Terahertz science and technology is undergoing a period of rapid development and diversified applications in security detection, imaging, sensing, and communication.^[1–3] These applications demand many kinds of high-performance terahertz wave functional components such as filters, splitters, modulators, switches, phase shifter, and absorbers.^[4–7] Among the terahertz wave functional devices required, manipulation of terahertz wave power exhibits tremendous potential applications in terahertz technology. In recent years, several types of terahertz wave switches have been reported in the literature.^[8–10] The long size terahertz switch imposes limitations on the achievable density of integration circuits.^[8] Moreover, the slow time response of the mechanically, thermally, or electrically tunable method has greatly restricted the practical application of the terahertz wave switch. Therefore, there is still a great challenge to realize a compact switch in the terahertz region. To the best of our knowledge, the rapid development of terahertz wave integrated circuit technology requires a large number of compact terahertz wave switches. To reduce the device size, a terahertz switch based on graphene is very desirable, but still lacking to date.

In recent years, graphene has aroused a great deal of research interest because of its outstanding electronic transport properties and optical properties. Due to this, graphene has been envisioned to facilitate new possibilities for constructing low power, rapidly tunable devices from the infrared to terahertz range.^[11–13] Currently, many researchers are focusing on the issue of localized and propagated properties of graphene surface plasmon polaritons (SPPs), such as nano-discs, nano-ribbons, and graphene metamaterials.^[14–17] Interestingly, it has been reported that some kinds of dynamically tunable infrared optical devices are based on graphene metasurfaces,^[18] graphene metamaterial,^[19] graphene nanostrips,^[20] and graphene nanocrosses^[21] respectively. These provide the possibility of devising flexibly tunable plasmon devices based on graphene. In addition, a mid-infrared fast-tunable graphene ring resonator has also been numerically analyzed.^[22] It can also be used to construct a tunable mid-infrared filter, modulator, directional coupler and so on. Especially, the relaxation time of carriers in graphene is a few picoseconds, which offers great opportunities for ultrafast terahertz manipulation devices.^[23] In this study, we investigate and demonstrate a novel terahertz switch based on three graphene ring resonators. By tuning the bias voltage on the center graphene ring, its chemical potential and mode effective index can be tuned significantly which plays a role in controlling the transmission characteristics of the SPP wave. The device is investigated in detail using the finite element method (FEM) with COMSOL, a commercial finite element based software package. The calculation results indicate that the transmission characteristics of the resonant mode can feasibly be tuned by varying the radius or Fermi level of the center graphene ring. The results show that the ON–OFF response time is less than 1.2 ms and the attenuation of the novel terahertz wave switch is more than 17 dB at a frequency of 7 THz. We believe that our studies will be of value in fabricating the versatile, fast-tunable integrated devices in the terahertz region for terahertz wave communication and processing.

In this study, we consider the structure, which is composed of two graphene waveguides and three graphene rings of which one has an inner radius of R₁ = 0.2 μm and the other two have an inner radius of R = 0.5 μm each. The coupling distance between ring and graphene waveguide is denoted by d₁ = 0.1 μm. Similarly, the distance between rings is denoted by d₂ = 0.05 μm. The SPP wave of the monolayer graphene is injected from the input port of the lower graphene waveguide and outputs from the upper graphene waveguide. The length of the graphene waveguide is L = 2.6 μm. The whole graphene structure is arranged on a polymethyl methacrylate medium with a refractive index of 1.48. The equivalent permittivity of graphene is given by ε_eq = 1 +jσ_g/(ε₀Δω),^[24,25] where j is the imaginary unit, σ_g represents the graphene surface conductivity, ε₀ is the permittivity of free space, Δ is the thickness of the graphene thin film, and ω is the angular frequency. The surface conductivity σ_g is governed by the Kubo formula including the interband and intraband transition contributions.^[26,27] Here, only the transverse magnetic (TM) polarized SPP supported by monolayer graphene is considered in the investigation. The dispersion relation of TM wave along the graphene layer can be given by ,^[28] where k₀ = 2π/λ and η₀ = 120πΩ are the free space wave-number and the intrinsic impedance of free space, respectively. The effective mode index, a parameter closely related to the confinement of TM wave, is calculated from n_eff = β /k₀. The propagation length is defined as L_spp = 1/Im(β), featuring the SPP propagation loss in graphene. Interestingly, the L_spp varies greatly when the chemical potential μ_c is slightly changed, which is the guidance for designing the active surface plasmon wave devices. Graphene is modelled as a thin layer of Δ = 0.34 nm in thickness^[29] and its optical parameters are determined via the relative permittivity. In the near-field coupling case, the propagation loss on the graphene waveguide between two resonators is ignored ‘for separation d₂ and the Im(β) are small enough. We make a subtle, yet important, distinction between the cavity buildup and magnification factor. The buildup factor is the ratio of the internal field in a particular graphene resonator to that in another resonator. The electric-field buildup factors are given by^[30]

Fig. 1.

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	Fig. 1. Schematic diagram of the terahertz switch consisting of two graphene waveguides and three graphene rings.

