- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Applied

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Diffraction Phenomena in Time-Varying Metal-Based Metasurfaces

Antonio Alex-Amor1,*, Salvador Moreno-Rodríguez2, Pablo Padilla2, Juan F. Valenzuela-Valdés2, and Carlos Molero2

  • 1Department of Information Technology, Universidad San Pablo—CEU, CEU Universities, Campus Montepríncipe, Boadilla del Monte (Madrid) 28668, Spain
  • 2Department of Signal Theory, Telematics and Communications, Universidad de Granada, Granada 18071, Spain

  • *Corresponding author. antonio.alexamor@ceu.es
PDF

Phys. Rev. Applied 19, 044014 – Published 5 April, 2023

DOI: https://doi.org/10.1103/PhysRevApplied.19.044014

Abstract

This paper presents an analytical framework for the analysis of time-varying metal-based metamaterials. Specifically, we particularize the study to time-modulated metal-air interfaces embedded between two different semi-infinite media that are illuminated by monochromatic plane waves of frequency ω0. The formulation is based on a Floquet-Bloch modal expansion, which takes into account the time periodicity of the structure (Ts=2π/ωs) and integral-equation techniques. It allows us to extract the reflection and transmission coefficients as well as to derive nontrivial features about the dynamic response and dispersion curves of time-modulated metal-based screens. In addition, the proposed formulation has an associated analytical equivalent circuit that gives a physical insight into the diffraction phenomenon. Similarities and differences between space- and time-modulated metamaterials are discussed via the proposed circuit model. Finally, some analytical results are presented to validate the present framework. Good agreement is observed with numerical computations provided by a self-implemented finite-difference time-domain (FDTD) method. Interestingly, the present results suggest that time-modulated metal-based screens can be used as pulsed sources (when ωs≪ω0), beam formers (ωs∼ω0) to redirect energy in specific regions of space, and analog samplers (ωs≫ω0).

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (56)

