperture, unit-cells can be prescribed on a per-location basis such that the transformed phase at the FCL aperture results in the desired linear phase gradient that generates beam squint. The permittivity profile (and FCL shape) that is generated can then be optimized for various far-field metrics. The overall design flow is as follows:

In order to generate a low profile FCL, it would be necessary to use a material paradigm with a high range of effective permittivity. However, the overall thickness of the FCL is also essential to the FCL’s second primary function of improving phase collimation: specifically, the FCL translates the phase center vertically upward towards the petzval surface. This is because the radiating aperture of the feed is now effectively the top of the FCL and — given that the FCL is still a low-directivity component — the FCL phase center will reside close to the FCL aperture. The exact placement is difficult to predict due to the highly diffractive nature of the FCL and depends on frequency because the feed’s aperture fields (and original phase center) also vary over frequency. Furthermore, it may not actually be optimal for the FCL phase center to reside exactly on the petzval surface because the FCL’s illumination characteristics (i.e. amplitude taper and spillover) may prefer a different focal distance. Rather, the eventual optimization of the FCL should emphasize the actual desired far-field characteristics like peak gain, side lobe level or beam angle as opposed to intermediate proxy metrics like phase center location and squint angle. Once the FCL permittivity distribution is finalized, it can be discretized according to the desired material paradigm.

2.3 Demonstration of the FCL design

For this demonstration, the aperture lens is fed from a WR-62 $10\,$dBi horn antenna translated along a flat feed surface with $5$ discrete scan positions. These scan positions correspond to lateral offsets left-from-center as shown in Fig. 1(a): $0\,$mm ($\#1$, broadside), $13\,$mm ($\#2$), $26\,$mm ($\#3$), $39\,$mm ($\#4$), and $52\,$mm ($\#5$). Note that position $\#5$ places the feed center slightly beyond the edge of the lens for a high spillover loss condition. The feed surface is $50\,$mm from the bottom surface of the lens ($4\,$mm below the Petzval surface at the center-line) as shown in Fig. 1(a). Three FCL designs are designed to correct the feeds at offset positions $\#3$, $\#4$, and $\#5$. These feed positions were selected because of their varying degrees of spillover loss and beamscan degradation. Note that the FCLs are discrete structures with each FCL corresponding to only one scan position: given the scan spacing, the FCLs cannot be used simultaneously and are intended as a proof of concept for the focal correction approach.

Like the aperture lens, the FCLs in this work are modeled as a core layer between two wideband impedance matching tapers to maintain high efficiency over the Ku-band. The impedance matching tapers are necessary to provide functionality over the horn’s entire bandwidth. The impedance matching tapers are based on the designs in [11,25]. Relatively few matching sections ($3$-$4$ layers) are employed here so as not to dominate the vertical profile of the FCLs. Unlike the aperture lens, the core region of the FCL does not collimate the feed’s radiation but rather re-directs it toward the center of the aperture lens. As a result the FCL GRIN profiles are skewed, not symmetric, about the center line with higher permittivity at the edge of the FCL nearest the lens center. The top surfaces of the FCLs are defined with a 2$^{\textrm {nd}}$ order polynomial and optimized to mitigate a stark impedance mismatch at the edge of the FCL due to the monotonic permittivity profile in the core—in order to mitigate strong reflections from the FCL edge, the top surface of the lens is ideally convex.

In each iteration of the optimizer, the feed, FCL and lens are simulated with an in-house 2D finite difference time domain (FDTD) solver [15]. The lateral offsetting of the feed/FCL breaks the rotational symmetry of the problem and thus the farfields are calculated assuming a fanbeam aperture. The best designs from all optimizations are validated in 3D full-wave simulation using Empire XPU FDTD software.

The final FCL permittivity profiles for positions $\#3$, $\#4$, and $\#5$ are shown in Fig. 2(b), (c), and (d), respectively. These permittivity profiles are discretized in anticipation of fabrication: each FCL profile is approximated to a grid spacing of $2.13\,$mm in $\hat {x}$ and $1.52\,$mm in $\hat {z}$ (note that the permittivity profile is uniform in $\hat {y}$). These FCLs are sized to fit the aperture of the horn antenna with aperture dimensions of $27.7\,$mm by $19.6\,$mm. The FCLs and horn are oriented such that the beam is squinted in the H-plane of the horn.

