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Abstract
Terahertz logic gates play a crucial role in optical signal processing and THz digitization. In this paper, we propose a design strategy for graphene-based metamaterial THz all-optical logic gate devices based on the induced transparency effect of surface isolated. Theoretically, we realize Boolean operations by coupling of a hexagonal graphene resonant cavity with dual embedded rotatable ellipses. Based on the coupled mode theory, the elliptical rotation angle of the resonator is an important factor affecting the PIT phenomenon. We control the logic input by adjusting the rotation angles of the two embedded ellipses. The analysis results show that: under the incidence of y-polarized light, the ellipse deflection angle of 0° represents the input signal ‘0’, and the ellipse deflection angle of 30° represents the input signal ‘1’. Through numerical simulation, the structure realizes two logical operations of NAND and AND. Under the incidence of x-polarized light, the ellipse deflection angle of 0° represents the input signal ‘0’, and the ellipse deflection angle of 90° represents the input signal ‘1’. Through numerical simulation, the structure realizes three logical operations of NAND, XNOR and OR. Finally, we analyze the performance of the logic gates by extinction ratio. The extinction ratio of the logic gate is up to 10.38 dB when performing OR Boolean operations. Numerically simulated all-optical logic gates can be key components of optical processing and telecommunication equipment.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Surface plasmon polaritons (SPP), which are mixed excited states formed by the interaction of conduction electrons on the surface of a dielectric material with photons in an incident light wave [1–4]. SPP have been discovered and researched on metal surfaces and graphene surfaces [5–10]. Optical logic gates are the core components of photonic central processing unit (CPU), which play a crucial role in optical computing and data processing [11,12]. Compared with traditional electrical logic gates, optical logic gates have the advantages of high speed, low power consumption and large bandwidth [13–15]. Currently, many scholars are committed to the research based on SPP all-optical logic gates and have achieved many results [16–19]. In 2020, Dolatabady A et al. demonstrate an optical logic gate based on graphene nanoribbon resonators. Based on the propagation of the edge modes in the waveguide and the coupling between the waveguide and the strip resonator, the structure realizes XOR, OR and NOT Boolean operations with an extinction ratio of 8 dB in the terahertz band [20]. In 2020, Roya Ebrahimi Meymand et al. designed all-optical logic gates using the principle of metasurface coherent perfect absorption. The structure takes the incident THz wave at both ends as the input signal and the outgoing wave as the output signal. By adjusting the relative phase difference between the two input signals, the designed device realizes AND, OR and XOR logic operations [21]. In 2022, Wang et al. proposed a design method for metamaterial all-optical logic gates composed of semiconductor-metal hybrids. The designed device uses pump light as input and transmission efficiency as output. The conductivity of the semiconductor is regulated by the presence or absence of pump light, and the numerical simulation of the structure realizes NOR and OR Boolean operations [22]. Optical logic devices based on SPPs have greatly improved in size miniaturization. However, for most designs, due to the different signals of the control inputs of different logic gates, the structure can only implement one logic function at a time and cannot implement parallel operation. Therefore, we would like to find a suitable method to solve these problems. Currently, the plasmon-induced transparency effect (PIT) induced by SPP is expected to solve these problems [29,46]. However, terahertz plasmonic logic devices based on the PIT phenomenon are less explored, and most logic devices can only provide one logic operation at a time.
In this research, we propose a strategy to construct terahertz logic gates using graphene bases. Theoretically, we have designed a specific THz device composed of a rectangular graphene ring coupled with a hexagonal graphene resonant cavity embedded with a rotatable ellipse and two circular graphenes, which can realize multiple PIT effects. The corresponding transmission characteristics of the device in the terahertz band are numerically simulated by rotating the embedded ellipse angle to control the input logic states. The structure can realize four logical operations of NAND, AND, XNOR and OR at the resonant frequency. With WDM technology, the structure can realize NAND and AND parallel logic operations under y-polarised light incidence, and the structure can realize NAND, XNOR and OR parallel logic operations under x-polarised light incidence. Thus, this research provides a new approach for terahertz logic device design.
2. Structure model and theoretical analysis
In the mid-infrared to terahertz band, graphene-excited SPP have a strong local field confinement effect [23–28]. In addition, graphene SPP can not only achieve precise control and manipulation of light by overcoming the classical diffraction limit, but also to achieve modulation of the SPP broadband by changing the Fermi energy level of graphene [29,30]. The metamaterial based on SPP consists of periodically arranged unit cells, and a schematic diagram of the unit cells is shown in Fig. 1. The geometric parameters of the crystal cells are $Px = 11\,\mu m$ and $Py = 6\,\mu m$. The patterned graphene consists of a rectangular ring and two hexagonal resonant cavities embedded with rotatable ellipses and two solid circles. Patterned graphene deposited on substrate Si. The thickness of the substrate is $h = 10\,\mu m$ and its refractive index ${n_{Si}} = 1.45$. The inner width of the rectangular graphene ring is $w = 0.5\,\mu m$. The side length of the hexagonal resonant cavity is $L1 = 2\,\mu m$. The long axis radius of the embedded ellipse is $a = 1.55\,\mu m$ and the short axis radius is $b = 0.85\,\mu m$. The radius of the circular graphene is $r = 0.5\,\mu m$. The distance between the centres of the two hexagonal resonators is $L2 = 4.8\,\mu m$. The distance between the centres of the two circular graphene is $L3 = 1.342\,\mu m$. ${\theta _1}$ and ${\theta _2}$ denote the angle between the long axis of the left and right ellipses and the negative half-axis of the X -axis, respectively. The distance between the resonant cavity and the rectangular ring are all $d = 0.2\,\mu m$. The thickness of the graphene is $t = 0.5\,\mu m$, and the relaxation time $\tau = 0.5ps$.
