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All-optical AND, OR, and XOR logic gates based on coherent perfect absorption in graphene-based metasurface at terahertz region
Journal Pre-proof All-optical AND, OR, and XOR logic gates based on coherent perfect absorption in graphene-based metasurface at terahertz region Roya Ebrahimi Meymand, Ali Soleymani, Nosrat Granpayeh
PII: DOI: Reference:
S0030-4018(19)30934-4 https://doi.org/10.1016/j.optcom.2019.124772 OPTICS 124772
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Optics Communications
Received date : 25 January 2019 Revised date : 12 October 2019 Accepted date : 15 October 2019 Please cite this article as: 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, Optics Communications (2019), doi: https://doi.org/10.1016/j.optcom.2019.124772. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
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All-Optical AND, OR, and XOR Logic Gates Based on Coherent Perfect Absorption in Graphene-Based Metasurface at Terahertz Region
Roya Ebrahimi Meymand, Ali Soleymani, and Nosrat Granpayeh* [email protected] [email protected] *
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Center of Excellence in Electromagnetics, Optical Communication Laboratory, Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran
Corresponding author: [email protected]
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Abstract: In this paper, we propose a novel method for designing all-optical logic gates based on the coherent perfect absorption principle in graphene-based metasurface in terahertz (THz) region. The proposed structure allows us to access AND, OR, and XOR logic operations by adjusting the relative phase difference of two input signals and creating destructive and/or constructive interference. We have calculated the contrast ratio to analyze the performance of these logic gates. The working frequency of the proposed logic gates can be manipulated by varying the gate-controlled Fermi energy of graphene. These structures can be used in ultrafast all-optical signal processing and ultra-compact integrated circuits.
1. Introduction
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Keywords: Coherent perfect absorption, Graphene, Metasurface, Terahertz, All-optical logic gates.
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All-optical logic gates provide potential applications for optical signal processing and optical networks due to their unique characteristics such as high-rate data transmission, high bandwidth, and low power consumption [1–3]. All-optical logic gates eliminate the need for conversion of optical signals to electronic ones and the existence of a nonlinear medium in electro-optical and nonlinear-optical logic functions. Therefore, it results in a decrease in power consumption [4]. A number of approaches with different schemes such as semiconductor optical amplifier (SOA) [5], electro-optical phenomena [6,7], nonlinear photonic crystal [8], optical fibers [9], self-collimation effect in two dimensional photonic crystal (2D-PC) [10,11], tunable saturable absorption (SA) to reverse saturable absorption (RSA) in graphene-oxide (GO) film and CuPc-doped PMMA thin films [12,13], two-photon absorption (TPA) [14], and multichannel logic gates based on coherent perfect absorption [15] have been proposed to design all optical logic gates. Some limitations such as the need for preparing nonlinear medium, complex design, large size, high-intensity inputs, high power consumption [16], and difficulties in controlling the relative phase differences of input signals [17], increase the demand for new schemes for optical data processing. Coherent perfect absorption (CPA), the concept of time-reversed lasing [18], has drawn great attention due to its functional features. CPA system consists of two counter-propagating waves for achieving perfect absorption, whereas in the coherent perfect transmission (CPT) system, perfect transmission occurs with minimum losses [19]. When the reflected waves from one direction cancel the transmitted waves of the other direction, perfect absorption is achieved and the scattering fields are perfectly suppressed [20]. As illustrated in Fig. 1, when an absorber film is illuminated by two incident waves, a standing wave is formed at the position of the film and or if it is placed in the node of the standing wave (Fig. 1a), the interaction of the electromagnetic field and the film is weak. Therefore, the incident waves will pass the film with low loss and the film acts as a transparent object, and thus perfect transmission occurs (CPT). On the other hand, if the absorber film is positioned at an antinode of the standing wave (Fig. 1b), the interaction would become very strong. Therefore, all the incoming energy to the system is completely absorbed by the metasurface, perfect absorption (CPA) occurs accordingly
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[21,22]. Thus by manipulating the phase and the intensity of one beam, the intensity of other beams on the other direction can be modulated easily by suppressing and/or enhancing the lightmatter interaction [15,23]. In recent years, several potential applications based on the CPA system, such as absorber [24], all-optical modulators and switches [25,26], slow-light waveguide [27], coherent perfect rotator [28], signal processing such as pulse restoration and coherence filtering [29] have been proposed and analyzed.
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Fig.1 Interaction of two coherent beams on an absorbing film, a) destructive interference, in which there is no signal on the film to be coupled to the metasurface absorber and thus coherent perfect transmission (CPT) occurs. b) Constructive interference in which strong intensity signal couples to the metasurface absorber and thus coherent perfect absorption (CPA) occurs.
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Graphene, a 2D metallic material with extraordinary photonic and optoelectronic properties including high conductivity, high carrier mobility, and tunable Fermi level has been intensively studied for decades [30,31]. Graphene exhibits a strong plasmonic response in the THz region. Moreover, high confinement of graphene plasmons compared to diffraction limits results in strong light-matter interactions and compact metasurface designs [32]. Doped and patterned graphene can enhance localized plasmons, hence increasing the absorption coefficient [33]. Therefore, graphene is a promising candidate for THz optical devices such as modulators [34,35], detectors [36,37], sensors [38], absorbers [39,40], antenna [41,42], switches, and logic gates [43]. Some graphene-based logic gates such as electro-optical [6], electronic [44] and alloptical [45] have been proposed and investigated.
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In this paper, we propose an ultra-compact, low power consumption, high contrast ratio THz logic gates based on CPA in graphene metasurface. The logic gates operations are based on coherent perfect transmission and absorption. Compared to the logic gates based on nonlinearity [46–48], our proposed design is fast because it profits from the linear process of coherent perfect absorption and optically linear materials and also because it is based on the interference of two lightwaves. Besides, a low-intensity input level is required. The input lightwaves can be generated by low-energy femtosecond laser pulses in the experiments [49]. Controlling the optical phase difference in our proposed design is easier than other structures which are based on photonic crystal waveguides [50]. The modulating signal in [51,52] is the voltage applied to the graphene layer. Additionally, our structure can adapt to other structures due to its compact design, which results in the reduction of costs. Also, by introducing a proper threshold intensity for each gate, the proposed structure can be used in more compact, complicated, and cascaded devices. In addition, in our proposed device multiple logic functions could be implemented in contrast to the devices designed for only a sole logic function [53]. The working principle of the proposed logic gates is discussed in detail and their efficiencies are verified by simulations. The working frequency of the proposed logic gates can be tuned by applying a bias voltage and shifting the Fermi level of graphene.
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The remaining of the paper is organized as follows: In Section 2, the theory and simulation method are described. In Section 3, the simulation results of the proposed structure are given and discussed. In Section 4, the electrical tunability of the structure is studied. The paper is concluded in Section 5.
