Abstract
In this chapter, we focus on the development on tunable terahertz/infrared metamaterials enabled with plasmonic excitations in graphene micro-/nanostructures. We aimed the issue that high loss in the plasmonic excitations of graphene limits the performance of graphene’s ability in manipulating light. We show the enhancement of light-graphene interactions by employing plasmonic metamaterial design for proper plasmonic excitations, and coherent modulation on optical fields to further increase the bonding of light field for boosted plasmonic excitations. The enhanced plasmonic excitations in graphene provide the possibility of practical applications for terahertz and infrared band graphene photonics and optoelectronics.
Keywords
- graphene
- plasmonics excitations
- tunable metamaterials
- terahertz
- infrared
- surface conductivity
1. Introduction
There have been numerous reports on scientific advances in graphene, a first realistic two-dimensional (2D) material with carbon atoms arranged in a hexagonal lattice. Since its first exfoliation from graphite by Geim and Novoselov [1, 2], graphene stimulated and led the research upsurge in two-dimensional materials [3, 4]. It is attractive for myriad applications that profits from its high electronic mobility (25,000 cm2/V-1 s-1) [5], exceptional mechanical strength (~1.0 TPa) [6], and thermal conductivity [7]. It has also been widely investigated for potential applications in photonics and optoelectronics [8–10]. Graphene exhibits much stronger binding of surface plasmon polaritons [11–16], and the Dirac fermions in graphene provide ultra wideband tunability in optical response through electrostatic field, magnetic field, or chemical doping [15–20]. All these are good for dynamical control on optical signals. However, there are still some challenges in developing graphene photonics for practical applications. One of them is that graphene is almost transparent to optical waves due to the relatively low carrier concentrations in the monolayer atomic sheet; this might be useful for some cases, for example, for the transparent electrodes, but strong light-matter interactions is the most crucial part for practical optical applications. Boosting the light-matter interaction in graphene is one important issue to address to take further advantage of graphene in optical devices or systems, for example, to realize functionality such as optical insulator similar to gapped graphene [21–23] for nanoelectronics, which is essential for myriad applications in all-optical systems and components of much miniaturized optical circuits [24–26]. It is important to take effectual strategies to improve the light-graphene interactions.
1.1. Plasmonic metamaterials
Artificially engineered microstructures, that is, the plasmonic metamaterial and photonic crystals, are well-known platforms for the enhancement of light-matter interactions [27–29]. Optical absorption enhancement in graphene had been demonstrated in a photonic crystal nanocavity for high-contrast electro-optic modulation, at the regime of critical coupling with photonic crystal-guided resonance, and in photonic crystals for broadband response [30–34]. And in the meanwhile, plasmonic metamaterials [35–42] with even miniaturized elements are promising for the manipulation of light at the deep subwavelength scale by making use of the plasmonic excitations. Especially a kind of metamaterials with a single 2D function layer, named as metasurface [43–49], has been intensively studied in recent years for various possibilities to manipulate light peculiarly. The metasurface is naturally connected to the 2D graphene for the following: (i) changing conversional plasmonic material-metal with graphene will provide frequency-agile responses and make the metasurface even more subwavelength and (ii) the light-graphene interactions can be significantly enhanced in an atomically thin graphene metasurface. Optical absorption enhancement has been studied in graphene nanodisks, in which periodic graphene disks are placed on a substrate or a dielectric layer with metallic ground, the plasmonic excitations in the structure resulting in the complete absorption of incident light. Graphene micro-/nanoribbons, split ring resonators, mantles, nano-crosses, and photonic crystals have also been exploited for controlling terahertz and infrared light.
1.2. Coherently modulated light-matter interactions
Another strategy that was proposed recently to remarkably improve the light-matter interaction is the coherent modulation technique, which is based on the coherence of optical fields. The coherence of laser made it unique in modern optics and photonics. A coherent perfect absorber (CPA), also called anti-laser, was recently proposed [50] and demonstrated [51] in a Si-resonator. The coherent absorption comes from the phase modulation on light fields. Since the first proposal, relevant coherent modulation-assisted processes have attracted considerable research interests with various photonic structures [52–58], for example, laser absorber and symmetry breaking in PT-symmetric optical potentials and strongly scattering systems, unidirectional invisibility in PT-symmetric periodic structures, and perfect mode (polarization or morphology) conversions. It has been proven that coherently modulated optical field provides additional localization of the light within artificially engineered microstructures, including both the photonic crystals and plasmonic metamaterials, to further boost light-matter interactions.
In this chapter, we summarize our recent studies on the excitation of electric/magnetic plasmonic modes in graphene structures [59, 60], and their synergic action with the coherently modulated optical fields that provide strong interaction between graphene and light for practical and tunable terahertz/infrared metamaterials or metasurfaces [61, 62].