Fig. 1. (a) Three-dimensional schematic of the proposed structure. (b) Top view of the structural unit.
Before data simulation, the conductivity of a single layer graphene needs to be obtained. The surface conductivity ${\sigma _g}$ of graphene consists of intra-band electron photon scattering ${\sigma _{{\mathop{\rm int}} ra}}$ and inter-band photon leaps ${\sigma _{{\mathop{\rm int}} er}}$. It can be calculated according to Kubo's formula [31,32]:
In the proposed structure, a single-layer of patterned graphene is deposited on a silicon substrate and in contact with air. Incident THz waves are excited on the graphene surface and fundamental frequency transverse magnetic (TM) polarised SPP modes propagate along the graphene surface. The dispersion relation of the SPP with TM polarisation excitation on the graphene surface is [38,39]
Here, ${\varepsilon _{S\textrm{i}}}$, ${\varepsilon _{air}}$, and ${\varepsilon _0}$ are the relative permittivity of silicon, the relative permittivity of air, the relative permittivity of vacuum, respectively. $\beta$ is the propagation constant of graphene metamaterial plasmon waves. ${k_0} = 2\pi /{\lambda _0}$ is the wave vector of light in the free space. ${\eta _0}$ is the intrinsic impedance. Therefore, the effective refractive index of the metamaterial can be expressed as: ${n_{eff}} = \beta /{k_0}$ [35].
The designed graphene metamaterial was numerically simulated by the finite element analysis method to realize the dual PIT phenomenon. We use periodic boundary conditions along the x -direction and the y- direction and perfectly matched layers (PMLs) along the z- direction [40]. Incident terahertz waves propagate along the z-direction with an magnetic field polarized along the x direction and an electric field polarized along the y direction. We characterize the transmission ability of THz waves by selecting the transmission coefficient in the S parameter. We take the different rotation angles of the two embedded ellipses as the input signal and the transmittance of the structure as the output signal.
3. Mechanical Analysis of Optical Logic Gates
3.1 Switching Mechanism
Optical logic gates can use optical switches to realize the control and switching of optical signals, thereby realizing the logic operation of optical signals [41]. The switching mechanism based on the PIT effect can be used to realize logic operations. By designing the structure and controlling the input signal, the optical transparency and optical absorption conversion in the PIT effect can be used to realize logic operations such as AND, OR, NOT, and XOR. This enables optical logic gates to perform complex optical calculations and signal processing.
Figure 2(a) shows the transmission spectrum of the metamaterial. The transmission spectrum has three resonance valleys points and two resonance peaks points. In this paper, the resonance points are named dip1, peak1, dip2, peak2 and dip3 (from left to right). The frequencies corresponding to the resonance points are ${f_1} = 1.7THz$, ${f_2} = 2.8THz$, ${f_3} = 4.48THz$, ${f_4} = 4.86THz$ and ${f_5} = 5.14THz$. The plunge of the structure at 8 THz is caused by nonlinear effects, which we do not analyze here. Figure 2(b)-(f) shows the electric field strength and electric field vector distributions at the five resonance points.
Fig. 2. (a) Transmission spectrum of the structure at ${\theta _1} = {\theta _2} = {0^ \circ }$ under y-polarised light incidence. (b) Electric field distribution at resonant frequency ${f_1} = 1.7THz$. (c) Electric field distribution at resonant frequency ${f_2} = 2.8THz$. (d) Electric field distribution at resonant frequency ${f_3} = 4.48THz$. (e) Electric field distribution at resonant frequency ${f_4} = 4.86THz$. (f) Electric field distribution at resonant frequency ${f_5} = 5.14THz$. (Arrows indicate the direction of the electric field at the surface of the structure)
In order to analyze the switching mechanism of the PIT effect, we investigated the electric field and the electric field vector distribution at the resonant frequency. As shown in Fig. 2(b), (d) and (f), phase reversal of the electric field occurs at the three resonance valley points. In Fig. 2(b), according to the electric field distribution, the rectangular graphene ring acts as the bright mode, and the resonant cavity and circular graphene act as the dark mod. The interaction between the bright mode and dark mode produces a transmission valley at ${f_1} = 1.7THz$, where the electric field was mainly concentrated between the hexagonal cavity and the rectangular graphene ring. In Fig. 2(c), there is almost no electric field at the rectangular graphene rings and circular graphene and the ellipse inside the resonant cavity. The reason for this phenomenon is that the transmission of patterned graphene at this frequency is higher than 90%. In Fig. 2(d), the strong electric field distribution is mainly concentrated on the inside and outside of the hexagonal resonant cavity embedded with an ellipse, while the weak electric field is distributed outside the rectangular graphene ring. Under the interaction of strong and weak electric fields, the resonance of the structure drop at ${f_3} = 4.48THz$. It can be seen from Fig. 2(e-f) that the electric field distribution is mainly concentrated on the outside of the rectangular graphene ring and the hexagonal resonant cavity.