2. Theory and Simulation Method
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The schematic of the proposed structure and its unit cell are shown in Fig. 2. Each cell consists of a graphene square ring on a SiO2 substrate with the refractive index of n 1.45 and thickness of 1.3µm. The graphene thickness is assumed to be 0.5 nm. The values of parameters interpolated from [54] to operate in THz frequency range and then optimized to achieve the best performance and the dimensions of 26m26m1.3m. The structure is illuminated by two coherent-counter propagating beams on both sides at normal incidence. In the simulations, we have assumed that the electric field of the two coherent waves is polarized along the x-axis. Periodic boundary conditions are set for the x-y plane and perfect match layers (PML) are applied along the z-direction. The graphene layer is modeled by complex conductivity g , based on random phase approximation (RPA), described by Drude formula as [55,56]:
ie 2 c 2 i 1
(1)
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g
where e, c , , , and are respectively the electric charge of an electron, the graphene chemical potential, the reduced Planck's constant, the electromagnetic wave angular frequency, e is the intraband relaxation time, where and f represent the carrier mobility and the Fermi velocity, respectively. The loss for graphene is included in our simulations by considering the complex conductivity of it. 2
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c
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The chemical potential c 0.6 eV, relaxation time τ=0.5 ps, and T=300K are initially considered. The gate voltage, Vg, is applied to the graphene layer to adjust its Fermi energy.
(a) (b) Fig. 2. (a) The schematic of the proposed metasurface absorber and (b) its unit cell.
In CPA system, output intensities O can be obtained from input beams ( I ) through scattering matrix (Sg) [20]:
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O Sg O
I t I r
r Ie i t Ie i
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where t and r are the transmission and reflection coefficients, respectively. Since the metasurface under investigation is a reciprocal structure with spatial symmetry, and the input beams ( I ) are set to have equal amplitudes, the scattering matrix can be simplified with t t
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and r r , so the amplitude of the scattering coefficients can be expressed as:
O O tIe i rIe i
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The scattering outputs are required to be suppressed at quasi-CPA frequencies i.e. (
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tIei rIei ), from which the necessary condition for CPA is: t r , Which means both the transmission and the reflection coefficients have the same amplitudes and phase difference 2n at the film position. On the other hand, perfect transmission can be achieved when the relative phase difference is equal to (2n 1) . So in CPA systems, absorption and transmission can be modulated by adjusting the phase difference between input beams to control the position of the absorber film along the standing wave [57].
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The proposed metasurface based on patterned graphene can be excited similarly to the one presented by Rao et al. [21]. A special setup is needed to create in-phase and out-phase input beams, which is schematically shown in Fig. 3a. Light can be generated by a CW source such as Quantum cascade lasers centered at a wavelength of 60µm [21,58] and then divided by a lossless 50:50 beam splitter (BS) into two equal optical waves of equal intensities. It should also be noted that in practice for excluding nonlinear and Opto-thermal effects, the powers at the sample position should be at a low level. Thus, the output power of the laser could be 0.5mW up to the level that is low enough to avoid occurring nonlinear effects. Therefore, it is possible to ignore the photo and thermal instability. We have assumed that the electric field of the two coherent waves is polarized along the x-axis. A phase shifter and a variable attenuator in the way of one of the two beams are required to control the relative phase and intensity of the two beams. The system should be calibrated before applications. The total output wave is then directed via a beam splitter and collected by a detector (Fig. 3b).
(a)
(b)
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Fig. 3 (a) The Schematic view of the proposed setup and (b) The schematic view of the CPA and/or CPT setup. The graphene-based metasurface is illuminated by two counter-propagating beams to control the absorption and/or transmission by variation of the relative phase difference between the two input beams.
3. Simulation Results and Discussion
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Simulations based on the FDTD method are performed to verify the function of proposed logic gates. As shown in Fig. 4a when the proposed structure is illuminated by a single beam, there is a plasmonic resonance centered at 4.85 THz. This strong excitation leads to the enhancement of absorption in graphene metasurface with a maximum of 49.65%. If two equal intensity light beams with zero phase difference from opposite sides impinge on the structure, the interaction of light and graphene increases. Therefore, constructive interference of electric fields leads to a coherent absorption of 99.55% (Fig 4b). Additionally, in calculating absorption and transmission of the proposed structure, the scattering and dissipation losses have been considered. The physical mechanism for strong absorption in Fig. 4 (b) can be explained as follows: The electric field distribution at the resonance frequency of 4.85THz for single beam incidence and two-beam illumination with 0 and π relative phase difference are shown in Fig.5. It is clear that when the phase difference between the two input beams at film position is 0 , the strong electric field is mainly concentrated around the two edges of the patterned graphene. Therefore, this strong resonance leads to the enhancement of coherent absorption (Fig. 5a). On the other hand, when the phase difference is , the electric (magnetic) resonance is
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very weak, which results in a small amount of absorption almost near 0.01% (Fig. 5b). The electric field distribution for single-beam illumination is given in Fig. 5c.
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(a) (b) Fig. 4 (a) Absorption, reflection and transmission under the illumination of only one beam at normal incidence (b) Coherent absorption spectrum for the proposed structure.
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(a) (b) (c) Fig. 5 Distribution of the electric field at the resonance frequency of 4.85 THz for (a)-(b) 0 and π phase difference of two incident beams (c) single-beam illumination.
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Thus at the resonance frequency of 4.85 THz, the output intensity can be modulated easily by adjusting the relative phase difference between the two light beams, as the phase difference increases from 0 to π, the output intensity increases from 0.01% to 99.55% (Fig. 6), which gives a modulation contrast of 40dB.
Fig. 6 Output intensity as a function of the relative phase difference at the selected resonant frequency of 4.85 THz.
This high contrast ratio can be utilized in many applications in which high-depth modulation is needed. For instance, by introducing proper threshold intensity we can describe the logic gates function by coherent perfect absorption phenomenon. We can consider the two incident light beams illuminated to the proposed structure as the two ports of logic gates. If the light is incident upon the two input ports simultaneously I , I , the output intensity will depend on the phase
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difference of the inputs at the film position. If the relative phase difference is 2n , there will be constructive interference, CPA occurs, output intensity will be nearly zero, which corresponds to logic 0. In contrast, (2n 1) phase difference leads to destructive interference, coherent perfect transmission (CPT), which corresponds to logic 1. If a single beam impinges to either port 1 or port 2 I , 0 or 0, I , nearly 50% of light is absorbed by the absorbing film and the rest is either transmitted or reflected [54]. Therefore, a high output intensity may not be achieved [59]. Lastly, if the two input intensities are zero (0, 0), the output intensity will be zero certainly.
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Table 1. The output intensity of AND, OR, and XOR logic gates.
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The output intensities for different cases discussed above have been simulated and the results are shown in table 1. We can see that if the phase difference between the two inputs is equal to π, the output intensity will be 0.99I in at the frequency of 4.85THz, which can be considered as logic 1 for both AND and OR logic gates. As we calculated in Fig. 4a, for an ideal planar absorber, half of the input beam intensity will be absorbed and 25% of the incident intensity will be transmitted as well as reflected. Therefore, we can assume that when only one of the input ports is excited I , 0 or 0, I , the output
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intensity is 0.25I in . By choosing different threshold intensity I th , the proposed metasurface
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can be utilized for different logic operations. As shown in Fig. 7, the intensity threshold for AND and OR gates can be considered at 0.25I in and 0. However, by choosing intensity threshold I th1 0.8I in and I th 2 0.2I in , an error can be prevented from occurring in a decision on logic 0 and 1. The truth states of output are “1”, “0”, “0”, “0” for AND gate (Fig. 7a), the truth states of output are “1”, “1”, “1”, “0” for OR gate (Fig. 7b). A zero phase difference is produced between the two input beams at the absorber film position to investigate the performance of the XOR logic gate. According to the CPA mechanism, if the phase difference between the two input beams is equal to 0 or 2nπ, constructive interference occurs and output transmission will be approximately 0. In this case, when two in-phase input beams with equal intensities are simultaneously excited from opposite sides, the output intensity is 0.01I in (Fig. 6), which gives logic 0. If only one of the input ports is illuminated ((𝐼 , 0) or
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(0, 𝐼 )), 0.25I in of the input beam transmit through the structure and by choosing threshold intensity ( I th 2 0.2I in ), the truth states of output are “0”, “1”, “1”, “0” (Fig. 7c). By introducing proper threshold intensity in this way, our planar structure can be used in more complicated and compact devices.
