A Graphene-Based THz Wave Duplexer and Filter: Switching via Gate Biasing

: This work introduces a Graphene-based multi-layer reconfigurable device as a wave duplexer in the THz frequency range. Adjusting transmitting and reflecting parts of incident waves alongside controlling absorption provides the interesting capability to select target waves in different frequencies. The proposed device includes periodic graphene patterns on both sides of silicon dioxide as substrate. Additionally, the patterns are biased differently compared to conventional patterns which makes it possible to achieve two distinct behaviors versus frequency. Exploiting equivalent circuit models (ECM) for graphene and dielectric, the whole device is modeled by passive RLC circuits. According to simulation results, the proposed device can transmit and reflect incident THz waves at desired frequencies in 0.1 THz to 30 THz which makes it an ideal candidate for manipulating THz waves in terms of transmission and reflection.

provides carrier frequencies in telecommunication protocols much higher than those used in current communication systems (wireless and commercial). It has also been used to increase data transmission capacity for short-range (short-distance) communications. The various applications of the terahertz band have made this area one of the most interesting research topics [4][5][6][7][8]. Implementing such applications requires materials to realize terahertz devices. Researchers interested in the terahertz band have studied the properties of materials with different dimensions. In terms of common three-dimensional materials, the electrical conductivity and conductivity of silica and gold have been investigated in the terahertz band. In addition, a range of two-dimensional materials such as graphene, phosphorene, and silicon have also been investigated [9].
Among these two-dimensional materials, graphene has been the subject of research in various fields due to its unique mechanical, thermal, and electromagnetic properties. One of the attractive properties of graphene as a semiconductor-metal material is its unique conductivity, which can be controlled by external voltage bias or static magnetic bias. Now, along with the terahertz frequency band and graphene material, we need a way to model and realize such devices. To help design accurate structure, it is essential to provide numerical modeling methods that take into account the properties of graphene [9], [30][31][32][33][34].
One of the simplification approaches to solving electromagnetic problems is to describe the elements as circuit elements. In the meantime, relatively accurate equations are presented to describe the graphene layer.
In 2014 and 2015, references [10] and [11] presented efficient circuit models for graphene nano-strips and graphene nano-disks, respectively, which consider the effects of physical parameters such as the geometry and electron relaxation time along with the effects of bias voltage has taken into account.
According to many previous works, the accuracy of the circuit model performance has been compared with numerical methods, most of which report a very good agreement with the slight error of the circuit model method versus numerical methods [10], [11]. Based on this, it can be concluded that the circuit model approach can be a substitute for time-consuming and complex numerical methods. In this regard, three graphene patterns are focused.
Nano-strips, nano-disks, and graphene continuous plates are modeled in series with resistor-inductor-capacitor circuit elements. This modeling, along with knowing the dielectric circuit model, leads to the calculation of the structure impedance. Matching this impedance with the impedance of the outer space of the structure means the transfer of maximum power from the external environment to the structure (maximum power in an absorber means complete absorption in the structure). In other words, the impedance adaptation is equivalent to the full absorption at the frequency at which this adaptation occurred. Thus, this approach paves the way for the design of graphene-based devices by simplifying an electromagnetic phenomenon to the level of an impedance matching problem [18][19][20][21][22][23].
In this way, here two graphene patterns on both sides of dielectric form a reconfigurable device that can select the desired reflection and/or transmission waves. Section 2 describes the proposed device in detail with corresponding circuit representation. Also, section 3 provides simulations results while section 4 concludes the work as the conclusion.

Proposed Device:
The proposed device is illustrated in Fig. 1, includes two periodic arrays of Graphene on both sides of a dielectric. Each Graphene pattern consists of a triple-bias scheme. According to [14], bias equalities can force patterns to experience different periods, and consequently, a degree of freedom is provided to adjust device reactions in desired frequencies. In addition, based on [12][13][14][15], [35][36][37], circuit representation of graphene patterns is reported with excellent accuracy compared to full numerical simulations. According to Fig. 1, the incident wave divides into three parts: Transmitted, Absorbed, and Reflected parts. By minimizing the absorption part, interesting functions can be realized via transmission and reflection parts. In this way, the proposed structure can act similar to a duplexer which can transmit or reflect target waves.
, , P, W, hr and D are dielectric thickness, disk radius, disk period, ribbons width, and ribbons period respectively. It should be noted that the illustration is symbolic while all disks are the same in shape and all ribbons have equal width. Also, based on [15], periods of disks and ribbons can vary be corresponding to bias equalities.  According to [10] and [14], each pattern can be modeled via a resistor, inductor, and capacitor. These elements are related to some physical constants and geometrical sizes as bellow: (1) To obtain n q , and 1n q , physical parameter such as , P, r W , and D , must be designed and then referred to Table 2. Z impedance sees to graphene disks at the end of the line. Therefore, 1 Z calculated by Eq.
(3). Then Eq. (4) is obtained based on the transmision line concept [16]. Also, the dielectric can be modeled via (5). And the input impedance is calculated as below: where the definition of parameters of Eq. (3) to Eq. (6) are reported in Table 3: Table 3. Definition of parameters.

Definition Parameter
The wave propagation constant in the dielectric substrate. Based on Eq. (6), the input impedance of the proposed structure is calculable versus frequency. All parameters in the proposed structure have their effects on the impedance. So finding the impedance sensitivity to parameters is interesting to obtain distinct responses.  (7) In this way, with an iterative algorithm, two sets of chemical potentials are obtained as Mode A and Mode B which are tabulated in the next section.

Simulation Results:
According to Eq. (8), changing gate bias leads to changing chemical potential which forces the device to react differently [17]. In this way, two operational modes are defined with corresponding chemical potentials, tabulated in Table 4.  Table 1.
The described device is simulated via two sets of bias values. The corresponding chemical potentials for each bias set are tabulated in Table 4. Table 4. Two sets of bias values for the proposed device.
First operational mode (eV) Second operational mode (eV) Similarly, the second mode of operation is reported in Fig. 6 and Fig. 7.
According to simulation results, both operational modes are in an acceptable condition against geometrical variations while the device can be switched easily between two modes just by setting bias values.  Finally, the comparison table is reported in Table 5.

Conclusion:
Using triple-bias graphene patterns of ribbons and disks, a reconfigurable device is presented which can manipulate THz radiation in terms of transmission, reflection, and absorption. Changing external gate bias stimulates the device to shift operational region against frequency. The device is modeled by circuit model elements to simplify simulation.
The sensitivity of the proposed device versus geometrical parameters is reported which verifies the superior performance of the design. Such a reconfigurable device is in great demand for several functions in optical systems. It can be used as a wave duplexer with the capability of tuning via gate biasing.

Data Availability Statement:
The data that support the findings of this study are available from the corresponding author upon reasonable request.