The prosperous developments in all-optical processing and telecommunication systems have induced extensive requirements to high-speed, low-loss, and compact components to be implemented as photonic integrated circuits (PICs).1 The application of surface plasmon (SP) wave propagation can be a promising idea to provide reliable optical devices.2 So far, many plasmonic components based on metals have been explored.34.5.–6 However, high intrinsic loss and lack of enough tenability have hampered metallic plasmonic structures to be vastly employed.7 Recently, graphene, a two-dimensional (2-D) and hexagonal arrangement of carbon atoms, has drawn much attention due to its excellent optical properties providing compact, low-loss, and tunable components.89.10.–11 Showing more advantageous behavior, such as tunability and more compactness compared to metal-based structures, graphene-based structures are considered as high-qualified candidate components for implementation of next generation nanoplasmonic optical devices and systems.12 During the past decade, various types of graphene-based devices, such as bends and splitters,13 different types of optical waveguides,14,15 metasurface absorbers,16 logic gates,17 lenses,18 filters,1920.21.–22 switches, and directional couplers,23 have been proposed and analyzed numerically and experimentally. Also, SP waves propagation supported by graphene ribbons in terms of the edge and the waveguide modes,24 and two types of symmetric and antisymmetric waveguide SP modes corresponding, respectively, to the symmetric and antisymmetric magnetic field distribution across the gap between the graphene layers have been analyzed and investigated.25 In addition, some structures, such as power splitters,26 switches,27 and directional couplers,28 in three layer graphene system have been studied.
In this study, a wavelength selective structure comprising of two graphene layers, as input and output ports, coupled through a cavity resonator is proposed and analyzed numerically using the finite-difference time-domain (FDTD) method. A midinfrared bandpass filter is achieved, in which the wavelength of the transmission peak is tuned by varying the length of the resonator, the lateral coupling distance between the graphene layers, the dielectric refractive index of the material inside the resonator, and the chemical potential of the graphene layers utilizing appropriate external voltage bias. FDTD simulation results are in good agreement with the theoretical predictions. The simple proposed structures can be easily fabricated to be utilized in compact nanoplasmonic devices and PICs for optical processors and communication systems in the midinfrared region.
Theory and Simulation Method
The schematic view of the proposed basic structure is shown in Fig. 1. Two graphene layers as input and output ports in an antisymmetric configuration are coupled through a cavity resonator. In a practical point of view, the structure should be inserted in a dielectric medium, but for simplicity without limiting the generality, the background index is assumed to be air. The structure is analyzed numerically using the 2-D-FDTD method with a perfectly matched layer absorbing boundary condition around the simulation region. In the simulations, graphene is treated as an ultrathin film. The Kubo formula is used for deriving the surface conductivity () of graphene.2930.–31 At room temperature and in the midinfrared spectral range, the chemical potential of graphene is always above half of the photon energy. So the intraband transition dominates, and the interband transition is neglected. Therefore, the overall conductivity is simplified as31,3233,34
To excite the SP waves along –direction, one electric dipole source has been used to excite the polarized wave propagating on graphene layers. The antisymmetric SP modes are formed and excited by the even superposition of the SPs in the resonator.25 The incident wavelength satisfying the resonance condition of the resonator can transmit to the output graphene waveguide while the other wavelengths are suppressed. In resonance wavelengths, the wave transmitted from the input port is coupled to the cavity resonator through the small gap ( in Fig. 1) and creates the standing wave in the cavity. Then, the wave is decoupled to the output port, through the other gap. A precise detection system can be employed at the output port to measure the power transmitted and wavelength of transmission peak.
The resonance wavelengths and the length of the cavity resonator () are related by the following resonance condition25:25
The structural parameters , , and are assumed as 250, 30, and 50 nm, respectively. The parameters of the surface conductivity of graphene are set as follows: , ,26 and . To provide the chemical potential of a graphene layer in a specific value, we should apply appropriate external voltage to the layer. The voltage can be applied through two metalized sides of the substrate. Recently, structures consisting of two electrostatically gated graphene layers separated by a thin layer of insulator have been proposed theoretically35,36 and implemented experimentally.37
Two monitors are located at the locations of and to detect the incident and transmitted powers, respectively. The transmission ratio (transmittance) is defined as .
To save the memory and execution time of simulations, a nonuniform mesh creation is employed. The mesh size inside the graphene region along - and -directions is set as 10 and 0.05 nm, respectively, and the mesh sizes increase gradually outside the graphene region.
Results and Discussion
In this section, different structures of resonance filter, power splitter, and refractive index sensor are proposed, analyzed, and discussed.
Transmission ratio spectrum of the cavity resonator formed between antisymmetric input–output parallel graphene pair is shown in Fig. 2(a). Transmission peaks appear at wavelengths of 10.65 and according to the first- and second-order resonance wavelengths, respectively. Obviously, bandpass filtering effect is realized. The distributions of the field in the cross section of the resonator at the incident wavelengths of and are demonstrated in Figs. 2(b) and 2(c), respectively. So, the resonator sandwiched between the graphene ribbons behaves as a Fabry–Perot cavity resonator. Only the incident wavelength satisfying the resonance condition of the resonator can be coupled effectively into the output graphene layer waveguide. If the wavelength does not satisfy the resonance condition, it will be reflected at the cavity interface as shown in Fig. 2(c). For practical implementation, the overall structure should be mounted in a dielectric. Figure 2(d) shows the transmission ratio spectrum of the filter structure inserted in carbazole, with refractive index of 1.3. As the medium refractive index increases, the resonance wavelength increases, which shows a redshift.
