1. Introduction

Perfect absorbers in optical frequency regime can be categorized into two types in case of bandwidths: broadband perfect absorbers and narrowband perfect absorbers. The broadband perfect absorbers are commonly based on localized surface plasmon (LSP) resonance and have been widely used in surface enhanced spectroscopy [1–3], energy harvesting [4–5], thermal emission [6–8], optical sensing [9–10], and light modulation combined with graphene [11–13]. The narrowband perfect absorbers are usually constituted based on another plasmon resonance mode, i.e. surface plasmon polariton (SPP) resonance. The reported applications of narrowband perfect absorbers mainly focused on the fields of thermal radiation tailoring [14–15], and refractive index sensing [16–19]. Up to date, no light modulation application with SPP based narrowband perfect absorbers have been reported to the best of our knowledge. Similar to LSP resonance, the light power of SPP resonance is also highly localized on metal surface, which may enable a strong interaction between plasmon mode and graphene.

Many works have been devoted to graphene enabled dynamic tuning of metal LSP resonance [20–36]. Graphene was used as a tunable loss, which is large due to interband transition in near-infrared wavelength range, to control plasmon damping [20–21]. Then, it is showed that both quality factor and resonance frequency of gold nanorod can be modified through top gate tuned graphene [22]. In mid-infrared wavelength range, graphene induced blue shift of Fano resonance was demonstrated and explained using generalized perturbation theory [23]. The theoretical work from Z. Li predicted that the design of metal reflection layer is crucial for high performance light modulation applications [24]. B. Vasić theoretically demonstrated that, for split ring resonator, it is gap size which dominates the resonance wavelength tuning range [25]. It is reported that a plasmonic metasurface with two Fano resonances can dramatically enhance the interaction of infrared light with single layer graphene, and a phase modulation based motion sensor was also demonstrated [26–27]. M. C. Sherrott achieved a broad phase modulation range of 237° at an operating wavelength of 8.5µm by using a gate-tunable graphene-gold resonator geometry [28]. In resonance wavelength shift maximization, a large value of 650nm has been reported by Y. Yao, and then an optimized bended nanorod resonator was introduced to further improve the tuning range to 1100nm [11–12]. A high performance light intensity modulator based on bended nanorod and graphene was then reported [13]. In our previous work, we theoretically described a tunable infrared grating based on the phase modulation of split ring resonator [29]. For the interaction between narrowband absorber and graphene, S. Kim proposed that distributed Bragg reflector can enable near-unity absorption of graphene [30]. A symmetric-to-asymmetric line shape transition and a significant narrowing of the linewidth of guided mode resonance was realized with graphene loading [31]. Despite the great progress made by all these works, the relatively small working bandwidth may be the main obstacle for real applications. On the other hand, the resonance wavelength of SPP is known to be highly dependent on the incident angle, which provides an alternative way to broadband mid-infrared light modulation.

In this work, we demonstrate a broadband mid-infrared light modulator based on graphene enabled dynamic tuning of SPP resonance, which is supported by an all-metal grating. A large modulation depth of 90% can be obtained in a broad spectral range from 5µm to 6µm, which is 2.5-fold enhanced compared with graphene tuned LSP resonance. The phase tuning application is also demonstrated, and the reflection phase tuning range can be as large as 180°. The coupled mode theory has then been used to analyze the influences of grating structure parameters on modulation performance.

2. Metal grating - graphene hybrid structure

Figure 1(a) illustrates the hybrid structure of graphene and gold grating, which is composed of a two-dimensional disk array and a flat substrate. The permittivity of bulk gold in infrared range is described by the Drude model, the plasma frequency ω_p = 1.37 × 10¹⁶ rad/s, and the damping constant γ_p = 4.08 × 10¹³ rad/s. Because of surface scattering and grain boundary effects in thin films, the damping constant of gold patch is set to be three times that of bulk gold [9–10]. The grating structure parameters are designed for critical coupling of SPP resonance with near-unity absorption. The period of the array and diameter of the disk are set as P = D = 6µm. The thicknesses of the disk and substrate are set as t_s = 450nm and t_d = 100nm, respectively. Graphene is modeled as thin surface characterized by a surface impendence Z (ω, µ_c, τ, T) where ω is radian frequency, µ_c is chemical potential, τ is relaxation time, and T is temperature [37]. The temperature and relaxation time are set to be T = 300K and τ = 0.1ps, respectively. All the simulations were performed using finite element method in CST studio suite. According to the black line in Fig. 1(b), the absorption of SPP mode is 98.3% at resonance wavelength of 5.9946µm, which is very close to P and thus indicates a first order SPP mode [16]. The bandwidth of the resonance peak is very small that the full width half maximum (∼30nm) is almost one order of magnitude smaller than that of LSP resonance [13]. The blue line in Fig. 1(b) shows the reflection phase around the resonance wavelength, and the ∼300° phase variation reveals the underdamped resonance situation. Figure 1(c) shows the cross view of electric field distribution at resonance, and it can be seen that the maximum field intensity locates on the grating surface, which enables a strong interaction between resonance mode and overlaid graphene. Figure 1(d) gives the top view of field distribution, and both the cross view and top view of the resonance pattern are clearly different from those of dipole mode with LSP resonance [10]. The graphene surface impendence Z is closely related to the chemical potential µ_c, which can be dynamically tuned through electrical gating [20–28]. According to the perturbation theory, the reflection phase and intensity of the hybrid structure can be then be dynamically controlled through real-time graphene conductivity modification [24–25].

