1. Introduction

Enhanced transmission of light using nanostructured metals has always been of great interest in the field of plasmonics [1–3]. With the aid of near-field effects, the transmission of the electromagnetic waves can be enhanced or depressed. Extraordinary light transmission through single sub-wavelength apertures [4–6] or nanohole arrays [7,8] have been studied thoroughly. With similar motivations, electromagnetic transmission through a metal film [9,10] with the mediation of surface plasmons has also been proposed. Much of the work on enhanced transmission has been shown to be frequency-selective due to size-dependent optical resonance frequencies. Here, we propose and demonstrate a counter-intuitive model to increase the mid-infrared (mid-IR) transmission over a broad range of frequencies by using an absorptive, continuous graphene film, which has shown broadband properties in many applications.

Graphene, with its unique and promising electronic and photonic properties, has attracted burgeoning amount of interests since its discovery [11]. It provides a unique platform to construct fundamental and technological research on a two dimensional material with tunable properties [12,13]. Today, graphene has been utilized in the applications of transparent conductive diodes [14,15], photodetectors and phototransistors [16,17], and photovoltaic and solar cells [18,19]. Recently emerging field of graphene plasmonics [20–24] offer new methods for the near-field control of light-matter interaction [25,26], enabling new devices to fulfill complete absorption [27], light modulation [28], plasmonic antennas [29,30], and nanoresonators [31]. In particular, the optical properties of graphene can be tuned by gating or doping, making it a promising material platform for achieving active control of nanoplasmonics [32–35].

In this paper, we propose and demonstrate enhanced infrared transmission through gold nanoslit arrays at mid-IR frequency range via excitation of surface plasmon polaritons (SPPs) at the graphene/metal interface. Previously, metal-gratings with graphene has been shown to enable enhanced transmission at IR wavelengths, however a simple equivalent LC-model was used to describe the enhanced transmission effect [36]. However, our numerical calculations and FDTD simulations indicate that the surface plasmon polaritons excited at the graphene/metal grating interface is responsible for enhancing transmission over wide range of wavelengths. In this paper, we theoretically demonstrate that with the excitation of the SPPs in continuous graphene, mid-IR radiation transmitted through nanoslit arrays with narrow slit widths can be enhanced over broad range of frequencies. This type of hybrid structure offers new opportunities for the study and the control of propagating SPPs in a continuous graphene sheet.

2. Results and discussions

Metallic slit arrays or so-called wire grid structures are widely used as optical polarizers especially in the infrared spectral range. A wire grid polarizer is composed of a grid of metallic strips with the periodicity much smaller than the wavelength of the radiation. For p-polarized light, that is, when the magnetic field is parallel to the metallic strips, it can travel through the slits while s-polarized light will be reflected back. When using narrow slit width between the metallic strips, the light transmission is also quite poor for p-polarized light. Here, we propose to enhance the mid-IR transmission from the gold nanoslit arrays by coupling with graphene SPPs.

In the mid-IR wavelength range, the optical properties of doped or gated graphene will be dominated by optical intraband transitions, instead of interband transition and phonon-induced scattering. In this case, the optical response of the graphene can be modeled with a semiclassical Drude-like expression [37]:

The optical gratings are commonly used to excite surface plasmons [37,38]. Here, the gold nanoslit arrays provide an ideal frame to compensate the momentum mismatch to excite the surface plasmons in graphene. As shown in Fig. 1(a), continuous graphene is placed underneath the gold grating with silicon as the substrate, which could be fulfilled in experiment by transferring graphene film on silicon followed by patterning gold nanoslit arrays. The silicon is used as the transparent substrate in the wavelengths of interest. The p-polarized EM wave is normally incident in all the simulations. We use finite-difference time-domain (FDTD) technique to simulate the optical response of the graphene/gold nanoslit arrays which has 500 nm periodicity and 20 nm slit width. The thickness of the gold is chosen to be 50 nm and the graphene is modeled as an anisotropic material with 1 nm thickness [37]. The transmittance spectra of gold nanoslit arrays without and with graphene are plotted in Fig. 1(b). For the gold nanoslit array case, the transmittance of the radiation covers the mid-IR region broadly with 20% to 40% due to the polarizer effect with small slit width between the gold strips. After placing graphene underneath the gold grating in the simulations, we observe a broad transmittance enhancement up to 40% to 60%, which is quite surprising since graphene is just a monolayer and lossy material. The physical mechanism for this enhanced transmission will be discussed later.

