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Abstract
Achieving ultra-broadband and completely modulated absorption enhancement of monolayer graphene in near-infrared region is practically important to design graphene-based optoelectronic devices, however, which remains a challenge. In this work, by spectrally designing multiple magnetic plasmon resonance modes in metamaterials to be adjacent to each other, near-infrared light absorption in monolayer graphene is greatly improved to have an averaged absorption efficiency exceeding 50% in a very broad absorption bandwidth of about 800 nm. Moreover, by exerting an external bias voltage on graphene to change Fermi energy of graphene, the ultra-broadband absorption enhancement of monolayer graphene exhibits an excellent tunability, which has a nearly 100% modulation depth and an electrical switching property. This work is promising for applications in near-infrared photodetectors, amplitude modulators of electromagnetic waves, etc.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In very wide wavelength range covering ultraviolet, visible light, near-infrared, middle-infrared, far-infrared, and terahertz (THz), the single-pass electromagnetic wave absorption of an undoped and suspended monolayer graphene is only about 2.3%. This universal absorption value is fully determined by the fine structure constant in graphene [1,2], which does not dependent on the wavelength of incident electromagnetic waves. Such a low absorption efficiency is a huge obstacle for promising applications of two-dimensional graphene materials in optoelectronic nanodevices [3–5]. To remove the huge obstacle, a variety of physical mechanisms have been proposed to largely improve the absorption efficiency of graphene in recent years [6–38]. The common property of different physical mechanisms is greatly enhancing the electromagnetic near fields on the surface of graphene to absorb more incident photon by electron transitions between energy bands [6].
In addition to high absorption efficiency, controlling the absorption bandwidth of graphene for achieving a broadband absorption enhancement is practically important in many fields [39–42], such as photocatalysts, photovoltage, photodetectors, and so on [3–5]. Therefore, more and more efforts are made recently to broaden the absorption bandwidth of graphene as possible, and at the same time maintain relatively high absorption efficiency, through various design schemes projected in different frequency ranges [43–58]. Generally speaking, multiple-resonator approach is a very effective design scheme for expanding the absorption bandwidth of graphene [43–45]. In multiple-resonator approach, a geometric structural unit is able to support multiple resonance modes, whose excitation frequencies are carefully tuned to have a part spectral overlap between each other, by properly changing the physical dimensions of multiple resonators arranged into the same structural unit [43–45]. Besides high absorption efficiency and wide absorption bandwidth, dynamical modulation of the absorption in graphene by bias voltage is also a research highlight at present [59–65]. One great advantage of the kind of active modulation is fully utilizing external stimuli to change the absorption of graphene, which does not need reconstructing designed structures, thanks to the electrical tunability of the surface conductivity of graphene.
Up to now, achieving ultra-broadband and completely modulated absorption enhancement of monolayer graphene in near-infrared region remains a challenge, however, which is practically important to design graphene-based optoelectronic devices. In this work, we numerically demonstrate an ultra-broadband near-infrared absorption enhancement of monolayer graphene, by spectrally designing multiple independent magnetic plasmon resonance modes excited in metamaterials. The excitation wavelengths of magnetic plasmon resonance modes are carefully designed to be adjacent to each other, so the near-infrared light absorption in monolayer graphene is greatly improved to have an averaged absorption efficiency exceeding 50% in a very broad absorption bandwidth of about 800 nm. More importantly, the absorption of monolayer graphene exhibits an excellent tunability, which has a nearly 100% modulation depth and an electrical switching property, by exerting an external bias voltage on graphene to change Fermi energy of graphene. This work should be helpful for some graphene-based optoelectronic devices, for examples, near-infrared photodetectors, amplitude modulators of electromagnetic waves, etc.
2. Method
The building blocks of designed metamaterials are illustrated in Fig. 1, which are composed of four silver nanocrosses, monolayer graphene, silica spacer, and silver substrate. The silver nanocrosses have the same width (w) and height (h), but they have different lengths (l1 > l2> l3> l4). The thickness of silica spacer is t, and the thickness of monolayer graphene is tg = 0.34 nm. The silver nanocrosses are arranged into a periodic array with periods of px and py in the x and y axis directions, respectively. The near-infrared light is normally incident on the designed metamaterials, and its polarization is along the x axis direction, as shown by three black arrows located in the left upper corner. Ein, Hin, and Kin represent the electric field, magnetic field, and wave vector of incident light, respectively. In this work, the commercial software package “EastFDTD” is employed to investigate the absorption property of monolayer graphene and to numerically simulate electromagnetic field distributions. For detailed instruction for this soft use, please visit the website of https://www.eastfdtd.com. In numerical simulation, the relative permittivity of silica is taken to be a constant of 2.1 in the near-infrared wavelength range from 1000 nm to 2000 nm. The specific values of the relative permittivity of silver for different wavelengths are taken from experimental data [66]. The surface conductivity of graphene is obtained from random-phase approximation, which depends on light frequency, Fermi energy Ef, carrier relaxation time τ, and temperature T [67–69].
