Wood Anomalies and Surface-Wave Excitation with a Time Grating

Emanuele Galiffi, Yao-Ting Wang, Zhen Lim, J. B. Pendry, Andrea Alù, and Paloma A. Huidobro

Phys. Rev. Lett. 125, 127403 – Published 17 September 2020

Abstract

In order to confine waves beyond the diffraction limit, advances in fabrication techniques have enabled subwavelength structuring of matter, achieving near-field control of light and other types of waves. The price is often expensive fabrication needs and the irreversibility of device functionality, as well as the introduction of impurities, a major contributor to losses. In this Letter, we propose temporal inhomogeneities, such as a periodic drive in the electromagnetic properties of a surface which supports guided modes, as an alternative route for the coupling of propagating waves to evanescent modes across the light line, thus circumventing the need for subwavelength fabrication, and achieving the temporal counterpart of the classical Wood anomaly. We show analytically and numerically how this concept is valid for any material platform and at any frequency, and propose and model a realistic experiment in graphene to couple terahertz radiation to plasmons with unit efficiency, demonstrating that time modulation of material properties could be a tunable, lower-loss and fast-switchable alternative to the subwavelength structuring of matter for near-field wave control.

Received 21 April 2020
Accepted 18 August 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.127403

Physics Subject Headings (PhySH)

Acoustic metamaterials Acoustic wave phenomena Charge density waves Electrical conductivity Electromagnetism Metamaterials Near-field optics Optical & microwave phenomena Optical conductivity Photonic crystals Photonics Plasma oscillations Plasmonics Plasmons Polaritons

Atomic, Molecular & OpticalGeneral PhysicsCondensed Matter, Materials & Applied PhysicsInterdisciplinary Physics

Authors & Affiliations

Emanuele Galiffi ^1,*, Yao-Ting Wang², Zhen Lim ¹, J. B. Pendry¹, Andrea Alù^3,5, and Paloma A. Huidobro ⁴

¹The Blackett Laboratory, Imperial College London, SW7 2AZ London, United Kingdom
²Department of Mathematics, Imperial College London, SW7 2AZ London, United Kingdom
³Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, USA
⁴Instituto de Telecomunicações, Insituto Superior Técnico, University of Lisbon, Avenida Rovisco Pais 1,1049-001 Lisboa, Portugal
⁵Physics Program, Graduate Center, City University of New York, New York, NY 10016, USA

^*Corresponding author. eg612@ic.ac.uk

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Vol. 125, Iss. 12 — 18 September 2020

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Images

Figure 1
(a),(b) Conventional coupling of propagating waves to surface waves is achieved by breaking momentum conservation via a periodic perturbation $σ (x)$ in space, inducing horizontal transitions of the radiation field, from the incident wave vector $k_{i}$ to that of the surface wave $k_{s w}$ . Conversely, a periodic perturbation $σ (t)$ in time (a),(c) breaks energy (frequency) conservation, coupling a wave with incoming frequency $ω$ to a surface wave with frequency $ω_{s w}$ , thus enabling (d) far-field excitation of surface waves, without the need for in-plane structuring.
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Figure 2
(a) Dispersion relation for surface waves on a current sheet (or deeply subwavelength conducting film) with Drude dispersion [Eq. (6)]. (b) Transmittance through the current sheet under a time modulation of its Drude weight at frequency $\tilde{Ω} \approx 0.94$ , with 30% modulation amplitude ( $α = 0.15$ ) at fixed in-plane wave vector ${\tilde{k}}_{x} \approx 1.12$ (vertical red line); the loss rate $\tilde{γ} = 0.0011$ (different loss levels considered in Fig. 2 of Ref. [29]). A surface mode is excited when the frequency of the incoming waves differs from that of the surface wave by the modulation frequency $\tilde{Ω}$ . Continuous line: analytic theory (three-bands approximation). Dots: exact transfer matrix result. (c)–(e) FETD simulations of the temporal Wood anomaly predicted in (a)–(b). (c) A pulse with carrier frequency ${\tilde{ω}}_{0} \approx 1.61$ impinges on the time-modulated surface ( $α = 0.15$ ), successfully exciting a surface wave. In (d), the same pulse impinges on the surface without modulation ( $α = 0$ ), and in (e) the modulation is present ( $α = 0.15$ ), but the pulse is detuned in frequency, while having the same in-plane momentum.
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Figure 3
(a) Numerically calculated transmittance (continuous lines) and absorbance (dashed lines) spectra for a graphene sheet whose doping is modulated at an adiabatic frequency $f_{m} = Ω / 2 π \times 80 GHz ≪ f_{s p}$ , with amplitudes of 0% (blue), 10% (red), 20% (purple), and 30% (green). The baseline Fermi level $E_{F} = 1 eV$ , the electron mobility $m = 20 000 {cm}^{2} / (V \cdot s)$ and the incident in-plane wave vector $k_{x} = 15 rad \cdot {mm}^{- 1}$ ( $θ \approx 23 °$ at the resonance). The inset shows the transition in the phase plane.
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Figure 4
(a) The dynamical excitation mechanism can yield critical coupling to the desired surface mode after including a backreflector behind the graphene sheet, and coupling the surface plasmon excitation to a Fabry-Perot mode of the cavity, as demonstrated in the surface plot (b), which shows complete suppression of reflectance for an optimal value of frequency and cavity width. The inset shows the anticrossing between the cavity mode and the surface plasmon, and the three cut lines at $d = 0.40$ (dotted), 0.44 (dot-dashed), and 0.48 mm (dashed) are shown in (c).
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