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Abstract
Graphene plasmons with tunable resonance wavelengths and low loss have attracted considerable attention in the past decade. However, the weatk interaction between graphene and light, which is attributed to the low carrier concentration and small thickness of graphene, severely hinders the practical application of graphene plasmon. In the infrared wavelength range, graphene can act as a tunable load to modify both the resonance wavelength and the damping of metal plasmon, which has been successfully used for light intensity and phase modulations. In this work, a synthetic phase meta-atom composed of a split ring resonator and a graphene patch is designed with a switchable reflection phase of either 0 or π. The large phase tuning range arises from the graphene induced strong modification of metal plasmon. By arranging the 0/π phase bits in different spatial orders, one-dimensional grating with a dynamically tunable period and orientation can be obtained.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Plasmonics of metal nanostructures have benefited many practical applications, including but not limited to light detection/emission [1,2], label free sensing [3], surface enhanced scattering/absorption spectroscopy [4–6], metasurfaces [7]. While the near- and far-field plasmonic response of metal nanostructure can be modified through geometry engineering, active control of these properties is in strong demand. So far, a variety of tuning methods based on semiconductors with electrically/optically modified carrier concentration [8–12], liquid crystals with tunable refractive index [13], nonlinear materials [14], and mechanical stretching [15] have been reported. However, these methods suffer from slow operation speed or small tuning range. In comparison, electrical tuning method based on graphene possesses advantages of high speed, large tuning range, compatibility with silicon technology, and large-scale fabrication [16].
A number of works have been contributed to graphene based metal plasmon tuning. N. K. Emani used Graphene as a tunable loss, which is large due to interband transition in near-infrared wavelength range, to control metal plasmon damping [17,18]. Then, it was shown by J. Kim that both quality factor and resonance frequency of gold nanorod can be modified through top gate tuned graphene [19]. In mid-infrared wavelength range, S. H. Mousavi demonstrated the graphene induced blue shift of Fano resonance and explained this phenomenon with generalized perturbation theory [20]. A large resonance wavelength tuning range of 650nm has been reported by Y. Yao, and then an optimized bended nanorod resonator was designed to further improve the tuning range to 1100 nm. A high performance light intensity modulator based on bended nanorod and graphene was also reported [21–23]. The theoretical work from Z. Li indicated that the design of metal reflector is beneficial for light modulation applications [24]. B. Vasic´ theoretically demonstrated that, for split ring resonator, the gap size dominates the resonance wavelength tuning range [25]. It is reported by N. Dabidian 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 8.5 μm by using a gate-tunable graphene-gold resonator geometry [28]. Despite the great progress made by all these works, only intensity and phase modulation applications have been considered. Graphene enabled metal plasmon tuning may also be utilized in some other optical devices, for example, tunable gratings.
In this theoretical work, we demonstrate a period and orientation tunable infrared grating based on graphene coupled split ring resonator. The phase bit of graphene patch and split ring resonator is designed to possess tunable phase response of either 0 or π. The influence of graphene on plasmonic near field is also demonstrated, which is responsible for the large phase tuning range. By arranging the 0/π phase bits in different spatial orders, the period and orientation of one-dimensional grating can then be different. The results demonstrated here may benefit not only tunable gratings but also reconfigurable metasurfaces [29].
2. Results and discussions
2.1 Schematic demonstration of tunable grating
The concept of tunable grating is briefly described in Fig. 1. When the one-dimensional grating is illuminated normally, two scattering light beams exist on two sides of the incident beam. For the purpose of real-time direction control of scattering beams, the period and orientation of the grating need to be tuned dynamically. Considering the specific case of plasmonic grating used in this work, the reflection phase and intensity manipulation of single phase bit (metal resonator) is the key problem. Once the reflection phase of single phase bit can be switched between 0 and π with unchanged reflection intensity, a post-fabrication tunability can be achieved for grating period and orientation. Figure 1(a) and (b) reveals a smaller polar angle can be obtained for scattering beams with larger period, which depends on putting more phase bits in one period. Figure 1(c) and (d) reveals grating orientation induced azimuthal angle variation of scattering beams.
Fig. 1 Schematic illustration of a dynamically tunable grating with normal incident light and two scattering beams. The single phase bit, which is composed of a split ring resonator and a graphene square patch, is designed to possess switchable 0/π phase response with unchanged reflectivity. The comparison between (a) and (b) reveals the influence of grating period (each period is composed of 12 and 20 phase bits, respectively) on the polar angle of scattering beams. (c) and (d) illustrates the tunable azimuthal angle of scattering beams through grating orientation modification, which is based on arranging 0/π phase bits in different spatial orders.
