Radio-transparent dipole antenna based on a metasurface cloak

Antenna technology is at the basis of ubiquitous wireless communication systems and sensors. Radiation is typically sustained by conduction currents flowing around resonant metallic objects that are optimized to enhance efficiency and bandwidth. However, resonant conductors are prone to large scattering of impinging waves, leading to challenges in crowded antenna environments due to blockage and distortion. Metasurface cloaks have been explored in the quest of addressing this challenge by reducing antenna scattering. However, metasurface-based designs have so far shown limited performance in terms of bandwidth, footprint and overall scattering reduction. Here we introduce a different route towards radio-transparent antennas, in which the cloak itself acts as the radiating element, drastically reducing the overall footprint while enhancing scattering suppression and bandwidth, without sacrificing other relevant radiation metrics compared to conventional antennas. This technique opens opportunities for cloaking technology, with promising features for crowded wireless communication platforms and noninvasive sensing.

The paper proposes a means for solving blockage and interference in dual-band closely-positioned antenna scenarios, e.g., as used in 3G and 4G cellular base stations. Typically, the low frequency (LB, large dimensions) antennas are positioned in front of the high frequency (HB, small dimensions) antennas in such a typical configuration, distorting the radiation patterns of the latter. A possible solution that has been attempted previously by numerous authors utilizes mantle cloaks (impedance surfaces) surrounding the LB antennas to reduce their scattering cross section at the high frequency band, allowing HB antennas to radiate properly. However, cloaking the LB antennas is typically narrow band, due to the resonant nature of the optimized conducting dipole radiators (alternatively, thicker cloaks can be used, which makes the overall design bulkier and less attractive). Instead, the authors propose to use the conducting impedance sheets comprising the cloak as the radiating element, and optimize them (together with a suitable dielectric core and cover) to exhibit low scattering cross section to begin with. From another point of view (as it is presented in the paper), instead of cloaking a resonant conductor, the idea is to cloak a dielectric cylinder (which is far less demanding since it has a significantly lower scattering cross section to begin with), and use the cloak surface as the means to conduct radiating currents required for an effective antenna. The concept is first principally discussed and illustrated using a simplified configuration, and then demonstrated experimentally using a commercially oriented base station antenna panel.
From a technical perspective, the work seems highly valuable. Indeed, it manages to solve the crowdedantennas problem in an elegant manner, maintaining the gain and beamwidth of the isolated HB antennas across the entire high frequency band even in the presence of the "blocking" (now cloaked) LB antenna, while avoiding undesired beam squint. At the same time, the proposed LB antenna, having a dielectric core and the cloak surface as the "active" element, performs as expected across the entire low frequency band. This may prove very useful for many modern (and future) communication systems. However, I have some concerns with regards to the paper as a scientific contribution intended for Nature Communications.
1. The immersed cloak design, which should have been the focus of this work, barely gets any attention at all. Besides being discussed mainly in the SM, the design formula is not even mentioned, there is no schematics of the surface itself, there is no schematics of the excitation circuit, no real discussion on how to "transform" the impedance surface into a commercial-grade antenna (besides one or two sentences on page 11 of the SM), no details on how it was fabricated. I think that the paper should be rewritten with these aspects receiving much more attention in the main text (including the discussion around Figs. S1 and S2). Even though the standard mantle cloak formulas may be well known, I think that the main design formulas, principal design considerations and guidelines, as well as the aforementioned schematics should appear in the main text.
2. Since the idea to use the cloak as the antenna has been proposed before (see [27] of the manuscript and [14] of the SM), it seems (the way the manuscript is written) that the main purpose of the work is to adapt this idea as to fit the commercial base station antenna panel scenario. While this makes the work very strong from a technical perspective, I think that adding another example (the authors mention "arbitrarily shaped antennas" on the last page) to demonstrate the universal nature of their concept (even in simulations) would significantly strengthen the scientific merit of the work.
3. Many details are missing or hard to locate, not all terms and acronyms are well defined, and terminology is not always consistent. All of these make the reading quite difficult. 3 3.5. What is f_0? lambda_0? 3.6. Main text refers to 3x3 unit cell for the antenna panel, while SM refers to 2x3 unit cell. 3.7. Page 4 -"a metallic cylinder cloaked with an optimal metasurface" -provide reference or a detailed design procedure (SM) to unambiguously identify the optimal metasurface. 3.8. Page 5 -"conducting dipole designed to efficiently radiate" -how does this design manifest itself in Fig.  2(a) and 2(b)? 3.9.  is referenced with respect to angular sensitivity, but we failed to locate where this issue is discussed therein. 3.10. Page 6 -"geometry is optimized to efficiently radiate in the LB" -how was the optimization performed? With respect to which figure of merit? 3.11. Page 15 -Please define the bandwidth mentioned in the caption. Is it the -3 dB bandwidth? 3.12. Page 17 -Please indicate what is plotted in the radiation patterns. Is it gain? Realized gain? 3.13. "SoM" and "SM" are inconsistently used to indicate Supplementary Material. 3.14. "Std. Dipole" and "CD" are inconsistently used to indicate conventional conducting dipole antennas. 3 Other comments: 1. Page 4 -the authors mention increased sensitivity to illumination angle observed in Fig. 2(c). However, it seems that the band is wider for all angles of incidence for the thicker device… 2. Figure 2 -The perforated screen illustration is misleading, in my mind. If ideal impedance sheets were used, the illustration should include a smooth surface. 3. Page 6 -The authors mention that the (cloaked) LB antenna eliminates scattering interference also within the LB band. Could you please elaborate on how this is consistent with the bounds found by the authors in "Physical bounds on absorption and scattering for cloaked sensors" [Phys. Rev. B 89, 045122. 2014]? From reciprocity, if the antenna radiates well doesn't it mean it should also absorb well in the same frequency? 4. Page 7 -"an isolate array" (not "arrays"). 5. Page 8 -the authors claim that Fig. 4 shows the benefits of the proposed antenna for both polarization planes. How can this be seen? In which polarization were the measurements conducted? Which plane cut is shown? 6. Page 9 -Beam squint should be averaged in absolute value (cannot be negative). Otherwise large angular deviations with opposite signs would cancel each other. 7. Page 9 -How come the isolated antenna exhibits a lower gain on average than the cloaked one? Please comment on that in the manuscript. 8. SM, page 1 -don't x_1, x_2, etc. also depend on the Bessel function order "n"? 4.3. Please define coordinate systems and polarizations (TE, TM) visually in the SM figure(s). 9. SM, page 4 -how to determine the maximum relevant order N_max? 10. SM, page 4 -how Z_zz can be considered isotropic? 11. SM, Figure S6 -legend is inconsistent with the description in the text.
Reviewer #3 (Remarks to the Author): The paper represents novel ideas that provide good information for current research but also ideas for advancing these ideas for future work.
It would be good to have more details on the actual experimental fabrication of the cloaking device and measurements. Confirmation of the dielectric constants of the materials used. Info on repeatability of the experimental data etc.
Reviewer #4 (Remarks to the Author): In the manuscript entitled "Radio-Transparent Dipole Antenna Based on a Metasurface Cloak", the authors proposed a radio-transparent antenna composed of a hollow dielectric cylinder and an inductive metasurface inserted within the dielectric cylinder. The inductive metasurface can suppress the total scattering of this antenna and meanwhile function as a radiating element, rendering it a radio-transparent antenna. This idea is a follow-up work of the previous concepts proposed by the authors as cloaked sensors, but the potential application in antennas seems quite interesting to me. However, the manuscript seems not so satisfying in its current form and some important issues need to be addressed.
1. The idea of constructing a low-scattering antenna by a dielectric cylinder and an inductive metasurface inserted within the cylinder seems similar to the so-called "Mantle cloaking", which can cloak a dielectric cylinder by metasurface, except that the inductive metasurface is optimized to a feeding line. Considering this, the connections and differences between these two approaches should be discussed. 3. What is the purpose of using the hollow cylinder instead of a solid one? How did the authors find this specific type of antenna? More elaboration on the reasoning behind the final result is preferred. 4. How important is the goal of cancelling the scattering of neighboring antennas in practice? I mean, if one looks at Fig. 1, the radition pattern is only slightly affected by the low-frequency antenna. Thus this figure seems to indicate the scattering between neighboring antennas is just a minor issue, if one does not care too much about wavefront. Will this issue be significant for antenna array, or is there any circumstance in which this issue becomes critical? 5. The figures are not very attracting. For example, Figs. 2(a) and 2(b) seem to be the duplicate of each other, except for the change in the parameters. So why not plot only one figure and mark two sets of parameters to save the space? The font size in Fig. 3 are much larger than those in other figures. 6. As for the far-field performance at HB shown in Fig. 4(d), the improvement of the radiation from the radio-transparent antenna seems not so large. Especially, at 2.3 and 2.7GHz, the radiation of std. dipole seems more close to that of the isolated HB antenna. I suggest the authors add some analysis on the upper limit of the improvement and possibly negative factors that should be avoided.