At this time, the circular graphene and the resonant cavity work together to act as a dark mode. Bright mode of action of rectangular graphene rings. The dark mode is excited by the coupled light field between the incident light and the bright mode. Under the illumination of incident light, the interaction of bright mode and dark mode produces a transmission valley at ${f_5} = 5.14THz$.
The conical arrows shown in Fig. 2(b-f) indicate the direction of the electric field vector. It can be seen from Fig. 2(b-c) that the direction of the electric field vector is reversed in the outer four corners of the rectangular graphene ring (Red coil in Fig. 2(c)). In Fig. 2(d), the direction of the electric field vector on and outside the rectangular graphene ring are consistent with that in Fig. 2(b), while the direction of the electric field vector inside the rectangular ring is completely opposite to that in Fig. 2(b). The reversal of the direction of the electric field vector is a typical feature of the PIT phenomenon. In Fig. 2(e-f), the electric field vector flipped on the outside of the rectangular graphene ring (Pink coil in Fig. 2(e)), which is attributed to the fact that the rectangular graphene ring acts as a bright mode at this time.
3.2 All-optical Logic Gates
In Fig. 2(d), a strong electric field is distributed on the resonant cavity, and the inner elliptical edge also has a stronger electric field distribution, which indicates that the position of the ellipse affects the coupling between the incident light and the bright mode. By adjusting the rotation angle of the embedded ellipse to affect the coupling between the incident light and the bright modes, thus changing the transmission of terahertz waves. Under y-polarized light incidence, the rotation angle was set to 0° and 30° to adjust the structure. The traditional optical logic gates use the presence or absence of signals as the identification of the input signa ‘0’ and ‘1’ logic states [42,43]. We can adjust the logic state of ‘0’ and ‘1’ by changing the rotation angle of the embedded ellipse. We take the ellipse deflection angle as the input signal. A deflection angle $\theta$ of 0° represents the input signal ‘0’, and a deflection angle $\theta $ of 30° represents the input signal ‘1’, as shown in Table 1. The output logic states ‘0’ and ‘1’ are determined by the transmission coefficient of the metamaterial. The input signal is adjusted by the rotation angles of the ellipse, and the transmission spectrum of the structure under different logic states are shown in Fig. 3.
Table 1. Input logic states for different input signals. The input signal is controlled by the elliptical rotation angle.
Figure 3 clearly shows that at the first and third resonance valleys, the output of the device under different input states is consistent, which is due to the fact that the rectangular graphene ring acts as a bright mode at this time. In addition, the green line shows a significant resonance dip and resonance peak at the second resonance valley point. At the same time, it can be found that when the internal ellipse of the hexagonal resonant cavity is deflected by 30°, the structure will have a significant resonance drop at 6.94 THz. At this point, the hexagonal resonant cavity embedded with a 30° deflection ellipse acts as the bright mode. It can be seen from Fig. 3 that the transmittance of the structure changes significantly at the resonant frequency under different logic state inputs. The transmission performance of the designed device under the incidence of the terahertz wave can be changed by changing the rotation angle of the ellipse, thereby realizing logic operations. The horizontal dashed line represents our threshold for distinguishing output signals, which is set to 0.5. Anything above the threshold was considered an output signal ‘1’ and anything below the threshold was considered an output signal ‘0’. We can observe that the same logic function can be implemented in the frequency domain with a specific bandwidth. This article mainly analyzes the logic operations at the resonant frequency to demonstrate the performance of the corresponding logic gates.
4. Discussion on the logical relationship and structure of all-optical logic gates
Since the hexagonal resonant cavities embedded with an ellipse can be destructively couple with the rectangular ring graphene, the proposed structure can be designed as an ultra-compact logic gate. Under the incidence of y-polarized light, the structure can realize two logic operations of AND and NAND. In the next section, we discuss the implementation of each logical function.