2.2 Design of 0/π phase bit
As illustrated by Fig. 2(a), the single phase bit of tunable plasmonic grating is composed of a split ring resonator (SRR) in metal-insulator-metal configuration and a graphene square patch placed between SRR and dielectric layer. The carrier concentration of graphene can be dynamically modified through back gating. The period of the phase bit is L = 600 nm, and the side length of the graphene square patch is 550 nm. The outer radius and inner radius of the SRR are 250 nm and 200 nm, respectively. The thickness of underneath gold reflector and SRR are 100 nm and 50 nm, respectively. The gap size of SRR is 50 nm. The simulations were performed using Lumerical FDTD solutions, and the material choice for gold is Au(Gold)-Palik. The permittivity of the dielectric layer is set as 2. Graphene is modeled as thin surface characterized by a surface conductivity σ (ω, μc, Г, T) where ω is radian frequency, μc is chemical potential, Г is a phenomenological scattering rate, and T is temperature [30]. The temperature and scattering rate are set as T = 300 K and Г = 0.01 ev (corresponds to a relaxation time of 0.03 ps), respectively. The graphene chemical potential μc is closely related to the carrier concentration, which can be tuned through chemical/electrical doping. According to the perturbation theory, the reflection phase and intensity of the phase bit can be dynamically controlled through graphene conductivity modification [17–28]. In our proposed strategy, the phase bit with graphene chemical potential of 0.2 ev and 0.6 ev are designed to possess a reflection phase difference of π, and unchanged reflection intensity at the same time.
Fig. 2 (a) Schematic illustration of a single phase bit of the tunable plasmonic grating, and the components are split ring resonator/electrode, graphene, dielectric layer and gold reflector from top to bottom. (b) Transition from underdamped resonance to overdamped resonance by changing the graphene chemical potential from 0.2 ev to 0.6 ev with dielectric layer thickness of h = 400 nm. (c) The center working wavelength is decided to be 5.14 μm with h = 500 nm and (d) the reflection phase difference is 180° at this wavelength.
The phase tuning range of MIM structure strongly depends on the lifetimes of resonance due to absorption inside the structure and radiation to the far field (τi and τr, respectively) [31]. According to Fig. 2(b), the transition from underdamped resonance to overdamped resonance is observed by increasing the graphene chemical potential with dielectric layer thickness h = 400 nm. This is because of larger graphene absorption comes with higher graphene carrier concentration, and the overdamped condition τr > τi is satisfied with graphene chemical potential of 0.6 ev. It is very clear that the phase jump of underdamped resonance in Fig. 2(b) is much larger than that of overdamped resonance. Therefore, the underdamped resonance is more desirable for phase modulation application. Since graphene can be considered as a tunable loss, which could drive the underdamped/overdamped transition, the structure parameters need to be carefully designed to avoid overdamped situation. The simplest way to avoid overdamped resonance is to increase the dielectric layer thickness h, which considerably reduces the intrinsic loss. For 180° phase difference design, h is swept from 400 nm to larger values. The intersection of reflection spectra with graphene chemical potential of 0.2 ev and 0.6 ev is chosen as the center working wavelength. According to Fig. 2(c) and (d), with 500 nm dielectric layer thickness, the reflection spectra intersect at wavelength of 5.14 μm and the reflection phase difference at this wavelength is exactly 180°.
According to Fig. 2(c), both the resonance wavelength and amplitude of split ring resonator have a considerable dependency on the graphene chemical potential, which comes from the strong coupling effect between plasmonic near field and graphene. Figure 3(a) shows the electric field distribution (normalized to incident electric field) of split ring resonator without graphene, and a majority of the plasmonic mode power is trapped in the gap area, which is known as the “hot spot”. According to Fig. 3(b), the formation of “hot spot” depends on the interaction between positive charges and negative charges, which gather at two sides of the gap, respectively. The graphene loading induced extinction of “hot spot” is demonstrated by Fig. 3(c), where the electric field at the gap area is no longer strong. This is because of that the graphene with relative high conductivity bridge the gold ligament, and a large part of the positive/negative charges can go through the gap, which is proved by the small charge density at gap area as shown in Fig. 3(d). It is also worth pointing out that the electric field on top/down sides of graphene patch are significant, which may be attributed to the excitation of dipole resonance of graphene plasmon.
Fig. 3 Normalized electric field distribution on the interface of SRR and dielectric layer (a) without and (c) with graphene (chemical potential of 0.2 ev). Charge density distribution on the interface of SRR and dielectric layer (b) without and (d) with graphene (chemical potential of 0.2 ev).
2.3 Dynamic period and orientation tuning
Since the size of single phase bit is fixed and the reflection phase can be dynamically switched between 0 and π, the grating is tunable by putting different number of phase bits in one period. The total number of phase bits in the grating is set to be 120*120, i. e., the size of the grating is 72 μm*72 μm. As shown by Fig. 4(a) and (d), two grating periods are considered here for demonstration. Under the normal incidence of plane waves, the far-field function scattered by the grating is expressed as:
where θ and φ are the polar and azimuth angles of an arbitrary direction, respectively. φ(m,n), which is either 0 or π, is the phase response of the phase bit labeled with (m,n), and k is the wavevector of light in free space.Fig. 4 Tunable infrared grating with dynamic period of (a) P1 = 12L and (d) P2 = 20L. (b) Analytical and (c) numerical radiation pattern with grating period P1. (e) Analytical and (f) numerical radiation pattern with grating period P2.
