# Tensor-Free Holographic Metasurface Leaky-Wave Multi-Beam Antennas with Tailorable Gain and Polarization

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Simplification of the Tensor Impedance

#### 2.1. Surface Impedance Tensor

_{x}and k

_{y}along those respective directions, then

_{obs}, y

_{obs}) at a radial distance of

_{0}= 1/√(μ

_{0}ε

_{0}) is the free-space impedance, the TM and TE modal fields are written succinctly as

_{z}is, for surface waves, the attenuation constant along z perpendicular to the surface and k

_{0}= ω√(μ

_{0}ε

_{0}) is the free-space wavenumber, with ω = 2πf being the angular frequency.

#### 2.2. Holography Theorem

_{ρϕ}of (19) is zero. Thus, (14) becomes

_{ρρ}, remains involved, and it equals this aforementioned surface impedance. Hence, we have proven the entailment of only a solitary scalar impedance for the synthesis of the hologram despite starting off first with principles from the impedance tensor formulation generally involving four tensor elements.

## 3. Simultaneous TM and TE Beams

_{0e}, ϕ

_{0e}) and the other TM (${\widehat{\mathsf{\theta}}}_{0m}$ directed) of amplitude ${E}_{{\theta}_{0m}}$ arriving from (θ

_{0m}, ϕ

_{0m}), is expressed as a function of spatial coordinates (x

_{s}, y

_{s}) = (ρ

_{s}, ϕ

_{s}) of locations on the hologram surface, each point with its associated unit vectors (${\widehat{\mathsf{\rho}}}_{s}$, ${\widehat{\mathsf{\varphi}}}_{s}$), according to

_{0}is an arbitrary coefficient and n is the average effective refractive index of the span attainable by the parametric range of the considered metasurface unit cell, the solely entailed Z

_{ρρ}element in the tensor matrix of (19) is written as

## 4. Design of the Unit Cell

_{r}= 2.2, loss tangent = 0.0009 and thickness 1.57 mm) was chosen for the design due to its low loss tangent that mitigates losses in the millimeter wave band. The unit cell has a square shape with a period of p = 2 mm. The structure is back-shielded by a copper sheet, and a metal patch is printed on the surface, as shown in Figure 2, with g denoting the gap size between adjacent patches.

_{s}versus frequency. Upon obtaining k

_{s}, the TM surface impedance Z

_{patch}of different unit cells is given by [27]:

_{0}= √(μ

_{0}/ε

_{0}) is the intrinsic free-space wave impedance (377 Ω) and α

_{z}represents, as in (18), the positive real-valued decay constant along the surface normal (z-direction) [24,28].

_{s}for any given frequency f (thus k

_{0}), each in the considered range of gap sizes, from 0.4 to 1.2 mm, pertains to a certain α

_{z}of (34) and thus Z

_{patch}of (33). This allows us to numerically compute Z

_{patch}versus the gap size, as shown in Figure 3a for f = 28 GHz, in which Z

_{patch}ranges from j280 to j214 Ω. Therefore, X in (32) is obtained as X = (280 + 214)/2 = 247. Due to the sinusoidally oscillating nature of Z

_{surf}in (32), we need a factor to expand X to a maximum value of 280 and a minimum of 214 so that the surface impedance of the unit cell can match the hologram. Hence, we set M = (280 − 247)/247 = 0.133. Again, due to different k

_{s}associated with different gap sizes, the variation of the refractive index n at f = 28 GHz with the gap size can be plotted as shown in Figure 3b.

_{0m}= 20°, ϕ

_{0m}= 45°), while that of the TE polarization is from (θ

_{0e}= 50°, ϕ

_{0e}= 135°), both arbitrarily chosen directions. Equal amplitudes of both beams are assumed, i.e., A

^{TM}= A

^{TE}= 0.5.

_{0m}= 20°, ϕ

_{0m}= 45°) is now portrayed, with the radiation of this component towards the other unintended direction (θ

_{0e}= 50°, ϕ

_{0e}= 135°) of the TE polarization remaining weak. Likewise but conversely, strong radiation of the co-polar phi component of the E-field towards just the designated direction (θ

_{0e}= 50°, ϕ

_{0e}= 135°) for the TE case is observed in Figure 5c. The cross-polar phi component of the TM radiation towards its desired beam direction (θ

_{0m}= 20°, ϕ

_{0m}= 45°) is seen from Figure 5c to be weak as well. Similarly, the cross-polar theta component of the TE case towards its intended (θ

_{0e}= 50°, ϕ

_{0e}= 135°) is shown in Figure 5b to be also suppressed, as required.