4.1 AND gate and structure discussion
In order to design an AND logic gate, it is necessary to ensure that the output signal is ‘1’ if and only if all input signals are ‘1’, otherwise the output signal is ‘0’. According to Fig. 3, it can be seen that the structure enables AND Boolean operations at 4.47 THz. The transmission coefficient at 4.47 THz is used as the output signal. The transmission coefficient takes 50% as the threshold, and we define large output value (greater than 50%) as ‘1’, and small output value (less than 50%) as ‘0’. The specific implementation process of OR Boolean operation is as follows: when the two embedded ellipse rotation angles ${\theta _1}$ and ${\theta _2}$ are both 0°, the input signal is [0,0], and the transmission coefficient of the structure is 22.7%, indicating that the output signal is ‘0’. When the two embedded elliptic rotation angles ${\theta _1} = {0^ \circ }$ and ${\theta _2} = {30^ \circ }$, the input signal is [0,1], and the transmission coefficient of the structure is 41.2%, indicating that the output signal is ‘0’. When the two embedded elliptic rotation angles ${\theta _1} = {30^ \circ }$ and ${\theta _2} = {0^ \circ }$, the input signal is [1,0], and the transmission coefficient of the structure is 40%, indicating that the output signal is ‘0’. When the two embedded elliptic rotation angles ${\theta _1} = {30^ \circ }$ and ${\theta _2} = {30^ \circ }$, the input signal is [1,1], and the transmission coefficient of the structure is 83.6%, indicating that the output signal is ‘1’. According to the above definition, the truth table of the device is shown in Table 2. According to Fig. 3, it can be observed that the AND logic function can be implemented in the range of 4.37 THz to 4.65 THz. Figure 4 shows the electric field distribution for the four input logic states at 4.47 THz. According to Fig. 4, it can be seen intuitively that in the case of ${\theta _1} = {\theta _2} = {30^ \circ }$, the electric field on the surface of the structure is weaker, and the electric field on the surface of the structure is stronger in other cases. When the input signals are [0,0], [0,1] and [1,0], the hexagonal resonant cavities embedded with ellipses are coupled. The typical electric field direction reversal phenomenon occurs inside the resonator and around the circular graphene. When the input signal is [1,1], the hexagonal resonant cavity with embedded ellipse does not have coupling itself. At the same time, there is no electric field flip reversal occurs around the graphene. In order to define the performance of logic function of the system, the extinction ratio (ER) is introduced. The ER represents the relationship between the power of the output logic level ‘1’ and the power of the output logic level ‘0’. Taking the ER as the optimization standard, and let its unit be dB. The ER of the logic gate based on this structure is [44,45]:
Where $P_{vr}^1$ is the average power of logic ‘1’ and $P_{vr}^0$ is the average power of logic ‘0’. After calculation, the ER of the AND gate is 3.83 dB.Fig. 4. Electric field distribution for different logic states at a resonant frequency of 4.47 THz. (a) ${\theta _1} = {\theta _2} = {0^ \circ }$. (b) ${\theta _1} = {0^ \circ }$ and ${\theta _2} = {30^ \circ }$. (c) ${\theta _1} = {30^ \circ }$ and ${\theta _2} = {0^ \circ }$. (d) ${\theta _1} = {\theta _2} = {30^ \circ }$.
Table 2. Truth table for the device. The input signal has an elliptical rotation angle manipulation, and the output signal is defined at a transmission coefficient of 4.47 THz.
4.2 NAND gate and structure discussion
In order to design NAND logic gate, it is necessary to ensure that the output signal is ‘0’ if and only if all input signals are ‘1’, otherwise the output signal is ‘1’. Figure 3 shows that the structure can realize NAND Boolean operations at 3.99 THz and 6.94THz. Here, the input signal definition is kept constant, and the transmission coefficient at the resonance frequency is used as the output signal. The transmission coefficient takes 50% as the threshold, and we define large output value (greater than 50%) as ‘1’, and small output value (less than 50%) as ‘0’. As shown in Table 3. When the input signal is [1, 1], the transmission coefficient of the structure at 3.99 THz is 39.9%, indicating that the output signal is ‘0’. When the input signals are [0,0], [0,0] and [1,0], the transmission coefficients of the structure at 3.99 THz are 73.9%, 60.4%, and 60.6%, respectively, and their corresponding logic states are all ‘1’. Similarly, when the resonant frequency is 6.94 THz, the transmittance of the structure in four logic states are 92.8%, 65.8%, 66.6% and 31.7%, and the corresponding output signals are ‘1’, ‘1’, ‘1’, and ‘0’, respectively. Therefore, the structure can realize NAND logic operation at both resonant frequencies. At the same time, we can observe from Fig. 3 that NAND logic functions can be implemented in the range of 3.89 to 4.07 THz and 6.81 THz to 7.08 THz. Figure 5 shows the electric field distribution of the structure for four input logic states at 3.99 THz. Figure 6 shows the electric field distribution of the structure for four input logic states at 6.94 THz. It can be seen from the figure that the field intensity of the hexagonal cavity is strongest when ${\theta _1} = {\theta _2} = {30^ \circ }$, that is, when the input logic state is [1, 1]. The field strength of hexagonal resonator is weak under the other three logic state inputs. The ER of the corresponding logic gates are shown in Table 3.
Fig. 5. Electric field distribution for different logic states at a resonant frequency of 3.99 THz. (a) ${\theta _1} = {\theta _2} = {0^ \circ }$. (b) ${\theta _1} = {0^ \circ }$ and ${\theta _2} = {30^ \circ }$. (c) ${\theta _1} = {30^ \circ }$ and ${\theta _2} = {0^ \circ }$. (d) ${\theta _1} = {\theta _2} = {30^ \circ }$.
Fig. 6. Electric field distribution for different logic states at a resonant frequency of 3.99 THz. (a) ${\theta _1} = {\theta _2} = {0^ \circ }$. (b) ${\theta _1} = {0^ \circ }$ and ${\theta _2} = {30^ \circ }$. (c) ${\theta _1} = {30^ \circ }$ and ${\theta _2} = {0^ \circ }$. (d) ${\theta _1} = {\theta _2} = {30^ \circ }$.
Table 3. Truth table for the device. The input signal is manipulated by the elliptical rotation angle, and the output signals are defined at transmission coefficients of 3.99 and 6.94 THz, respectively.
