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Finding passive, reciprocal metasurfaces for arbitrary wave transformations

K.O. Arnold*,†, C. Hooper†, J.G. Smith†, A.P. Hibbins, J.R. Sambles, and S.A.R. Horsley

N. Clow

  • DSTL, Porton Down, Salisbury SP4 0JQ, United Kingdom

  • *Contact author: koa201@exeter.ac.uk
  • †These authors contributed equally to this work.
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Phys. Rev. Applied 24, 044034 – Published 10 October, 2025

DOI: https://doi.org/10.1103/8g1m-hjbz

Abstract

We give a general design method for finding the passive, reciprocal surface impedance tensor required to enact any wave transformation. We do this through characterizing the surface in terms of a tensorial surface impedance, showing that a large family of impedance distributions can be found that perform an identical wave transformation. Even when the conditions of reciprocity and passivity are imposed, there still remain many solutions to the design problem. We exploit this as a design method for metasurfaces, giving two examples where the metasurface rotates the input polarization and reshapes the output field, showing we can parameterize the set of equivalent reciprocal metasurfaces in terms of a single complex parameter. In addition, through allowing dissipation and gain within the response, the surface can have many different functionalities in the orthogonal polarization, opening up a new route for the design of multiplexed metasurfaces.

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References (44)

  1. H. T. Chen, A. J. Taylor, and N. Yu, A review of metasurfaces: Physics and applications, Rep. Prog. Phys. 79, 076401 (2016).
  2. B. Assouar, B. Liang, Y. Wu, Y. Li, J.-C. Cheng, and Y. Jing, Acoustic metasurfaces, Nat. Rev. Mat. 3, 460 (2018).
  3. K. Achouri and C. Caloz, Electromagnetic Metasurfaces: Theory and Applications (Wiley and Sons, New Jersey, USA, 2021).
  4. S. A. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech House, London, UK, 2003).
  5. K. Wu, P. Coquet, Q. J. Wang, and P. Genevet, Modelling of free-form conformal metasurfaces, Nat. Commun. 9, 3494 (2018).
  6. N. Lebbe, A. Maurel, and K. Pham, Homogenized transition conditions for plasmonic metasurfaces, Phys. Rev. B 107, 085124 (2023).
  7. C. J. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, A discussion on the interpretation and characterization of metafilms/metasurfaces: The two-dimensional equivalent of metamaterials, Metamaterials 3, 100 (2009).
  8. D. Zaluški, A. Grbic, and S. Hrabar, Analytical and experimental characterization of metasurfaces with normal polarizability, Phys. Rev. B 93, 155156 (2016).
  9. T. B. A. Senior and J. L. Volakis, Approximate Boundary Conditions in Electromagnetics (The Institution of Electrical Engineers, London, UK, 1995).
  10. S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, Metasurfing: Addressing waves on impenetrable metasurfaces, IEEE Antennas Wirel. Propag. Lett. 10, 1499 (2011).
  11. N. Yu and F. Capasso, Flat optics with designer metasurfaces, Nat. Mater. 13, 139 (2014).
  12. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Light propagation with phase discontinuities: Generalized laws of reflection and refraction, Science 334, 333 (2011).
  13. W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun et al., High-efficiency broadband meta-hologram with polarization-controlled dual images, Nano Lett. 14, 225 (2014).
  14. Y. Wang, C. Guan, X. Ding, K. Zhang, B. Ratni, S. N. Burokur, X. Gu, and Q. Wu, Multi-focus hologram utilizing Pancharatnam–Berry phase elements based metamirror, Opt. Lett. 44, 2189 (2019).
  15. B. H. Fong, J. S. Colburn, J. J. Ottusch, J. L. Visher, and D. F. Sievenpiper, Scalar and tensor holographic artificial impedance surfaces, IEEE Trans. Antennas Propag. 58, 3212 (2010).
  16. B. A. Munk, Frequency Selective Surfaces, Theory and Design (Wiley and Sons, New Jersey, USA, 2005).
  17. C. Pfeiffer and A. Grbic, Metamaterial Huygens’ surfaces: Tailoring wave fronts with reflectionless sheets, Phys. Rev. Lett. 110, 197401 (2013).
  18. A. Epstein and G. V. Eleftheriades, Huygens’ metasurfaces via the equivalence principle: Design and applications, JOSA B 33, A31 (2016).
  19. M. Chen, M. Kim, A. M. H. Wong, and G. V. Eleftheriades, Huygens’ metasurfaces from microwaves to optics: A review, Nanophotonics 7, 1207 (2018).