FCL $\#3$ has a flat top surface and a thickness of $9.14\,$mm. FCL $\#3$ notably also has a high maximum permittivity ($\epsilon _r$=$6.0$) despite being the thinnest FCL, allowing it to achieve mild beam squint of $9^{\circ }$ with a minimal vertical translation of the phase center of $+5.8\,$mm at $18\,$GHz. This is important because the inner FCL is closer to the Petzval surface than the outer FCLs. FCLs $\#4$ and $\#5$ have convex top surfaces with maximum thicknesses of $18.29\,$mm and $21.34\,$mm, respectively. FCL$\#4$ achieves a beam squint of $18^{\circ }$ with a phase center shift of $+11\,$mm at $18\,$GHz. FCL $\#5$ is the thickest FCL and contributes the largest squint and vertical phase center shift: $23^{\circ }$ and $+14\,$mm at $18\,$GHz. This phase center shift is necessary to place the phase center onto the Petzval surface and incidentally increases the focal angle from $46^{\circ }$ to $55^{\circ }$.

The simulated FCL$\#3$, FCL$\#4$, and FCL$\#5$ $18\,$GHz far-field radiation patterns are provided in Fig. 2(b), (c), and (d), respectively. The gain pattern of the horn without FCL is shown in black, the simulated gain pattern of the FCL-horn combination is shown in yellow, and the measured gain pattern of the FCL-horn combination is shown in red. The beam squinting functionality of the FCLs is clearly demonstrated, with greater beam squint being associated with the higher offsets. FCL $\#3$ generates only a mild beam squint because position $\#3$ has the lowest spillover losses. Conversely, position $\#5$ experiences the highest spillover losses and thus FCL $\#5$ generates the most extreme beam squint of $23^{\circ }$.

2.4 Geometrical optics perspective

To demonstrate the FCL functionality intuitively, a ray tracing approach based on Geometric Optics (GO) is implemented. The GO approach is prominent in GRIN lens design and optimization [26,27]. In the GO simulation, rays represent the propagation of the electromagnetic wave and the rays are typically launched from a point source — which in this context represents the feed antenna’s far field phase center. By updating the ray equation and wave transfer equations iteratively, the E-field propagation can be approximately characterized. Here we employ GO ray tracing with an in-house simulator to demonstrate the FCLs’ effect on the power flow within the lens system. The ray trace simulator is written in Matlab software and based on [26].

To characterize the effect of the FCLs in the ray tracing environment it is necessary to appropriately map the feed radiation onto point source excitations. First, the far-field patterns of the horn and FCL-assisted horn are extracted from 3-D full-wave electromagnetic simulation (Fig. 2(b-d)). These field patterns are then sampled and mapped onto rays emerging from point sources located at the phase center positions.

FCL $\#5$ is selected for illustration here due to its relatively extreme beam squint and phase center shift (see Sec.2.3). Fig. 3(a) and (b) shows the ray tracing for position $\#5$ with and without FCL$\#5$, respectively. Note that $\epsilon _r=1$ for all regions outside the aperture lens in both simulations; FCL$\#5$ is plotted in Fig. 3(b) only to emphasize the phase center translation and is not involved in ray tracing. High ray density corresponds to higher power density and the rays are also color-coded with warmer tones (ie, red) indicating higher normalized radiation intensity $\tilde {U}$. For clarity, only rays contained within the incident plane are shown.

 

Fig. 3. GRIN lens ray tracing result for position $\#5$ without (a) and with (b) FCL $\#5$. The aperture lens and FCL$\#5$ GRIN profiles (Fig. 2(a) and (e)) are shown in grayscale and the normalized radiation intensity $\tilde {U}$ is shown varying from blue to red. The $+14\,$mm phase center translation is shown in (b). The FCL$\#5$ profile is plotted for reference but not involved in ray tracing.