 

Fig. 1. (a) Schematic illustration of metal grating – graphene hybrid structure, and x-polarized light is normally incident on the structure. (b) Reflectivity and reflection phase of the hybrid structure with graphene chemical potential of 0.2eV. (c) Cross view (at middle of the disk) and (d) top view (50nm above grating surface) of the electric field distribution at resonance.

Download Full Size | PDF

3. Resonance wavelength tuning of the SPP mode

According to Fig. 2(a), a considerable blue shift of the resonance wavelength can be observed with increasing graphene chemical potential. This wavelength shift is obtained through the strong modulation effect of imaginary part of graphene surface impendence, which varies from 20000 Ω/sq with 0.2eV to 3000 Ω/sq with 0.9eV as shown by Fig. 2(b). In comparison, the variation of real part of graphene surface impendence, shown by Fig. 2(c), influences the intrinsic loss of the structure and is much smaller (from 1500 Ω/sq with 0.2eV to 1000 Ω/sq with 0.9eV) than that of imaginary part, which explains the small reflectivity change during the graphene chemical potential increasing. The modulation performance of the hybrid modulator is given by Fig. 2(d), where both modulation depth (MD) and insertion loss (IL) have been considered. The modulation depth for a specific wavelength λ is calculated using the equation of MD = 1- Rmin(λ)/Rmax(λ), where Rmax(λ) and Rmin(λ) are the maximum and minimum achievable reflectivity for that wavelength, respectively. The critical coupling is utilized here to obtain an ultra-small reflectivity at resonance, and thus enable a near-unity modulation depth. The insertion loss is calculated by using the equation of IL = 10*log(Rmax(λ)), and the value from −2 dB to −9 dB is achievable for a modulation depth over 90%. The insertion loss can be further decreased by improving the wavelength tuning range. The modulation performance given here is comparable to the 95% modulation depth and −2 dB to −8 dB insertion loss obtained with LSP resonance [13]. This is because of the ultra-narrow band resonance of SPP mode, which may also be beneficial for high wavelength selectivity light modulation. However, the modulation wavelength range is rather small and may hinder the practical application. It is well known that the resonance wavelength of SPP mode highly depends on the incident angle, which may provide an alternative way to broadband light modulation rather than change the grating structure parameters.

 

Fig. 2. (a) The resonance wavelength of the hybrid structure blue shifts with increasing graphene chemical potential (the step of chemical potential is 0.1eV). (b) imaginary part and (c) real part of graphene surface impendence. (d) The modulation depth and insertion loss of this grating – graphene hybrid infrared light modulator.

Download Full Size | PDF

4. Incident angle dependent light modulation

For a clear demonstration of broadband modulation with SPP mode, the modulation performance with LSP resonance is first demonstrated here for comparison. As shown by the inset in Fig. 3(a), the gold disk array in Fig. 1(a) is modified to support LSP resonance. For specific, a dielectric layer is introduced between the gold disk and the continuous gold film, and the structure parameters of gold disk are changed to enable a LSP mode near 6µm. The period of the array and diameter of the disk are set as P = 1.8µm and D = 1.7µm, respectively. The thicknesses of the gold disk, dielectric layer and gold substrate are set to be t_s = 50nm, t_g = 80nm and t_d = 100nm, respectively. The permittivity of the dielectric layer is ε_g = 2. The 100nm gap between each disk leads to a highly confined electric field, which can be seen from the field distribution shown by Fig. 3(a), and thus enables the strong interaction between graphene and LSP resonance mode [20–28]. Figure 3(b) shows the dependency of LSP resonance wavelength on graphene chemical potential, the corresponding modulation depth has been shown by the black dot line in Fig. 3(d). The working bandwidth with LSP mode has been limited by the wavelength shift value shown in Fig. 3(b) and is hard to improve considering that the interaction between LSP resonance mode and graphene is already very strong. Unlike LSP resonance mode, the resonance wavelength of SPP mode is very sensitive to the incident angle, and may provide an alternative way to broadband modulation with high modulation depth without tuning the structure parameters. Figure 3(c) shows the SPP resonance spectra with different incident angles (angle defined in x-z plane and with respect to the z axis), and the relationship between resonance wavelength and incident angle can be calculated according to momentum-matching conditions [16]. It can be seen that from 0° to 35° the variation of reflectivity is very small that can be neglected, which means the incident angle variation has a small influence on intensity modulation performance in this range. The color lines in Fig. 3(d) show the graphene enabled modulation depth of SPP resonance mode with four separated incident angles. The incident angle can be adjusted continuously from 0° to 35° to modulate the wavelengths not included in the four modulation bands. Considering modulation depth larger than 90%, it can be seen that the modulation bandwidth with SPP mode is ∼1µm, which is 2.5-fold enhanced compared with the ∼400 nm modulation bandwidth with LSP mode, as shown by the black dot line in Fig. 3(d). By further increasing the incident angle, the SPP mode strong couples with Rayleigh anomaly, which leads to weakened modulation effect. Anyway, larger modulation bandwidth may be obtained by proper structure design to eliminate the influence of Rayleigh anomaly.