(a) (b) (c) Fig. 7. Output intensity in the input states (1,1), (1,0), (0,1) and (0,0) for (a) AND, (b) OR and (c) XOR logic gates.
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Our proposed device can be used as an ultrafast gate. Operation speed is limited by the response time (RT) which is calculated by Rt C of the circuit, where Rt and C are the total resistance and capacitance of the proposed device, respectively. The total resistance Rt of the proposed device comes from both graphene layer resistance and the resistance Rm of the metal-graphene contact resistance; the former is generally several hundred kilo-ohms, but with highly doped graphene it can be reduced to 125 sq , while the latter is several ohms [54]. The capacitance of the proposed device due to the graphene layer can be calculated as C 0 d Ag d , where 0 , d , A g , and d are respectively the permittivity of the vacuum, the relative permittivity of the
(4)
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I CR 10 log ON I OFF
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dielectric substrate of the structure, the area of the graphene sheet, and the distance between the capacitor plates. The calculated capacitance of the structure is about 7.3 10 15 F . According to RT Rt C , the response time with Rt~20 Ω [60] is calculated to be ~146 fs, which shows a fast operation. The contrast ratio, i.e. output level difference between the two logic states of 1 and 0, is one of the important characteristics of logic gates. The more interval between output levels causes a lower error in sensing logic 0 and 1 [61]. Contrast ratio (CR) is defined as:
where ION and I OFF are the output intensity for logic 1 and 0, respectively. Therefore contrast ratio for AND and XOR gates are 6dB and 14dB respectively. In this regard, these gates are proper candidates for future optical signal processing.
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To design a cascaded structure, it needs experimental data and analysis to calculate output intensities and determining the sensitivity of the THz detectors to release how many iterations are permissible. As illustrated in Fig. 8, the schematics of the binary NAND, NOR, and XNOR gates can be realized by cascading NOT gate and AND, OR, and NOR, respectively.
Fig. 8. Schematic illustration of logic gates NAND, NOR and NXOR built by cascaded AND, OR and XOR gates.
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The cascaded logic gates can be realized in such structure, while the “controller” is used to control signal. Besides, a phase shifter and a variable attenuator are required in this way to control the relative phase and intensity of the two beams. Therefore, by introducing proper phase difference and intensity, NAND, NOR, and NXOR gates can be obtained.
4. Electrical Tunability The frequency tunability of graphene is a remarkable property in optical devices. The CPA frequency of a graphene-based metasurface can be tuned by varying the driven voltage applied to graphene, and it can be described as follows: the Fermi energy depends on charge-carrier density as: E F F n . Therefore, by increasing the electrostatic doping, the charge-carrier
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concentration and the Fermi energy will be increased, which leads to graphene have a higher Drude weight and re-enforced metallicity. Thus, the scattering and reflection increase as well as the transmission decrease. In this way, a necessary condition for CPA i.e. t r will shift
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to higher frequencies. As shown in Fig. 8, by decreasing the bias voltage applied to the graphene, a redshift of the CPA frequency occurs and the contrast ratios for both AND and XOR logic gates also decrease by decreasing the Fermi level. Additionally, by increasing the bias voltage, the graphene conductivity increases and graphene sheet resistance decreases, which leads to an increase in the operating speeds [62]. Therefore, depending on a decreasing or increasing the electrical tunability, switching speed changes.
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(a) (b) Fig. 8. (a) Contrast ratio for AND (purple line) and XOR (blue line) logic gates versus the Fermi energy of graphene. (b) the Dependence of the CPA frequency on the Fermi energy of the graphene.
5. Conclusion
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A method for designing all-optical AND, OR, and XOR logic gates is proposed and simulated, based on coherent perfect absorption (CPA) or transmission (CPT) principles in a graphene metasurface at terahertz (THz) region. We have shown that by adjusting the relative phase difference between the two incident beams at the absorber position, the output intensity can be manipulated, and we can switch between CPA and CPT. A variable optical attenuator and phase shifter are used for amplitude and phase modulation. When the light waves are in-phase, the light output intensity decreases and the interaction of light and graphene causes the coupling of light to surface. The gates must be calibrated before their applications. We used these mechanisms to create constructive and destructive interference for designing optical logic gates. The proposed device has been designed to operate in the THz region. The working frequency of the proposed logic gates can be tuned by varying the chemical potential of the graphene instead of the expensive method of re-design and re-fabrication of the structure with new dimensions. These tunable all-optical logic gates can be used for ultrafast all-optical signal processing, complex or basic computing, optical switching, and photonic integrated circuits. References
[1] M. Zhang, L. Wang, P. Ye, All optical XOR logic gates: technologies and experiment demonstrations, IEEE Commun. Mag. 43 (2005) S19–S24. [2] Q. Wang, G. Zhu, H. Chen, J. Jaques, J. Leuthold, A. Piccirilli, N. Dutta, Study of alloptical XOR using Mach-Zehnder interferometer and differential scheme, IEEE J. Quantum Electron. 40 (2004) 703–710. [3] S. Roy, C. Yadav, All-optical sub-ps switching and parallel logic gates with
Journal Pre-proof
bacteriorhodopsin (BR) protein and BR-gold nanoparticles, Laser Phys. Lett. 11 (2014). C. Kachris, I. Tomkos, Power consumption evaluation of all-optical data center networks, Cluster Comput. 16 (2013) 611–623. [5] T. Fjelde, D. Wolfson, A. Kloch, B. Dagens, A. Coquelin, I. Guillemot, F. Gaborit, F. Poingt, M. Renaud, Demonstration of 20 Gbit/s all-optical logic XOR in integrated SOAbased interferometric wavelength converter, Electron. Lett. 36 (2000) 1863–1864. [6] W. Chen, L. Yang, P. Wang, Y. Zhang, L. Zhou, T. Yang, Y. Wang, J. Yang, Electrooptical logic gates based on graphene–silicon waveguides, Opt. Commun. 372 (2016) 85–90. [7] Q. Li, M. Zhu, D. Li, Z. Zhang, Y. Wei, M. Hu, X. Zhou, X. Tang, Optical logic gates based on electro-optic modulation with Sagnac interferometer, Appl. Opt. 53 (2014) 4708–4715. [8] Y. Liu, F. Qin, Z.M. Meng, F. Zhou, Q.H. Mao, Z.Y. Li, All-optical logic gates based on two-dimensional low-refractive-index nonlinear photonic crystal slabs, Opt. Express. 19 (2011) 1945–1953. [9] M.N. Islam, Ultrafast all-optical logic gates based on soliton trapping in fibers, Opt. Lett. 14 (1989) 1257. [10] Y. Zhang, Y. Zhang, B. Li, Optical switches and logic gates based on self-collimated beams in two-dimensional photonic crystals, Opt. Express. 15 (2007) 9287–9292. [11] X.S. Christina, A.P. Kabilan, Design of optical logic gates using self-collimated beams in 2D photonic crystal, Photonic Sensors. 2 (2012) 173–179. [12] S. Roy, C. Yadav, Femtosecond all-optical parallel logic gates based on tunable saturable to reverse saturable absorption in graphene-oxide thin films, Appl. Phys. Lett. 103 (2013). [13] S. Roy, C. Yadav, All-optical ultrafast logic gates based on saturable to reverse saturable absorption transition in CuPc-doped PMMA thin films, Opt. Commun. 284 (2011) 4435– 4440. [14] P. Sethi, S. Roy, All-optical ultrafast XOR / XNOR logic gates , binary counter , and double-bit comparator with silicon microring resonators, J. Opt. Soc. Am. 53 (2014) 9– 11. [15] M. Papaioannou, E. Plum, J. Valente, T.F. Rogers, N.I. Zheludev, All-optical multichannel logic based on coherent perfect absorption in a plasmonic metamaterial, APL Photonics. 1 (2016) 090801. [16] T. Houbavlis, K. Zoiros, A. Hatziefremidis, H. Avramopoulos, L. Occhi, G. Guekos, S. Hansmann, H. Burkhard, R. Dall’Ara, 10 Gbit/s all-optical Boolean XOR with SOA fibre Sagnac gate, Electron. Lett. 35 (1999) 1650–1652. [17] P. Andalib, N. Granpayeh, All-optical ultra-compact photonic crystal NOR gate based on nonlinear ring resonators, JOSA B. 11 (2009) 085203. [18] Y.D. Chong, L. Ge, H. Cao, A.D. Stone, Coherent Perfect Absorbers: Time-Reversed Lasers, Phys. Rev. Lett. 105 (2010) 053901. [19] J. Zhang, K.F. MacDonald, N.I. Zheludev, Controlling light-with-light without nonlinearity, Light Sci. Appl. 1 (2012) 12524–12532. [20] Y. Fan, F. Zhang, Q. Zhao, Z. Wei, H. Li, Tunable terahertz coherent perfect absorption in a monolayer graphene, Opt. Lett. 39 (2014) 6269–6272. [21] S.M. Rao, J.J. Heitz, T. Roger, N. Westerberg, D. Faccio, Coherent control of light interaction with graphene, Opt. Lett. 39 (2014) 5345–5347.