  1. T. Tamir, H. C. Wang, and A. A. Oliner, Wave propagation in sinusoidally stratified dielectric media, IEEE Trans. Microw. Theory Techn. 12, 323 (1964).
  2. C. Elachi, Ph.D. Thesis, Division: Engineering and Applied Science, Caltech, 1971.
  3. S. Taravati and G. V. Eleftheriades, Generalized Space-Time Periodic Diffraction Gratings: Theory and Applications, Phys. Rev. Appl. 12, 024026 (2019).
  4. A. M. Shaltout, A. Kildishev, and V. Shalaev, Time-varying metasurfaces and Lorentz on-reciprocity, Opt. Express 5, 246293 (2015).
  5. L. Zhang, Z. Q. Chen, S. Liu, Q. Zhang, J. Zhao, J. Y. Dai, G. D. Bai, X. Wan, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, Space-time coding digital metasurfaces, Nat. Commun. 9, 4334 (2018).
  6. D. M. Solís and N. Engheta, Functional analysis of the polarization response in linear-time varying media: A generalization of Kramer-Kronig relations, Phys. Rev. B 103, 144303 (2018).
  7. V. Pacheco-Peña and N. Engheta, Temporal equivalence of Brewster angles, Phys. Rev. B 104, 214308 (2021).
  8. J. Pendry, P. Huidobro, M. Silveirinha, and E. Galiffi, Crossing the light line, Nanophotonics 11, 161 (2022).
  9. C. Caloz and Z. Deck-Léger, Spacetime metamaterials—Part I: General concepts, IEEE Trans. Antennas Propag. 68, 1569 (2020).
  10. C. Caloz and Z. Deck-Léger, Spacetime metamaterials—Part II: Theory and applications, IEEE Trans. Antennas Propag. 68, 1583 (2020).
  11. V. Tiukuvaara, T. J. Smy, and S. Gupta, Floquet analysis of space-time modulated metasurfaces with Lorentz dispersion, IEEE Trans. Antennas Propag. 69, 7667 (2021).
  12. G. Ptitcyn, M. S. Mirmoosa, and S. A. Tretyakov, Time-modulated meta-atoms, Phys. Rev. Res. 1, 023014 (2019).
  13. S. Yin, E. Gaffili, and A. Alu, Floquet metamaterials, eLight 1, 1 (2022).
  14. R. Marqués, F. Martín, and M. Sorolla, Metamaterials with Negative Parameters: Theory, Design and Microwave Applications, (John Wiley & Sons, Hoboken, New Jersey, 2008).
  15. B. A. Munk, Metamaterials: Critique and Alternatives, (John Wiley & Sons, Hoboken, New Jersey, 2009).
  16. A. Alex-Amor, A Palomares-Caballero, and C. Molero, 3-D metamaterials: Trends on applied designs, computational methods and fabrication techniques, Electronics 11, 410 (2022).
  17. A. M. Shaltout, V. M. Shalaev, and M. L. Brongersma, Spaciotemporal light control with active metasurfaces, Science 364, 648 (2019).
  18. Y. Hadad, D. L. Sounas, and A. Alu, Space-time-gradient metasurfaces, Phys. Rev. B 92, 100304 (2015).
  19. Y. Hadad, J. C. Solic, and A. Alu, Breaking temporal frequencies for emission and absorption, Proc. Natl. Acad. Sci. (PNAS) 113, 3471 (2016).
  20. D. L. Sounas and A. Alu, Non-reciprocal photonics based on time modulation, Nat. Photonics 11, 774 (2017).
  21. S. Yin and A. Alu, Efficient phase conjugation in space-time leaky waveguide, ACS Photonics 9, 979 (2022).
  22. N. Chamanara, S. Taravati, Z.-L. Deck-Léger, and C. Caloz, Optical isolation based on space-time engineered asymmetric photonic band gaps, Phys. Rev. B 96, 1554092017 (2017).
  23. M. M. Salary, S. Jafar-Zangani, and A. Mosallaei, Electrically tunable harmonics in time-modulated metasurfaces for wavefront engineering, New J. Phys. 20, 123023 (2018).
  24. Y. Shi and S. Fang, Dynamic non-reciprocal meta-surfaces with arbitrary phase reconfigurability based on photonics transitions in meta-atoms, App. Phys. Lett. 108, 021110 (2016).
  25. X. Fang, M. Li, and J. Hang, Accurate direction-of-arrival estimation method based on space-time modulated metasurfaces, TechRxiv Preprint, https://doi.org/10.36227/techrxiv.17698181.v2 (2022).
  26. X. Wang and C. Caloz, Spacetime-modulated metasurface for spacial multiplexing communications, 13th International congress on artificial materials for novel wave phenomena—metamaterials 2019, Rome, Italy, 465–467 (2019).
  27. T. Itoh, Numerical Techniques for Microwave and Millimeter-Wave Passive Structures, (John Wiley & Sons, Hoboken, New Jersey, 1989).
  28. J. R. Zurita-Sánchez, P. Halevi, and J. C Cervantes-González, Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function ϵ(t), Phys. Rev. A 79, 053821 (2021).
  29. A. Sotoodehfar, M. S. Mirmoosa, and S. A. Tretyakov, Waves in Linear Time-Varying Dielectric Media, 2022 16th European Conference on Antennas and Propagation (EuCAP), Madrid, Spain, 1–5 (2022).
  30. Z. Wu, C. Scarborough, and A. Grbic, Space-Time Modulated Metasurfaces with Spatial Discretization: Free-Space N-Path Systems, Phys. Rev. Appl. 14, 064060 (2020).
  31. S. F. Bass, A. M. Palmer, K. R. Schab, K. C. Kerby-Patel, and J. E. Ruyle, Conversion matrix method of moments for time-varying electromagnetic analysis, IEEE Trans. Antennas Propag. 70, 6763 (2022).
