A Wideband Orbital Angular Momentum Antenna Array Design for Wireless Communication

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

the paper introduces a new design with verified measurements. the author may add the design evolution steps and how the shape is selected.

a parametric study on the effect of element dimensions on performance.

why the cavity has different height grooves, please verify.

 

Author Response

1. The paper introduces a new design with verified measurements. the author may add the design evolution steps and how the shape is selected.

 

Reply:

Thank you for your comment. As the reviewer recommended, we add the design evolution steps to the manuscript. The contents are as follows:

The mechanism of the proposed antenna is based on the operating characteristics of Pancharatnam-Berry (PB) phase i.e., the 0 to 360° rotation of a circularly polarized (CP) antenna can generate extra 0 to 360° radiation phase delay. Based on the PB phase, four CP cross-dipole antennas are used to generated 1 mode OAM beam. The rotation angles of the cross-dipole antennas are 0°, 90°, 180°, and 270°, thus the dipole can be excited with 90° phase delay. Next, to match the radiation bandwidth with the impedance matching band, the top Z-shaped radiator patch and the bottom grooves with the different heights are used to optimize the radiation patterns. Finally, the S-shaped parasitic patches are combined with the antenna feeding network, which can help further optimize the operating band of the proposed antenna.

The above contents have been added to Section 2.1.

 

 

2. A parametric study on the effect of element dimensions on performance.

 

Reply:

Thank you for your comments. As the reviewer recommended, we have added the parametric study on the effect of element dimensions. The parameters r_a and D₁ are swept to optimized the S-parameters of the cross-dipole antenna. It can be seen that the optimized value can help improve the impedance matching bandwidth of the proposed antenna unit. The results have been add to Figure 1 in the current version of the manuscript.

 

Figure. R1. Simulated S-parameters of the element with the different (a) r_a and (b) D₁.

 

3. Why the cavity has different height grooves, please verify.

 

Reply:

Thank you for your comment. As can be seen in Fig. R2, with the number of cavities increases, the impedance matching of the antenna continues to slightly improve and the gain continues to increase. This is the main reason for the introduction of different height grooves.

 

Figure. R2. Performance comparison of antennas introducing different number of cavities.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The work presents the results of an antenna array capable of generating a +1 OAM mode through a simple and effective design strategy. The paper follows a clear logical flow, and the experimental results confirm the effectiveness of the proposed design approach. Nevertheless, due to some concerns that arose during my review, I have some suggestions to further improve the quality of the paper with the following considerations:

- The literature review should be improved. You are dealing with OAM arrays, and in recent years, two emerging array technologies (Transmitarrays and Reflectarrays) have been extensively employed for OAM mode generation. It would be worthwhile to introduce them in the introduction, e.g.:

1) Rao J, Wang C, Yu H, Xu G, Ren X, Zhao L, Li Y, Huang Z. Conical conformal OAM-generating transmitarray with high transmission double C-shaped grating metasurface. Opt Express. 2024 Sep 9;32(19):34128-34140. doi: 10.1364/OE.532826.
2) Babar Hayat, Jinling Zhang, Muhammad Ishfaq, Shabeer Ahmad, Adil Khan, and Abdul Majeed, "Broadband OAM vortex beams generating through transmitarray for millimeter wave applications," Opt. Express 33, 10036-10046 (2025)
3) M. Beccaria, G. Dassano and P. Pirinoli, "Single-Layer, Multimode OAM Reflectarray Antennas," in IEEE Antennas and Wireless Propagation Letters, vol. 22, no. 5, pp. 980-984, May 2023, doi: 10.1109/LAWP.2022.3229559.
4) L. Han, Y. Zhu, Y. Xu, Y. Liu, W. Xie and B. Xiong, "Novel Folded Reflectarray and Transmitarray Antenna Generating Long Nondiffractive Bessel Beams Carrying OAM With Integrated Feed," in IEEE Transactions on Antennas and Propagation, vol. 72, no. 6, pp. 4719-4728, June 2024, doi: 10.1109/TAP.2024.3383248.

Any papers recommended in the report are for reference only. They are not mandatory. You may cite and reference other papers related to this topic.