Jo
urn al P
re-
pro
of
[4]
Journal Pre-proof
L. Baldacci, S. Zanotto, G. Biasiol, L. Sorba, A. Tredicucci, Interferometric control of absorption in thin plasmonic metamaterials: general two port theory and broadband operation, Opt. Express. 23 (2015) 9202–9210. [23] X. Zhang, C. Meng, Z. Yang, Wave Manipulations by Coherent Perfect Channeling, ArXiv Prepr. ArXiv. 1703 (2017) 04979. [24] O. Kotlicki, J. Scheuer, Wideband coherent perfect absorber based on white-light cavity, Opt. Lett. 39 (2014) 6624–6627. [25] X. Fang, M. Lun Tseng, J.. Ou, K.F. MacDonald, D. Ping Tsai, N.I. Zheludev, Ultrafast all-optical switching via coherent modulation of metamaterial absorption, Appl. Phys. Lett. 104 (2014) 141102. [26] R. Bruck, O.L. Muskens, Plasmonic nanoantennas as integrated coherent perfect absorbers on SOI waveguides for modulators and all-optical switches, Opt. Express. 21 (2013) 27652–27661. [27] N. Gutman, A.A. Sukhorukov, Y.D. Chong, C.M. de Sterke, Coherent perfect absorption and reflection in slow-light waveguides, Opt. Lett. 38 (2013) 4970–4973. [28] M. Crescimanno, N.J. Dawson, J.H. Andrews, Coherent perfect rotation, Phys. Rev. A . 86 (2012) 031807. [29] J. Zhang, K.F. MacDonald, N.I. Zheludev, Controlling light-with-light without nonlinearity, Light Sci. Appl. 1 (2012) 1–5. [30] E. Shokati, N. Granpayeh, M. Danaeifar, Wideband and multi-frequency infrared cloaking of spherical objects by using the graphene-based metasurface, Appl. Opt. 56 (2017) 3053–3058. [31] S. Asgari, A. Dolatabady, N. Granpayeh, Tunable midinfrared wavelength selective structures based on resonator with antisymmetric parallel graphene pair, Opt. Eng . 56 (2017) 067102–067102. [32] F.H.L. Koppens, D.E. Chang, F.J.G. De Abajo, Graphene Plasmonics : A Platform for Strong LightÀMatter, Nano Lett. 11 (2011) 3370–3377. [33] R.R. Nair, P. Blake, A.N. Grigorenko, K.S. Novoselov, T.J. Booth, T. Stauber, N.M. Peres, A.. Geim, Fine structure constant defines visual transparency of graphene, Sci. 320 (2008) 1308–1308. [34] B. Sensale-Rodriguez, R. Yan, M.M. Kelly, T. Fang, K. Tahy, W.S. Hwang, D. Jena, L. Liu, H.. Xing, Broadband graphene terahertz modulators enabled by intraband transitions, Nat. Commun. 3 (2012) 780. [35] W. Gao, J. Shu, K. Reichel, D.V. Nickel, X. He, G. Shi, R. Vajtai, P.M. Ajayan, J. Kono, D.M. Mittleman, Q. Xu, High-Contrast Terahertz Wave Modulation by Gated Graphene Enhanced by Extraordinary Transmission through Ring Apertures, Nano Lett. 14 (2014) 1242–1248. [36] M. Mittendorff, S. Winnerl, J. Kamann, J. Eroms, D. Weiss, H. Schneider, M. Helm, Ultrafast graphene-based broadband THz detector, Appl. Phys. Lett. 103 (2013) 021113. [37] F. Xia, T. Mueller, Y.M. Lin, A. Valdes-Garcia, Ultrafast graphene photodetector, Nat. Nanotechnol. 4 (2009) 839–843. [38] Y. Huang, S. Zhong, Y. Shen, L. Yao, Y. Yu, D. Cui, Graphene/Insulator Stack Based Ultrasensitive Terahertz Sensor With Surface Plasmon Resonance, IEEE Photonics J. 9 (2017) 1–11. [39] B. Xiao, M. Gu, S. Xiao, Broadband, wide-angle and tunable terahertz absorber based on cross-shaped graphene arrays., Appl. Opt. 56 (2017) 5458–5462.