Fig. 1. Schematic diagram of designed metamaterials for ultra-broadband and nearly 100% modulated near-infrared light absorption enhancement of monolayer graphene.
3. Results and discussion
We have calculated the near-infrared light absorption spectra of monolayer graphene at normal incidence for different lengths of silver nanocrosses. As shown by the black line at the bottom of Fig. 2(a), when the lengths (l1, l2, l3, l4) (400, 350, 300, 250 nm), four obvious absorption peaks are observed, whose maxima are 0.73, 0.76, 0.65, and 0.77, from right to left. In the next paragraph, we will demonstrate that the absorption peaks origin from four independent magnetic plasmon resonance modes. Because these four peaks are adjacent to each other, we can obtain an ultra-broadband light absorption enhancement of monolayer graphene. In the wavelength range from 1150 nm to 1950 nm, the minimum absorption value is 0.22 and the averaged absorption value exceeds 0.5. The ultra-broadband absorption enhancement is desired for graphene-based infrared detection. When the lengths of silver nanocrosses synchronously decrease in small steps of 10 nm, the absorption peaks red-shift gradually, because the excitation wavelengths of magnetic plasmon resonance modes become longer. In Figs. 2(b) and 2(c), we present the corresponding absorption spectra of silver and whole structure, respectively. Compared with graphene, the silver materials absorb relatively fewer incident light, whose absorption value is less than 0.25 at four peaks in all cases of different lengths. Very interestingly, the peak absorption of whole structure can reach up nearly 100%, that is, the well-known perfect absorption of electromagnetic waves [70–73]. In this work, we mainly focus on how to enhance light absorption in graphene, because the absorption part of silver material is not useful for graphene-based optoelectronic devices.
Fig. 2. Numerically calculated normal-incidence absorption spectra of graphene (a), silver (b), and total metamaterials (c) for different lengths of silver nanocrosses. Specific parameters: px = py = 900 nm, t = 30 nm, w = 100 nm, h = 50 nm, Ef = 0.30 eV, τ = 0.50 ps, and T = 300 K. For clarity, spectral lines are vertically offset in a step of 0.25 in (b) and 1.0 in (a) and (c).
To investigate the physical mechanism of the absorption peaks, we plot the electromagnetic field intensity on the xy plane at the center of silica spacer for four resonance wavelengths of λ1, λ2, λ3 and λ4. The electromagnetic field intensity is normalized by the incident electric field Ein or magnetic field Hin. For the wavelength of λ1, two electric field “hotspots” and one magnetic field “hotspot” are clearly seen in Figs. 3(a) and 3(b), respectively. Because the incident light is polarized along the x axis direction, two electric field “hotspots” are around the left and right sides of the first silver nanocross with a length of l1, and the magnetic field “hotspot” is underneath the first silver nanocross. Such field distribution properties indicate the excitation of magnetic plasmon resonance mode in well-known metamaterials [74,75]. In essence, the magnetic plasmon resonance mode is a hybrid mode due to plasmonic interaction of silver substrate and nanocross. For the wavelengths of λ2, λ3 and λ4, as shown in Figs. 3(c)–3(h), nearly the same electromagnetic field patterns are observed, but electromagnetic field “hotspots” are distributed near the second, third, and fourth silver nanocrosses with a length of l2, l3, l4, respectively. So, the absorption peaks result from four independent magnetic plasmon resonance modes. Because of the localization property of these resonance modes, the absorption in graphene has angle tolerance, as shown in Fig. S1 in supplementary material. The red arrows in Fig. 3 indicate that the directions of magnetic fields of these resonance modes are along the y-axis, which are parallel to the magnetic field direction of incident light. So, the magnetic plasmon resonance modes can counteract the incident light, which distinguishes them from conventional plasmon resonance modes in metal nanoparticles [74,75].
Fig. 3. Normalized electric (a, c, e, g) and magnetic (b, d, f, h) field intensity on the xy plane at the center of silica spacer, for four resonance wavelengths of λ1 =1760 nm (a, b), λ2 = 1560 nm (c, d), λ3 =1370 nm (e, f), and λ4 =1185 nm (g, h). Red arrows indicate the directions of magnetic fields.
