A Mathematical Model Based on Electrical and Magnetic susceptibilities for an Ideal Reflective Metasurface - Without Unwanted Waves -
Subject Areas : electrical and computer engineering
Elham Moradi
1
,
Masoud Movahhedi
2
*
1 - Electrical Engineering Department, Yazd University, Yazd, Iran
2 - Yazd University
Keywords: Anomalous reflection, metasurfaces, periodic structures, reconfigurable intelligent surfaces (RISs), generalized sheet transition conditions (GSTCs).,
Abstract :
One of the most useful features of metasurfaces is controlling a plane-wave reflection. However, recent research has shown that realizations of anomalously reflecting surfaces based on simple phase-gradient metasurface designs suffer from limited efficiency, where there are always parasitic reflections to undesired directions. Using a circuit-based approach, it has been shown that a polarizer metasurface can achieve reflection without spurious diffraction. Here, such condition is derived using a medium-based—and hence, more insightful—an approach based on generalized sheet transition conditions and surface susceptibility tensors. Thus, we derive the susceptibility tensors of the metasurface in closed-form equations. Moreover, to determine the performance improvement of this metasurface compared to its common examples, the susceptibility parameters of the metasurface based on the Generalized Snell's law are also obtained. Then, full-wave simulations of two surfaces illuminated by perpendicular Gaussian waves are compared. The obtained susceptibility parameters are considered the macroscopic design of the metasurface.
[1] A. Araghi, "Reconfigurable intelligent surface (RIS) in the sub-6 GHz band: design, implementation, and real-world demonstration," IEEE Access, vol. 10, pp. 2646-2655, 2022.
[2] E. Basar, M. Di Renzo, J. De Rosny, M. Debbah, M. Alouini, and R. Zhang, "Wireless communications through reconfigurable intelligent surfaces," IEEE Access, vol. 7, pp. 116753-116773, 2019.
[3] Q. Wu, S. Zhang, B. Zheng, C. You, and R. Zhang, "Intelligent reflecting surface aided wireless communications: atutorial," IEEE Trans. Commun., vol. 69, no. 5, pp. 3313-3351, May 2021.
[4] S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, "Metasurfaces: from microwaves to visible," Phys. Rep., vol. 634, pp. 1-72, May 2016.
[5] M. Di Renzo, "Smart radio environments empowered by reconfigurable intelligent surfaces: how it works, state of research, and the road ahead," IEEE J. Sel. Areas Commun., vol. 38, no. 11, pp. 2450-2525, Nov. 2020.
[6] M. Di Renzo, F. H. Danufane, and S. Tretyakov, Communication Models for Reconfigurable Intelligent Surfaces: From Surface Electromagnetics to Wireless Networks Optimization, https://arxiv.org/abs/2110.00833, 2021.
[7] C. Huang, A. Zappone, G. C. Alexandropoulos, M. Debbah, and C. Yuen, "Reconfigurable intelligent surfaces for energy efficiency in wireless communication," IEEE Trans. Wireless Commun., vol. 18, no. 8, pp. 4157-4170, Aug. 2019.
[8] Q. Wu and R. Zhang, "Intelligent reflecting surface enhanced wireless network via joint active and passive beamforming," IEEE Trans. Wireless Commun., vol. 18, no. 11, pp. 5394-5409, Nov. 2019.
[9] N. Yu, "Light propagation with phase discontinuities: generalized laws of reflection and refraction," Science, vol. 334, no. 6054, pp. 333-337, 1 Sept. 2011.
[10] N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, "Terahertz metamaterials for linear polarization conversion and anomalous refraction," Science, vol. 340, no. 6138, pp. 1304-1307, 16 May 2013.
[11] M. I. Shalaev, et al., "High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode," Nano Lett., vol. 15, no. 9, pp. 6261-6266, 2015.
[12] S. E. Hosseininejad, et al., "Digital metasurface based on graphene: an application to beam steering in terahertz plasmonic antennas," IEEE Trans. Nanotechnol., vol. 18, pp. 734-746, 2019.
[13] R. Kargar, K. Rouhi, and A. Abdolali, "Reprogrammable multifocal THz metalens based on metal-insulator transition of VO2-assisted digital metasurface," Opt. Commun., vol. 462, Article ID: 125331, May 2020.
[14] V. S. Asadchy, et al., "Perfect control of reflection and refraction using spatially dispersive metasurfaces," Phys. Rev. B., vol. 94, Article ID: 075142, Aug. 2016.
[15] J. Huang and J. A. Encinar, Reflectarray Antennas, Wiley, 2008.
[16] F. Liu, D. H. Kwon, and S. A. Tretyakov, "Reflectarrays and metasurface reflectors as diffraction gratings," IEEE Antennas and Propagation Magazine, vol. 65, no. 3, pp. 21-32, Jun. 2023.
[17] M. Di Renzo, F. H. Danufane, and S. Tretyakov, "Communication models for reconfigurable intelligent surfaces: from surface electromagnetics to wireless networks optimization," Proc. of the IEEE, vol. 110, no. 9, pp. 1164-1209, Sept. 2021.
[18] A. Diaz-Rubio and S. Tretyakov, "Macroscopic modeling of anomalously reflecting metasurfaces: angular response and far-field scattering," IEEE Trans. Antennas Propag., vol. 69, no. 10, pp. 6560-6571, Oct. 2021.