5. X-polarized light discussion and logic function
5.1 Discussion of X-polarized incident light
In order to explore the influence of different polarized light on the metamaterial structure, when x-polarized light incidence, the transmission spectra of the structure under four logic state inputs are shown in Fig. 7. Comparing Fig. 3 and Fig. 7, it can be found that the formation of the transmission spectrum is based on the PIT effect of SPP. Under different polarized light incidence, the transmission spectra of logic devices are different due to the different structures in light and dark modes. With X-polarized light incident, the structure can realize three logical operations of NAND, XNOR, and OR at the resonance frequency. Here, we still use the different rotation angles of the two embedded ellipses as input signals to the logic device. When both embedded ellipse rotation angles ${\theta _1}$ and ${\theta _2}$ are both 0°, the input signal is [0,0]. When the rotation angles of the two embedded ellipses are ${\theta _1} = {0^ \circ }$ and ${\theta _2} = {90^ \circ }$, the input signal is [0, 1]. When the rotation angles of the two embedded ellipses are ${\theta _1} = {90^ \circ }$ and ${\theta _2} = {0^ \circ }$, the input signal is [1,0]. When the rotation angles of the two embedded ellipses are ${\theta _1} = {90^ \circ }$ and ${\theta _2} = {90^ \circ }$, the input signal is [1,1]. At the same time, the transmission coefficient at the resonant frequency is used as the output signal. The transmission coefficient takes 50% as the threshold, and we define large output value (greater than 50%) as ‘1’, and small output value (less than 50%) as ‘0’. The horizontal dashed line represents our threshold for distinguishing output signals, which is set to 0.5. Anything above the threshold was considered an output signal ‘1’ and anything below the threshold was considered an output signal ‘0’. We can observe that the same logic function can be implemented in the frequency domain with a specific bandwidth. From Fig. 7, we observe the same logic functionality in the ranges 3.86 THz to 4.41 THz and 4.53 THz to 4.8 THz and 6.18 THz to 6.8 THz. We mainly explore the performance of logic gates at the resonant frequency. Based on the above definition, the truth table of the device at the three resonant frequencies is shown in Table 4. At the same time, we calculated the ER at the resonant frequency of each logical operation in Table 4.
Table 4. Truth table for the device. The input signal has an elliptical rotation angle manipulation, and the output signal is defined at transmission coefficients of 4.10, 4.68 and 6.68 THz.
5.2 Summary of logical relationships
The logical functions realized by the structure at resonant frequencies under different polarized light incidence are summarized in Table 5. It can be noticed that the numerical simulation realizes four logical functions. ER is one of the important characteristics to measure the performance of logic gates. The larger the ER value, the smaller the error of detecting logic ‘0’ and ‘1’. It can be seen from Table 5 that the structure can realized three logic functions under x-polarized light incidence, and the ER is also large. At 6.68 THz, the ER of the OR logic gate reaches 10.38 dB. It can be found from Table 5 that each logic function can be implemented within a certain bandwidth. In the range of 4.53 THz to 4.65 THz, changing the incident polarized light can achieve a variety of logic functions. Different incident polarized light and different resonance frequencies are used as control signals can be used in cascaded structures. Through the cascade structure, we can implement more Boolean operations.
Table 5. Summary of logic functions
We compare with many structures in recent years, as shown in Table 6. The comparison results show that compared with the literature [20–22,48], in the terahertz band, the ER of our proposed optical logic gate structure is the highest 10.38 dB. By comparing the literature, it can be found that logic gates designed with metal or other semiconductor materials are more used in the visible light band. From the literature [47–51], it can be found that most designed all-optical logic gates are mainly controlled based on the coupling between two or more waveguides. This article controls the input signal through the particularity of the structure itself. In the terahertz band, patterned graphene has its advantages. Our structure has a higher value in the extinction ratio, and at the same time has a wider bandwidth to implement logic functions and has a wide range of applications. At the same time, we found that the value of the threshold affects the implementation of the logic function. At the same time, we found that the implementation of different logical functions is related to thresholds. The threshold of our structure is 0.5, and relatively higher or lower threshold settings have better reliability. These multiple logical operations can be implemented at the same frequency by correctly defining the threshold intensity. In summary, the metamaterial we designed has good application value in the field of terahertz optical logic gates.
Table 6. Comparison between the proposed structural logic gate and other structural logic gates
6. Conclusion
In this paper, we theoretically designed a terahertz metamaterial device consisting of a rectangular graphene ring, two hexagonal graphene resonators embedded with ellipses, and two circular graphene. Based on the PIT effect of SPP, the numerical simulation implements four logic operations of NAND, AND, XNOR and OR are realized through numerical simulation. We have shown that the output intensity can be changed by adjusting the rotation angle of the ellipse. We analyze that the structure can be numerically simulated to achieve Boolean operation under different polarization incident light. It can be found that when the rotation angle of the ellipse is 0°, the structure presents a typical PIT phenomenon. When the rotation angle is not 0°, more resonance peaks appear in the transmission spectrum corresponding to the input logic state, which comes from the coupling between the terahertz wave and the resonant cavity embedded in the ellipse. By calculating the ER, the maximum ER of the logical operation realized by the structure is 10.38 dB. At the same time, we find the bandwidth that can realize the corresponding logical function. The designed structure has superior performance in the adjustable bandwidth range. The designed structure has superior performance within the adjustable bandwidth range and has broader application prospects. Under the incidence of polarized light, the structure can not only realize multiple Boolean operations, but also realize the simultaneous operation of multiple logic operations. The numerical simulation of the multi-Boolean terahertz logic gate in this paper provides a new idea for the design of highly integrated terahertz optical logic devices.
