Electromagnetic characterization of tuneable graphene‐strips‐on‐substrate metasurface over entire THz range: Analytical regularization and natural‐mode resonance interplay

Abstract

Scattering and absorption of the H-polarized plane wave by the infinite grating of flat graphene strips are considered in the environment met most frequently-on or at the surface of a dielectric-slab substrate. The full-wave meshless code is based on the analytical semi-inversion using the Riemann-Hilbert problem solution. This leads to a Fredholm second-kind matrix equation for the Floquet harmonic amplitudes that guarantees code convergence and provides easy control of computational error, which can be reduced to machine precision. The matrix elements are combinations of elementary functions, and therefore, the code is accurate and quite economical. This enables computation of the reflectance, transmittance, and absorbance as a function of the frequency in the wide band from static case to 10 THz. Numerical results show that such a metasurface with micrometre-sized strips is a composite periodic open resonator. It is highly frequency-selective thanks to the interplay of three types of natural modes-low-Q slab, moderate-Q plasmon strip, and ultrahigh-Q lattice-that do not exist in the absence of the substrate. Varying the chemical potential of graphene, one can manipulate the electromagnetic characteristics of the metasurface at a fixed frequency from almost total transmission to almost total reflection.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

Spoiling of tunability of on-substrate graphene strip grating due to lattice-mode-induced transparency

“… 6 , 9 , 11 and 12 (see also references therein), and used in the real-life tunable plasmonic mid-infrared biosensors 3 and THz nanoantennas. 4 Recently, we have analyzed the scattering and absorption of THz waves by such a grating, lying on a dielectric substrate, 13 using the method of analytical regularization based on the explicit solution of the Riemann–Hilbert Problem. This meshless technique has an advantage in the absence of numerical integrations needed to fill in the resulting matrix and possesses a mathematically guaranteed convergence.…”

“…Using this extremely fast and reliable numerical code, we have studied in ref. 13 the interplay, in the entire THz range of the resonances in the scattering and absorption caused by the H-polarized natural modes of three types: low-Q slab modes (SMs) of the substrate, moderate-Q plasmon modes (PMs) of the graphene strips, and ultrahigh-Q lattice modes (LMs). In this research, the EIT regimes appeared if the PM frequencies coincided with the frequencies of sharper LM resonances.…”

“… 16–19 This is because in theory they may have whatever high (albeit still finite) Q-factors; 14 in our case, this happens if the substrate gets thinner. 13 More specifically, if h → 0, then the complex LM poles of the field as a function of the frequency tend towards the purely real-valued frequencies of Rayleigh Anomalies (RAs), which are the field branch points. The other natural modes of our metasurface, namely the plasmon modes of the strips and the slab modes of the substrate, do not have such a property.…”

“…They are controlled by the grating period p and the wavelength of the lowest guided mode of the dielectric slab (see ref. 13 for details). A moderate-Q peak, which shifts to the blue for the larger chemical potentials is for the PM resonance, P 1 .…”

“…We have considered only the H-polarization case because in the E-polarization the DC-tunable plasmon modes and resonances associated to them do not exist, although both lattice modes and slab modes are present. Note that the lattice modes, in either polarization, do not exist on a graphene-strip grating in the free space; 6 however, they exist on such a grating supported by a thin substrate; 13 their Q-factors, for infinite grating, grow up unlimitedly if the substrate gets thinner, or its contrast with the host medium vanishes. 13 Taking this into account, we would like to stress that accurate assessment of such fine resonance effects is possible only with equally fine numerical techniques, more accurate than today's commercial codes.…”