- Figure 7 shows the mode purity calculation. How did you compute it? Please provide the formulation you used.
- Figure 9 shows a far-field cut of the radiation pattern, but which cut? In which plane? Please clarify and improve the presentation of the results in general.
- Did you perform a numerical validation before fabrication (a full-wave simulation)? If so, it would be worthwhile to compare the measurements with the simulation to identify any discrepancies.
- It would be beneficial to include a 3D plot of the radiation pattern (at least from the simulation) to visualize the behavior across the entire angular region.
- If, for example, you wanted to change the OAM radiation mode, what would happen to your layout? How would it change? Demonstrating that your design could be scalable to other OAM modes would be a valuable improvement.

Author Response

Comments to the Author

 

The work presents the results of an antenna array capable of generating a +1 OAM mode through a simple and effective design strategy. The paper follows a clear logical flow, and the experimental results confirm the effectiveness of the proposed design approach. Nevertheless, due to some concerns that arose during my review, I have some suggestions to further improve the quality of the paper with the following considerations:

 

Reply:

Thanks very much for your work and for giving us the chance to improve our manuscript.

 

1. The literature review should be improved. You are dealing with OAM arrays, and in recent years, two emerging array technologies (Transmitarrays and Reflectarrays) have been extensively employed for OAM mode generation. It would be worthwhile to introduce them in the introduction, e.g.:

 

1) Rao J, Wang C, Yu H, Xu G, Ren X, Zhao L, Li Y, Huang Z. Conical conformal OAM-generating transmitarray with high transmission double C-shaped grating metasurface. Opt Express. 2024 Sep 9;32(19):34128-34140. doi: 10.1364/OE.532826.

2) Babar Hayat, Jinling Zhang, Muhammad Ishfaq, Shabeer Ahmad, Adil Khan, and Abdul Majeed, "Broadband OAM vortex beams generating through transmitarray for millimeter wave applications," Opt. Express 33, 10036-10046 (2025)

3) M. Beccaria, G. Dassano and P. Pirinoli, "Single-Layer, Multimode OAM Reflectarray Antennas," in IEEE Antennas and Wireless Propagation Letters, vol. 22, no. 5, pp. 980-984, May 2023, doi: 10.1109/LAWP.2022.3229559.

4) L. Han, Y. Zhu, Y. Xu, Y. Liu, W. Xie and B. Xiong, "Novel Folded Reflectarray and Transmitarray Antenna Generating Long Nondiffractive Bessel Beams Carrying OAM With Integrated Feed," in IEEE Transactions on Antennas and Propagation, vol. 72, no. 6, pp. 4719-4728, June 2024, doi: 10.1109/TAP.2024.3383248.

Any papers recommended in the report are for reference only. They are not mandatory. You may cite and reference other papers related to this topic.

 

Reply:

Thank you for your comments. As the reviewer recommended, we have added the above reference to abstract.

 

2. Figure 7 shows the mode purity calculation. How did you compute it? Please provide the formulation you used.

 

Reply:

Thank you for your comment. The calculation procedure of the mode purity has been added to the manuscript. The contents are as follows:

In order to quantify the purity of the OAM beams, the Fourier transform is used to decompose the OAM beams into different OAM modes. [R1, R2]. The decomposition method is shown in eq. R1 and R2. Where A_l is the Fourier coefficient of the OAM beams with mode number l, y(j) is the discrete E-field distribution along the circumference of the OAM beam’s null location, and the E-field distribution is the maximum value along the radius direction.

                                           (R1)

                                                 (R2)

In the purity calculation, the OAM beams with mode number l = −3 to 3 are considered. The purity of the OAM mode l is defined as follows:

                                          (R3)

[R1] B. Jack, M. J. Padgett, and S. Franke-Arnold, "Angular diffraction," New J. Phys 10(10), 2008103013 (2008).

[R2] E. Yao, S. Franke-Arnold, J. Courtial, S. Barnett, and M. Padgett, "Fourier relationship between angular position and optical orbital angular momentum," Opt. Express 14, 9071-9076 (2006).

 

3. Figure 9 shows a far-field cut of the radiation pattern, but which cut? In which plane? Please clarify and improve the presentation of the results in general.

 

Reply:

Thank you for your comments. The beam is cut in xoz plane (phi = 0°), the corresponding coordinate system is marked in Figure 1. We have added the description to the manuscript and improve the other presentation of the results. We also add the 3D radiation patterns to the manuscript.