Response letter to the referees' comments on the manuscript NCOMMS-21-06952-T entitled "Radio-Transparent Dipole Antenna Based on a Metasurface Cloak"
We thank the Referees and the Editors for the time they spent evaluating our paper, for their constructive suggestions, and their overall positive feedback. We are very encouraged by the positive statements by all reviewers. In the following, we provide detailed response to all their comments, and outline the changes we implemented in the manuscript to address them. We hope that the revised manuscript may meet in the eyes of the Editors and the Referees the publication criteria of Nature Communications. Authors: We agree with the referee that more details regarding the design and simulation procedure may make the paper more accessible for the reader. Following this comment, we have rewritten the paper and made sure that the revised version of the main paper includes the detailed design process of the cloak design. We also have revised some of the figures to help navigate through the design steps. Authors: We agree with the referee that in the original submission these details were missing. In the revised version of the paper of the paper and SM, we have done our best to address these issues. Authors: We thank the referee for this comment. In the revised version of the paper, the missing definitions have been added to the main text. Authors: We thank the referee for noticing this misprint. The panel is a 2x3 unit cell. We have fixed the issue on the revised version of the paper. Referee A.3.7. Page 4 -"a metallic cylinder cloaked with an optimal metasurface" -provide reference or a detailed design procedure (SM) to unambiguously identify the optimal metasurface. Authors: We thank the referee for pointing out this issue and we agree that this could be a point of confusion for the readers. In the figures mentioned by the referee, the metallic cylinder is covered with an ideal impedance sheet. The required impedance can be found by applying the proper boundary conditions in Eqs. (1)-(2) of the main paper. We agree that in the original submission, the design procedure was not clear. To address this issue, in the revised paper we have added a detailed design procedure to prevent any confusion.

Authors:
We thank the referee for this comment. The design presented here has a significantly reduced aspect ratio in comparison to the ones presented in the mentioned references by the referee. This is because of the added extra layers for cloaking in those works in contrast to an immersed cloaking layer that we have proposed in our work. For example: in [33] the total diameter of the monopole radiating at 2.4 GHz is 15.79 mm ( 0 0.128 at 2.4GHz). The diameter of our proposed design is 22.88 mm which is 0 0.063 at a center BW of 830 MHz. Notice that this is the key advantage of our work: in conventional cloaked antennas, we cannot place the cloak too close to the metallic surface of the antenna without hindering the operational bandwidth. Here instead, we get rid of the metal, and use the cloak, immersed in a suitably designed dielectric, to radiate. We achieve therefore reduced cross-section and improved bandwidth at the same time. Fig. 4(d) the TDCMA closely matches the isolated panel. But there are significant differences in all the high-frequency (f>=2.3 GHz) patterns.

Authors:
We thank the referee for pointing out this important issue. To explain the performance of the proposed design, let us first start by considering a simple scenario where a LB antenna is illuminated at HB frequencies. Supplementary Fig. 8, shows that at all the tested HB frequencies, our proposed design performs extremely well in cloaking the LB antenna. However, in Fig. 4 of the paper we are considering a realistic and practical design where the LB antenna is positioned in front of an array of HB antennas and all are backed by a finite metallic back reflector rather than considering an abstract case where the LB antenna is located in front of one HB antenna. In such a practical scenario, there are several parasitic effects (e.g., coupling between the HB antennas, coupling between different HB antennas with the LB antenna, and the presence of a back reflector) 6 that are not considered in the design process since it will introduce tremendous complications to the design process, if not make it impossible. However, regardless of the complications mentioned, the proposed design performs quite well. There are a few notes that we need to consider when investigating the results in Fig. 4(d) of the paper. By comparing the radiation patterns for the Conductive Dipole case and the proposed Radio-Transparent Dipole Antenna, it is clear that the proposed design performs extremely well at all HB frequencies by improving the radiation characteristics at these frequencies. However, ideally, we would want the proposed Radio-Transparent Dipole Antenna to match the radiation characteristics of the isolated HB antenna array. In fact, this is accomplished for lower frequencies, as can be seen from the results.
As the referee correctly points out, for higher frequencies f>=2.3 GHz, the radiation characteristics of the proposed Radio-Transparent Dipole Antenna are slightly deviated from the radiation characteristics of the Isolated HB antenna array which can be explained by the fact that here we are considering a system level proof of concept which has lots of extra parasitic effects that are extremely difficult if not impossible to take into account carefully at the design level. It should also be noted that the proposed design improved the blockage issue almost in all the HB frequencies. To clarify the results more, we have added an explanation in the revised version of the paper.

Other comments:
Referee A. 1 Fig. 2(c). However, it seems that the band is wider for all angles of incidence for the thicker device… Authors: We thank the referee for raising this issue. We apologize if our original statement was confusing. Basically, what we meant is that a thicker design will provide higher bandwidth but at the cost of increased angular sensitivity defined as . This can be seen from Fig. 2(d) where the derivative of the blue line, corresponding to the thicker design, is sharper than the green one which corresponds to the thinner design. To clarify this, in the revised version of the paper we have added an explanation.

Referee A.2. Figure 2 -The perforated screen illustration is misleading, in my mind. If ideal impedance sheets were used, the illustration should include a smooth surface.
Authors: We thank the referee for the constructive comment. We agree with the referee that the original way of representing the impedance sheet could be misleading to the readers. In the revised version of the paper, we have addressed this issue by replacing the ideal impedance sheet with a smooth transparent surface and added a clarifying explanation to the text.

Referee A.3. Page 6 -The authors mention that the (cloaked) LB antenna eliminates scattering interference also within the LB band. Could you please elaborate on how this is consistent with 7 the bounds found by the authors in "Physical bounds on absorption and scattering for cloaked sensors" [Phys. Rev. B 89, 045122. 2014]? From reciprocity, if the antenna radiates well doesn't it mean it should also absorb well in the same frequency?
Authors: We thank the referee for bringing up this issue. Interestingly, and consistent with the results in the paper mentioned by this reviewer, a cloaked antenna can provide zero scattering and yet transmit / receive efficiently. The reason is that the absence of scattering from an antenna does not prevent the antenna from inducing currents on it, in reality the currents induced on our metal traces forming the antenna are responsible for cancelling the scattering from the dielectric host. Reciprocity requires that if we can induce currents on the metal traces, then by injecting those same currents we should be able to radiate out with the same efficiency, and indeed this is what we achieve. We have clarified this aspect in the main text.

Referee A.4. Page 7 -"an isolate array" (not "arrays").
Authors: We thank the referee for noticing this misprint. We have corrected the issue in the revised version of the paper. Fig. 4

shows the benefits of the proposed antenna for both polarization planes. How can this be seen? In which polarization were the measurements conducted? Which plane cut is shown?
Authors: The polarization of the received antenna is aligned with the length of the base station [vertical direction with respect to Fig. 4(b)]. With this in mind, the HB dipoles are diagonally oriented with respect to the receiving antenna, as commonly done in radio base station applications. Considering this and the fact that both arms of the HB antennas are excited simultaneously, the proof of concept considered here shows very good performance for both polarizations.

Referee A.6. Page 9 -Beam squint should be averaged in absolute value (cannot be negative). Otherwise large angular deviations with opposite signs would cancel each other.
the antennas designed based on this methodology not only suffer from narrow bandwidths and polarization sensitivity, but are also limited by the appendage of an extra cloaking increasing the aspect ratio. This is important in particular because the antenna to be cloaked is typically metallic, hence a cloaking metasurface needs to be placed at a distance to avoid shorting. Narrow gaps between the metasurface and the antenna lead to sacrificed bandwidth, whereas large gaps make the response angular dependent. Increased dimensions not only adversely affect the already closely packed system, but also result in undesired scattering through otherwise non-dominant scattering orders.
In this work, instead of cloaking an existing antenna, we start our design with a low scattering dielectric object and embed in it with an ultra-low profile metasurface to further reduce its scattering in the HB over a large bandwidth. This is easy to achieve, given the already low and non-resonant scattering of the dielectric host. We showed that this technique is capable of addressing the current challenges of cloaked antennas, realizing an efficient LB radiator and at the same time mitigating the total HB scattering of the element.
On the other hand, the approach presented here is similar to the conventional mantle cloak approach in the sense that they both are based on scattering cancellation concept. However, the impedance sheet used in our concept has a negligible cloaking responsibility since the dielectric has a very low scattering in the first place, making it less sensitive to the angle of illumination and provide higher bandwidth.
In the introduction of the paper, we already discuss the designs based on mantle cloaks and their challenges under the general concept of "scattering cancellation techniques" and mention their challenges. However, to make it clearer, we have added a discussion to the revised paper to reiterate the similarities and differences between the proposed design and with the ones based on mantle cloaks.

Referee D.2. I wonder if the authors could directly compare with previous metal antennas with metasurface cloaks and scattering cancellation techniques, e.g. in Figs. 3,4 and 5.
Authors: We thank the referee for this comment. We feel that this addition would be not particularly beneficial, as it is clear from the results shown in Fig. 2 that the scattering cross section of the immersed metasurface in a dielectric is notably reduced compared to the mantle cloak on a conductive dipole approach. In the interest of keeping our paper centered on our design, we prefer to avoid these additional plots. The challenge in drawing this comparison is that we improve both the cross section and the frequency / angular bandwidth of the response compared to conventional cloaked antennas. We have clarified these aspects further in the revised paper.

Referee D.3.
What is the purpose of using the hollow cylinder instead of a solid one? How did the authors find this specific type of antenna? More elaboration on the reasoning behind the final result is preferred.

11
Authors: The center of the cylinder has been hollowed out for antenna mounting, weight reduction, as well as capacitive feeding for passive intermodulation reduction. Usually in real-life base stations the similar strategy is utilized for the same purposes. However, in principle, one can choose a solid cylinder if the above-mentioned factors are not important. In SM, we have a note explaining this.

Referee D.4.
How important is the goal of cancelling the scattering of neighboring antennas in practice? I mean, if one looks at Fig. 1, the radition pattern is only slightly affected by the lowfrequency antenna. Thus this figure seems to indicate the scattering between neighboring antennas is just a minor issue, if one does not care too much about wavefront. Will this issue be significant for antenna array, or is there any circumstance in which this issue becomes critical?
Authors: We apologize if Fig. 1 of the paper in the original submission was misleading. In fact, Fig. 1 is a simplified schematic (and not a real simulated structure) for a real-life base station scenario. In the revised version of the paper, we have modified this figure to prevent confusion. Authors: We thank the referee for the comment. Figures 2(a) and 2(b) are two-dimensional intensity plots and, although we understand and appreciate the referee's point in making the figures more compact and appealing, unfortunately it is not possible to merge them into one plot. However, in the revised version of the paper, we have modified these figures to make them more attractive inspired by these suggestions. Referee D. 6. As for the far-field performance at HB shown in Fig. 4(d), the improvement of the radiation from the radio-transparent antenna seems not so large. Especially, at 2.3 and 2.7GHz, the radiation of std. dipole seems more close to that of the isolated HB antenna. I suggest the authors add some analysis on the upper limit of the improvement and possibly negative factors that should be avoided.