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In Fig. 3(a) half of the emitted rays clearly bypass the lens, representing a spillover efficiency $\eta _s<50\%$. The bulk of the remaining power is captured by the very edge of the lens (ie, $x$ between $-50\,$mm to $-40\,$mm). In Fig. 3(b), the beam squint is obvious with nearly all red high-power rays intercepting the lens. Notably, nearly $70\%$ of rays now propagate through the GRIN lens and the ray distribution is much closer to the lens center ($x$ from $-45\,$mm to $-30\,$mm). From this study alone it is apparent that the spillover can be greatly reduced with the use of a FCL. A 3-D full-wave characterization and detailed analysis are provided in Sec.3.

3. Prototype and results

3.1 Fabrication and measurement

The aperture lens and FCL GRIN media are constructed according to the method presented in [11,15] from drilled low-loss RF substrates. The aperture lens is fabricated from Rogers AD250, AD350 and AD1000 materials with host permittivity (loss tangent) values of $2.5$ ($0.0013$), $3.5$ ($0.0033$), and $10.15$ ($0.0023$), respectively. These materials are extremely low-loss and have been demonstrated in other dielectric GRIN designs [11,15]. Photographs of the aperture lens are shown in Fig. 4(a) and (b) where the concave top and convex bottom are visible. The gray color is due to the AD250 material which makes up the exterior of the lens. The lens diameter is 101.6 mm. The FCLs use the same materials except that Rogers TC600 ($\epsilon _{r}=6.15$, tand$\delta =0.002$) is used instead of AD1000. Photographs of fabricated FCLs $\#3$, $\#4$, and $\#5$ are shown in Fig. 4(c), (d), and (e), respectively. The gray material is AD250, the light tan material is AD350 and the darker tan material (rightmost in the stack-up) is TC600. Each FCL is the size of a WR90 waveguide cross section (0.9 inch $\times$ 0.4 inch). The individual layers are fabricated to a tolerance within $0.05\,$mm but the actually assembly process has a larger tolerance within $0.2\,$mm of placement layer to layer. Unfortunately this second tolerance can occasionally be systematic: it was found that there was a positive off-axis shift of $\Delta x=0.5\,$mm over $5$ consecutive layers in the core FCL $\#5$. The layer thickness is electrically small ($1.524\,$mm thick) but the misalignment errors contribute to a minor deviation of the measured beam angle of FCL $\#5$ as will be shown.

 

Fig. 4. (a) Photograph showing concave top of aperture lens. (b) Photograph showing convex bottom of aperture lens. (c), (d), and (e): Photographs of FCL $\#3$, FCL $\#4$, FCL $\#5$, respectively.

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The FCL-alone patterns are measured in a time-gated farfield setting. The measured radiation patterns for FCL $\#3$, FCL $\#4$, and FCL $\#5$ are shown in the red trace in Fig. 2(b), (c), and (d), respectively. There is good agreement between measured and simulated (yellow trace) radiation patterns for all FCLs with a slight deviation in beam angle for FCL $\#5$. This deviation is likely due to fabrication and assembly tolerances mentioned above; also expect FCL $\#5$ to be the most sensitive given that it is the largest FCL with the highest permittivity. Futhermore, we expect that some multipath errors are present: these are difficult to fully eliminate in time-gated farfield measurement especially for low-directivity antennas. Regardless, this error is not expected to significantly alter the aperture lens-coupled performance.

The aperture lens/FCL system is measured in both a time-gated farfield setting and a planar nearfield chamber shown in Fig. 1(b). Fig. 5 shows a flowchart of the NSI-MI planar near field measurement. The incoming RF signal, transmitted by a network analyzer (VNA), is radiated through the horn antenna and the proposed lenslet. The corrected wave is then incident on the GRIN lens for phase collimation. Finally, the collimated wave is scanned discretely by the near field probe which provides complex s-parameter data of the aperture fields via the VNA. The NSI-MI software then calculates the far fields gain patterns. The near field scanner is automatically controlled by PC and scanning time depends on scanning area and resolution. In this case, a single measurement took on the order of twenty minutes. For measurements of different scan positions, the horn is translated to various offsets (shown as x’s in the figure) and the corresponding FCL is applied to the horn antenna. The measured $18\,$GHz gain patterns are provided in Fig. 6 along with the corresponding simulated gain patterns. Positions $\#1$, $\#2$, $\#3$, $\#4$, and $\#5$, are shown in (a), (b), (c), (d), and (e), respectively. Measured data is given in orange and the simulated data is given in black; for positions $\#3$, $\#4$, and $\#5$ the FCL-assisted data is shown in solid and the horn-alone data is dotted. There is excellent agreement between simulation and measurement for all cases.