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[22]
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H. Xiong, Y.N. Jiang, C. Yang, X.P. Zeng, Frequency-tunable terahertz absorber with wire-based metamaterial and graphene, J. Appl. Phys. 51 (2017) 015102. [41] R. Filter, M. Farhat, M. Steglich, R. Alaee, C. Rockstuhl, F. Lederer, Tunable graphene antennas for selective enhancement of THz-emission, Opt. Express. 21 (2013) 3737– 3745. [42] M. Dragoman, A.A. Muller, D. Dragoman, F. Coccetti, R. Plana, Terahertz antenna based on graphene, J. Appl. Phys. 107 (2010) 104313. [43] J.S. Gómez-Díaz, J. Perruisseau-Carrier, Graphene-based plasmonic switches at near infrared frequencies, Opt. Express. 21 (2013) 15490–15504. [44] R. Sordan, F. Traversi, V. Russo, Logic gates with a single graphene transistor, Appl. Phys. Lett. 94 (2009) 128–130. [45] X.B. Li, W.B. Lu, J. Wang, J. Hu, Z.G. Liu, B.H. Huang, H. Chen, Edge mode graphene plasmons based all-optical logic gates, Photonics Nanostructures - Fundam. Appl. 33 (2019) 66–69. [46] S. Afzal, V. Ahmadi, M. Ebnali-Heidari, All-optical tunable photonic crystal nor gate based on the nonlinear Kerr effect in a silicon nanocavity, J. Opt. Soc. Am. B. 30 (2013) 2535. [47] M. Ghadrdan, M.A. Mansouri-Birjandi, Concurrent implementation of all-optical halfadder and AND & XOR logic gates based on nonlinear photonic crystal, Opt. Quantum Electron. 45 (2013) 1027–1036. [48] J.W.M. Menezes, W.B. De Fraga, A.C. Ferreira, K.D.A. Saboia, A.F.G.F. Filho, G.F. Guimarães, J.R.R. Sousa, H.H.B. Rocha, A.S.B. Sombra, Logic gates based in two- and three-modes nonlinear optical fiber couplers, Opt. Quantum Electron. 39 (2007) 1191– 1206. [49] C.P. Singh, K.S. Bindra, Saturation and reverse saturable absorption in semiconductor doped glass and its application to parallel logic gates, Opt. Quantum Electron. 47 (2015) 3313–3321. [50] C.J. Wu, C.P. Liu, Z. Ouyang, Compact and low-power optical logic NOT gate based on photonic crystal waveguides without optical amplifiers and nonlinear materials, Appl. Opt. 51 (2012) 680. [51] X. Wu, J. Tian, R. Yang, A type of all-optical logic gate based on graphene surface plasmon polaritons, Opt. Commun. 403 (2017) 185–192. [52] K.J.A. Ooi, H.S. Chu, P. Bai, L.K. Ang, Electro-optical graphene plasmonic logic gates, Opt. Lett. 39 (2014) 2–5. [53] J. Dong, X. Zhang, D. Huang, A proposal for two-input arbitrary Boolean logic gates using single semiconductor optical amplifier by picosecond pulse injection, Opt. Express. 17 (2009) 7725. [54] X. Hu, J. Wang, High-speed gate-tunable terahertz coherent perfect absorption using a split-ring graphene, Opt. Lett. 40 (2015) 5538–5541. [55] V.P. Gusynin, S.G. Sharapov, J.P. Carbotte, Magneto-optical conductivity in graphene, J. Phys. Condens. Matter. 19 (2007) 026222. [56] L.A. Falkovsky, A.A. Varlamov, Space-time dispersion of graphene conductivity, Eur. Phys. J. B. 56 (2007) 281–284. [57] X. Fang, K.F. MacDonald, E. Plum, N.I. Zheludev, Coherent control of light-matter interactions in polarization standing waves, Sci. Rep. 6 (2016) 1–7. [58] H. Tao, C.M. Bingham, A.C. Strikwerda, D. Pilon, D. Shrekenhamer, N.I. Landy, K.
Jo
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re-
pro
of
[40]
Journal Pre-proof
of
pro
[62]
re-
[61]
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[60]
Jo
[59]
Fan, X. Zhang, W.J. Padilla, R.D. Averitt, Highly flexible wide angle of incidence terahertz metamaterial absorber : Design , fabrication , and characterization, Phys. Rev. B. 78(24) (2008) 2–5. H. Wang, X. Yu, X. Rong, All-optical AND, XOR, and NOT logic gates based on Ybranch photonic crystal waveguide, Opt. Eng. 54 (2015) 077101–077101. C. Qiu, W. Gao, R. Vajtai, P.M. Ajayan, J. Kono, Q. Xu, Efficient modulation of 1.55 μm radiation with gated graphene on a silicon microring resonator, Nano Lett. 14 (2014) 6811–6815. F. Parandin, M.M. Karkhanehchi, Terahertz all-optical NOR and AND logic gates based on 2D photonic crystals, Superlattices Microstruct. 101 (2017) 253–260. J. Gosciniak, D.T.H. Tan, graphene-based photonic modulators, Sci. Rep. 3 (2013) 1897.
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Highlights
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A novel method for designing all optical logic gates based on coherent perfect absorption and transmission principles. Some designs are proposed and the numerical results are discussed. The design structures are compact and simple to fabricate.
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PII: DOI: Reference:
S0030-4018(19)30934-4 https://doi.org/10.1016/j.optcom.2019.124772 OPTICS 124772
To appear in:
Optics Communications
Received date : 25 January 2019 Revised date : 12 October 2019 Accepted date : 15 October 2019 Please cite this article as: 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, Optics Communications (2019), doi: https://doi.org/10.1016/j.optcom.2019.124772. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
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All-Optical AND, OR, and XOR Logic Gates Based on Coherent Perfect Absorption in Graphene-Based Metasurface at Terahertz Region
Roya Ebrahimi Meymand, Ali Soleymani, and Nosrat Granpayeh* [email protected] [email protected] *
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Center of Excellence in Electromagnetics, Optical Communication Laboratory, Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran
Corresponding author: [email protected]
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Abstract: In this paper, we propose a novel method for designing all-optical logic gates based on the coherent perfect absorption principle in graphene-based metasurface in terahertz (THz) region. The proposed structure allows us to access AND, OR, and XOR logic operations by adjusting the relative phase difference of two input signals and creating destructive and/or constructive interference. We have calculated the contrast ratio to analyze the performance of these logic gates. The working frequency of the proposed logic gates can be manipulated by varying the gate-controlled Fermi energy of graphene. These structures can be used in ultrafast all-optical signal processing and ultra-compact integrated circuits.
1. Introduction
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Keywords: Coherent perfect absorption, Graphene, Metasurface, Terahertz, All-optical logic gates.
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All-optical logic gates provide potential applications for optical signal processing and optical networks due to their unique characteristics such as high-rate data transmission, high bandwidth, and low power consumption [1–3]. All-optical logic gates eliminate the need for conversion of optical signals to electronic ones and the existence of a nonlinear medium in electro-optical and nonlinear-optical logic functions. Therefore, it results in a decrease in power consumption [4]. A number of approaches with different schemes such as semiconductor optical amplifier (SOA) [5], electro-optical phenomena [6,7], nonlinear photonic crystal [8], optical fibers [9], self-collimation effect in two dimensional photonic crystal (2D-PC) [10,11], tunable saturable absorption (SA) to reverse saturable absorption (RSA) in graphene-oxide (GO) film and CuPc-doped PMMA thin films [12,13], two-photon absorption (TPA) [14], and multichannel logic gates based on coherent perfect absorption [15] have been proposed to design all optical logic gates. Some limitations such as the need for preparing nonlinear medium, complex design, large size, high-intensity inputs, high power consumption [16], and difficulties in controlling the relative phase differences of input signals [17], increase the demand for new schemes for optical data processing. Coherent perfect absorption (CPA), the concept of time-reversed lasing [18], has drawn great attention due to its functional features. CPA system consists of two counter-propagating waves for achieving perfect absorption, whereas in the coherent perfect transmission (CPT) system, perfect transmission occurs with minimum losses [19]. When the reflected waves from one direction cancel the transmitted waves of the other direction, perfect absorption is achieved and the scattering fields are perfectly suppressed [20]. As illustrated in Fig. 1, when an absorber film is illuminated by two incident waves, a standing wave is formed at the position of the film and or if it is placed in the node of the standing wave (Fig. 1a), the interaction of the electromagnetic field and the film is weak. Therefore, the incident waves will pass the film with low loss and the film acts as a transparent object, and thus perfect transmission occurs (CPT). On the other hand, if the absorber film is positioned at an antinode of the standing wave (Fig. 1b), the interaction would become very strong. Therefore, all the incoming energy to the system is completely absorbed by the metasurface, perfect absorption (CPA) occurs accordingly
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[21,22]. Thus by manipulating the phase and the intensity of one beam, the intensity of other beams on the other direction can be modulated easily by suppressing and/or enhancing the lightmatter interaction [15,23]. In recent years, several potential applications based on the CPA system, such as absorber [24], all-optical modulators and switches [25,26], slow-light waveguide [27], coherent perfect rotator [28], signal processing such as pulse restoration and coherence filtering [29] have been proposed and analyzed.