 

4. Did you perform a numerical validation before fabrication (a full-wave simulation)? If so, it would be worthwhile to compare the measurements with the simulation to identify any discrepancies.

 

Reply:

Thank you for your comments. We have performed a numerical validation before fabrication (a full-wave simulation). The comparison between simulated results and measurement results have been added to the manuscript. The modified parts have been highlighted for review.

The modified parts are as follows:

By comparing test results with the S-parameters obtained from simulation, it can be found that the simulation results indicate that the frequency ranges of the antenna with |S11| lower than -10 dB are 2.65 GHz~3.42 GHz and 3.58 GHz~5.03 GHz, while the measured results show that the antenna with |S11| lower than -10 dB are 2.58 GHz~2.77 GHz, 2.88 GHz~3.14 GHz and 3.31 GHz~5.28 GHz. The relative bandwidth is 61.58%. It shows that the employed ring step metal reflective back cavity as well as parasitic radiation patches are effective. The error between simulation and measurement is due to the material of the simulation model is more ideal while the actual medium substrate used is not uniformly filled and there is a certain offset at the welding place, the error does not affect the relative bandwidth, and the simulation and measurement curves coincide with each other in the trend, especially in the resonance at 3 GHz.

 

5. It would be beneficial to include a 3D plot of the radiation pattern (at least from the simulation) to visualize the behavior across the entire angular region.

 

Reply:

Thank you for your comments, the reviewer is totally right. The 3D plot of the radiation patterns have been added to the manuscript, as shown in Figure R3 (Figure 9 in the manuscript).

 

Figure. R3. 3D radiation pattern of the antenna at (a) 3.0 GHz; (b) 4.5 GHz; (c) 6.0 GHz.

 

6. If, for example, you wanted to change the OAM radiation mode, what would happen to your layout? How would it change? Demonstrating that your design could be scalable to other OAM modes would be a valuable improvement.

 

Reply:

Thank you for your comments. The OAM radiation mode of the proposed antenna depends on the rotation angle of each circularly polarized dipole unit. Since the radiation phase of the circularly polarized dipole can be tuned by its rotation angle [R3], the OAM radiation mode can be flexible changed to other OAM modes.

[R3] Guoqiang Li; Hongyu Shi; Bolin Li; Jianjia Yi; Anxue Zhang; Haiwen Liu. Arbitrary polarization angle and wavefront manipulation of linearly polarized waves using PB phase. J. Phys. D: Appl. Phys. 2022, VOL:55, 335105.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

In this paper, a wideband OAM antenna array is proposed, which shows a relative wide bandwidth and high radiation efficiency. The technology of the metal back cavity array is somehow novel, but there are several technical issues need to be improved.

1) The authors mentioned that the CDAA realizes the broadband OAM radiation characteristics by rotating the elements of the array, the feed network only meets the requirement of equal amplitude and phase. In this situation, how much phase difference is created between different array elements?

2) In figure1, the exact location of the coordinate origin should be added to make it easier for the reader to understand the distribution of four circular holes.

3) The distance D should be marked in figure3, which will be easier for the reader to understand that it is the distance between the S-shaped parasitic radiating patches on both sides of the bottom main feed network and the main feed network.

4) The font size in Figure 7 is not uniform enough with the other images.

5) Figure 9 shows the far-field orientation of this antenna at 3 GHz, what is the phi component of this 2D plane?

6) While the measured results show that the antenna with |S11| lower than -10 dB are 2.58 GHz~2.77 GHz, 2.88 GHz~3.14 GHz and 3.31 GHz~5.28 GHz. In this sentence, |S11| should be modify to |S₁₁|.

7) In the conclusion part, the author states that the bandwidth of the proposed antenna can cover the S-C band. But the simulation results indicate that the frequency ranges of the antenna with |S₁₁| lower than -10 dB are 2.65 GHz~3.42 GHz and 3.58 GHz~5.03 GHz. This band range lies in the S- and C-bands, but does not cover the S- and C-bands. I think the statement here should be modified.

8) More reference papers can be added and compared in Table 1.

Comments on the Quality of English Language

The text contains some grammatical inconsistencies that slightly affect readability. For instance, “It can detect the motion characteristics of the target itself through the helical wavefront structure for further analysis of the target’s intention” (Page 2, Line 57) feels a bit complex and unclear. I suggest refining similar cases to enhance grammatical flow and clarity.