 

Fig. 1 (a) Schematics of continuous graphene film at the bottom of the gold nanoslit arrays. (b) Transmittance of the structures of gold nanoslit arrays with and without graphene for periodicity p = 500 nm and d = 20 nm.

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The transmission enhancement is strongly dependent on the structure parameters, i.e. the periodicity and the slit width. To figure out the effect of these parameters, the transmittance spectra with different periodicities and slit widths are simulated for two cases: without graphene and with graphene.

The transmittance spectra shown in Fig. 2 were obtained by changing the periodicity from 200 nm to 1000 nm and keeping the slit width fixed at 20 nm. As shown in Fig. 2(a), when there is no graphene, the transmission increases with decreasing periodicity and larger transmission happens at longer wavelengths. When the periodicity is extremely small compared with the wavelength, the gold nanoslit structure can be described with an effective index model which indicates the flat transmittance spectra [39]. After combining with graphene, we observe that the transmittance is enhanced for the entire spectrum, especially for larger periodicities at longer wavelengths, as shown in Fig. 2(b). The transmittance spectra of several periodicities are selected and plotted separately in Fig. 2(c) for comparison. There are oscillations in the transmittance spectrum due to Fabry-Perot type reflection of the graphene surface plasmons from the nanoslit period boundaries. Increasing the periodicity will induce higher order reflections and thus increase the number of oscillations. We note that a similar enhanced transmission study was performed by Liu et al. [36], however they described the enhanced transmission effect using an LC-model therefore not taking into account the plasmonic properties of graphene. Here, our simulations prove that indeed surface plasmons excited at the graphene/metal interface is responsible for observing such broadband transmission enhancement. The enhancement factor is obtained by dividing the transmittance with graphene to that without graphene ($\text{EF}=\frac{{\text{T}}_{\text{Graphene}}}{{\text{T}}_{Gold}}$), as plotted in Fig. 2(d). Since we are keeping the slit width fixed at 20 nm while increasing the periodicity, the transmission reduces significantly in the case of gold nanoslit arrays. Therefore, it is easier to enhance transmission with larger periodicity, hence larger enhancement factors.

 

Fig. 2 (a) and (b) Transmittance spectrum of gold nanoslit arrays without and with graphene for different periodicities (fixed slit width 20 nm). (c) Transmittance of selected periodicities of the structures with graphene at the bottom. (d) Enhancement factor $\text{EF}=\frac{{\text{T}}_{\text{Graphene}}}{{\text{T}}_{Gold}}$for selected periodicities compared by two cases.

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Additional simulations are performed by keeping the periodicity fixed at 500 nm and changing the slit width. Simulated transmittance spectra for varying slit widths from 0 nm (continuous gold) to 100 nm are shown in Figs. 3(a) and 3(b). The transmission is rather low for slit widths smaller than 20 nm. Increasing the slit width results in higher transmission. Similar to the periodicity effect, larger transmission also happens at longer wavelengths. After combining with graphene, we observe how the oscillations perform with varied slit widths. When the slit widths are larger than 40 nm, the transmission dips can be observed. And the dips move to higher wavelengths for wider slit widths, which indicates the localized features of the graphene surface plasmons in the slits. The electric field distribution at the spectrum dip is plotted in the Appendix (A.1).

 

Fig. 3 (a) and (b) Transmittance spectrum of gold nanoslit arrays without and with graphene for different slit widths (fixed periodicity 500 nm). (c) Transmittance of selected slit widths of the structures with graphene at the bottom. (d) Enhancement factor $\text{EF}=\frac{{\text{T}}_{\text{Graphene}}}{{\text{T}}_{Gold}}$for selected slit widths compared by two cases.

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The spectra of several slit widths as well as the corresponding enhancement factors are plotted in Figs. 3(c) and 3(d). The enhancement is getting larger with smaller slit widths which resembles the performance of the case with large periodicities when considering in terms of the duty cycles. Actually the enhancement factors can be quite large when the slit width is about 10 nm in simulations. In the case of small slit widths, the transmission without graphene is approaching zero with large portion of reflective gold in one period. And the transmission dips shift to longer wavelengths when the slit widths get wider, which is the typical trend in localized surface plasmons. For 100 nm slit width case, higher order resonance can also be observed in this wavelength region.