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Fig.1 Interaction of two coherent beams on an absorbing film, a) destructive interference, in which there is no signal on the film to be coupled to the metasurface absorber and thus coherent perfect transmission (CPT) occurs. b) Constructive interference in which strong intensity signal couples to the metasurface absorber and thus coherent perfect absorption (CPA) occurs.
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Graphene, a 2D metallic material with extraordinary photonic and optoelectronic properties including high conductivity, high carrier mobility, and tunable Fermi level has been intensively studied for decades [30,31]. Graphene exhibits a strong plasmonic response in the THz region. Moreover, high confinement of graphene plasmons compared to diffraction limits results in strong light-matter interactions and compact metasurface designs [32]. Doped and patterned graphene can enhance localized plasmons, hence increasing the absorption coefficient [33]. Therefore, graphene is a promising candidate for THz optical devices such as modulators [34,35], detectors [36,37], sensors [38], absorbers [39,40], antenna [41,42], switches, and logic gates [43]. Some graphene-based logic gates such as electro-optical [6], electronic [44] and alloptical [45] have been proposed and investigated.
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In this paper, we propose an ultra-compact, low power consumption, high contrast ratio THz logic gates based on CPA in graphene metasurface. The logic gates operations are based on coherent perfect transmission and absorption. Compared to the logic gates based on nonlinearity [46–48], our proposed design is fast because it profits from the linear process of coherent perfect absorption and optically linear materials and also because it is based on the interference of two lightwaves. Besides, a low-intensity input level is required. The input lightwaves can be generated by low-energy femtosecond laser pulses in the experiments [49]. Controlling the optical phase difference in our proposed design is easier than other structures which are based on photonic crystal waveguides [50]. The modulating signal in [51,52] is the voltage applied to the graphene layer. Additionally, our structure can adapt to other structures due to its compact design, which results in the reduction of costs. Also, by introducing a proper threshold intensity for each gate, the proposed structure can be used in more compact, complicated, and cascaded devices. In addition, in our proposed device multiple logic functions could be implemented in contrast to the devices designed for only a sole logic function [53]. The working principle of the proposed logic gates is discussed in detail and their efficiencies are verified by simulations. The working frequency of the proposed logic gates can be tuned by applying a bias voltage and shifting the Fermi level of graphene.
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The remaining of the paper is organized as follows: In Section 2, the theory and simulation method are described. In Section 3, the simulation results of the proposed structure are given and discussed. In Section 4, the electrical tunability of the structure is studied. The paper is concluded in Section 5.
2. Theory and Simulation Method
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The schematic of the proposed structure and its unit cell are shown in Fig. 2. Each cell consists of a graphene square ring on a SiO2 substrate with the refractive index of n 1.45 and thickness of 1.3µm. The graphene thickness is assumed to be 0.5 nm. The values of parameters interpolated from [54] to operate in THz frequency range and then optimized to achieve the best performance and the dimensions of 26m26m1.3m. The structure is illuminated by two coherent-counter propagating beams on both sides at normal incidence. In the simulations, we have assumed that the electric field of the two coherent waves is polarized along the x-axis. Periodic boundary conditions are set for the x-y plane and perfect match layers (PML) are applied along the z-direction. The graphene layer is modeled by complex conductivity g , based on random phase approximation (RPA), described by Drude formula as [55,56]:
ie 2 c 2 i 1
(1)
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g
where e, c , , , and are respectively the electric charge of an electron, the graphene chemical potential, the reduced Planck's constant, the electromagnetic wave angular frequency, e is the intraband relaxation time, where and f represent the carrier mobility and the Fermi velocity, respectively. The loss for graphene is included in our simulations by considering the complex conductivity of it. 2
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c
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The chemical potential c 0.6 eV, relaxation time τ=0.5 ps, and T=300K are initially considered. The gate voltage, Vg, is applied to the graphene layer to adjust its Fermi energy.
(a) (b) Fig. 2. (a) The schematic of the proposed metasurface absorber and (b) its unit cell.
In CPA system, output intensities O can be obtained from input beams ( I ) through scattering matrix (Sg) [20]:
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O Sg O
I t I r
r Ie i t Ie i
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where t and r are the transmission and reflection coefficients, respectively. Since the metasurface under investigation is a reciprocal structure with spatial symmetry, and the input beams ( I ) are set to have equal amplitudes, the scattering matrix can be simplified with t t
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and r r , so the amplitude of the scattering coefficients can be expressed as:
O O tIe i rIe i
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The scattering outputs are required to be suppressed at quasi-CPA frequencies i.e. (
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tIei rIei ), from which the necessary condition for CPA is: t r , Which means both the transmission and the reflection coefficients have the same amplitudes and phase difference 2n at the film position. On the other hand, perfect transmission can be achieved when the relative phase difference is equal to (2n 1) . So in CPA systems, absorption and transmission can be modulated by adjusting the phase difference between input beams to control the position of the absorber film along the standing wave [57].
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The proposed metasurface based on patterned graphene can be excited similarly to the one presented by Rao et al. [21]. A special setup is needed to create in-phase and out-phase input beams, which is schematically shown in Fig. 3a. Light can be generated by a CW source such as Quantum cascade lasers centered at a wavelength of 60µm [21,58] and then divided by a lossless 50:50 beam splitter (BS) into two equal optical waves of equal intensities. It should also be noted that in practice for excluding nonlinear and Opto-thermal effects, the powers at the sample position should be at a low level. Thus, the output power of the laser could be 0.5mW up to the level that is low enough to avoid occurring nonlinear effects. Therefore, it is possible to ignore the photo and thermal instability. We have assumed that the electric field of the two coherent waves is polarized along the x-axis. A phase shifter and a variable attenuator in the way of one of the two beams are required to control the relative phase and intensity of the two beams. The system should be calibrated before applications. The total output wave is then directed via a beam splitter and collected by a detector (Fig. 3b).
(a)
(b)
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Fig. 3 (a) The Schematic view of the proposed setup and (b) The schematic view of the CPA and/or CPT setup. The graphene-based metasurface is illuminated by two counter-propagating beams to control the absorption and/or transmission by variation of the relative phase difference between the two input beams.
3. Simulation Results and Discussion
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Simulations based on the FDTD method are performed to verify the function of proposed logic gates. As shown in Fig. 4a when the proposed structure is illuminated by a single beam, there is a plasmonic resonance centered at 4.85 THz. This strong excitation leads to the enhancement of absorption in graphene metasurface with a maximum of 49.65%. If two equal intensity light beams with zero phase difference from opposite sides impinge on the structure, the interaction of light and graphene increases. Therefore, constructive interference of electric fields leads to a coherent absorption of 99.55% (Fig 4b). Additionally, in calculating absorption and transmission of the proposed structure, the scattering and dissipation losses have been considered. The physical mechanism for strong absorption in Fig. 4 (b) can be explained as follows: The electric field distribution at the resonance frequency of 4.85THz for single beam incidence and two-beam illumination with 0 and π relative phase difference are shown in Fig.5. It is clear that when the phase difference between the two input beams at film position is 0 , the strong electric field is mainly concentrated around the two edges of the patterned graphene. Therefore, this strong resonance leads to the enhancement of coherent absorption (Fig. 5a). On the other hand, when the phase difference is , the electric (magnetic) resonance is
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very weak, which results in a small amount of absorption almost near 0.01% (Fig. 5b). The electric field distribution for single-beam illumination is given in Fig. 5c.