  32. X. Wang, A. Díaz-Rubio, H. Li, S. A. Tretyakov, and A. Alu, Theory and Design of Multifunctional Space-Time Metasurfaces, Phys. Rev. Appl. 13, 044040 (2020).
  33. M. H. Mostafa, A. Díaz-Rubio, M. S. Mirmoosa, and S. A. Tretyakov, Coherently Time-Varying Metasurfaces, Phys. Rev. Appl. 17, 064048 (2022).
  34. S. Taravati and G. V. Eleftheriades, Microwave space-time-modulated metasurfaces, ACS Photonics 9, 305 (2022).
  35. Y. Vahabzadeh, N. Chamanara, and C. Caloz, Generalized sheet transition condition FDTD simulation of metasurface, IEEE Trans. Antennas Propag. 66, 271 (2018).
  36. R. Rodriguez-Berral, C. Molero, F. Medina, and F. Mesa, Analytical wideband model for strip/slit gratings loaded With dielectric slabs, IEEE Trans. Microw. Theory Tech. 60, 3908 (2012).
  37. R. Rodriguez-Berral, F. Medina, F. Mesa, and M. Garcia-Vigueras, Quasi-analytical modeling of transmission/reflection in strip/slit gratings loaded with dielectric slabs, IEEE Trans. Microw. Theory Tech. 60, 405 (2012).
  38. C. Molero, R. Rodríguez-Berral, F. Mesa, and F. Medina, Wideband analytical equivalent circuit for coupled asymmetrical nonaligned slit arrays, Phys. Rev. E 95, 023303 (2017).
  39. R. Dubrovka, J. Vazquez, C. Parini, and D. Moore, Equivalent circuit method for analysis and synthesis of frequency selective surfaces, IEE Proceedings—Microw., Antennas Propag. 153, 213 (2006).
  40. R. Rodríguez-Berral, F. Mesa, and F. Medina, Analytical multimodal network approach for 2-D arrays of planar patches/apertures embedded in a layered medium, IEEE Trans. Antennas Propag. 63, 1969 (2015).
  41. C. Molero, M. García-Vigueras, R. Rodríguez-Berral, F. Mesa, and N. Llombart, Equivalent circuit approach for practical applications of meander-line gratings, IEEE Antennas Wireless Propag. Lett. 16, 3088 (2017).
  42. A. Alex-Amor, F. Mesa, Á. Palomares-Caballero, C. Molero, and P. Padilla, Exploring the potential of the multi-modal equivalent circuit approach for stacks of 2-D aperture arrays, IEEE Trans. Antennas Propag. 69, 6453 (2021).
  43. W. Yu, L. Sisi, Y. Haiyan, and L. Jie, Progress in the functional modification of graphene/graphene oxide: A review, RSC Adv. 10, 15328 (2020).
  44. X. Li and H. Zhu, Two-dimensional MoS2: Properties, preparation, and applications, Journal of Materiomics 1, 33 (2015).
  45. A. Laturia, M. L. Van de Put, and W. G. Vandenberghe, Dielectric properties of hexagonal boron nitride and transition metal dichalcogenides: From monolayer to bulk, npj 2D Mater Appl. 2, 6 (2018).
  46. N. Salazar, C. Marquez, and F. Gamiz, Synthesis of Graphene and Other Two-Dimensional Materials, Nanophotonics, 2D Materials for Nanophotonics (Elsevier, Amsterdam, Netherlands, 2021), p. 1.
  47. N. Mishra, J. Boeckl, N. Motta, and F. Iacopi, Graphene growth on silicon carbide: A review, Phys. Status Solidi A 213, 2277 (2016).
  48. C. Molero, A. Palomares-Caballero, A. Alex-Amor, I. Parellada-Serrano, F. Gamiz, P. Padilla, and J. F. Valenzuela-Valdes, Metamaterial-based reconfigurable intelligent surface: 3D meta-atoms controlled by graphene structures, IEEE Commun. Mag. 59, 42 (2021).
  49. M. J. Allen, V. C. Tung, and R. B. Kaner, Honeycomb carbon: A review of graphene, Chem. Rev. 110, 132 (2010).
  50. S.-E. Zhu, S. Yuan, and G. C. A. M. Janssen, Optical transmittance of multilayer graphene, Europhys. Lett. 108, 17007 (2014).
  51. Q. Hu, J. Zhao, K. Chen, K. Qu, W. Yang, J. Zhao, T. Jiang, and Y. Feng, An intelligent programmable omni-metasurface, Laser Photon. Rev. 16, 2100718 (2022).
  52. C. Molero, A. Alex-Amor, F. Mesa, Á. Palomares-Caballero, and P. Padilla, Cross-polarization control in FSSs by means of an equivalent circuit approach, IEEE Access 9, 99513 (2021).
  53. M. S. Markov, Expanding use of pulsed electromagnetic field therapies, Electromagn. Biol. Med. 26, 257 (2007).
  54. A. Dolla, Pulsed and continuous-wave magnetic resonance spectroscopy using a low-cost software-defined radio, AIP. Adv. 9, 115110 (2019).
  55. K. Takaki, K. Takahashi, N. Hayashi, D. Wang, and T. Ohshima, Pulsed power applications for agriculture and food processing, Rev. Mod. Plasma Phys. 5, 12 (2021).
  56. C. Rizza, G. Castaldi, and V. Galdi, Short-Pulsed Metamaterials, Phys. Rev. Lett. 128, 257402 (2022).

Outline

Information

Phys. Rev. Applied 19, 044014– Published 5 April, 2023
  • Received 28 July 2022
  • Revised 16 December 2022
  • Accepted 23 February 2023
Crossmark - Check for updates button

© 2023 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation