# Nonreciprocal Wavefront Manipulation in Synthetically Moving Metagratings

^{1}

^{2}

^{*}

## Abstract

**:**

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Holloway, C.L.; Kuester, E.F.; Gordon, J.A.; O’Hara, J.; Booth, J.; Smith, D.R. An Overview of the Theory and Applications of Metasurfaces: The Two-Dimensional Equivalents of Metamaterials. IEEE Antennas Propag. Mag.
**2012**, 54, 10. [Google Scholar] [CrossRef] - Zhao, Y.; Liu, X.X.; Alù, A. Recent Advances on Optical Metasurfaces. J. Opt.
**2014**, 16, 123001. [Google Scholar] [CrossRef] - Yu, N.; Capasso, F. Flat Optics with Designer Metasurfaces. Nat. Mater.
**2014**, 13, 139. [Google Scholar] [CrossRef] [PubMed] - Tretyakov, S.A. Metasurfaces for general transformations of electromagnetic fields. Philos. Trans. R. Soc. Lond. A
**2015**, 373, 20140362. [Google Scholar] [CrossRef] - Glybovski, S.B.; Tretyakov, S.A.; Belov, P.A.; Kivshar, Y.S.; Simovski, C.R. Metasurfaces: From Microwaves to Visible. Phys. Rep.
**2016**, 634, 1. [Google Scholar] [CrossRef] - Wu, Z.; Ra’di, Y.; Grbic, A. Tunable metasurfaces: A polarization rotator design. Phys. Rev. X
**2019**, 9, 011036. [Google Scholar] [CrossRef][Green Version] - Yu, N.; Genevet, P.; Kats, M.A.; Aieta, F.; Tetienne, J.-P.; Capasso, F.; Gaburro, Z. Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction. Science
**2011**, 334, 333–337. [Google Scholar] [CrossRef][Green Version] - Aieta, F.; Genevet, P.; Kats, M.A.; Yu, N.; Blanchard, R.; Gaburro, Z.; Capasso, F. Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces. Nano Lett.
**2012**, 12, 4932. [Google Scholar] [CrossRef] - Pfeiffer, C.; Grbic, A. Metamaterial Huygens’ Surfaces: Tailoring Wave Fronts with Reflectionless Sheets. Phys. Rev. Lett.
**2013**, 110, 197401. [Google Scholar] [CrossRef] - Selvanayagam, M.; Eleftheriades, G.V. Discontinuous electromagnetic fields using orthogonal electric and magnetic currents for wavefront manipulation. Opt. Express
**2013**, 21, 14409. [Google Scholar] [CrossRef] - Ni, X.; Wong, Z.J.; Mrejen, M.; Wang, Y.; Zhang, X. An ultrathin invisibility skin cloak for visible light. Science
**2015**, 349, 1310. [Google Scholar] [CrossRef] [PubMed] - Estakhri, N.M.; Alù, A. Wavefront Transformation with Gradient Metasurfaces. Phys. Rev. X
**2016**, 6, 041008. [Google Scholar] - Principe, M.; Consales, M.; Micco, A.; Crescitelli, A.; Castaldi, G.; Esposito, E.; la Ferrara, V.; Cutolo, A.; Galdi, V.; Cusano, A. Optical fiber meta-tips. Light Sci. Appl.
**2017**, 6, e16226. [Google Scholar] [CrossRef] [PubMed][Green Version] - Hadad, Y.; Sounas, D.L.; Alu, A. Space-time gradient metasurfaces. Phys. Rev. B
**2015**, 92, 100304. [Google Scholar] [CrossRef][Green Version] - Shaltout, A.; Kildishev, A.; Shalaev, V. Time-Varying Metasurfaces and Lorentz Non-Reciprocity. Opt. Mater. Express
**2015**, 5, 2459. [Google Scholar] [CrossRef][Green Version] - Caloz, C.; Alù, A.; Tretyakov, S.; Sounas, D.; Achouri, K.; Deck-Léger, Z.-L. Electromagnetic nonreciprocity. Phys. Rev. Appl.
**2018**, 10, 047001. [Google Scholar] [CrossRef][Green Version] - Wu, H.; Luo, Q.; Chen, H.; Han, Y.; Yu, X.; Liu, S. Magnetically controllable nonreciprocal Goos-Hänchen shift supported by a magnetic plasmonic gradient metasurface. Phys. Rev. A
**2019**, 99, 033820. [Google Scholar] [CrossRef] - Xiao, Y.; Qian, H.; Liu, Z. Nonlinear metasurface based on giant optical kerr response of gold quantum wells. ACS Photonics
**2018**, 5, 1654. [Google Scholar] [CrossRef] - Sounas, D.L.; Alù, A. Non-reciprocal photonics based on time modulation. Nat. Photonics
**2017**, 11, 774. [Google Scholar] [CrossRef] - Taravati, S.; Khan, B.A.; Gupta, S.; Achouri, K.; Caloz, C. Nonreciprocal nongyrotropic magnetless metasurface. IEEE Trans. Antennas Propag.
**2017**, 65, 3589. [Google Scholar] [CrossRef][Green Version] - Ptitcyn, G.; Mirmoosa, M.S.; Tretyakov, S.A. Time-modulated meta-atoms. Phys. Rev. Res.
**2019**, 1, 023014. [Google Scholar] [CrossRef][Green Version] - Shi, Y.; Fan, S. Dynamic Non-Reciprocal Meta-Surfaces with Arbitrary Phase Reconfigurability Based on Photonic Transition in Meta-Atoms. Appl. Phys. Lett.
**2016**, 108, 021110. [Google Scholar] [CrossRef] - Shi, Y.; Han, S.; Fan, S. Optical Circulation and Isolation Based on Indirect Photonic Transitions of Guided Resonance Modes. ACS Photonics
**2017**, 4, 1639. [Google Scholar] [CrossRef] - Zang, J.W.; Correas-Serrano, D.; Do, J.T.S.; Liu, X.; Alvarez-Melcon, A.; Gomez-Diaz, J.S. Nonreciprocal wavefront engineering with time-modulated gradient metasurfaces. Phys. Rev. Appl.
**2019**, 11, 054054. [Google Scholar] [CrossRef][Green Version] - Minkowski, H. Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern,”. Nachr. Ges. Wiss. Göttingen Math.-Phys. Kl.
**1908**, 1908, 53. [Google Scholar] - Tai, C.T. A study of electrodynamics of moving media. Proc. IEEE
**1964**, 52, 685. [Google Scholar] [CrossRef] - Tretyakov, S.A. Nonreciprocal composite with the material relations of the transparent absorbing boundary. Microw. Opt. Technol. Lett.
**1998**, 19, 365. [Google Scholar] [CrossRef] - Tretyakov, S.A. Analytical Modeling in Applied Electromagnetics; Artech House: Norwood, MA, USA, 2003. [Google Scholar]
- Ra’di, Y.; Asadchy, V.S.; Tretyakov, S.A. Total absorption of electromagnetic waves in ultimately thin layers. IEEE Trans. Antennas Propag.
**2013**, 61, 4606–4614. [Google Scholar] [CrossRef] - Ra’di, Y.; Asadchy, V.S.; Tretyakov, S.A. One-way transparent sheets. Phys. Rev. B
**2014**, 89, 075109. [Google Scholar] [CrossRef][Green Version] - Kodera, T.; Sounas, D.L.; Caloz, C. Artificial Faraday Rotation Using a Ring Metamaterial Structure without Static Magnetic Field. Appl. Phys. Lett.
**2011**, 99, 031114. [Google Scholar] [CrossRef] - Ra’di, Y.; Grbic, A. Magnet-Free Nonreciprocal Bianisotropic Metasurfaces. Phys. Rev. B
**2016**, 94, 195432. [Google Scholar] [CrossRef][Green Version] - Asadchy, V.S.; Albooyeh, M.; Tcvetkova, S.N.; Díaz-Rubio, A.; Ra’di, Y.; Tretyakov, S.A. Perfect Control of Reflection and Refraction Using Spatially Dispersive Metasurfaces. Phys. Rev. B
**2016**, 94, 075142. [Google Scholar] [CrossRef][Green Version] - Epstein, A.; Eleftheriades, G.V. Huygens’ Metasurfaces via the Equivalence Principle: Design and Applications. JOSA B
**2016**, 33, A31–A50. [Google Scholar] [CrossRef] - Ra’di, Y.; Sounas, D.L.A.; Alù, A. Metagratings: Beyond the Limits of Graded Metasurfaces for Wave Front Control. Phys. Rev. Lett.
**2017**, 119, 067404. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**(

**a**) Schematic of a nonreciprocal metagrating (side view). Amplitudes of the reflected wave into different Floquet channels when exciting from (

**b**) Port A, (

**c**) Port B, and (

**d**) Port C. For this specific design, we assume ${\omega}_{\mathrm{ee}}={\omega}_{\mathrm{em}}={\omega}_{\mathrm{mm}}={\omega}_{0}$ and ${\delta}_{\mathrm{ee}}=2{\delta}_{\mathrm{em}}=4{\delta}_{\mathrm{mm}}=0.4{\omega}_{0}$.

**Figure 2.**Array of bianisotropic moving particles designed to circulate space waves between three Floquet channels located with 45 degree angular distance. (

**a**) Nonreciprocal metagrating. Inset shows a single inclusion composed of a loop loaded with an isolator to create one-way rotating magnetic dipole and a wire strip providing the required electric dipole response. (

**b**) Results for isolation achieved between different Floquet channels. Geometric parameters of the design: outer radius of the loop is $3.53\mathrm{mm}$, inner radius of the loop is $2.63\mathrm{mm}$, $g=0.5\mathrm{mm}$, $b=42.43\mathrm{mm}$, $a=9\mathrm{mm}$, $h=2.3\mathrm{mm}$, $dh=2.15\mathrm{mm}$, $lx=1.75\mathrm{mm}$, $ly=12.2\mathrm{mm}$, the width of the electric dipole is $0.4\mathrm{mm}$, dielectric permittivity is $10.2$, and loop is rotated for $15$ degrees in the direction shown in the figure. The structure is simulated using infinite periodic boundary conditions. Here, for the sake of simplicity, we consider ideal lumped isolators.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ra’di, Y.; Alù, A. Nonreciprocal Wavefront Manipulation in Synthetically Moving Metagratings. *Photonics* **2020**, *7*, 28.
https://doi.org/10.3390/photonics7020028

**AMA Style**

Ra’di Y, Alù A. Nonreciprocal Wavefront Manipulation in Synthetically Moving Metagratings. *Photonics*. 2020; 7(2):28.
https://doi.org/10.3390/photonics7020028

**Chicago/Turabian Style**

Ra’di, Younes, and Andrea Alù. 2020. "Nonreciprocal Wavefront Manipulation in Synthetically Moving Metagratings" *Photonics* 7, no. 2: 28.
https://doi.org/10.3390/photonics7020028