Authors:
We thank the referee for this comment. To explain the performance of the proposed design, let us first start by considering a simple scenario where a LB antenna is illuminated at HB frequencies. Supplementary Fig. 8 shows that at all the tested HB frequencies the proposed design performs extremely well in cloaking the LB antenna. However, in Fig. 4 of the paper, we are considering a realistic practical design where the LB antenna is positioned in front of an array of HB antennas and all are backed by a metallic back reflector rather than considering an abstract case where the LB antenna is located in front of one HB antenna. In such a practical scenario, there are several parasitic effects (e.g., coupling between the HB antennas, coupling between different HB antennas with the LB antenna, and the presence of a back reflector) that are not considered in the design process since it will introduce tremendous complications to the design process if not make it impossible. However, regardless of the complications mentioned, the proposed design performs quite well. There are a few notes that we need to consider when investigating the results in Fig. 4(d) of the paper. By comparing the radiation patterns for the Conductive Dipole case and the proposed Radio-Transparent Dipole Antenna, it is clear that the proposed design performs extremely well at all HB frequencies by improving the radiation characteristics at these frequencies. However, ideally, we would want the proposed Radio-Transparent Dipole Antenna to match the radiation characteristics of the isolated HB antenna array. In fact, this is accomplished for lower frequencies as can be seen from the results. However, as the referee correctly points out, for higher frequencies f>=2.3 GHz, the radiation characteristics of the proposed Radio-Transparent Dipole Antenna are slightly deviated from the radiation characteristics of the Isolated HB antenna array which can be dedicated to the fact that here we are considering a system level proof of concept which has lots of extra parasitic effects that are extremely difficult if not impossible to take into account on the design level. It should be noted that the proposed design improved the blockage issue almost in all the HB frequencies.
The significant improvement induced by the proposed design can also be seen from Fig. 5 of the main paper. For most of the band, the gain is fully restored, which goes directly into the power transmission of the base-station, especially since the antenna is directly in front of the transmitter, where every fraction of a dB is precious. Considering even a modest 1dB band averaged gain improvement, the base station would be 20% more efficient with the proposed approach. Most of the in-band gain improvement is ~3dB, which is impressive. Next consider the additional degradation due to beam squint. Even if the base station was 100% efficient, for half of the band, the power would be directed 45deg. from its intended direction. The bandwidth is dramatically larger than any similar approach. To clarify the results more, we have added an explanation in the revised version of the paper.
Referee D.7. The large and small antennas in Figure 4 are oriented to the same direction, what happens if they are not aligned to the same direction?
Authors: We thank the referee for this comment. Although not considered in this paper, we believe that there should not be a significant change in the response. As it can be seen from Fig. 4, here half of the HB dipoles are aligned with the LB dipoles and the other half are orthogonal to them, showing the reliability of the design under the two extremes. Furthermore, it should be noted that here we are exciting all the dipoles simultaneously. A rotation of one dipole with respect to the other would not change significantly the results because of the small size of the antennas and the fact that we are exciting already both polarizations.
Referee D.8. The curves in Figure 5 are not very smooth, probably due to insufficient frequency points.
I thank the authors for the thorough consideration of my comments; most of them were addressed satisfactorily. However, further to additional clarifications required for some of the responses, one major issue has emerged.
Particularly, the additional details and improved schematics of the "metasurface cloak" design provided in the revised manuscript shed new light on the presented results and brought up new issues. In fact, as it became clear now from the improved drawings in Figure 3 and Supplementary Figures 3 and 4, the "metasurface" contains only two thin strips along the cylinder circumference. This is highly unconventional as far as metasurfaces are concerned (e.g., see the metasurface cloaks in [35], [37]). This aspect has to be clarified by the authors before I can make my recommendation, since it is central to the claims made in the manuscript.
1. Is such a sparse configuration sufficient for homogenization? Could this two-strip structure be considered an impedance surface? If the authors claim this is the case, they should provide direct evidence to that, by extracting in simulations the surface impedance of such a structure (regardless of the cloaking functionality), and comparing it to analytical models based on homogenization (e.g., [37]). Fig. 3, it is not obvious to me that the thin strips play an important role in the cloaking effect as described by the authors. To establish this, the authors should indicate clearly how this final configuration is obtained based on Eq. (3). Which frequency is used in this equation as the cloaking frequency that yields the implemented design parameters? Is the cloaking quality reduced when the thin strip width deviates from the derived value? 3. Could it be that the main scattering reduction stems from the use of the dielectrics, and the strips merely serve as means for establishing radiation (i.e., exciting the dielectric body)? In that sense, other conductor geometries (regardless of the metasurface cloak design rules) might be as good as these thin strips in providing similar performance. 4. Either way, the fact that two thin strips are considered a "metasurface" should be clearly highlighted and commented about in the main text (considering also the points mentioned above). A clear figure of the cloak itself (e.g., as in [35], [37]) should be presented, with all the relevant dimensions denoted on it. In the current manuscript form, this fact can be easily missed, and is mostly documented in the Supplementary Material (also not emphasized sufficiently therein).