 

Fig. 3. (a) Electric field distribution of LSP resonance with gold disk array in metal-insulator-metal configuration, and the inset shows the structure schematically. (b) Dynamic tuning of LSP resonance by increasing the graphene chemical potential. (c) The SPP resonance spectra with different incident angles. (d) Broadband working and high modulation depth achieved with SPP resonance by varying the incident angle, and the black dot line shows the modulation depth of LSP resonance for comparison.

Download Full Size | PDF

The hybrid structure is also capable of broadband reflection phase tuning. Figure 4(a) shows the dependency of reflection phase on graphene chemical potential at normal incidence. The largest phase tuning range 180° appears at the center wavelength of 5.99µm as shown by Fig. 4(b). As the wavelength departs from the center wavelength, the phase tuning range becomes smaller and smaller. This limited working bandwidth can be compensated by adjusting incident angle again. The large phase tuning range remains with larger incident angles, as illustrated by Fig. 4(c) and 4(d) with incident angle of 30° and center wavelength of 5.2µm.

 

Fig. 4. Dependency of reflection phase on graphene chemical potential with incident angle of (a) 0° and (c) 30°. The reflection phase tuning range at (b) 5.99µm with incident angle of 0° and (d) 5.2µm with incident angle of 30°.

Download Full Size | PDF

5. Influence of grating structure parameters on critical coupling

The light modulation performance of the hybrid structure highly depends on the critical coupling, which means that radiation loss is equal to absorption loss (Q_r = Q_a, Q_r and Q_a are defined as the radiative quality factor and absorptive quality factor, respectively) [38]. Q_r and Q_a can be calculated using r = −1+(2/τ_r) /[-i*(ω-ω₀) + 1/τ_a+1/τ_r], where r is the reflection coefficient, and τ_a (Q_a=ω₀τ_a/2) and τ_r (Q_r=ω₀τ_r/2) represent the lifetimes of the resonance due to absorption inside the structure and radiation to the far field, respectively. The critical coupling leads to maximum absorption of incident light and very sharp phase variation near resonance wavelength. Near unity absorption is critical to obtain high intensity modulation depth according to MD = 1- Rmin(λ)/Rmax(λ). It is shown by Fig. 5(a) that the reflectivity can be even smaller with t_s=0.4µm than that with t_s=0.45µm (P = D = 6µm). The reason why disk thickness is chosen as 0.45µm is that smaller disk thickness decreases the radiation loss and leads overdamped resonance (Q_r > Q_a), which has a much smaller reflection phase tuning range according to the black and red lines in Fig. 5(b). While the diameter of gold disk (D) is reduced with fixed period (P), the critical coupling condition is no longer satisfied, which causes larger reflectivity and less sharp phase variation as shown by Fig. 5(c) and 5(d). In conclusion, the grating parameters should be designed to locate the resonance not only near the critical coupling to obtain large modulation depth but also on the underdamped side to ensure large phase tuning range. Figure 6 shows the dependency of radiative/absorptive quality factors on D and t_s. It is illustrated that the underdamped resonance is maintained with decreasing D, and the resonance goes through underdamped to overdamped with decreasing t_s.

 

Fig. 5. Dependency of hybrid structure reflectivity on (a) t_s and (c) D. Dependency of hybrid structure reflection phase on (b) t_s and (d) D. The chemical potential of graphene in the hybrid structure is set as 0.9eV.

Download Full Size | PDF

 

Fig. 6. Dependency of radiative and absorptive quality factors on (a) D with fixed P = 6 µm and t_s=0.45 µm and (b) t_s with fixed P = D = 6 µm (Q_r in black and Q_a in red).

Download Full Size | PDF

6. Conclusion

In summary, graphene enabled dynamic tuning of SPP based narrowband perfect absorber is discussed. Due to the highly localized electric field, the interaction between graphene and resonance mode is strong enough to manipulate the resonance wavelength. Then the hybrid structure can be utilized as a light modulator. The modulation depth can be as high as 100% and the insertion loss ranges from −2db to −9db with 90% modulation depth. For phase tuning application, a large tuning range of 180° can be obtained. The narrowband light modulation nature can be overcome by adjusting the incident angle. The structure parameters design of metal grating for critical coupling has also been discussed. This graphene loaded metal grating hybrid structure may beneficial for not only light modulation but also label free sensing.