## 5. Amplitude Control of Differently Polarized Beams

_{TM}TM beams with the i-th one arriving from (θ

_{0m,i}, ϕ

_{0m,i}) and N

_{TE}TE beams with the i-th one arriving from (θ

_{0e,i}, ϕ

_{0e,i}), we rewrite the Formula (32) as

_{i}

^{TM}and A

_{i}

^{TE}are the amplitudes of the ith beams of their respective polarizations, subjected to the condition of $\sum _{i=1}^{{N}_{TM}}{A}_{i}^{TM}}+{\displaystyle \sum _{i=1}^{{N}_{TE}}{A}_{i}^{TE}}=1$.

_{0m}= 15°, ϕ

_{0m}= 45° for the TM beam and θ

_{0e}= 45°, ϕ

_{0e}= 135° for the TE beam. For both these dual-beam cases, N

_{TM}= N

_{TE}= 1, and note the dropping of the beam index i since there is only one beam per polarization. As before, the CST solver is used for the simulations.

^{TM}= A

^{TE}= 0.5) are presented in Figure 6. As the 3D radiation pattern of the absolute gain in Figure 6a portrays, the two beams are radiated with similar strengths toward their prescribed directions. For the TM-polarized beam, strong co-polar radiation along (θ

_{0m}= 15°, ϕ

_{0m}= 45°) is observed in the antenna pattern of Figure 6b for the theta component of the radiated gain defined by the E-field, whereas—as given in Figure 6c—the co-polar phi component of the gain pattern for the TE case displays a main beam towards (θ

_{0e}= 45°, ϕ

_{0e}= 135°). All respectively, the cross-polar phi and theta components of the E-field gain patterns in Figure 6b,c show weak radiation towards the designated beam directions of (θ

_{0m}= 15°, ϕ

_{0m}= 45°) and (θ

_{0e}= 45°, ϕ

_{0e}= 135°). These aspects are more clearly depicted by the planar plots in Figure 7 of these 3D patterns in those two phi cuts. θ

_{0m}= 15° of the gain pattern in the ϕ

_{0m}= 45° plane has strong and weak co-polar theta and cross-polar phi components, respectively. Exhibited in Figure 7b for the ϕ

_{0e}= 135° cut are strong co-polar phi but weak cross-polar theta components along θ

_{0e}= 45°. As required by the equal prescribed amplitudes for both cases of polarizations, the co-polar components are demonstrated by Figure 7a,b to be each radiated with an intensity of about 18 dBi.

^{TM}= 0.333, A

^{TE}= 0.667, the latter being double the former. The simulated gain patterns in the same fashion as Figure 6 and Figure 7 are presented respectively in Figure 8 and Figure 9. Particularly, the 3D patterns of the absolute gain, the theta, and phi gain components are conveyed by Figure 8a–c respectively, and the patterns in the two phi planes containing the intended beams of both polarizations are given in Figure 9a,b, in each of which the patterns of both the co- and cross-polar components are presented. Without describing the details again, the same as before about the co- and cross-polar components of both polarizations (TM and TE) being strongly and weakly radiated towards their designated beam directions can also be said here for this case. The theoretical difference of 20log

_{10}(2) = 6.02 dB between both beam levels is seen to be demonstrated by the amount which the maximum gain level of the phi component in Figure 9b, being about 20 dBi, is stronger than that of the theta component in Figure 9a, being about 14 dBi.

_{0m,1}= 150°, ϕ

_{0m,2}= 120°, ϕ

_{0m,3}= 60°, ϕ

_{0m,4}= 30°) and (θ

_{0m,1}= θ

_{0m,2}= θ

_{0m,3}= θ

_{0m,4}= 30°) and have amplitude coefficients (A

_{1}

^{TM}= C

_{1}= 0.2, A

_{2}

^{TM}= C

_{2}= 0.15, A

_{3}

^{TM}= C

_{3}= 0.4, A

_{4}

^{TM}= C

_{4}= 0.25). It is observed from this schematic that because C

_{3}is larger than the others, the interference pattern about the corresponding ϕ

_{0m,3}= 60° region of the holographic plate is also more prominent.