To further investigate the physical explanations of the phenomenon observed in the spectra, we plot the vertical component of the electric field in side-view for the structure proposed before (500 nm periodicity and 20 nm slit width) at the wavelength of 13. When there is no graphene, as shown in Fig. 4(a), since gold serves much like the perfect conductor in mid-IR wavelength region, the electric field is mostly concentrated around the small slit. After combining with the graphene, the electric field is enhanced overall (Fig. 4(b)), especially in the slit and on the graphene. The zoomed-in version shown in Fig. 4(c) indicates the plasmonic characteristic of the graphene with which the surface plasmons propagate. Due to the excitation of the SPPs in graphene sheet, more light can be coupled to the structure therefore increasing the overall transmission. The supporting videos (see Visualization 1 and Visualization 2) compare the electric field of the gold nanoslit arrays and the hybrid structure, which confirms the existence of the propagating SPPs of graphene in this particular structure. Since the graphene surface plasmons are propagating back and forth horizontally in the period, the interference of them will lead to the oscillations in the spectra. When the periodicity is increasing with the fixed slit width, the overall effective permittivity of the gold grids is also increasing. And in this case, since the wavevector of the graphene SPPs also becomes larger from Eq. (2), more SPPs are expected to propagate through one period, which accounts for the increasing of the oscillations in Fig. 2(c). In the Appendix, we estimate the wavelengths of the graphene SPPs and analyze the effect quantitatively. (A.2)

 

Fig. 4 (a) Side-view electric field distribution of the gold nanoslit arrays structures. (b) and (c) Side-view electric field distribution of the hybrid structures

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3. Conclusions

In conclusion, we theoretically investigate the graphene/gold nanoslit arrays hybrid structure. By making use of the excitations of SPPs in continuous graphene, it is possible to enhance the mid-IR transmission broadly through the gold nanoslit arrays structures. In addition, various structure parameters and the electric field distribution have been investigated with FDTD simulations to understand the underlying mechanism. This hybrid structure can potentially help the study and control of propagating SPPs in continuous graphene sheet.

Appendix

A.1 Side-view electric distribution of the localized plasmon resonance

The side-view electric field component along x direction for the case of 100 nm slit at the wavelength of 12.2 $\mu m$ is shown in Fig. 5 (Pink line in Fig. 3(d)). The dipolar nature of the resonance is a sign of the localized surface plasmons excited at the graphene between the gold nanoslits. Since the highest electric field enhancement are calculated to be around the edge of the gold nanoslits, we expect the graphene between nanoslits to have the highest absorption.

 

Fig. 5 Side-view electric field distribution of the localized plasmon resonance

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A.2 Quantitative counting of the graphene SPPs compared with the spectrum fringes

In the electric field distribution, we could quantitatively count the number of graphene SPPs in 500 nm period (actually 480 nm under gold). For different excitation wavelengths, the wavelengths of graphene SPPs can be estimated. The fringe distance can also be counted from Fig. 1(b). For Febry-Perot type transmission, around the resonance we have $2l=k{\lambda }_{SPP}$, where l is the distance within which the SPPs interference happens, ${\lambda }_{SPP}$ is the graphene surface plasmons wavelength in the medium, and k is the counted number of the wavelengths. Here as we count the number of SPPs, from $10 \text{μm}$ everytime we come across one oscillation, the number of k will decrease by 1. Below in Table 1, we show the counted SPPs number, calculated wavelengths as well as the counted fringe distances. The number counted from the electric field distribution matches pretty good with the spectrum. According to Eq. (2), we can approximate ${\text{λ}}_{\text{SPP}} ~ {\text{λ}}^2$, which leads to $\text{Δλ }~ \text{Δ}\sqrt{{\text{λ}}_{\text{SPP}}}$. As the excitation wavelengths increase, the distance between the oscillation will increase as well.

Table 1. SPPs wavelengths and spectrum fringes

View Table

Acknowledgments

This material is based upon work supported by the Materials Research Science and Engineering Center (NSF-MRSEC) (DMR-1121262) of Northwestern University. We also acknowledge partial support from the Institute for Sustainability and Energy at Northwestern (ISEN) through ISEN Booster Award.

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