Funding
Natural Science Foundation of Guangxi Zhuang Autonomous Region (2023GXNSFAA026015); Major Special Projects of Guangxi Science and Technology (AA22067056); National Natural Science Foundation of China (51965007); Innovation Project of Guangxi Graduate Education (YCSW2022123).
Disclosures
No conflict of interest exits in the submission of this manuscript.
Data availability
Data underlying the results presented in this paper can be obtained from the authors upon reasonable request.
References
1. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3-4), 131–314 (2005). [CrossRef]
2. T. L. Wang, Y. P. Zhang, H. Y. Zhang, and M. Y. Cao, “Dual-controlled switchable broadband terahertz absorber based on a graphene-vanadium dioxide metamaterial,” Opt. Mater. Express 10(2), 369–386 (2020). [CrossRef]
3. Qu Yan, Ning Chaoyu, Zou Shuzhen, Yu Haijuan, Chen Xuechun, Xu Shuang, Zuo Jiexi, Han Shifei, Li Xinyao, and Lin Xuechun, “Recent advances in nanosecond-pulsed Ytterbium-doped all-fiber lasers[J],” Infrared and Laser Engineering 51(6), 20220055 (2022). [CrossRef]
4. A. D. Almeida, D. A. Bahamon, N. M. R. Peres, and C. J. S. de Matos, “A critical analysis on the sensitivity enhancement of surface plasmon resonance sensors with graphene,” Nanomaterials 12(15), 2562 (2022). [CrossRef]
5. Y. Zheng, Z. Yi, L. Liu, X. W. Wu, H. Liu, G. F. Li, L. C. Zeng, H. L. Li, and P. H. Wu, “Numerical simulation of efficient solar absorbers and thermal emitters based on multilayer nanodisk arrays,” Appl. Therm. Eng. 230(PB), 120841 (2023). [CrossRef]
6. H. Emami-Nejad, A. Mir, A. Farmani, and R. Tablebzadeh, “Proposal of an infrared electro-optic switch based on grapheme–silicone–graphene metamaterial with electrically dynamic tunability,” Opt. Rev. 29(6), 476–486 (2022). [CrossRef]
7. F. Y. Wu, P. C. Shi, Z. Yi, H. L. Li, and Y. G. Yi, “Ultra-Broadband Solar Absorber and High-Efficiency Thermal Emitter from UV to Mid-Infrared Spectrum,” Micromachines 14(5), 985 (2023). [CrossRef]
8. S. M. G. Mousavi-Kiasari, K. Rashidi, D. Fathi, H. Taleb, S. M. Mirjalili, and V. Faramarzi, “Computational design of highly-sensitive graphene-based multilayer SPR biosensor,” Photonics 9(10), 688 (2022). [CrossRef]
9. F. Qin, J. Chen, J. W. Liu, L. Liu, C. J. Tang, B. Tang, G. F. Li, L. C. Zeng, H. L. Li, and Z. Yi, “Design of high efficiency perovskite solar cells based on inorganic and organic undoped double hole layer,” Sol. Energy 262, 111796 (2023). [CrossRef]
10. Y. Y. Zhu, P. G. Cai, W. L. Zhang, T. Y. Meng, Y. J. Tang, Z. Yi, K. H. Wei, G. F. Li, B. Tang, Y. G. Yi, S. Ameen, and N. Tait, “Ultra-Wideband High-Efficiency Solar Absorber and Thermal Emitter Based on Semiconductor InAs Microstructures,” Micromachines 14(8), 1597 (2023). [CrossRef]
11. J. Y. Wu, Y. Y. Yang, Y. Qu, L. N. Jia, Y. N. Zhang, X. Y. Xu, S. T. Chu, B. E. Little, R. Morandotti, B. H. Jia, and D. J. Moss, “2D layered graphene oxide films integrated with micro-ring resonators for enhanced nonlinear optics,” Small 16(16), 1906563 (2020). [CrossRef]
12. Z. Peng, J. B. Feng, H. Yuan, W. Cheng, Y. Wang, X. D. Ren, H. Cheng, S. Y. Zang, Y. B. Shuai, H. Liu, J. G. Wu, and J. B. Yang, “A Non-Volatile Tunable Ultra-Compact Silicon Photonic Logic Gate,” Nanomaterials 12(7), 1121 (2022). [CrossRef]
13. H. M. Hussein, T. A. Ali, and N. H. Rafat, “A review on the techniques for building all-optical photonic crystal logic gates,” Opt. Laser Technol. 106, 385–397 (2018). [CrossRef]
14. J. J. Singh, D. Dhawan, and N. Gupta, “All-optical photonic crystal logic gates for optical computing: an extensive review,” Opt. Eng. 59(11), 110901 (2020). [CrossRef]
15. X. W. Xue and N. Calabretta, “Nanosecond optical switching and control system for data center networks,” Nat. Commun. 13(1), 2257 (2022). [CrossRef]
16. P. Li, Y. X. Wang, and P. Xu, “All-optical logic gates based on unidirectional surface plasmon polaritons,” Appl. Opt. 58(16), 4205–4210 (2019). [CrossRef]