_{0m,i}= 30° angle, it is more readily observed that the level differences among the gains indeed come to terms with the respective differences in their amplitude coefficients. For instance, the 4 dB drop from the peak gain (of about 19 dBi) of the beam with tailored strength of C

_{3}= 0.4 to that (15 dBi) of the beam with C

_{4}= 0.25 checks well with 20log

_{10}(0.4/0.25) = 4.08. The radiation and total efficiencies are ε

_{rad}= –0.18 dB (96%) and ε

_{tot}= –0.486 dB (89.4%), respectively.

_{1}

^{TM}= A

_{2}

^{TM}= A

_{1}

^{TE}= A

_{2}

^{TE}= 0.25. The radiation directions are (θ

_{0m,1}= 15°, ϕ

_{0m,1}= 150°), (θ

_{0m,2}= 5°, ϕ

_{0m,2}= 60°), (θ

_{0e,1}= 45°, ϕ

_{0e,1}= 120°), and (θ

_{0e,2}= 55°, ϕ

_{0e,2}= 30°), respectively.

_{0m,1}= 15° and θ

_{0m,2}= 5° of both beams—whereas Figure 13b displays strongly and weakly radiated co-polar phi and cross-polar theta components towards θ

_{0e,1}= 45° and θ

_{0e,2}= 55°, respectively. Similar peak gains of about 16 dBi of the co-polar components are observed in Figure 13a,b, as expected of the equal prescribed amplitudes. For this case, the efficiencies are ε

_{rad}= –0.174 dB (96%) and ε

_{tot}= –0.4 dB (91%).

## 6. Circular Polarization

_{0#}, ϕ

_{0#}) = (θ

_{0}, ϕ

_{0}) in (8) for this case, the latter being the angular coordinates of the common radiation direction shared by both polarization components. For the left-hand circular polarization (LHCP) of (36), the co- and cross-polar unit vectors are given by [29]

_{isol}, for any far-field direction $\widehat{r}(\theta ,\varphi )$ is defined as the ratio of the co-to cross-polar field amplitudes towards that direction, and is the reciprocal of the corresponding relative cross-polar level X

_{rel}with respect to the co-polar level, i.e.,

_{0}, ϕ

_{0}) = (20°, 45°). The simulated 3D absolute gain pattern is offered by Figure 15, while the planar pattern and the axial ratio ℜ, both in the ϕ

_{0}plane, are presented in Figure 16 and Figure 17, respectively. Evident from Figure 16, strong main beams are produced towards the designated θ

_{0}= 20° direction by the absolute gain pattern of Figure 16a as well as both theta and phi components of the gain as conveyed by Figure 16b, as required. An axial ratio of 1.09 dB (linear scale value of 1.134, close to unity) towards that direction is observed in Figure 17a simulated by CST and translated to an X

_{isol}of 24.042 dB via (41) as shown in Figure 17b. The corresponding co- and cross-polar patterns calculated by (39) using the simulated theta and phi gain components are given in Figure 18. As seen, the cross-polar radiation intensity towards the main beam is below that of the co-polar component by the considerable amount of 24 dB of X

_{isol}, as expected.

## 7. Sidelobe Suppression by Beam Cancellation

_{0m,i=1}= 30°, ϕ

_{0m,i=1}= 45°. The surface impedance distribution of the so-called originating first-stage hologram synthesized for radiating just this main beam is described by the first of the three sum terms within the inner parenthesis of the following.

_{0m,i=1}= 45° plane of this originating hologram, in each of which a strong radiation towards the prescribed θ

_{0m,i=1}= 30° is seen with a gain of 21.15 dBi (linear scale value of 130.2). Likewise, in those respective scales, the black dotted traces in Figure 19(bi,bii) again represent the co-polar patterns of this first-stage hologram, but this time in the ϕ

_{0m,i=2}= 57° plane in which a TM-polarized sidelobe is incurred towards θ

_{0m,i=2}= 38°, with a level of 13.1 dBi (linear scale value of 20.5). Plots in linear scales are included as they can portray differences in values more distinctly, as appreciated later when comparisons among the iterations are made.

_{TM,SL}= 45°, θ

_{TM,SL}= 25°) prior to Hamming window is seen to be mitigated to about 8.47 dBi upon the Hamming window, which shows a significant reduction of about 2.1 dB. Substantial mitigation towards most other theta directions about that 25° is also observable, even by as much as 6.8 dB towards θ = 17°. Although the sidelobe levels towards θ = 45° deteriorate, significant improvement towards most other theta directions of approximately 50°–90° is also distinct.

_{TE}= 135°, θ

_{TE}= 35°), as conveyed by the former plot. The same explanations of the solid red and dotted black lines previously for the TM case reapply here for the TE case, being traces prior to and upon the Hamming window respectively. Before and after Hamming window, the co-polar main beam levels are 18.12 dBi and 16 dBi, respectively. In the Hamming window, the nearest-in sidelobe levels of the co-polar pattern are observed to have fallen by about 28 dB. For the cross-polar pattern of Figure 21b, substantial mitigation towards most theta directions is easily observable, and the cross-polar pattern with the most severe sidelobe towards (ϕ

_{TM,SL}= 135°, θ

_{TM,SL}= 30°) was reduced by about 2.64 dB. Additionally, the second most severe sidelobe towards (ϕ

_{TM,SL}= 135°, θ

_{TM,SL}= 25°) reduced by about 5.2 dB. It can thus be seen that using the Hamming window can mitigate most sidelobe levels so that the minor reduction of the co-polar main beam can be neglected.

## 8. Measurements on Manufactured Prototype

^{TM}= 0.667, A

^{TE}= 0.333).

_{11}over a band about the operation frequency is conveyed by Figure 26. Good impedance matching throughout the band centered at 28 GHz achieved by the simulated design is verified experimentally.

_{0m}= 35°, ϕ

_{0m}= 45°) of nearly 20 dBi for both. The corresponding patterns (simulated and measured patterns) of the cross-polar (phi) component towards that main beam direction are seen from Figure 27b to be indeed much lower than the co-polar intensity by around 10 dB. For the other beam, which is TE polarized, the consistency between the measured and simulated co-polar gain patterns (phi component) is evident from Figure 27c, while the agreements of the cross-polar (theta) pattern are observed in Figure 27d. The co-polar main beam level of around 12 dBi is accurately reproduced in the experiment towards the designated direction of θ

_{0e}= 20° and ϕ

_{0e}= 135° and is considerably stronger than the cross-polar level of about 0 dBi. In addition, the difference of about 6 dB between the intensities of the two measured co-polar main beams is also consistent with expectation by theory.

## 9. Comparisons with Existing Literature

## 10. Comparison of Holographic Beamforming Arrays Afforded by the Present Design with Conventional Phased Arrays and Sector Antennas

## 11. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Surface waves (undulating arrows) excited on an artificial impedance surface that scatter waves by changes in the surface impedance to produce the desired radiation beams (straight arrows); (

**b**) image reconstruction of objects comprising distributed sources.

**Figure 2.**Schematic of the $2\times 2\times 1.575$ ${\mathrm{mm}}^{3}$ unit cell with a variable gap size g.

**Figure 3.**(

**a**) Surface impedance Z

_{patch}of the unit cell as a function of gap size; the range of gap size is from 0.4 mm to 1.2 mm. (

**b**) Effective refractive index n of the unit cell as a function of gap size; the range of gap size is from 0.4 mm to 1.2 mm.

**Figure 4.**Holographic pattern base on interferences that generate dual beams at θ

_{0m}= 20°, ϕ

_{0m}= 45° (TM) and θ

_{0e}= 50°, ϕ

_{0e}= 135° (TE).

**Figure 5.**Simulated 3D far field gain patterns: (

**a**) absolute gain; (

**b**) theta component of the E-field gain with beam towards θ

_{0m}= 20°, ϕ

_{0m}= 45° (TM); and (

**c**) phi component of the E-field gain with beam towards θ

_{0e}= 50°, ϕ

_{0e}= 135° (TE).

**Figure 6.**Simulated 3D far field gain patterns for dual-beam, dual-polarized antenna with A

^{TM}= A

^{TE}= 0.5: (

**a**) absolute gain; (

**b**) theta component of E-field gain with beam towards θ

_{0m}= 15°, ϕ

_{0m}= 45° (co-polar for TM); and (

**c**) phi component of E-field gain with beam towards θ

_{0e}= 45°, ϕ

_{0e}= 135° (co-polar for TE).

**Figure 7.**Simulated planar far field patterns for dual-beam, dual-polarized antenna with A

^{TM}= A

^{TE}= 0.5 in (

**a**) ϕ = ϕ

_{0m}= 45° plane, showing strong radiation of co-polar theta component but weak cross-polar phi towards θ

_{0m}= 15° and (

**b**) ϕ = ϕ

_{0e}= 135° plane, showing strong radiation of co-polar phi component but weak cross-polar theta towards θ

_{0e}= 45°.

**Figure 8.**Simulated 3D far field gain patterns for dual-beam, dual-polarized antenna with A

^{TM}= 0.333, A

^{TE}= 0.667: (

**a**) absolute gain; (

**b**) theta component of E-field gain with beam towards θ

_{0m}= 15°, ϕ

_{0m}= 45° (co-polar for TM); and (

**c**) phi component of E-field gain with beam towards θ

_{0e}= 45°, ϕ

_{0e}= 135° (co-polar for TE).

**Figure 9.**Simulated planar far field patterns for dual-beam, dual-polarized antenna with A

^{TM}= 0.333, A

^{TE}= 0.667, in (

**a**) ϕ = ϕ

_{0m}= 45° plane, showing strong radiation of co-polar theta component but weak cross-polar phi towards θ

_{0m}= 15°, and (

**b**) ϕ = ϕ

_{0e}= 135° plane, showing strong radiation of co-polar phi component but weak cross-polar theta towards θ

_{0e}= 45°. Maximum 20 dBi strength of phi component in is (

**b**) about 20log

_{10}(2) = 6 dB stronger than the 14 dBi strength of theta component in (

**a**).

**Figure 10.**Simulated 3D radiation pattern of all-TM-polarized quadruple-beam holographic antenna for (ϕ

_{0m,1}= 150°, ϕ

_{0m,2}= 120°, ϕ

_{0m,3}= 60°, ϕ

_{0m,4}= 30°) and (θ

_{0m,1}= θ

_{0m,2}= θ

_{0m,3}= θ

_{0m,4}= 30°) with (A

_{1}

^{TM}= C

_{1}= 0.2, A

_{2}

^{TM}= C

_{2}= 0.15, A

_{3}

^{TM}= C

_{3}= 0.4, A

_{4}

^{TM}= C

_{4}= 0.25).

**Figure 11.**Simulated gain pattern of all-TM-polarized quadruple-beam holographic LWA of Figure 10. All beams converge towards a common θ

_{0m}= 30°.

**Figure 12.**Simulated 3D far field gain patterns for quad-beam LWA, with two TM- and two TE-polarized beams with (A

_{1}

^{TM}= A

_{2}

^{TM}= A

_{1}

^{TE}= A

_{2}

^{TE}= 0.25): (

**a**) absolute gain; (

**b**) theta component of gain with two strong beams towards (θ

_{0m,1}= 15°, ϕ

_{0m,1}= 150°) and (θ

_{0m,2}= 5°, ϕ

_{0m,2}= 60°) (co-polar for TM); and (

**c**) phi component of gain with beams towards (θ

_{0e,1}= 45°, ϕ

_{0e,1}= 120°) and (θ

_{0e,2}= 55°, ϕ

_{0e,2}= 30°) (co-polar for TE).

**Figure 13.**Simulated planar far field patterns for quad-beam LWA, with two TM- and two TE-polarized beams, (A

_{1}

^{TM}= A

_{2}

^{TM}= A

_{1}

^{TE}= A

_{2}

^{TE}= 0.25), in various phi planes containing the beams, (

**a**) TM beams in 150° and 60° phi-cuts, showing strong radiation of co-polar theta component but weak cross-polar phi towards θ

_{0m,1}= 15° and θ

_{0m,2}= 5°, and (

**b**) TE beams in 120° and 30° phi planes, showing strong radiation of co-polar phi component but weak cross-polar theta towards θ

_{0e,1}= 45° and θ

_{0e,2}= 55°.

**Figure 14.**Hologram as LWA for radiating circular polarized beam towards (θ

_{0}, ϕ

_{0}) = (20°, 45°).

**Figure 15.**Simulated 3D far field absolute gain pattern with circular polarized main beam towards (θ

_{0}, ϕ

_{0}) = (20°, 45°).

**Figure 16.**Radiation patterns in ϕ

_{0}= 45° plane of circular-polarized LWA for (

**a**) absolute gain and (

**b**) in the same plot, theta and phi components of gain.

**Figure 17.**Radiation patterns in ϕ

_{0}= 45° plane of circular-polarized LWA for (

**a**) absolute gain and (

**b**) in the same plot, theta and phi components of gain.

**Figure 18.**Co- and cross-polar far-field patterns of circular polarized LWA in ϕ = ϕ

_{inc}plane for main beam towards θ

_{0}= 20° in CST.

**Figure 19.**The above figure is a composite diagram of original, sidelobe cancellation, sidelobe cancellation, and main beam compensation and is divided into (

**a**) main beam (TM) co-polarization; (

**ai**) dB scale, (

**aii**) linear scale, and (

**b**) sidelobe TM co-polarization; (

**bi**) dB scale, (

**bii**) linear scale.

**Figure 20.**Radiation patterns in ϕ

_{TM}= 45° plane containing TM polarized beam, with red and black dotted traces for cases before and after the Hamming window. (

**a**) Co-polar pattern with main beam towards (ϕ

_{TM}= 45°, θ

_{TM}= 20°) and (

**b**) cross-polar pattern with the most severe sidelobe towards (ϕ

_{TM,SL}= 45°, θ

_{TM,SL}= 25°), reduced by about 2.1 dB.

**Figure 21.**Radiation patterns in ϕ

_{TE}= 135° plane containing TE polarized beam, with red and black dotted traces for cases before and after the Hamming window. (

**a**) Co-polar pattern with main beam towards (ϕ

_{TE}= 135°, θ

_{TE}= 35°) and (

**b**) cross-polar pattern with the most severe sidelobe towards (ϕ

_{TM,SL}= 135°, θ

_{TM,SL}= 30°), reduced by about 2.64 dB.

**Figure 23.**(

**a**) Top and (

**b**) SMA soldering views of the holographic antenna fabricated in θ = 45° and 135° modes.

**Figure 24.**Comparison of measured radiation patterns of WR-28 standard horn antenna obtained by the near-field measurement technology of Taiwan Microwave Circuit Company with those obtained by measurements in far-field anechoic chamber.

**Figure 25.**Measurement environment of 28 GHz holographic antenna in Taiwan Microwave Circuit company.

**Figure 26.**Variation with frequency of simulated and measured S

_{11}over band centered around 28 GHz operating frequency.

**Figure 27.**Measured and simulated gain patterns of dual-polarization multiple beams holographic LWA with (A

^{TM}= 0.667, A

^{TE}= 0.333): (

**a**) co-polar and (

**b**) cross-polar in ϕ

_{0m}= 45° plane with θ

_{0m}= 35°; (

**c**) Co-polar and (

**d**) Cross-polar in (

**b**) ϕ

_{0e}= 135° plane with θ

_{0e}= 20°.

Reference | Multiple Beams | Beams in Any Phi Plane | Gain Amplitude Control | Beam Polarization Control | Beam Phase Control | No Hologram Partitioning | Sidelobe Suppression and Compensation | Contains Measurement Results |
---|---|---|---|---|---|---|---|---|