2. Tunable plasmonic excitations in graphene metamaterials
2.1. Optical conductivity of graphene
The optical response of a monolayer graphene can be described with the complex surface conductivity in the local-random phase approximation (RPA) approximation as
with
Figure 1 shows the surface conductivity of a monolayer graphene (Fermi level: 0.1 eV) at 0 K. We can see that the total conductivity of the graphene includes two parts: (i) contribution from the intraband transition (blue), the response is similar to Drude dispersive metals; and (ii) contribution from the interband transition (green), with near nondispersive real conductivity at frequencies higher than double Fermi level. For that graphene is interesting for dynamically controlled photonic applications, we plot the surface conductivities under different Fermi levels (from 0.06 to 0.14 eV) in Figure 2; we can see from the figure that the conductivity of graphene can be s-tuned by changing the Fermi level, especially the low-frequency Drude-like response. The tunable Drude-like metallic behavior has received intensive attention in the past years, and this chapter focuses on the tunable plasmonic excitations in graphene at terahertz/infrared frequencies.
2.2. A comparative study on the plasmonic excitations in graphene split ring resonators (SRRs)
We proposed to enhance infrared extinction and absorption in a monolayer graphene sheet by patterning split ring resonators, a kind of basic structure in the design of plasmonic metamaterials. By introducing asymmetric split ring resonators (ASRRs) into the monolayer graphene sheet, we excited both fundamental magnetic mode and electric mode, and the contributions on the enhancement of infrared extinction and the absorption of these two modes are comparatively studied. The designed periodic SRR-patterned graphene metamaterial is shown in Figure 3, the rings are with width
In calculations, the graphene sheet was approximately treated as optical interface with complex surface conductivity, since a one-atom-thick graphene sheet is sufficiently thin compared with the concerned wavelength; the complex surface conductivity can be well described by a Drude model as
First, we set
We investigate the influences of geometric parameters on the optical extinction and absorption of the ASRR graphene metamaterial. Figure 5 shows resonant frequencies of the electric mode and the magnetic mode, and the extinction and absorption at resonant frequencies for graphene metamaterial with different line widths. The extinction on the resonance for both the electric mode and the magnetic mode rises as the line width becomes wider, and the extinction of the electric resonance is nearly one order higher than that of the magnetic resonance. We can see that the extinction can be efficiently boosted at the frequency of electric resonance, for example, the optical extinction of about 87% at a wavelength of
Then, we investigate the influence of symmetry (of the SRR structure) on the optical extinction and absorption. We find that the resonant frequency of the electric mode almost did not shift when changing the asymmetric parameter, and the enhanced extinction and absorption of the symmetric SRR (
2.3. Electric plasmonic excitation in graphene cut-wires and physics of a maximum 50% absorption in graphene metamaterials
We have found that the electric dipolar mode is stronger in enhancing light-graphene interactions at terahertz frequencies compared to the magnetic mode and other higher-order modes. As the simplest structure that supports electric dipolar excitation, cut-wire is essential in designing plasmonic metamaterials. It has been widely adopted for exploring fundamental physics as well as novel functionalities, such as plasmon-induced transparency, polarization manipulations, and optical antennas. We suggested a tunable metasurface by exploiting a monolayer graphene patterned in a cut-wire array. We mainly focused on the strengthening of graphene’s terahertz response by the electric dipolar excitation of the basic cut-wire structure and the influences of the graphene qualities. A 50% maximum absorption at the electric dipolar mode is confirmed by the extraction of effective surface conductivities of a cut-wire array of the theoretical and experimental graphene. Systematic investigations to the graphene metasurface by changing values of graphene sample between two sets of well-known experimental data, that is, Li et al. data [18] and Yan et al. data [10], respectively, show that optical response of the graphene cut-wire-based metasurface can be tuned substantially in terahertz frequencies.