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(a) (b) Fig. 4 (a) Absorption, reflection and transmission under the illumination of only one beam at normal incidence (b) Coherent absorption spectrum for the proposed structure.
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(a) (b) (c) Fig. 5 Distribution of the electric field at the resonance frequency of 4.85 THz for (a)-(b) 0 and π phase difference of two incident beams (c) single-beam illumination.
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Thus at the resonance frequency of 4.85 THz, the output intensity can be modulated easily by adjusting the relative phase difference between the two light beams, as the phase difference increases from 0 to π, the output intensity increases from 0.01% to 99.55% (Fig. 6), which gives a modulation contrast of 40dB.
Fig. 6 Output intensity as a function of the relative phase difference at the selected resonant frequency of 4.85 THz.
This high contrast ratio can be utilized in many applications in which high-depth modulation is needed. For instance, by introducing proper threshold intensity we can describe the logic gates function by coherent perfect absorption phenomenon. We can consider the two incident light beams illuminated to the proposed structure as the two ports of logic gates. If the light is incident upon the two input ports simultaneously I , I , the output intensity will depend on the phase
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difference of the inputs at the film position. If the relative phase difference is 2n , there will be constructive interference, CPA occurs, output intensity will be nearly zero, which corresponds to logic 0. In contrast, (2n 1) phase difference leads to destructive interference, coherent perfect transmission (CPT), which corresponds to logic 1. If a single beam impinges to either port 1 or port 2 I , 0 or 0, I , nearly 50% of light is absorbed by the absorbing film and the rest is either transmitted or reflected [54]. Therefore, a high output intensity may not be achieved [59]. Lastly, if the two input intensities are zero (0, 0), the output intensity will be zero certainly.
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Table 1. The output intensity of AND, OR, and XOR logic gates.
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The output intensities for different cases discussed above have been simulated and the results are shown in table 1. We can see that if the phase difference between the two inputs is equal to π, the output intensity will be 0.99I in at the frequency of 4.85THz, which can be considered as logic 1 for both AND and OR logic gates. As we calculated in Fig. 4a, for an ideal planar absorber, half of the input beam intensity will be absorbed and 25% of the incident intensity will be transmitted as well as reflected. Therefore, we can assume that when only one of the input ports is excited I , 0 or 0, I , the output
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intensity is 0.25I in . By choosing different threshold intensity I th , the proposed metasurface
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can be utilized for different logic operations. As shown in Fig. 7, the intensity threshold for AND and OR gates can be considered at 0.25I in and 0. However, by choosing intensity threshold I th1 0.8I in and I th 2 0.2I in , an error can be prevented from occurring in a decision on logic 0 and 1. The truth states of output are “1”, “0”, “0”, “0” for AND gate (Fig. 7a), the truth states of output are “1”, “1”, “1”, “0” for OR gate (Fig. 7b). A zero phase difference is produced between the two input beams at the absorber film position to investigate the performance of the XOR logic gate. According to the CPA mechanism, if the phase difference between the two input beams is equal to 0 or 2nπ, constructive interference occurs and output transmission will be approximately 0. In this case, when two in-phase input beams with equal intensities are simultaneously excited from opposite sides, the output intensity is 0.01I in (Fig. 6), which gives logic 0. If only one of the input ports is illuminated ((𝐼 , 0) or
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(0, 𝐼 )), 0.25I in of the input beam transmit through the structure and by choosing threshold intensity ( I th 2 0.2I in ), the truth states of output are “0”, “1”, “1”, “0” (Fig. 7c). By introducing proper threshold intensity in this way, our planar structure can be used in more complicated and compact devices.
(a) (b) (c) Fig. 7. Output intensity in the input states (1,1), (1,0), (0,1) and (0,0) for (a) AND, (b) OR and (c) XOR logic gates.
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Our proposed device can be used as an ultrafast gate. Operation speed is limited by the response time (RT) which is calculated by Rt C of the circuit, where Rt and C are the total resistance and capacitance of the proposed device, respectively. The total resistance Rt of the proposed device comes from both graphene layer resistance and the resistance Rm of the metal-graphene contact resistance; the former is generally several hundred kilo-ohms, but with highly doped graphene it can be reduced to 125 sq , while the latter is several ohms [54]. The capacitance of the proposed device due to the graphene layer can be calculated as C 0 d Ag d , where 0 , d , A g , and d are respectively the permittivity of the vacuum, the relative permittivity of the
(4)
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I CR 10 log ON I OFF
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dielectric substrate of the structure, the area of the graphene sheet, and the distance between the capacitor plates. The calculated capacitance of the structure is about 7.3 10 15 F . According to RT Rt C , the response time with Rt~20 Ω [60] is calculated to be ~146 fs, which shows a fast operation. The contrast ratio, i.e. output level difference between the two logic states of 1 and 0, is one of the important characteristics of logic gates. The more interval between output levels causes a lower error in sensing logic 0 and 1 [61]. Contrast ratio (CR) is defined as:
where ION and I OFF are the output intensity for logic 1 and 0, respectively. Therefore contrast ratio for AND and XOR gates are 6dB and 14dB respectively. In this regard, these gates are proper candidates for future optical signal processing.
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To design a cascaded structure, it needs experimental data and analysis to calculate output intensities and determining the sensitivity of the THz detectors to release how many iterations are permissible. As illustrated in Fig. 8, the schematics of the binary NAND, NOR, and XNOR gates can be realized by cascading NOT gate and AND, OR, and NOR, respectively.
Fig. 8. Schematic illustration of logic gates NAND, NOR and NXOR built by cascaded AND, OR and XOR gates.
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The cascaded logic gates can be realized in such structure, while the “controller” is used to control signal. Besides, a phase shifter and a variable attenuator are required in this way to control the relative phase and intensity of the two beams. Therefore, by introducing proper phase difference and intensity, NAND, NOR, and NXOR gates can be obtained.
4. Electrical Tunability The frequency tunability of graphene is a remarkable property in optical devices. The CPA frequency of a graphene-based metasurface can be tuned by varying the driven voltage applied to graphene, and it can be described as follows: the Fermi energy depends on charge-carrier density as: E F F n . Therefore, by increasing the electrostatic doping, the charge-carrier
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concentration and the Fermi energy will be increased, which leads to graphene have a higher Drude weight and re-enforced metallicity. Thus, the scattering and reflection increase as well as the transmission decrease. In this way, a necessary condition for CPA i.e. t r will shift
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to higher frequencies. As shown in Fig. 8, by decreasing the bias voltage applied to the graphene, a redshift of the CPA frequency occurs and the contrast ratios for both AND and XOR logic gates also decrease by decreasing the Fermi level. Additionally, by increasing the bias voltage, the graphene conductivity increases and graphene sheet resistance decreases, which leads to an increase in the operating speeds [62]. Therefore, depending on a decreasing or increasing the electrical tunability, switching speed changes.