 

Fig. 5. Measurement setup schematics. RF signal is launched in the vector network analyzer(VNA) and transmitted to the horn antenna. Incident wave is corrected by the proposed lenslets at 5 positions (from the lens center to the edge) and received by the near field scanner probe. PC controls the scanning area.

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Fig. 6. (a-e) Radiation patterns at $18\,$GHz for scan positions $\#1-\#5$. Simulated patterns are shown in black and measured patterns are shown in orange. For positions $\#3$, $\#4$, and $\#5$, the FCL-assisted radiation patterns are shown in solid traces with the horn-alone patterns dotted.

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The beam-squinting effect of the FCLs is immediately apparent: in all cases the FCLs dramatically reduce spillover radiation (observed for $\theta <0^{\circ }$) by coupling it into the main beam. This effect is most dramatic for the FCL $\#5$ case where the spillover radiation (with a peak at $\theta$=$-20^{\circ }$) is reduced by up to $10\,$dB and the main beam gain is increased $2\,$dB at $18\,$GHz. The FCL-assisted beams generally scan farther than their un-assisted counterparts due to their shifted phase centers. This is particularly noticeable for position $\#5$, where the beam angle increases from $43^{\circ }$ to $53^{\circ }$ with the inclusion of the FCL at $18\,$GHz. This is because FCL $\#5$ increases the focal angle by $10^{\circ }$ (see Sec.2.). In addition, the coma lobe is reduced due to better phase collimation (see the approximately linear $\angle E$ with an FCL in Fig. 1(a)). This is because the FCLs translate feed phase centers toward the Petzval surface. The improvement in side lobe level (SLL) is particularly stark for position $\#5$ where the SLL increases from $8\,$dB to $14\,$dB (Fig. 6(e).

The measured maximum gain for all positions and FCLs is shown in Fig. 7(a) to illustrate the measured gain improvement of scanned beams due to the FCLs. It should also be emphasized that the broadside aperture efficiency is greater than $70\%$ over the entire band with $74\%$ at $18\,$GHz, indicating a high performance base aperture lens. X-markers indicate measured values without FCLs and triangle markers indicate FCL-assisted measured values. The improvement is most notable for the FCL $\#5$ case, wherein gain from the nominal position $\#5$ measurements is increased by up to $2\,$dB. For FCL $\#3$ gain is modestly increased at lower frequencies but otherwise remains nearly the same as without an FCL. It is notable that FCL $\#4$ did not yield an increase in maximum gain, however, it did still increase the overall scan performance. The total scan improvement is more than just a maximum gain metric because the beam angle is increased for scanned beams. Fig. 7(b) shows the measured radiation patterns and corresponding scan envelopes for all positions at $18\,$GHz. The dashed black trace indicates the scan envelope for the lens system without FCLs and the dot-dash black trace indicates the scan envelope for the FCL-assisted case. The scan envelopes are based on a $G_{max}(\theta ) = G_{max}(0^{\circ })\textrm {cos}^{n}(\theta )$ curve where the scan loss exponent $n$ is unity for perfect beamscan. The scan loss improvement is substantial for the $18\,$GHz case with $n$ decreasing from $5$ to $2.5$. While the beam performance for high scan angles is still not comparable to that of a phased array, this is a dramatic improvement in scan capability relative to state of the art flat lenses. Furthermore, it is anticipated that by tweaking the optimization figures of merit (i.e., specifically targetting maximum gain, beam angle, or SLL), the overall scan performance can better cater to specific antenna applications.

 

Fig. 7. (a) Maximum measured gain over Ku-band of all scan positions with FCLs in place (triangle markers) and without FCLs (x markers). Black dashed trace indicates broadside gain at $100\%$ aperture efficiency. (b) Radiation patterns for all scan positions at $18\,$GHz. The black dashed (dot dash) trace indicates the scan loss envelope for the lens system without (with) FCLs on positions $\#3$, $\#4$, and $\#5$.