Figure 3 shows the effect of the variation of the length of the resonator () on the transmission ratio spectra. Obviously, the transmission peaks exhibit redshift as the length of the resonator increases. The second-order resonance wavelength of the structure versus the resonator length derived by the analytical method of Eqs. (3) and (4), and the numerical FDTD method are compared in Fig. 4, which are in good agreement. According to Eq. (3), the resonance wavelengths of the transmission peaks present a redshift as increases. Therefore, it is obvious that the transmittance spectrum would be tuned by the variation of the length of the resonator.
The transmittance spectrum can be also tuned by varying the lateral coupling distance between the graphene layers, . According to Eq. (4), the propagation constant of the antisymmetric SP mode depends on . As shown in Fig. 5, as the coupling distance increases, the real part of the wave vector, , decreases. The incident wavelength, is assumed to be . is 300 nm, and the other parameters are the same as those used in Fig. 2. Numerical simulation results for the spectra around the first-order resonance modes are shown in Fig. 6(a). Here, the transmission peaks present a redshift as the coupling distance increases. In addition, applying the external gate voltage can tune the chemical potential of the cavity resonator graphene layers to vary the resonance wavelength. The simulated transmission ratio spectra for different chemical potentials of graphene are shown and compared in Fig. 6(b). As shown, a small change in the chemical potential can tune the resonance wavelength. The transmission peaks exhibit a blueshift as the chemical potential increases. Without refabrication of new structures, the values of external gate voltage can tune the resonance wavelength of the resonator.
According to Eqs. (3) and (4), the gap space between the cavity resonator and input–output graphene waveguides () does not change the resonance wavelength. So, changes in only have an effect on the transmission peak value. Transmission ratio spectra for different values of are shown in Fig. 7. As increases, the coupling losses increase, and the maximum transmission decreases.
A power splitter is also designed and analyzed by adding another graphene output waveguide, as shown in Fig. 8. Figure 9(a) demonstrates the output spectra of the proposed splitter for the parameters of , , , and for both graphene layers in output waveguides. By changing the distance between one of the output ports and the resonator, the power transmissions have been changed and it is easy to deduce that the output port with a longer distance from the resonator would receive a lower portion of the input power, as shown in Fig. 9(b) for . Hence, different values of power division ratios can be realized by altering the gap space between the cavity resonator and the output waveguides. Moreover, active power splitter for providing different required transmission power ratios can be obtained by variation of the chemical potentials of the output ports, as shown in Fig. 10. The output port with higher chemical potential has higher transmittance.
As can be considered from Eq. (1), the conductivity spectrum is proportional to the chemical potential of the graphene. Higher chemical potential leads to higher conductivity. Therefore, the wave transmission loss along the graphene decreases and the transmission ratio at the output graphene waveguides with a higher level of chemical potential increases, which comply well with the results in Fig. 10.
Refractive Index Sensor
The transmission ratio spectra of the structure of Fig. 1 with the cavity resonator filled with materials with different refractive indices are presented in Fig. 11. Increasing the refractive index, the transmission ratio spectrum tends to exhibit a redshift without a strong change in the shape. As shown in Fig. 11, there is approximately a linear relationship between the resonance wavelength of the sensor structure and the refractive index of material filling it. Therefore, by measuring the variation of the resonance wavelength peak, the structure can be exploited as a refractive index sensor. The sensor sensitivity (SS) is the rate of variation of resonance wavelength peak with respect to resonator refractive index, , in nanometer per refractive index unit (). This ratio can be considered as a useful parameter to investigate the performance of the sensor structure. We have calculated for our proposed sensor, the result of which is .
In this study, an antisymmetric parallel graphene layer pair coupled through a cavity resonator is proposed and analyzed theoretically and numerically. The wavelength selective graphene resonator sandwiched between the graphene ribbons behaves as a bandpass filter in the midinfrared region. The wavelength of the transmission peak is tuned by varying the length of the resonator, the coupling distance between the graphene layers, refractive index of the material inserted in the resonator, and the chemical potential of the graphene layers utilizing an external gate voltage. Numerical simulation results are in a good agreement with those of theoretical predictions. As the structure’s applications, a power splitter is designed and analyzed. The power transmission ratios can be meticulously changed via varying the gap space between the cavity resonator and input–output graphene waveguides, and also, through the variation of the chemical potentials of the output graphene layers. Another possible application is a simple refractive index sensor with sensitivity of . The proposed structures can be fabricated as ultracompact midinfrared devices utilizing in PICs.
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Somayyeh Asgari received her BSc degree in electrical and power electronics engineering from Zanjan University, Zanjan, Iran, in 2014, and her MSc degree in telecommunication engineering from K. N. Toosi University of Technology, Tehran, Iran, in 2017. She is doing her research at Optical Communication Laboratory, Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran, under the supervision of Professor Nosrat Granpayeh. Her research interests include design and simulation of optical graphene plasmonic devices and structures.
Alireza Dolatabady received his BSc degree in electrical and electronics engineering from Iran University of Science and Technology, Tehran, Iran, in 2010, and his MSc degree in telecommunication engineering from K. N. Toosi University of Technology, Tehran, Iran, in 2012. He is currently pursuing his study toward PhD and doing his research at Optical Communication Laboratory, Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran, under the supervision of Professor Nosrat Granpayeh.
Nosrat Granpayeh received his BSc, MSc, and PhD degrees in telecommunication engineering from Telecommunication College, Radio and Television College, Tehran, Iran, and University of NSW, Sydney, Australia, in 1975, 1980, and 1996, respectively. In 1975, as an honor graduate of the Faculty of Electrical and Computer Engineering of K. N. Toosi University of Technology (formerly, Telecommunication College), Tehran, Iran, he was employed as an instructor, where he was later promoted to lecturer, assistant professor, associate professor, and professor in 1980, 1996, 2007, and 2016, respectively.