To demonstrate the electrical tunability of graphene absorption, in Fig. 4(a) we show a series of absorption spectra for Fermi energy Ef to be increased from 0.30 to 0.60 eV in steps of 0.02 eV. Such a change of Fermi energy Ef can be realized by exerting an external bias voltage on monolayer graphene [76]. With increasing Fermi energy Ef, the near-infrared light absorption of graphene drops abruptly from long-wavelength side. The wavelength position of abrupt drop corresponds to the interband transition of graphene. For wavelengths larger than the position of interband transition, the graphene absorption is modulated to almost zero, because the imaginary part of effective permittivity of graphene becomes very low [67]. Figure 4(b) shows the modulation depth of graphene absorption for several typical Fermi energies. The modulation depth is defined as (A – A0)/A0, where A0 is the reference value of graphene absorption for Fermi energy Ef = 0.30 eV, and A is the absorption value for other Fermi energies. For Fermi energy Ef = 0.38 eV, the absorption of graphene drops abruptly around the wavelength of 1640 nm (i.e. the position of interband transition of graphene). For the wavelengths larger than 1640 nm, the graphene absorption is less than 0.01. In contrast, for the wavelengths smaller than 1640 nm, the graphene absorption has no large change, especially for short wavelengths. As a result, the corresponding modulation depth increases quickly around the wavelength of 1640 nm, as clearly exhibited by the black line in Fig. 4(b). Near the wavelength of 1640 nm, the modulation depth is about 92%, and for longer wavelengths the modulation depth can exceed 99%. For Fermi energy Ef = 0.44, 0.50, and 0.60 eV, the change trend of modulation depth is very similar, but the interband transition of graphene is blue-shifted to about 1420, 1245, and 1040 nm, respectively.
Fig. 4. (a) Absorption spectra of graphene at normal incidence and (b) modulation depth for different Fermi energy Ef. For clarity, absorption spectra in (a) are offset horizontally and vertically by 10% and 70%, respectively.
The large modulation depth makes the absorption of graphene has an electrical switching property, which holds great potential for amplitude modulators of electromagnetic waves in optical communication systems [77,78]. To demonstrate the electrical switching property, in Figs. 5(a) and 5(b) we present the dependence of graphene absorption and modulation depth on Fermi energy Ef for four resonance wavelengths of λ1, λ2, λ3, and λ4. The specific values of graphene absorption and modulation depth are directly taken from the numerically calculated results for different Fermi energies. At these four resonance wavelengths, there are four absorption peaks for Fermi energy Ef = 0.30 eV. For the resonance wavelength of λ1, when Fermi energy Ef is increased from 0.30 to 0.34 eV, the absorption of graphene does not have a large change, and correspondingly the modulation depth is very small. However, for Fermi energy Ef to be increased from 0.34 to 0.36 eV, the absorption of graphene drops abruptly from about 0.72 to 0.057, and thus the modulation depth rises dramatically from about 2.9% to 92.3%. The physical mechanism is that the effective permittivity of graphene has a very low imaginary part, when the interband transition of graphene approaches the resonance wavelengths of λ1. With Fermi energy Ef further increased from 0.36 to 0.60 eV, the graphene absorption is finally modulated to be nearly zero, and so the modulation depth can reach up to 100%. For the other three resonance wavelengths of λ2, λ3, and λ4, the graphene absorption and the modulation depth exhibit similar dependence on Fermi energy Ef. The difference is that the required Fermi energy Ef gradually increases for the interband transition to approach the resonance wavelengths. As labeled in Fig. 5(a), the high absorption can be considered as state “on”, and correspondingly the low absorption is believed as state “off” [79]. The absorption of graphene is able to exhibit an electrical switching property by changing Fermi energy Ef in a very small value range.
Fig. 5. (a) Absorption of graphene and (b) modulation depth as a function of Fermi energy Ef for four resonance wavelengths of λ1 =1760 nm, λ2 =1560 nm, λ3 =1370 nm, and λ4 =1185 nm.
4. Conclusions
In this work, we obtained an ultra-broadband light absorption enhancement of monolayer graphene in near-infrared region, by the spectral design on four independent magnetic plasmon resonance modes excited in metamaterials. Because the excitation wavelengths of multiple magnetic plasmon resonance modes are carefully designed to be adjacent to each other, the near-infrared light absorption in monolayer graphene is greatly improved, with an averaged absorption efficiency exceeding 50% in a very broad absorption bandwidth of about 800 nm. By exerting an external bias voltage on graphene to change Fermi energy of graphene, the absorption of monolayer graphene exhibits an excellent tunability, which has a nearly 100% modulation depth and an electrical switching property. Our work should be useful for some graphene-based optoelectronic devices, for examples, near-infrared photodetectors, amplitude modulators of electromagnetic waves, etc.
Funding
National Natural Science Foundation of China (11704183, 11704184, 11974188, 12104402, 91963211).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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