As shown by Fig. 4(a) and (d), the grating period can be tuned by putting different number of phase bits in it. P1 = 12L and P2 = 20L are used to demonstrate the grating period tuning enabled polar angle control of scattering beams. Figure 4(b) and (e) are the analytical radiation patterns calculated from Eq. (1) with P1 and P2, respectively. The polar angle in Fig. 4(b) with P1 is 45.3°, which is larger than the polar angle (25.2°) in Fig. 4(e) with P2. The numerical results, which are calculated with Lumerical FDTD solutions, fit well with the analytical results as shown by Fig. 4(c) and (f). One period is modeled in FDTD solutions, and the finite periodic structures are considered in far field projections with top hat illumination, which means the grating is uniformly illuminated by the light source. Other polar angles are also available by modifying the grating period. For even number of 0/π phase bits in one period, the polar angle varies from 59° with P = 10L to 18.9° with P = 26L. For periods smaller than 10L or larger than 26L, the side lobes of scattered field are large and cannot be ignored.
The orientation of grating can also be modified by arranging the 0/π phase bits in different spatial orders. Here, we assume that one phase byte is composed of 6 × 6 phase bits. As shown by Fig. 5(a), a displacement (D) of 3L is introduced between phase bytes in adjacent rows. The grating is oriented with an angle of 116.6° with respect to the positive direction of x axis, and the angle between scattered beam and x axis should be 116.6°-90° = 26.6°. The analytical radiation pattern is given by Fig. 5(b), and the strongest radiation exists at the directions of (θ, φ) = (52.7°, 26.5°) and (52.7°, 206.5°), which agree well with the numerical results shown by Fig. 5(c). Figure 5(d) shows the grating with D = 9L, and the analytical and numerical radiation patterns are given by Fig. 5(e) and (f), respectively. The polar angle remains 52.7° and the corresponding azimuth angles are 153.5° and 333.5°. It is obvious that the radiation patterns with D = 3L and D = 9L are symmetric with respect to both x and y axes. Other grating orientations may also be obtained by changing the value of D, for example, (θ, φ) = (59°, 33.7° /213.7°) with D = 4L.
Fig. 5 Tunable infrared grating with dynamic phase bite displacement of (a) D = 3L and (d) D = 9L. (b) Analytical and (c) numerical radiation pattern with displacement D = 3L. (e) Analytical and (f) numerical radiation pattern with displacement D = 9L.
2.4 Working bandwidth
Although the structure parameters are designed for the specific working wavelength of 5.14μm, the functionality is actually applicable in a relatively broad spectra range. When looking through the dependence of normalized far field radiation intensity distributions on incident wavelength with period P2 = 20L in Fig. 6, two main scatting beams are observed to be located at ± 25.2° (for 5.14 μm). As the wavelength departs from the center working wavelength, the radiation at 0° becomes larger. Considering different requirements of normal radiation suppression, the bandwidth of grating can be hundreds of nanometers centered at 5.14 μm.
2.5 Grating efficiency
According to Fig. 2(c), the efficiency of the proposed tunable grating is about 14.3%. The efficiency is relatively low because the working wavelength is in strong resonance and a large part of incident power has been dissipated by metal. One way to solve this problem is to increase the resonance wavelength shift. Figure 7(a) and (b) show that a higher efficiency of 20.4% can be obtained by increasing the higher graphene chemical potential from 0.6 ev to 0.7 ev. All the other parameters are kept unchanged except for the thickness of the dielectric layer, which is tuned to be h = 560 nm to enable 180° phase difference. The efficiency can be further improved to 24.6% by increasing the higher graphene chemical potential to 0.8 ev, as shown by Fig. 7(c) and (d) with h = 650 nm. Other efforts to increase wavelength tuning range can be realized by utilizing multilayer graphene according to our previous work [32].
Fig. 7 (a) Absorption and (b) phase response of single phase bit with graphene chemical potential of 0.2ev/0.7ev and dielectric layer thickness of h = 560 nm. (c) Absorption and (d) phase response of single phase bit with graphene chemical potential of 0.2ev/0.8ev and dielectric layer thickness of h = 650 nm.
3. Conclusion
Dynamically tunable infrared grating based on hybrid structure of split ring resonator and graphene is proposed and numerically investigated in this work. By applying different graphene chemical potential of 0.2ev and 0.6ev, the reflection phase of split ring resonator/graphene hybrid structure with fixed geometry can be either 0 or π, which enables us to tailor the functionality of grating by arranging the 0/π phase bits in different spatial orders. By putting different number of phase bits in one period, the polar angle of scattered beams can be tuned from 18.9° to 59°. By adjusting the displacement of phase byte in adjacent rows, the azimuthal angle of scattered beams can also be modified. Due to the large phase tuning range, this MIM/graphene hybrid structure is not only promising for the development of tunable grating/metasurface, but also indicates a new photonic application for two dimensional materials.
Funding
National Natural Science Foundation of China (11574349, 61801472, 61875223); Natural Science Foundation of Jiangsu Province (BK20150365, BK20170424); Hundred Talent Program of Chinese Academy of Sciences.
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