Figure 6 shows the schematic of the proposed tunable graphene metasurface. The meta-atoms, that is, graphene cut-wires, are periodically arranged in
We first took
Actually, the 50% maximum absorption of graphene metasurface can be understood simply with a transfer matrix study on a conductive sheet: since the graphene cut-wires are of deep subwavelength, we can neglect high-order scatterings of graphene metasurface, for that the unit cells of graphene metasurface are all of deep subwavelength, then we have the absorption (
where
The retrieval method [66, 67] for the calculation of effective EM parameters from measured
with
Since the effective electric surface conductivity of the graphene metasurface shows a Lorentz response, we used a Lorentzian function to fit the conductivity for quantitative descriptions of the electric resonances
where
To further investigate the graphene metasurface with different surface conductivities, we comparatively studied the graphene metasurface by changing the values of
3. Graphene plasmonic excitations in coherently modulated optical fields
3.1. A monolayer graphene as a tunable terahertz CPA
We suggest enhancing the terahertz absorption with the technique of coherent modulation in an unstructured and nonresonant monolayer graphene. We found that the quasi-CPA frequency, at which the formation condition of CPA is fulfilled, does exist in the terahertz band for suspending graphene. The scattering of coherent beams can be perfectly suppressed with proper coherent modulation on the input beams. In our theoretical study, a layer of graphene is free standing in vacuum, and it is illuminated by two counter-propagating and coherently modulated input beams (
In the monolayer graphene system, the complex scattering coefficients (
where
In a terahertz coherent perfect absorber, the coherent modulation of the input beams performance is required to inhibit the scatterings and thus stimulate the complete absorption of coherent terahertz beams, which requires
In calculations, the graphene sheet can be considered as an optical interface described by complex surface conductivity (
where
In the work, we also found that the CPA based on a monolayer graphene is of angularly sensitivity, which is good for wide angular tunability. For oblique incidence, we should consider both
The charge-carrier density and thus the Fermi level can be easily changed through electrostatic doping, which makes graphene promising for wide-tunable and broadband optoelectronic and photonic applications. With the increase in the electrostatic doping, we get higher charge-carrier concentration and thus higher Fermi energies, and we found a blue shift of the quasi-CPA frequency. This process can be understood as follows: the Drude weight of graphene (with higher carrier concentration) becomes higher, or we can say the graphene is with reenforced metallicity, which will have more scattering, then the reflection will be increased and the transmission will be decreased, and the quasi-CPA point will show a blue shift.
3.2. Graphene metamaterial interaction with coherent-modulated optical field as a tunable infrared CPA
The discussed suspending monolayer graphene CPA is physically based on the intrinsic Drude response of graphene, which is realizable only in the few-terahertz range with achievable graphene samples. And then we exploited the possibility of coherent perfect absorption at infrared frequencies. We designed a graphene nanoribbon-based metasurface and found that quasi-CPA frequencies, which is the necessary formation condition of coherent absorption, do exist in the mid-infrared regime for properly designed graphene nanoribbon arrays. The scattering of coherent beams can be perfectly suppressed at the quasi-CPA frequencies with proper phase modulations on the input beams. For the case with two crosses on the transmission and reflection spectra, we can achieve coherent perfect absorption at the two quasi-CPA frequencies, simultaneously. The flexible tunabilities of the graphene metasurface-based CPA are of interests for tunable infrared detections and signal modulations.
Figure 10 shows the schematic of the proposed graphene nanoribbons-based metasurface and the corresponding excitation configuration with two counter-propagating and coherently modulated optical beams (
We took
Since the high-order scatterings of the deep subwavelength graphene nanoribbons are negligible, the graphene metasurface can be formalized with effective surface conductivities, then its interactions with the coherent modulated optical fields are the same as previously discussed suspending graphene case. The scatterings of the input beams are required to be inhibited to demonstrate a CPA, the necessary condition for CPA performance is
It can be seen from Figure 11(a) that there exists two frequencies (22.65 and 23.33 THz), which we call
Equation (9) gives the formation condition for CPA in an effective medium scheme. To verify this, we used a recently proposed sheet retrieval method (see Eq. (3)) to extract the effective surface conductivity
To implement the perfect absorption with the graphene metasurface, we set a chirped phase modulation
The metasurface structures together with the electrically controlled graphene will provide more wide tunable space for the design of mid-infrared CPA; we first consider the geometric tunability of the graphene nanoribbon-based CPA. Figure 13 shows the dependence of the difference (
On the other hand, the graphene metasurface is also expected to have higher resonant strength for graphene with larger Fermi level. The dependence on Fermi energy of the difference of the scattering coefficients is plotted in Figure 14 (the width of the graphene nanoribbon was set to be
4. Conclusion
In summary, this chapter summarized the recent progresses in the subfield of graphene plasmonics. Aimed to the issue in practical applications based on graphene: high loss in the plasmonic excitations of graphene limits the performance of graphene’s ability in manipulating light. We show some reported results on the enhancement of light-graphene interactions by employing the new strategies including plasmonic metamaterial design and coherent modulation on optical fields. We found that the terahertz/ infrared extinction and absorption can be enhanced in a single graphene sheet by patterning plasmonic metamaterial structures, such as SRRs and cut-wires. It is found that we can significantly control the plasmonic excitations by manipulating geometric symmetry. It is shown that the electric plasmonic mode is stronger in enhancing infrared extinction and absorption compared to the magnetic mode and higher-order modes. We prove that the condition for maximum 50% absorption is
Acknowledgments
Y. Fan would like to acknowledge Prof. C. M. Soukoulis, Prof. Q. Zhao, Dr. N.-H. Shen, and Mr. P. Zhang for collaboration and helpful discussion. This work was supported by the NSFC (Grant Nos. 11674266, 61505164 and 11372248), the Program for Scientific Activities of Selected Returned Overseas Professionals in Shaanxi Province, the Fundamental Research Funds for the Central Universities (Grant Nos. 3102015ZY079 and 3102015ZY058), and the Shaanxi Project for Young New Star in Science and Technology (Grant No. 2015KJXX-11).
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