[19] V. Degli-Esposti, E. M. Vitucci, M. Di Renzo, and S. A. Tretyakov, "Reradiation and scattering from a reconfigurable intelligent surface: a general macroscopic model," IEEE Trans. Antennas Propag., vol. 70, no. 10, pp. 8691-8701, Oct. 2022.
[20] A. Diaz-Rubio, V. Asadchy, A. Elsakka, and S. Tretyakov, "From the generalized reflection law to the realization of perfect anomalous reflectors," Science Advances, vol. 3, no. 8, Article ID: 1602714, 11 Aug. 2017.
[21] N. Estakhri and A. Alu, "Wave-front transformation with gradient metasurfaces," Physical Review X, vol. 6, no. 4, Article ID: 041008, 2016.
[22] D. H. Kwon, "Lossless scalar metasurfaces for anomalous reflection based on efficient surface field optimization," IEEE Antennas Wireless Propag. Lett., vol. 17, no. 7, pp. 1149-1152, Jul. 2018.
[23] J. Budhu and A. Grbic, "Perfectly reflecting metasurface reflectarrays: mutual coupling modeling between unique elements through homogenization," IEEE Trans. Antennas Propag., vol. 69, no. 1, pp. 122-134, Jan. 2021.
[24] X. Wang, A. Diaz-Rubio, and S. A. Tretyakov, "Independent control of multiple channels in metasurface devices," Phys. Rev. Applied, vol. 14, Article ID: 024089, Aug. 2020.
[25] D. H. Kwon, "Planar metasurface design for wide-angle refraction using interface field optimization," IEEE Antennas Wireless Propag. Lett., vol. 20, no. 4, pp. 428-432, Apr. 2021.
[26] O. Rabinovich and A. Epstein, "Analytical design of printed circuit board (PCB) metagratings for perfect anomalous reflection," IEEE Trans. Antennas Propag., vol. 66, no. 8, pp. 4086-4095, Aug. 2018.
[27] O. Rabinovich, I. Kaplon, J. Reis, and A. Epstein, "Experimental demonstration and in-depth investigation of analytically designed anomalous reflection metagratings," Phys. Rev. B, vol. 99, Article ID: 125101, Mar. 2019.
[28] O. Rabinovich and A. Epstein, "Arbitrary diffraction engineering with multilayered multielement metagratings," IEEE Trans. Antennas Propag., vol. 68, no. 3, pp. 1553-1568, Mar. 2020.
[29] C. Pfeiffer and A. Grbic, "Bianisotropic metasurfaces for optimal polarization control: analysis and synthesis," Phys. Rev. Applied, vol. 2, Article ID: 044011, Oct. 2014.
[30] M. Selvanayagam and G. Eleftheriades, "Polarization control using tensor huygens surfaces," IEEE Trans. Antennas Propag., vol. 62, no. 12, pp. 6155-6168, Dec. 2014.
[31] T. Niemi, A. Karilainen, and S. Tretyakov, "Synthesis of polarization transformers," IEEE Trans. Antennas Propag., vol. 61, no. 6, pp. 3102-3111, Jun. 2013.
[32] M. A. Salem and C. Caloz, "Manipulating light at distance by a metasurface using momentum transformation," Opt. Express, vol. 22, no. 12, pp. 14530-14534, Jun. 2014.
[33] K. Achouri, M. A. Salem, and C. Caloz, "General metasurface synthesis based on susceptibility tensors," IEEE Trans. Antennas Propag., vol. 63, no. 7, pp. 2977-2991, Jul. 2015.
[34] X. Jia, X. Dang, X. Pan, and M. Wang, "Metasurfaces design using primary elements and characteristic models: connection between SSM/SPM and circuit quantities," IEEE Trans. Antennas Propag., vol. 71, no. 3, pp. 2837-2842, Mar. 2023.
[35] G. Cai, X. Liu, T. Shen, et al., "A full-vectorial spectral element method with generalized sheet transition conditions for high-efficiency metasurface/metafilm simulation," IEEE Trans Antenn Propag, vol. 71, no. 3, pp. 2652-2660, Mar. 2023.
[36] G. Lavigne, K. Achouri, V. S. Asadchy, S. A. Tretyakov, and C. Caloz, "Susceptibility derivation and experimental demonstration of refracting metasurfaces without spurious diffraction," IEEE Trans. Antennas Propag., vol. 66, no. 3, pp. 1321-1330, Mar. 2018.
[37] S. Sun, et al., "High-efficiency broadband anomalous reflection by gradient meta-surfaces," Nano Lett., vol. 12, no. 12, pp. 6043-6506, Dec. 2012.
[38] A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, "Broadband focusing flat mirrors based on plasmonic gradient metasurfaces," Nano Lett., vol. 13, no. 2, pp. 829-834, Feb. 2013.
[39] M. Kim, A. M. H. Wong, and G. V. Eleftheriades, "Optical huygens metasurfaces with independent control M. Veysi, C. Guclu, O. Boyraz, and F. Capolino, "Thin anisotropic metasurfaces for simultaneous light focusing 2015.
[40] K. Achouri and O. J. F. Martin, "Fundamental properties and classification of polarization converting bianisotropic metasurfaces," IEEE Trans. Antennas Propag., vol. 69, no. 9, pp. 5653-5663, Sept. 2021.
[41] K. Achouri and C. Caloz, Electromagnetic Metasurfaces: Theory and Applications, Wiley-IEEE Press, 2021.
[42] K. Achouri, et al., "Synthesis of electromagnetic metasurfaces: principles and illustrations," EPJ Appl. Metamater., vol. 2, no. 12, Article ID: 2015016, Jan. 2015.