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Tunable light trapping and absorption enhancement with graphene-based complementary metamaterials

Surface plasmon resonance (SPR) has been intensively investigated and widely exploited to trap the incident light and enhance absorption in the optoelectronic devices. The availability of graphene as a plasmonic material with strong half-metallicity and continuously tunable surface conductivity makes it promising to dynamically modulate the absorption enhancement with graphene-based metamaterials. Here we numerically demonstrate tunable light trapping and absorption enhancement can be realized with graphene-based complementary metamaterials. Furthermore, we also explore the polarization sensitivity in the proposed device, in which case either TM or TE plane wave at the specific wavelength can be efficiently absorbed by simply manipulating the Fermi energy of graphene. Therefore, this work can find potential applications in the next generation of photodetectors with tunable spectral and polarization selectivity in the mid-infrared and terahertz (THz) regimes.


I. INTRODUCTION
Surface plasmon resonance (SPR), the collective electronic excitation at metal/dielectric interface, provides an effective route to manipulate light-matter interaction. [1][2][3] The unprecedented ability of SPR to trap the incident light in the near field and induce the effects of electromagnetic field enhancement and light energy concentration has been intensively investigated and widely exploited to enhance light absorption in the optoelectronic devices.
In the past, a vareity of metal-based plasmonic metamaterials, such as ribbon, disk, ring, cross and other shapes have been presented to integrate with light-absorbing materials to improve their absorption performance in the infrared and terahertz (THz) regimes. 4-9 Unfortunately, the resonant responses of metal-based plasmonic metamaterials are dependent on the geometric parameters, and therefore the operating wavelength of these hybrid optoelectronic devices are unchangeable once they are fabricated, which severely hinders flexible applications requiring tunable spectral selectivity in practice.
Graphene is a promising two-dimensional (2D) material with exceptional optical and electrical properties and serves as a building block in the field of modern optoelectronics. 10,11 In the mid-infrared and THz regimes, graphene exhibits strong half-metallicity when coupling with the incident light and supports SPR for active applications. [12][13][14] Moreover, the resonant responses of graphene-based plasmonic metamaterials can be dynamically modulated by the continuously tunable surface conductivity of graphene with manipulating its Fermi energy, which are considered as serious competitors to their metal-based counterparts. [15][16][17][18][19][20] Very recently, the pioneering works have demonstrated the possibility for light trapping and absorption engineering with high efficiency and tunable spectral selectivity by integrating graphene-based plasmonic metamaterials with bulky or 2D materials. 21,22 Nevertheless, the graphene resonators in these designs exist in the isolated fashion, which may not be expediently tuned in practice. In addition, the tunable polarization selectivity in this kind of devices also remains to be further explored.
In this work, we numerically demonstrate light trapping and absorption enhancement can be realized with graphene-based complementary metamaterials. The hybrid device consists of a monolayer graphene perforated with a periodic array of nanoholes on the top of the light-absorbing material separated by an insulating spacer. The simulation results show that the excitation of SPR in the monolayer graphene can effectively trap the incident light in the near field and enhance the absorption in the nearby light-absorbing material by more than one order of magnitude. Furthermore, we explore the polarization sensitivity in the proposed device when transforming the shape of complementary resonators from circular nanohole to elliptical nanohole. With manipulating the Fermi energy of graphene, the polarization-sensitive absorption here can be dynamically modulated over a broad spectral regime, which can find potential applications in the next generation of photodetectors with tunable spectral and polarization selectivity in the mid-infrared and THz regimes. [23][24][25] II. THE GEOMETRIC STRUCTURE AND NUMERICAL MODEL In this hybrid device, the unit cell is arranged in a periodical array with a lattice constant P = 400 nm and consists of a monolayer graphene perforated with a circular nanohole on the top of the light-absorbing material separated by an insulating spacer. The radius of the circular nanohole is R = 120 nm, and the effective thickness of the monolayer graphene is set as t g = 1 nm. The thicknesses of the insulating spacer and the light-absorbing material are t i = 20 nm and t a = 100 nm, respectively, and the substrate is assumed to be semiinfinite. The insulating spacer and the substrate are treated as lossless dielectrics with a real permittivity of ε d = 1.96. The light-absorbing material is modeled using a complex permittivity of ε a = ε ′ + iε ′′ , where ε ′ = 10.9 and ε ′′ is related to the absorption coefficient α = 0.05 µm −1 accounting for losses, comparable to the typical material Hg 1−x Cd x Te ternary alloy exploited for photodetection in the mid-infrared and THz regimes. 26,27 The surface conductivity of graphene can be described with the random-phase approximation (RPA) in the local limit, including both intraband and interband processes 28-30 where e is the charge of an electron, k B is the Boltzmann constant, T is the operation temperature, is the reduced Planck's constant, ω is the angular frequency of the incident light, τ is the carrier relaxation time and E F is the Fermi energy. In the lower THz regime, the contribution originated from the interband process can be safely neglected due to the Pauli exclusion principle and the surface conductivity is reduced to a Drude-like model, 31,32 where the carrier relaxation time τ = (µE F )/(ev 2 F ) is dependent on the carrier mobility µ = 10000 cm 2 /V · s, the Fermi energy E F and the Fermi velocity v F = 10 6 m/s. 33,34 Furthermore, the anisotropic permittivity of graphene can be described in a diagonal tensor form, with isotropic dispersive components in the plane and non-dispersive component out of the plane [35][36][37] where ε 0 is the permittivity of vacuum. the resonance in the inset shows a strong enhancement of (|E z |) around the circular nanohole, which is symmetric to the y-axis. This is a characteristic behavior of the excitation of SPR in the nanohole-shaped resonator, which results from the accumulated charges around the circular nanohole due to the TM plane wave. 29 Hence, SPR effectively trap the light energy and provide sufficient time to dissipate it by the losses in the light-absorbing material.  With manipulating the Fermi energy of graphene, the tunable light trapping and ab-

IV. CONCLUSIONS
In conclusions, we numerically investigate the tunable light trapping and absorption enhancement in graphene-based complementary metamaterials. The excitation of SPR in the monolayer graphene perforated with a periodic array of nanoholes traps the incident light in the near field and leads to absorption enhancement in the light-absorbing material by more than one order of magnitude. Furthermore, polarization-sensitive absorption enhancement can be realized by transforming the shape of complementary resonators from circular nanohole to elliptical nanohole. The tunability of graphene makes it possible to dynamically modulate the absorption enhancement in the light-absorbing material over a broad spectral regime. In particular, either TM or TE plane wave at the specific wavelength can be efficiently absorbed by simply manipulating the Fermi energy of graphene, which is promising for potential applications in the mid-infrared and THz photodetection with spectral and polarization selectivity. Although SPR in the graphene-based metamaterials has mainly been observed in the mid-infrared and THz regimes, it has recently been experimentally demonstrated at much shorter wavelengths (∼ 2 µm), 38 therefore our proposed hybrid device together with its design principle can be also applied to the near-IR regime.