Mode manipulation and near-THz absorptions in binary grating-graphene layer structures
© Yuan et al.; licensee Springer. 2014
Received: 13 December 2013
Accepted: 28 January 2014
Published: 21 February 2014
The excitation and absorption properties of grating coupled graphene surface plasmons were studied. It was found that whether a mode can be excited is mainly determined by the frequency of incident light and the duty ratio of gratings. In the structure consisting graphene bilayer, a blueshift of the excitation frequency existed when the distance between neighbor graphene layer were decreased gradually. In graphene-grating multilayer structures, a strong absorption (approximately 90% at maximum) was found in near-THz range.
KeywordsGraphene surface plasmons Excitation condition Multilayer structure absorption
Recently, a lot of work has been done based on graphene due to its unique properties in electric, magnetic, thermal, etc.[1–3]. Graphene is carbon atoms arranged in a two-dimensional honeycomb lattice, in which the electrons behave like massless Dirac fermions with linear dispersion[4, 5]. Graphene has strong plasmonic effects which can be modified by gating, by doping, and so on. A controllable optical absorption was also found in structured graphene[6, 7].
Up to date, the graphene is modeled usually to be an extremely thin film with a conductivity σ, which consists of both intraband and interband from Kubo formula[7–9]. The intraband conductivity with Drude type plays a leading role when ℏω/μc was small. Both transverse electric (TE) and transverse magnetic (TM) have the dispersion relations at monolayer graphene with dielectric materials on two sides[10–12]. In other words, the charge carriers coupling to electromagnetic waves will produce a new surface wave, namely graphene surface plasmons (GSPs).
In the previous works, many numerical approaches were used to study the structured graphene, for example the finite element method (FEM), finite difference time domain (FDTD), and others[6, 15]. A strong plasmonic response of graphene has been demonstrated in a square-wave grating with a flat graphene on top. In which, the graphene-based plasmon response lead to a 45% optical absorption. In a periodic array of graphene ribbons, remarkably large GSPs result in prominent optical absorption peaks. In multilayer graphene, the absorption spectrum can be decomposed into subcomponents, which is helpful in understanding the behavior of GSP coupling.
In this paper, we studied the binary grating bounded by graphene on both sides. The rigorous coupled wave analysis (RCWA)[16, 17] was used the first time as we know to characterize the graphene-containing periodic structures. The excitation condition and excitation intensity seemed to be influenced by the grating constant, duty ratio and the distance between the graphene layers. When introducing more graphene layers into the structure periodically, a strong absorption band was found in the near-THz range.
Electromagnetic mode of binary grating-graphene
Because the imaginary part of conductivity (2) was positive, no solution of Equation 3 was found in real, which meant the TE mode GSP could not be excited.
Rigorous coupled wave analysis in graphene-containing structures
In common, the conventional RCWA based on the Floquet's theorem was unable to be used for the graphene-containing structures as the electric field will induce a current with current density J = σ E, while graphene was included.
in which n was the order, ± in subscripts represented approaching to y0 from two different directions. After the modification on the RCWA program, we can utilize it to deal with the graphene-containing structures.
Results and discussion
Phase matching condition
The resonant frequency of different orders
Order of GSP (N)
ω0 (meV) (RCWA)
ω1 (meV) (theoretical)
Duty ratio and stand wave interference
First two terms were GSP excited by one set of points (A in Figure 6) with two propagating directions (blue and green) and the last two terms were that from another set of points (B in Figure 6), where x0 is the distance of A and B in the form of light path (k0x0 = L1β1 = φ1 = (φ1 +φ2)f = 2πNf). Because in real space, different interfaces (ε1/ε1 and ε1/ε2) had different propagating constants, the expression might be complex. Here, the light path of x was used. It is found that scatting points A and B had a phase difference of π. This was caused by the different geometric symmetries. From Equation 11, when sin(k0x0/2) = 0, i.e., f = m/N ( m = 0, 1, …, N), field amplitude F would always be 0, which meant that the field cannot be excited. It was a cancelation process of two sets of standing waves that are coherent. So, for GSP mode of N, N + 1 of none absorption points appeared.
Coupling of GSPs on different graphene layers and resonant frequency shift
In Equation 12, κ(n, h, ∆θ) was the coupling coefficient and n, h, and ∆θ were order of GSP mode, thickness of grating, and phase difference of GSPs on two graphene layers, respectively. Essentially, the GSPs were surface waves so they interact with each other via evanescent interactions, and the coupling intensity decayed exponentially with h increasing. For fixed h, the lower order modes had larger skin depth (stronger coupling intensity) than the higher orders; then, the stronger coupling resulted in a large spectra shift. The phase difference of ∆θ also had affection to the absorption frequencies. However, in our case, the wavelength (15 meV ~ 82.8 μm) was much larger than the thickness of grating layer (h = 10 μm), it is reasonable to assume ∆θ is approximately 0. This can also be obtained clearly from the field distribution in Figure 4 that the electric fields on upper and lower graphene layers oscillated synchronously. This conclusion can still hold in multilayer graphene-grating structures. Finally, κ(n, h, ∆θ) ∝ e-hq(n), where.
When h was small (h < 4 μm), the larger κ(n, h, ∆θ) ∝ e -h was the larger shift of resonant frequency would be. And obviously, κ(n, h, ∆θ) was approaching 0 rapidly when h was large enough, which meant that the resonant frequency became a stable value of. Otherwise, κ(n, h, ∆θ) was also related to the order of GSP. The high order mode had a small skin deep with weak coupling intensity and less blueshift. When h tends to be 0, the grating became too thin to excite the surface mode. This was why the absorption disappeared when h = 0 in Figure 7.
Strong absorption in grating-graphene multilayers
On conclusion, the rigorous coupled wave analysis was modified to compute the excitation of graphene surface plasmon in graphene-containing binary gratings structures. Under the phase matching conditions, the excitation of the graphene surface plasmonics was determined by the distance between graphene layers and duty ratio of gratings, and the mode suppression can be realized by modifying the grating constant and duty ratio. A blueshift of the excitation frequency was obtained for enhanced coupling between GSP of neighbor graphene layers. Increasing the number of graphene layers had almost no effect on the excitation frequency of GSP but would lead to a high absorption with negligible reflection in near-THz range. Finally, the resonant frequency and absorptions can be easily modified by manipulating the structure parameter, including grating constant, duty ratio, and distance between the graphene layers and number of grating, and graphene-containing grating might become potential applications of THz region, such as optical absorption devices, optical nonlinear, optical enhancement, and so on.
This project was supported by the National Basic Research Program of China (no. 2013CB328702) and by the National Natural Science Foundation of China (no. 11374074).
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