17. P. Keshtkar, M. Miri, and N. Yasrebi, “Low power, high speed, all-optical logic gates based on optical bistability in graphene-containing compact microdisk resonators,” Appl. Opt. 60(24), 7234–7242 (2021). [CrossRef]
18. T. Sadeghi, S. Golmohammadi, A. F. Armani, and H. Baghban, “Improving the performance of nanostructure multifunctional graphene plasmonic logic gates utilizing coupled-mode theory,” Appl. Phys. B: Lasers Opt. 125(10), 189 (2019). [CrossRef]
19. Y. M. Gong, B. G. Quan, F. R. Hu, H. Wang, L. H. Zhang, M. Z. Jiang, L. Z. Zeng, X. W. Zhang, and W. L. Xu, “Active control of terahertz amplitude and phase based on graphene metasurface,” Phys. E 143, 115334 (2022). [CrossRef]
20. A. Dolatabady, N. Granpayeh, and M. Abedini, “Frequency-tunable logic gates in graphene nano-waveguides,” Photonic Network Communications 39(3), 187–194 (2020). [CrossRef]
21. R. E. Meymand, A. Soleymani, and N. Granpayeh, “All-optical AND, OR, and XOR logic gates based on coherent perfect absorption in graphene-based metasurface at terahertz region-ScienceDirect,” Opt. Commun. 458, 124772 (2020). [CrossRef]
22. Z. Q. Wang, Z. J. Zhang, F. Qiu, M. Wang, W. G. Yang, Z. H. Li, X. F. Hu, Y. P. Li, X Yan, H. Y. Yao, and L. Y. Liang, “Design of an all-optical multi-logic operation-integrated metamaterial-based terahertz logic gate,” Opt. Express 30(22), 40401–40412 (2022). [CrossRef]
23. Z. M. Liu, S. S. Zhuo, F. Q. Zhou, X. Zhang, Y. P. Qin, X. Luo, C. Ji, and G. X. Yang, “Double narrowband induced perfect absorption photonic sensor based on graphene-dielectric-gold hybrid metamaterial,” Nanoscale Res. Lett. 17(1), 85 (2022). [CrossRef]
24. J. Zhu and C. S. Wu, “Detection of amino acid with metamaterial perfect absorbers in the terahertz band,” Meas. 192, 110738 (2022). [CrossRef]
25. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nat. 424(6950), 824–830 (2003). [CrossRef]
26. Z. H. Chen, P. G. Cai, Q. Y. Wen, H. Chen, Y. J. Tang, Z. Yi, K. H. Wei, G. F. Li, B. Tang, and Y. G. Yi, “Graphene Multi-Frequency Broadband and Ultra-Broadband Terahertz Absorber Based on Surface Plasmon Resonance,” Electron. 12(12), 2655 (2023). [CrossRef]
27. J. Zhu and J. G. Yin, “Optical-fibre characteristics based on Fano resonances and sensor application in blood glucose detection,” Opt. Express 30(15), 26749–26760 (2022). [CrossRef]
28. T. Sang, S. A. Dereshgi, W. Hadibrata, I. Tanriover, and K. Aydin, “Highly Efficient Light Absorption of Monolayer Graphene by Quasi-Bound State in the Continuum,” Nanomater. 11(2), 484 (2021). [CrossRef]
29. Z. M. Liu, X. Zhang, F. Q. Zhou, X. Luo, Z. B. Zhang, Y. P. Qin, S. S. Zhuo, E. D. Gao, H. J. Li, and Z. Yi, “Triple plasmon-induced transparency and optical switch desensitized to polarized light based on a mono-layer metamaterial,” Opt. Express 29(9), 13949–13959 (2021). [CrossRef]
30. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008). [CrossRef]
31. M. Alaloul and J. B. Khurgin, “Electrical control of all-optical graphene switches,” Opt. Express 30(2), 1950–1966 (2022). [CrossRef]
32. X. L. Wu, Y. Zheng, Y. Luo, J. G. Zhang, Z. Yi, X. W. Wu, S. B. Cheng, W. X. Yang, Y. Yu, and P. H. Wu, “A four-band and polarization-independent BDS-based tunable absorber with high refractive index sensitivity,” Phys. Chem. Chem. Phys. 23(47), 26864–26873 (2021). [CrossRef]
33. H. Chen, Z. H. Chen, H. Yang, L. H. Wen, Z. Yi, Z. G. Zhou, B. Dai, J. G. Zhang, X. W. Wu, and P. H. Wu, “Multi-mode surface plasmon resonance absorber based on dart-type single-layer graphene,” RSC Adv. 12(13), 7821–7829 (2022). [CrossRef]
34. X. Zhang, F. Q. Zhou, Z. M. Liu, Z. B. Zhang, Y. P. Qin, S. S. Zhuo, X. Luo, E. D. Gao, and H. J. Li, “Quadruple plasmon-induced transparency of polarization desensitization caused by the Boltzmann function,” Opt. Express 29(18), 29387–29401 (2021). [CrossRef]