Author Response

Comments to the Author

In this paper, the authors proposed a wideband OAM antenna array. However, I have some comments on it.

 

1 The CDAA realizes the broadband OAM radiation characteristics by rotating the elements of the array, the feed network only meets the requirement of equal amplitude and phase. In this situation, how much phase difference is created between different array elements?

 

Reply:

Thank you for your comments.The OAM radiation mode of the proposed antenna depends on the rotation angle of each circularly polarized dipole unit. Since the radiation phase of the circularly polarized dipole can be tuned by its rotation angle [R3], the OAM radiation mode can be flexible changed to other OAM modes.

 

[R3] Guoqiang Li; Hongyu Shi; Bolin Li; Jianjia Yi; Anxue Zhang; Haiwen Liu. Arbitrary polarization angle and wavefront manipulation of linearly polarized waves using PB phase. J. Phys. D: Appl. Phys. 2022, VOL:55, 335105.

2. The dimensions of substrate are 140×140×1.6 mm, not 140×140×1.6 mm³.

 

Reply:

Thank you for your comments, the reviewer is totally correct. Corresponding parts of the article have been changed and the modified parts have been highlighted.

 

3.In figure1, the exact location of the coordinate origin should be added to make it easier for the reader to understand the distribution of four circular holes.

 

Reply:

Thank you for your comments, the reviewer is totally correct. The exact location of the coordinate origin has been added to figure1, as shown in Figure R4. The modified parts have been highlighted for review.

 

Figure R4. Schematic diagram of the broadband cross-dipoles radiator model: (a) top view; (b) bot-tom view; (c) main view. r_a = 15.51 mm, w₁ = 2.69 mm, l₁ = 34.07 mm, l₂ = 14.70 mm, l₃ = 70 mm, D₁ = 1.2 mm.

 

4. The distance D should be marked in figure3, which will be easier for the reader to understand that it is the distance between the S-shaped parasitic radiating patches on both sides of the bottom main feed network and the main feed network.

 

Reply:

Thank you for your comments, the reviewer is totally correct. The distance D has been marked in figure3, as shown in figure R5. The modified parts have been highlighted for review.

 

Figure. R5. Schematic diagram of the underlying feeder network structure.

 

5. The font size in Figure 7 is not uniform enough with the other images.

 

Reply:

Thank you for your comments, we have revised the font size in Figure 7, as shown in Figure R7.

 

Figure. R7. Purity of the measured near field.

 

6 Figure 9 shows the far-field orientation of this antenna at 3 GHz, what is the phi component of this 2D plane?

 

Reply:

Thank you for your comments. The phi component of this 2D plane is phi=0.

 

7 while the measured results show that the antenna with |S11| lower than -10 dB are 2.58 GHz~2.77 GHz, 2.88 GHz~3.14 GHz and 3.31 GHz~5.28 GHz. In this sentence, |S11| should be modify to |S₁₁|.

 

Reply:

Thank you for your comments, the reviewer is totally correct. The corresponding part of the original text has been modified. The modified parts have been highlighted for review.

The modified contents are as follows:

By comparing test results with the S-parameters obtained from simulation, it can be found that the simulation results indicate that the frequency ranges of the antenna with |S₁₁| lower than -10 dB are 2.65 GHz~3.42 GHz and 3.58 GHz~5.03 GHz, while the measured results show that the antenna with |S₁₁| lower than -10 dB are 2.58 GHz~2.77 GHz, 2.88 GHz~3.14 GHz and 3.31 GHz~5.28 GHz.

 

8 In the conclusion part, the author states that the designed antenna’s bandwidth can cover the S-C band. But the simulation results indicate that the frequency ranges of the antenna with |S₁₁| lower than -10 dB are 2.65 GHz~3.42 GHz and 3.58 GHz~5.03 GHz. This band range lies in the S- and C-bands, but does not cover the S- and C-bands. I think the statement here should be modified.

 

Reply:

Thank you for your comments, the reviewer is totally correct. The corresponding part of the original text has been modified. The modified parts have been highlighted for review.