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3.2 Comparison with flat GRIN lenses in literature

For comparison, we have simulated several state of the art flat GRIN lenses reported in the literature and provided their beamscan performance in Fig. 8: (a-e) correspond to [12], [12]*, [20], [13] and [15], respectively. Plots of the permittivity profiles are included in each sub-figure to illustrate the different design approaches. It should be noted that the manuscripts considered here do not report scan loss results for flat feed planes—likely because they are not typically used for beamscanning due to the challenges in this manuscript. Therefore we reconstructed each lens GRIN profile based on their respective manuscripts and simulated them in full-wave electromagnetic simulation with their prescribed feeds. The feeds are placed at the nominal focal distance at the center line of the lens where we confirmed that simulated broadside gain was approximately as reported in the manuscript. Then the feeds are stepped laterally along a plane to emulate a flat feed surface. The frequency of operation, maximum scanned beam angle, $F/D$ (referenced to the lens bottom surface), lens diameter (in $\lambda _0$), permittivity range, and scan loss exponent $n$ (based on all scanned beams) are summarized in Table 1 for each GRIN lens. The maximum scan angle is a qualitative metric based on the overall quality of the scanned beam—these values are typically below $40^{\circ }$ for such flat-feed GRIN lenses.

 

Fig. 8. Scan loss radiation patterns and corresponding scan loss envelopes (black) for (a) [12], (b) [12]*, (c) [20], (d) [13], (e) [15] and (f) this work. Warmer trace colors indicate larger lateral feed offsets and thus higher scan angles. Individual lens permittivity profiles are included in the insets.

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Table 1. Flat Feed Surface Scan Loss Comparison

View Table

Note that in the case of [12] (Fig. 8(a)), the lens achieves fairly good beamscan quality out to $25^{\circ }$ but the $F/D$ ratio is sufficiently large that the feed must be offset beyond the edge of the lens for any higher beam angles. For a fairer comparison, a lens with reduced $F/D = 0.5$ is designed using the methodology in [12] and included in Fig. 8(b) and Table 1—this result is referred to as [12]*.

In general, Fig. 8 and Table 1 indicate that flat GRIN lenses (including the nearly flat aperture lens in this work) consistently achieve scan loss exponents near $n=5$ out to $40^{\circ }$ for a flat focal surface. These particular lens designs were chosen based on their relative similarities: all designs are flat-lenses that operate in roughly the same frequency ranges and have similar electrical size. However, these designs all follow different methodologies and have varying permittivity ranges and GRIN profiles. It should be emphasized that the high scan loss exponent affects all of these lenses regardless of their differences. The lens from [15] is also included to illustrate that the same phenomenon occurs for higher frequency lenses with larger electrical diameter. Regardless of the GRIN profile used, the spillover radiation ($G(\theta <0^{\circ }$)) and coma aberration produce the drastic scan loss at high angle. This underscores the key limitations of flat lenses with flat feed surfaces for beamscanning: spillover losses and poor collimation. In contrast, the FCL-coupled lens system directly addresses these two nonidealities and improves the scan loss exponent by a factor of $2$ while improving maximum scan angle. In a more general sense, a FCL solution would be expected to improve the scan loss performance of any of the lenses mentioned.

4. Conclusion

A scanning GRIN lens system comprising an aperture lens and smaller feed-corrective GRIN components has been designed and demonstrated. The FCLs increase the maximum gain of the lens at beamscan while simultaneously reducing the spillover losses and increasing the beam angles of corresponding offset feeds. Maximum gain of the farthest scanned beams is increased by up to $2\,$dB and the scan loss exponent is halved from $n$=$5.0$ to $n$=$2.5$.

These results indicate that the poor scan loss characteristics associated with flat feed surface beam-scanning GRIN lenses can be partially remedied by correction at the feed level. The improved performance of the demonstrated system validates the concept and lays the groundwork for similar solutions. For example, a single ‘monolithic’ FCL could be placed over the entire feed array to allow for arbitrary/continuous offset of any given feed in the focal array. Future work aside, however, the demonstrated system is a substantial step toward GRIN flat lenses with flat feed surfaces as a viable beamscanning solution for MMW applications.