35. J. Zhu, J. G. Yin, and C. S. Wu, “Tunable Perfect Absorber of Graphene Metamaterial in the Terahertz Band and Its Sensing Properties,” Adv. Photonics Res. 3(4), 2100291 (2022). [CrossRef]
36. Y. P. Zhang, Y. Li, Y. Y. Cao, Y. Z. Liu, and H. Y. Zhang, “Graphene induced tunable and polarization-insensitive broadband metamaterial absorber,” Opt. Commun. 382, 281–287 (2017). [CrossRef]
37. Q. Y. Shangguan, Z. H. Chen, H. Yang, S. B. Cheng, W. X. Yang, Z. Yi, X. W. Wu, S. F. Wang, Y. G. Yi, and P. H. Wu, “Design of ultra-narrow band graphene refractive index sensor,” Sensors 22(17), 6483 (2022). [CrossRef]
38. C. Gan, H. Chu, and E. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the mid-infrared and terahertz frequencies,” Phys. Rev. B 85(12), 125431 (2012). [CrossRef]
39. H. Lu, X. M Liu, and D. Mao, “Plasmonic analog of electromagnetically induced transparency in multi-nanoresonator-coupled waveguide systems,” Phys. Rev. A 85(5), 053803 (2012). [CrossRef]
40. K. Bae, G. Kang, S. K. Cho, W. Park, K. Kim, and W. J. Padilla, “Flexible thin-film black gold membranes with ultrabroadband plasmonic nanofocusing for efficient solar vapour generation,” Nat. Commun. 6(1), 10103 (2015). [CrossRef]
41. Z. Y. Guo, X. R. Nie, F. Shen, H. P. Zhou, Q. F. Zhou, J. Gao, and K. Guo, “Actively tunable terahertz switches based on subwavelength graphene waveguide,” Nanomaterials 8(9), 665 (2018). [CrossRef]
42. M. P. Singh, J. K. Rakshit, and M. Hossain, “Modeling of polarization-conversion and rotation-based ultrafast All-optical ternary logic switch using microring resonator,” Braz. J. Phys. 53(2), 40 (2023). [CrossRef]
43. W. Su and Z. Geng, “Terahertz All-Optical Logic Gates Based on a Graphene Nanoribbon Rectangular Ring Resonator,” IEEE Photonics J. 10(6), 1–8 (2018). [CrossRef]
44. E. D. Gao, H. J. Li, Z. M. Liu, C. X. Xiong, C. Liu, B. X. Ruan, M. Li, and B. H. Zhang, “Terahertz multifunction switch and optical storage based on triple plasmon-induced transparency on a single-layer patterned graphene metasurface,” Opt. Express 28(26), 40013–40023 (2020). [CrossRef]
45. M. H. Wang, W. Qi, H. Yu, X. Q. Jiang, and J. Y. Yang, “Research of high speed optical switch based on compound semiconductor,” Chin. Sci. Bull. 54(20), 3679–3684 (2009). [CrossRef]
46. L Meiping, S Yanpeng, L Xiaoyu, S Jinmei, W Xiaodong, and Y Fuhua, “Tunable plasmon-induced transparency in graphene-based plasmonic waveguide for terahertz band-stop filters,” J. Opt 24(6), 065002 (2022). [CrossRef]
47. Y. L. Fu, X. Y. Hu, C. C. Lu, S. Yue, H. Yang, and Q. H. Gong, “All-optical logic gates based on nanoscale plasmonic slot waveguides,” Nano Lett. 12(11), 5784–5790 (2012). [CrossRef]
48. M. R Yuan, Q. W. Wang, Y. F. Li, Y. H. Xu, Q. Xu, X. Q. Zhang, X. X. Zhang, J. G. Han, and W. L. Zhang, “Terahertz spoof surface plasmonic logic gates,” iScience 23(11), 101685 (2020). [CrossRef]
49. R. El Haffar, O. Mahboub, A. Farkhsi, and M. Figuigue, “All-Optical Logic Gates Using a Plasmonic MIM Waveguide and Elliptical Ring Resonator,” Plasmonics 17(2), 831–842 (2022). [CrossRef]
50. K. Amer, E. Z. Kyriakos, and L. Wei, “Silicon-on-silica waveguides-based all-optical logic gates at 1.55 μm,” Phys. Scr. 98(3), 035517 (2023). [CrossRef]
51. P. Rani, Y. Kalra, and P. K. Sinha, “Design of all optical logic gates in photonic crystal waveguides,” Optik 126(9-10), 950–955 (2015). [CrossRef]
52. Y. Y. Xie, Y. Y. Yin, T. T. Song, Y. C. Zhu, J. X. Chai, B. C. Liu, and Y. C. Ye, “The design and simulation of a multifunctional logic device based on plasmon-induced transparency using two semicircular resonators,” Opt. 255, 168684 (2022).
53. S. H. Abdulnabi and M. N. Abbas, “Design an All-Optical Combinational Logic Circuits Based on Nano-Ring Insulator-Metal-Insulator Plasmonic Waveguides,” Photonics 6(1), 30 (2019). [CrossRef]