The modified contents are as follows:

This paper investigates the wireless OAM antenna that can be applied for S and C bands, the antenna has broadband and high gain characteristics, its bandwidth lies in the S-C band, the far-field and near-field performance is better, and adopts the metal back cavity as the support structure, so that the overall structural stability is higher.

 

9 The text contains some grammatical inconsistencies that slightly affect readability. For instance, “It can detect the motion characteristics of the target itself through the helical wavefront structure for further analysis of the target’s intention” (Page 2, Line 57) feels a bit complex and unclear. I suggest refining similar cases to enhance grammatical flow and clarity.

 

Reply:

Thank you for your comments, the reviewer is totally correct. The corresponding part of the original text has been modified. The modified parts have been highlighted for review.

The modified contents are as follows:

Unlike a common planar wave antenna, this antenna can generate a spiral wavefront structure to detect the motion characteristics of the target itself. This can be used to further analyze the target's intent.

 

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

This paper proposes an antenna for wireless communications. There are several issues in the paper which are listed below:
1) What's the inspiration of the cross-dipole rotating array, the reflecting back cavity and the feeding network? Is there a reference to design?
2) The only parametric analysis is conducted for the power divider. How all the other parameters of the device are determined? Is there an optimization process?
3) The results in Fig.4 are somewhat weird. It seems that from D=3.13mm and over, the results are identical. Is this correct? Moreover, why not to check distances below 2.13mm if this value is optimal? Maybe a better result lies for smaller gap.
4) Again for Fig.4, the reflection is not very indicative concerning the operation of the divider. Maybe, the power at the output ports is more impoertant to prove that it is equally divided.
5) How is Fig.7 extracted? What is the mode purity and is it calculated?
6) The comparison between measurement and simulation has many issues. There is an explanation in the manuscript, but the fact is that the resonances are completely different. Better simulation models are required and maybe more prototypes to evaluate a mean value.
7) The comparison is conducted with antennas of the literature that are not recent (2 at 2014 and 1 at 2020). However, in introduction it is mentioned that OAM antennas have received a lot of attention in recent years. Consequently, the comparison must be conducted with additional and more recent devices of the literature.
8) The proposed antenna has slightly better bandwidth and gain characteristics compared to the ones in Table 1, but the problem is its larger dimensions. This is a severe trade-off. What are the possible specific applications that the dimensions are not a problem? A proper reference is required.

Comments on the Quality of English Language

The English could be improved to more clearly express the research.

Author Response

Comments to the Author

This paper proposes an antenna for wireless communications. There are several issues in the paper which are listed below:

 

Reply:

Thanks very much for your work and for giving us the chance to improve our manuscript.

 

1 What's the inspiration of the cross-dipole rotating array, the reflecting back cavity and the feeding network? Is there a reference to design?

 

Reply:

Thank you for your comments. The cross-dipole rotating array, the reflecting back cavity and the feeding network are inspired by the following references, which have been added to the manuscript.

 

[R4] Yejun He; Wei He; Hang Wong. A wideband circularly polarized cross-dipole antenna. IEEE Antennas Wireless Propag. Lett. 2014, VOL.13, 67-70.

[R5] Wanjun Yang; Yongmei Pan; Shaoyong Zheng. A compact broadband circularly polarized crossed-dipole antenna with a very low profile. IEEE Antennas Wireless Propag. Lett. 2019, VOL.18, 2130-2134.

 

2 The only parametric analysis is conducted for the power divider. How all the other parameters of the device are determined? Is there an optimization process?

 

Reply:

Thank you for your comments. The other parameters of the power divider are chiefly determined by calculation from the substrate's thickness and dielectric constant, according to the formula for the characteristic impedance of a microstrip line. The optimization is mainly performed with the goal that the amplitude and phase of the four output ports are essentially the same

 

3 The results in Fig.4 are somewhat weird. It seems that from D=3.13mm and over, the results are identical. Is this correct? Moreover, why not to check distances below 2.13mm if this value is optimal? Maybe a better result lies for smaller gap.

 

Reply:

Thank you for your comments. It is true that from D = 3.13mm and over, the results are almost identical. We have added the results below 2.13 mm in Figure R6 (Figure 4 in the manuscript). From Figure R6 it can be seen that D = 2.13mm is optimal, reducing the gap does not have much effect on finding the optimal value.

 

Figure. R6. Analysis of the variation of the S-parameters with different distance D.