  20. R. Fleury, D. L. Sounas, and A. Alú, Negative refraction and planar focusing based on parity-time symmetric metasurfaces, Phys. Rev. Lett. 113, 023903 (2014).
  21. J. Tapar, S. Kishen, and N. K. Emani, Dynamically tunable asymmetric transmission in PT-symmetric phase gradient metasurface, ACS Photonics 8, 3315 (2021).
  22. Y. Fan, H. Liang, J. Li, D. P. Tsai, and S. Zhang, Emerging trend in unconventional metasurfaces: From nonlinear, non-Hermitian to nonclassical metasurfaces, ACS Photonics 9, 2872 (2022).
  23. S. A. R. Horsley and I. R. Hooper, One dimensional electromagnetic waves on flat surfaces, J. Phys. D 47, 435103 (2014).
  24. D. J. Bisharat and D. F. Sievenpiper, Guiding waves along an infinitesimal line between impedance surfaces, Phys. Rev. Lett. 119, 106802 (2017).
  25. M. Lawrence, D. R. Barton III, and J. A. Dionee, Nonreciprocal flat optics with silicon metasurfaces, Nano Lett. 18, 1104 (2018).
  26. A. Li, Y. Li, J. Long, E. Forati, Z. Du, and D. Sievenpiper, Time-modulated nonreciprocal metasurface absorber for surface waves, Opt. Lett. 45, 1212 (2020).
  27. X. Wang, A. Díaz-Rubio, H. Li, S. A. Tretyakov, and A. Alú, Theory and design of multifunctional space-time metasurfaces, Phys. Rev. Appl. 13, 044040 (2020).
  28. G. K. Shirmanesh, R. Sokhoyan, P. C. Wu, and H. A. Atwater, Electro-optically tunable multifunctional metasurfaces, ACS Nano 14, 6912 (2020).
  29. J. R. Capers, S. J. Boyes, A. P. Hibbins, and S. A. R. Horsley, Designing disordered multi-functional metamaterials using the discrete dipole approximation, New J. Phys. 24, 113035 (2022).
  30. A. Dai, P. Fang, J. Gao, Q. Min, R. Hu, S. Qiu, X. Wu, J. Guo, and G. Situ, Multifunctional metasurfaces enabled by multifold geometric phase interference, Nano Lett. 23, 5019 (2023).
  31. Y. M. Rind, N. Mahmood, I. Javed, L. Gao, T. Tauqeer, H. Cabrera, M. Zubair, Y. Massoud, and M. Q. Mehmood, Broadband multifunctional metasurfaces enabling polarization multiplexed focused vortex array generation, Mater. Today Commun. 38, 107648 (2024).
  32. H-X. Xu, S. Tang, T. Cai, S. Sun, Q. He, and L. Zhou, Multifunctional Metasurfaces, Design Principles and Device Realisations (Springer, New York, USA, 2021).
  33. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, Cambridge, UK, 2012).
  34. D.-H. Kwon, Illusion electromagnetics for free-standing objects using passive lossless metasurfaces, Phys. Rev. B 101, 235135 (2020).
  35. H. Chen, J. Wang, H. Ma, S. Qu, Z. Xu, A. Zhang, M. Yan, and Y. Li, Ultra-wideband polarization conversion metasurfaces based on multiple plasmon resonances, J. Appl. Phys. 115, 154504 (2014).
  36. Y. Z. Cheng, W. Withayachumnankul, A. Upadhyay, D. Headland, Y. Nie, R. Z. Gong, M. Bhaskaran, S. Sriram, and D. Abbott, in 2014 39th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) (IEEE, New York, USA, 2014), pp. 1–2.
  37. M. Feng, J. Wang, H. Ma, W. Mo, H. Ye, and S. Qu, Broadband polarization rotator based on multi-order plasmon resonances and high impedance surfaces, J. Appl. Phys. 114, 074508 (2013).
  38. X. Huang, D. Yang, and H. Yang, Multiple-band reflective polarization converter using U-shaped metamaterial, J. Appl. Phys. 115, 103505 (2014).
  39. D. Yan, Q. Gao, C. Wang, C. Zhu, and N. Yuan, in 2005 Asia-Pacific Microwave Conference Proceedings (IEEE, New York, USA, 2005), Vol. 3, p. 2.
  40. W. Yang, K.-W. Tam, W.-W. Choi, W. Che, and H. T. Hui, Novel polarization rotation technique based on an artificial magnetic conductor and its application in a low-profile circular polarization antenna, IEEE Trans. Antennas Propag. 62, 6206 (2014).
  41. X.-C. Zhu, W. Hong, K. Wu, H.-J. Tang, Z.-C. Hao, J.-X. Chen, and G.-Q. Yang, A novel reflective surface with polarization rotation characteristic, IEEE Antennas Wirel. Propag. Lett. 12, 968 (2013).
  42. A. M. Patel and A. Grbic, Modeling and analysis of printed-circuit tensor impedance surfaces, IEEE Trans. Antennas Propag. 61, 211 (2013).
  43. J. G. Smith, I. R. Hooper, N. Clow, A. P. Hibbins, and S. A. R. Horsley, Method for extracting the surface impedance of a generic reflective metasurface, Sci. Rep. 14, 27141 (2024).
  44. COMSOL Multiphysics, COMSOL Multiphysics, v6.2. www.comsol.com.

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Phys. Rev. Applied 24, 044034– Published 10 October, 2025
  • Received 15 April 2025
  • Revised 20 August 2025
  • Accepted 8 September 2025
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