The electric-field magnification factors are related to the buildup factors by the relations

The two-dimensional numerical simulations are carried out in the present terahertz switch configurations by using the finite element method with the aid of the commercial software module COMSOL Multiphysics. Graphene SPPs are computed by the boundary mode analysis, propagating from one port to another, and perfectly matched layers allow scattering into eventual radiative modes in the transversal direction. Figure 2 shows the transmission spectra for the center graphene ring with various radius (R₁). One can see that the spectra in Fig. 2 ‘tend to be red-shifted’ with the increase of R₁, which evidently validates the proportional relationship between the center frequency of the resonator and the radius of the center graphene ring. In order to explore the physical essence of the observed transmission spectra, we visually illustrate the electric-field (E_y) distributions of the SPPs at 7 THz corresponding to the different values of ring radius (R₁) of the center graphene ring as shown in Figs. 3(a)–3(c). One can obviously see that the SPP wave can be excited and confined strongly on a graphene ring at 7 THz when the resonance condition is satisfied. For the case of R₁ = 0.20 μm, most of the incident energy is trapped in the ring. At this time, the incident terahertz wave energy can successfully pass through the three graphene rings with sharp transmission bandwidth.

In order to investigate the coupling effect of the present configuration quantitatively, figure 4 shows the normalized transmissions of the terahertz switch with different chemical potential values in the center graphene ring. From Fig. 4, one sees that the SPP wave transmission ratio is over 87.1% at afrequency of 7 THz when μ_c = 0 eV. But, when μ_c = 0.2 eV, the transmission is low to 0.2%. That is to say, by changing the chemical potential value of the center graphene ring, the coupling mode in the ring resonator can be significantly tuned. It can be noted that when the resonance condition is satisfied, most of the incident energy can efficiently be obtained through the output graphene waveguide. The simulation results of electric field distribution of the SPPs in the plasmonic structure with the different chemical potentials at f = 7 THz are presented in Fig. 5. The incident signal is injected through the left port of the lower graphene waveguide. The electric field distribution clearly shows the coupling process of SPPs among the graphene rings. Note that the electric field intensities are uniformly distributed in the two parallel graphene waveguides and three graphene rings without any back scattering. In Fig. 5(a), one can see that when the resonance condition is satisfied, the incident energy which is trapped in the ring resonator couples to the output port of the lower graphene waveguide almost simultaneously. Since the surface conductivity of graphene is tunable by changing the chemical potential, the energy flow in two parallel graphene waveguides and three graphene rings can be controlled by bias voltage. When the central graphene ring in the three graphene rings system is biased, its Fermi level, and hence the surface conductivity, should be modified accordingly. Supposing that a bias voltage yields a chemical potential of μ_c = 0.1 eV in the center graphene ring, the SPPs from the input graphene waveguide will be partly coupled to the lower one which is finally collected by output port (see Fig. 5(b)). Similarly, if a bias voltage (i.e., a chemical potential of μ_c2 = 0.2 eV) is added onto the center graphene ring, the biased graphene ring will behave as a dielectric and cannot support the plasmonic mode, the incident energy from the lower graphene waveguide cannot be coupled to the upper graphene waveguide output as demonstrated in Fig. 5(c). Since the resonance condition in three graphene rings is not satisfied, the terahertz wave cannot propagate efficiently through the three graphene rings to the upper graphene waveguide output. From Fig. 5, one can see that there would be different electric field intensities in the output port of the present device for different bias voltages. Accordingly, the structure forms an effective terahertz wave switch. Here, we define the extinction ratio of the proposed device as ER = −10log(P_out/P_in), where P_in and P_out represent the power flows of input and output port, respectively. In this paper, the extinction ratio is 17.7 dB. Furthermore, the controlling rate is related to not only the response time of graphene material, but also the system response time. In order to analyze the time domain steady state intensity response of the presented terahertz wave switch, a continuous wave is excited at the input port position. Figure 6 shows the corresponding time domain steady state intensity response, and the switching rate of the proposed device is as short as around 1.2 ms, which is about 1/10 response time of a previous terahertz switch.^[8] These results can be valuable references for studying the ultrafast response terahertz wave switches.

Fig. 2.

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	Fig. 2. Transmission spectra of the present terahertz switch for the three different values of center graphene ring radius (R1).

Fig. 3.

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	Fig. 3. Snapshots of Ey intensity distribution at 7 THz for central graphene ring radius (a) R1 = 0.16 μm, (b) R1 = 0.18 μm, (c) R1 = 0.20 μm.

Fig. 4.

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	Fig. 4. Transmission characteristics of the terahertz switch with different chemical potential values of the center graphene ring.

Fig. 5.

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	Fig. 5. Snapshots of Ey intensity distribution at 7 THz for different chemical potential values of the center graphene ring: (a) μc = 0 eV, (b) μc = 0.1 eV, (c) μc = 0.2 eV.

Fig. 6.

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	Fig. 6. Time domain steady state terahertz wave intensity response.

We numerically investigate the design and transmission characterization of terahertz wave switch based on graphene rings and waveguides. Since the surface conductivity of graphene is tunable by gate voltage, the coupling process can be controlled. When the center graphene ring is biased, its chemical potential hence the surface conductivity should be accordingly modified. By varying the Fermi level or radius of the center ring resonator, SPP wave strongly confined in the graphene ring can be tuned feasibly. The simulated results show that the terahertz wave transmission ratio can be tuned from 87.1% to 1.7% with the chemical potential in the center graphene ring changing from 0 eV into 0.2 eV. These results are consistent with our theoretical predictions. We believe that the proposed terahertz wave switch can be useful for future terahertz wave communication systems.