 

4 Again for Fig.4, the reflection is not very indicative concerning the operation of the divider. Maybe, the power at the output ports is more important to prove that it is equally divided.

 

Reply:

Thank you for your comments. In order to prove that the power divider is an equal division power divider, we give the transmission coefficients from input ports to different output ports, as shown in Figure R9. From figure R9 it can be seen that the transmission coefficients are around -6.5 dB in frequency bands of interest, proving that the power is equally divided. The corresponding part has been added to the manuscript. The modified parts have been highlighted for review.

 

Figure. R9. Power distribution of the power divider.

 

The modified contents are as follows:

Figure 5 shows the power distribution of the power divider, the transmission coefficients are around -6.5 dB in frequency bands of interest, proving that the power is equally divided.

 

5 How is Fig.7 extracted? What is the mode purity and is it calculated?

Reply:

Thank you for your comment. The calculation procedure of the mode purity has been added to the manuscript. The contents are as follows:

In order to quantify the purity of the OAM beams, the Fourier transform is used to decompose the OAM beams into different OAM modes. [R6, R7]. The decomposition method is shown in eq. R1 and R2. Where A_l is the Fourier coefficient of the OAM beams with mode number l, y(j) is the discrete E-field distribution along the circumference of the OAM beam’s null location, and the E-field distribution is the maximum value along the radius direction.

                                           (R1)

                                                 (R2)

In the purity calculation, the OAM beams with mode number l = −3 to 3 are considered. The purity of the OAM mode l is defined as follows:

                                          (R3)

[R6] B. Jack; M. J. Padgett; S. Franke-Arnold. Angular diffraction. New J. Phys. 2008, VOL.10, 103013.

[R7] Eric Yao; Sonja Franke-Arnold; Johannes Courtial; Stephen Barnett; Miles Padgett. Fourier relationship between angular position and optical orbital angular momentum. Opt. Express. 2006, VOL.14, 9071-9076.

 

6 The comparison between measurement and simulation has many issues. There is an explanation in the manuscript, but the fact is that the resonances are completely different. Better simulation models are required and maybe more prototypes to evaluate a mean value.

 

Reply:

Thank you for your comment. Because of the joint simulation methods and the welding process[R8], there is an unavoidable error between the simulation results and the measured results.

 

[R8]Zhanbiao Yang; Jinzhu Zhou; Le Kang; Bei Liu; Guigeng Yang; Xiaowei Shi. A closed-loop cross-dipole antenna array for wideband OAM communication. IEEE Antennas Wireless Propag. Lett. 2020, VOL.19, 2492-2496.

 

7 The comparison is conducted with antennas of the literature that are not recent (2 at 2014 and 1 at 2020). However, in introduction it is mentioned that OAM antennas have received a lot of attention in recent years. Consequently, the comparison must be conducted with additional and more recent devices of the literature.

 

Reply:

Thank you for your comment, the reviewer is totally right. We have added additional and more recent devices of the literature to the manuscript. The added literature are as follows, which corresponds to [40][41] in the manuscript:

[R9]Xi Wang Dai; Ze Li; Hanpeng Ruan; Weiliang Yu; Leilei Liu; Guo Qing Luo. An ultralow-profile folded transmitarray antenna with both-sides beam regulate for K-band circularly polarized OAM waves. IEEE Antennas Wireless Propag. Lett. 2025, VOL.24, 142-146.

[R10] Fan Qin; Xuhui Cao; Chao Gu; Jinyang Bi; Steven Gao; Wenchi Cheng. Mode conversion of multimode OAM waves based on transmitted metasurface. IEEE Antennas Wireless Propag. Lett. 2024, VOL.23, 4373-4377.

 

8 The proposed antenna has slightly better bandwidth and gain characteristics compared to the ones in Table 1, but the problem is its larger dimensions. This is a severe trade-off. What are the possible specific applications that the dimensions are not a problem? A proper reference is required.

 

Reply:

Thank you for your comment, the reviewer is totally right. In order to pursue higher gain, electromagnetic metasurfaces are introduced into the antenna structure, which increases both the aperture and the profile thickness of whole structure, and at the same time the antenna has a narrower operating bandwidth[R11][R12]. In search of high gain, dimensions are not a problem.