Looking again in
Below I refer to additional revisions or clarifications required with regards to specific comments made in my previous report.
A.1: I advise the authors to provide in the future specific and detailed references to where revisions have been made in the text, which would surely expedite the review process. I may have missed it, but I could not find the schematics of the excitation circuit that was requested in this comment, as well as clear schematics of the metasurface itself. Please add these to the paper.
A.2: As far as I understand from the authors' response and provided example, "arbitrarily shaped antennas" in page 15 actually means "arbitrary arrangements of dipole antennas"? Please clarify or rephrase the statement.
A.3.2: I could not find the modified reference notations in the SM. Please verify.
A.3.12: Please specify also the polarization details of the measurements in the caption (see also Other comments/A.5).
A.4.1: Ok, thank you for the clarification. A minor issue -in Supp. Fig. 3 the value of r3 is different than in Supp. Fig. 4. Please check.
A.4.2: Ok, thank you for clarifying. I think, however, that there was a confusion in the revised text, since the section "In such a practical scenario, there are several parasitic effects (e.g., coupling between the HB antennas, coupling between different HB antennas with the LB antenna, and the presence of a back reflector) that are not considered in the design process since it will introduce tremendous complications to the design process if not make it impossible." appears with an almost identical wording at least twice therein. Please check.
Other comments/A.5: These polarization aspects should be clarified in the manuscript, including in the caption of Fig. 4. Is there any phase shift between the crossed-dipole arms? Do the cross dipoles emit circularly polarized radiation?
Other comments/A.6: I'm not sure what the authors mean in their response. The text specifically reads "Across the entire HB, the average beam squint caused by the conductive dipole element was measured to be …" (page 13), namely, there is a specific reference to averaging. Please clarify this in view of our comment.
Other comments/A.8: I may have not phrased my comment properly. Since these coefficients appear in the summation, it may be appropriate to indicate explicitly (using a subscript or a superscript) the fact that they are dependent on n.
Reviewer #4 (Remarks to the Author): I read the revised manuscript and the response letter carefully. The authors have made a substantial revision to their manuscript. The current version is much better than the previous one. They have also nicely addressed all my comments. I still think this original work would have an important impact to the field of antennas and metamaterials. Thus I am happy to recommend for publication. I only have some minor issues as listed below: a) In the revised manuscript, the authors mentioned that some metasurface cloak schemes have been applied to reduce antenna scattering. I'd like to suggest the authors add some brief review on metasurface cloak and transparent structures as well as some closely related references, so as to help the readers establish a more comprehensive understanding of the background of cloaking or transparent structures.