[1] | ✗ | ✓ | ✗ | ✓ | ✓ | ✓ | ✗ | ✗ |

[3] | ✗ | ✓ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ |

[12] | ✗ | ✓ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ |

[13] | ✗ | ✓ | ✗ | ✗ | ✗ | ✓ | ✗ | ✓ |

[14] | ✗ | ✓ | ✗ | ✓ | ✓ | ✗ | ✗ | ✓ |

[15] | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ |

[16] | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ |

[17] | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ |

[18] | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✓ |

[19] | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ |

[20] | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ |

[21] | ✓ | ✓ | ✓ | ✗ | ✗ | ✓ | ✗ | ✓ |

[22] | ✓ | ✗ | ✓ | ✗ | ✗ | ✓ | ✗ | ✓ |

[23] | ✓ | ✗ | ✓ | ✗ | ✗ | ✓ | ✗ | ✗ |

[26] | ✗ | ✓ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ |

[27] | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |

[28] | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ | ✓ |

[32] | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ | ✗ | ✓ |

Present work | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

Ref. | Freq (GHz) | Area of the Aperture | Number of Ports | Number of Beams | Realized Gain (dBi) | SLLs (dB) |
---|---|---|---|---|---|---|

[19] | 24 | $\pi \times {\left(10{\lambda}_{0}\right)}^{2}$ | 2 | 2 | 21.5 | 9 |

[21] | 14 | $10{\lambda}_{0}\times 10{\lambda}_{0}$ | 7 | 7 | 20 | 10 |

[32] | 12 | $9.6{\lambda}_{0}\times 8{\lambda}_{0}$ | 2 | 2 | 16 | 6 |

This work | 28 | $0.5\pi \times {\left(9.4{\lambda}_{0}\right)}^{2}$ | 1 | 1TM + 1TE | 18 @ for TM 17.3 for TE | 7.84 for TM 9.61 for TE |

Reference | ${\mathit{S}}_{11}$ (Meas.) | Co-Pol (Meas.) | Cross-Pol (Meas.) |
---|---|---|---|

[1] | ✗ | ✗ | ✗ |

[3] | ✗ | ✗ | ✗ |

[12] | ✗ | ✗ | ✗ |

[13] | −25 dB (17 GHz) −17 dB (20 GHz) | 16.7 dB (17 GHz) 20.5 dB (20 GHz) | ✗ |

[14] | ✗ | 15 dB (12 GHz) | 5 dB (12 GHz) |

[15] | −18 dB (23 GHz) (sim.) | 15 dB (23 GHz) | ✗ |

[16] | ✗ | −5 dB (16 GHz) (normalized) | ✗ |

[17] | ✗ | ✗ | ✗ |

[18] | ✗ | 28 dBi (8.4 GHz) | ✗ |

[19] | ✗ | ✗ | ✗ |

[20] | ✗ | ✗ | ✗ |

[21] | −22.5 dB (14 GHz) | 20 dB (14 GHz) | 10 dB (14 GHz) |

[22] | ✗ | 12 dB (18 GHz) | ✗ |

[23] | ✗ | ✗ | ✗ |

[26] | ✗ | ✗ | ✗ |

[27] | ✗ | ✗ | ✗ |

[28] | −9 dB (10 GHz) | 14.7 dB (10 GHz) | −22 dB (10 GHz) |

[32] | ✗ | 15 dB (12 GHz) | 7.5 dB (12 GHz) |

Present work | −13 dB (28 GHz) | 19 dB (TM) 13 dB (TE) | 10 dB (TM) 9 dB (TE) |

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© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Weng, C.-K.; Tsai, Y.-Z.; Vilenskiy, A.; Ng Mou Kehn, M.
Tensor-Free Holographic Metasurface Leaky-Wave Multi-Beam Antennas with Tailorable Gain and Polarization. *Sensors* **2024**, *24*, 2422.
https://doi.org/10.3390/s24082422

**AMA Style**

Weng C-K, Tsai Y-Z, Vilenskiy A, Ng Mou Kehn M.
Tensor-Free Holographic Metasurface Leaky-Wave Multi-Beam Antennas with Tailorable Gain and Polarization. *Sensors*. 2024; 24(8):2422.
https://doi.org/10.3390/s24082422

**Chicago/Turabian Style**

Weng, Chuan-Kuei, Yu-Zhan Tsai, Artem Vilenskiy, and Malcolm Ng Mou Kehn.
2024. "Tensor-Free Holographic Metasurface Leaky-Wave Multi-Beam Antennas with Tailorable Gain and Polarization" *Sensors* 24, no. 8: 2422.
https://doi.org/10.3390/s24082422