 

[R11]Xi Wang Dai; Ze Li; Hanpeng Ruan; Weiliang Yu; Leilei Liu; Guo Qing Luo. An ultralow-profile folded transmitarray antenna with both-sides beam regulate for K-band circularly polarized OAM waves. IEEE Antennas Wireless Propag. Lett. 2025, VOL.24, 142-146.

[R12] Fan Qin; Xuhui Cao; Chao Gu; Jinyang Bi; Steven Gao; Wenchi Cheng. Mode conversion of multimode OAM waves based on transmitted metasurface. IEEE Antennas Wireless Propag. Lett. 2024, VOL.23, 4373-4377.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have adequately addressed all my comments. I recommend the acceptance of the manuscript.

Author Response

Thanks very much for your work and for giving us the chance to improve our manuscript.

Reviewer 4 Report

Comments and Suggestions for Authors

The authors conducted some changes, but they are not satisfactory.

1) What's the reasoning for using half disks as cross-dipole antennas? What's the benefit compared to other designs (e.g. [34], [35])?

2) What optimization process is used to determine the dimensions of the device? A specific algorithm is used?

3) The discrepancy between the experimental and simulation results is not explained.

4) With a simple search, there are much more antennas that the comparison can be handled.
[R.1] Liu, Q., Chen, Z. N., Liu, Y., Li, F., Chen, Y., & Mo, Z. (2018). Circular polarization and mode reconfigurable wideband orbital angular momentum patch array antenna. IEEE Transactions on Antennas and Propagation, 66(4), 1796-1804.
[R.2] Liu, W., Deng, L., Chen, L., Zhang, C., & Li, S. (2024). A Broadband High-Gain Low-Profile Folded Transmitarray Antenna for OAM Generation. IEEE Antennas and Wireless Propagation Letters.
[R.3] Naseri, H., PourMohammadi, P., Melouki, N., Iqbal, A., & Denidni, T. A. (2022). A low-profile antenna system for generating reconfigurable OAM-carrying beams. IEEE Antennas and Wireless Propagation Letters, 22(2), 402-406.

5) Most importantly, the analysis of the gap distance D has a serious issue. In Fig. 4, it seems that the optimal value is at 2.13mm and all the other values has almost identical results, as the authors mention. But this figure is the same with the previous version, where different values for D where used. It seems that the authors only changed the labels and curve types. This is the most serious issue concerning the reliability of the results.

Author Response

1 What's the reasoning for using half disks as cross-dipole antennas? What's the benefit compared to other designs (e.g. [34], [35])?

Reply:

Thank you for your comments. We have to acknowledged that the use of half-disk, rectangular, or rhombic crossed dipoles does not cause drastic changes in the performance of the proposed antenna. However, we would like to emphasize that the innovation of this article mainly lies in the use of circularly polarized dipoles to realize OAM beams through PB phase, rather than the design of the dipoles themselves.

2 What optimization process is used to determine the dimensions of the device? A specific algorithm is used?

Reply:

Thank you for your comments and we apologize. The antenna design procedure and optimization process are as follows:

The mechanism of the proposed antenna is based on the operating characteristics of Pancharatnam-Berry (PB) phase i.e., the 0 to 360° rotation of a circularly polarized (CP) antenna can generate extra 0 to 360° radiation phase delay. Based on the PB phase, four CP cross-dipole antennas are used to generated 1 mode OAM beam. The rotation angles of the cross-dipole antennas are 0°, 90°, 180°, and 270°, thus the dipole can be excited with 90° phase delay. Next, to match the radiation bandwidth with the impedance matching band, the top Z-shaped radiator patch and the bottom grooves with the different heights are used to optimize the radiation patterns. Finally, the S-shaped parasitic patches are combined with the antenna feeding network, which can help further optimize the operating band of the proposed antenna. Genetic algorithm (GA) in the commercial full-wave simulation software HFSS is used as the algorithm of the optimization process.

3 The discrepancy between the experimental and simulation results is not explained.

Reply:

Thank you for your comments. The discrepancy between the simulated and measured refection coefficient is introduced by the four coaxial cables which are used to connected the dipoles and the feeding network. During the fabrication procedure, it is difficult to achieve coaxial cables with four segments of exactly equal length, due to manual manufacturing errors. The different length of the coaxial cables will generate the reflection fields with different phase delay, thus resulting in the slight offset in the reflection coefficients. The above discussion has been added to the manuscript.

4 With a simple search, there are much more antennas that the comparison can be handled.

[R.1] Liu, Q., Chen, Z. N., Liu, Y., Li, F., Chen, Y., & Mo, Z. (2018). Circular polarization and mode reconfigurable wideband orbital angular momentum patch array antenna. IEEE Transactions on Antennas and Propagation, 66(4), 1796-1804.

[R.2] Liu, W., Deng, L., Chen, L., Zhang, C., & Li, S. (2024). A Broadband High-Gain Low-Profile Folded Transmitarray Antenna for OAM Generation. IEEE Antennas and Wireless Propagation Letters.

[R.3] Naseri, H., PourMohammadi, P., Melouki, N., Iqbal, A., & Denidni, T. A. (2022). A low-profile antenna system for generating reconfigurable OAM-carrying beams. IEEE Antennas and Wireless Propagation Letters, 22(2), 402-406.

Reply:

Thank you for your comments. As the reviewer recommended, we have added the above reference to Table 1. The added reference corresponds to [42][43][44] in the manuscript.

5 Most importantly, the analysis of the gap distance D has a serious issue. In Fig. 4, it seems that the optimal value is at 2.13mm and all the other values has almost identical results, as the authors mention. But this figure is the same with the previous version, where different values for D where used. It seems that the authors only changed the labels and curve types. This is the most serious issue concerning the reliability of the results.

Reply:

Thank you for your comments and we apologize for our incorrect operation. We have re-simulated the parameter scan for distance D. The corresponding part of the original image has been modified, as shown in Fig.R1 (Fig.4 in the manuscript).

 

Author Response File: Author Response.pdf

Round 3

Reviewer 4 Report

Comments and Suggestions for Authors

As mentioned in the previous round, the reliability of the results is in a question. In particular, the curve for D=2.13mm in Fig.4 shall be the same with S11 in Fig.5. However, there are many obvious discrepancies.

Author Response

1 As mentioned in the previous round, the reliability of the results is in a question. In particular, the curve for D=2.13mm in Fig.4 shall be the same with S11 in Fig.5. However, there are many obvious discrepancies.

 

Reply:

Thanks very much for your work and for giving us the chance to improve our manuscript. We apologize for the unclear description. In Figures 4 and 5, the objects pointed to by the S-parameters are different. Figure 4 is used to illustrate the S-parameters of the entire antenna, which includes the power divider and the four dipole elements. In contrast, Figure 5 is only used to describe the S-parameters of the power divider. Figure 4 aims to demonstrate that these S-shaped patches can help optimize the reflection coefficient of the proposed antenna. To correct this issue, we have revised the names of Figures 4 and 5 to “reflection coefficient of the proposed antenna with different distance D” and “simulated S-parameters of the power divider”, respectively. We have also revised the descriptions of Figures 4 and 5 in the main text to prevent such misunderstandings.

Author Response File: Author Response.pdf

Round 4

Reviewer 4 Report

Comments and Suggestions for Authors

The clarification of the authors is ok. However, it is more convenient for Fig.4 to check parametrically (for distance D) the S11 coefficient for the power divider since this section is dedicated to the power divider. Normally, the same distance D should give the optimal results. Then, the S11 for the entire antenna shall be given in a new figure.

Author Response

1 The clarification of the authors is ok. However, it is more convenient for Fig.4 to check parametrically (for distance D) the S11 coefficient for the power divider since this section is dedicated to the power divider. Normally, the same distance D should give the optimal results. Then, the S11 for the entire antenna shall be given in a new figure.

Reply:

Thank you for your comments and affirmation. As the review recommended, we have added the S₁₁ coefficient of the power divider with varied spacing D to the manuscript. The modified figure is shown in Figure R1 (Figure 4 in the manuscript).

The optimum spacing between the parasitic radiation patch and the main feed network, derived from Figure R1, is 2.13 mm. With this spacing, the power divider can achieve the optimized impedance matching over a wide range of frequencies. The |S₁₁| for the entire antenna with D = 2.13 mm is given in Figure 5 in the manuscript. The modified figure is shown in Figure R2 (Figure 5 in the manuscript).

Author Response File: Author Response.pdf