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(a) (b) Fig. 8. (a) Contrast ratio for AND (purple line) and XOR (blue line) logic gates versus the Fermi energy of graphene. (b) the Dependence of the CPA frequency on the Fermi energy of the graphene.
5. Conclusion
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A method for designing all-optical AND, OR, and XOR logic gates is proposed and simulated, based on coherent perfect absorption (CPA) or transmission (CPT) principles in a graphene metasurface at terahertz (THz) region. We have shown that by adjusting the relative phase difference between the two incident beams at the absorber position, the output intensity can be manipulated, and we can switch between CPA and CPT. A variable optical attenuator and phase shifter are used for amplitude and phase modulation. When the light waves are in-phase, the light output intensity decreases and the interaction of light and graphene causes the coupling of light to surface. The gates must be calibrated before their applications. We used these mechanisms to create constructive and destructive interference for designing optical logic gates. The proposed device has been designed to operate in the THz region. The working frequency of the proposed logic gates can be tuned by varying the chemical potential of the graphene instead of the expensive method of re-design and re-fabrication of the structure with new dimensions. These tunable all-optical logic gates can be used for ultrafast all-optical signal processing, complex or basic computing, optical switching, and photonic integrated circuits. References
[1] M. Zhang, L. Wang, P. Ye, All optical XOR logic gates: technologies and experiment demonstrations, IEEE Commun. Mag. 43 (2005) S19–S24. [2] Q. Wang, G. Zhu, H. Chen, J. Jaques, J. Leuthold, A. Piccirilli, N. Dutta, Study of alloptical XOR using Mach-Zehnder interferometer and differential scheme, IEEE J. Quantum Electron. 40 (2004) 703–710. [3] S. Roy, C. Yadav, All-optical sub-ps switching and parallel logic gates with
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bacteriorhodopsin (BR) protein and BR-gold nanoparticles, Laser Phys. Lett. 11 (2014). C. Kachris, I. Tomkos, Power consumption evaluation of all-optical data center networks, Cluster Comput. 16 (2013) 611–623. [5] T. Fjelde, D. Wolfson, A. Kloch, B. Dagens, A. Coquelin, I. Guillemot, F. Gaborit, F. Poingt, M. Renaud, Demonstration of 20 Gbit/s all-optical logic XOR in integrated SOAbased interferometric wavelength converter, Electron. Lett. 36 (2000) 1863–1864. [6] W. Chen, L. Yang, P. Wang, Y. Zhang, L. Zhou, T. Yang, Y. Wang, J. Yang, Electrooptical logic gates based on graphene–silicon waveguides, Opt. Commun. 372 (2016) 85–90. [7] Q. Li, M. Zhu, D. Li, Z. Zhang, Y. Wei, M. Hu, X. Zhou, X. Tang, Optical logic gates based on electro-optic modulation with Sagnac interferometer, Appl. Opt. 53 (2014) 4708–4715. [8] Y. Liu, F. Qin, Z.M. Meng, F. Zhou, Q.H. Mao, Z.Y. Li, All-optical logic gates based on two-dimensional low-refractive-index nonlinear photonic crystal slabs, Opt. Express. 19 (2011) 1945–1953. [9] M.N. Islam, Ultrafast all-optical logic gates based on soliton trapping in fibers, Opt. Lett. 14 (1989) 1257. [10] Y. Zhang, Y. Zhang, B. Li, Optical switches and logic gates based on self-collimated beams in two-dimensional photonic crystals, Opt. Express. 15 (2007) 9287–9292. [11] X.S. Christina, A.P. Kabilan, Design of optical logic gates using self-collimated beams in 2D photonic crystal, Photonic Sensors. 2 (2012) 173–179. [12] S. Roy, C. Yadav, Femtosecond all-optical parallel logic gates based on tunable saturable to reverse saturable absorption in graphene-oxide thin films, Appl. Phys. Lett. 103 (2013). [13] S. Roy, C. Yadav, All-optical ultrafast logic gates based on saturable to reverse saturable absorption transition in CuPc-doped PMMA thin films, Opt. Commun. 284 (2011) 4435– 4440. [14] P. Sethi, S. Roy, All-optical ultrafast XOR / XNOR logic gates , binary counter , and double-bit comparator with silicon microring resonators, J. Opt. Soc. Am. 53 (2014) 9– 11. [15] M. Papaioannou, E. Plum, J. Valente, T.F. Rogers, N.I. Zheludev, All-optical multichannel logic based on coherent perfect absorption in a plasmonic metamaterial, APL Photonics. 1 (2016) 090801. [16] T. Houbavlis, K. Zoiros, A. Hatziefremidis, H. Avramopoulos, L. Occhi, G. Guekos, S. Hansmann, H. Burkhard, R. Dall’Ara, 10 Gbit/s all-optical Boolean XOR with SOA fibre Sagnac gate, Electron. Lett. 35 (1999) 1650–1652. [17] P. Andalib, N. Granpayeh, All-optical ultra-compact photonic crystal NOR gate based on nonlinear ring resonators, JOSA B. 11 (2009) 085203. [18] Y.D. Chong, L. Ge, H. Cao, A.D. Stone, Coherent Perfect Absorbers: Time-Reversed Lasers, Phys. Rev. Lett. 105 (2010) 053901. [19] J. Zhang, K.F. MacDonald, N.I. Zheludev, Controlling light-with-light without nonlinearity, Light Sci. Appl. 1 (2012) 12524–12532. [20] Y. Fan, F. Zhang, Q. Zhao, Z. Wei, H. Li, Tunable terahertz coherent perfect absorption in a monolayer graphene, Opt. Lett. 39 (2014) 6269–6272. [21] S.M. Rao, J.J. Heitz, T. Roger, N. Westerberg, D. Faccio, Coherent control of light interaction with graphene, Opt. Lett. 39 (2014) 5345–5347.
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urn al P
re-
pro
of
[4]
Journal Pre-proof
L. Baldacci, S. Zanotto, G. Biasiol, L. Sorba, A. Tredicucci, Interferometric control of absorption in thin plasmonic metamaterials: general two port theory and broadband operation, Opt. Express. 23 (2015) 9202–9210. [23] X. Zhang, C. Meng, Z. Yang, Wave Manipulations by Coherent Perfect Channeling, ArXiv Prepr. ArXiv. 1703 (2017) 04979. [24] O. Kotlicki, J. Scheuer, Wideband coherent perfect absorber based on white-light cavity, Opt. Lett. 39 (2014) 6624–6627. [25] X. Fang, M. Lun Tseng, J.. Ou, K.F. MacDonald, D. Ping Tsai, N.I. Zheludev, Ultrafast all-optical switching via coherent modulation of metamaterial absorption, Appl. Phys. Lett. 104 (2014) 141102. [26] R. Bruck, O.L. Muskens, Plasmonic nanoantennas as integrated coherent perfect absorbers on SOI waveguides for modulators and all-optical switches, Opt. Express. 21 (2013) 27652–27661. [27] N. Gutman, A.A. Sukhorukov, Y.D. Chong, C.M. de Sterke, Coherent perfect absorption and reflection in slow-light waveguides, Opt. Lett. 38 (2013) 4970–4973. [28] M. Crescimanno, N.J. Dawson, J.H. Andrews, Coherent perfect rotation, Phys. Rev. A . 86 (2012) 031807. [29] J. Zhang, K.F. MacDonald, N.I. Zheludev, Controlling light-with-light without nonlinearity, Light Sci. Appl. 1 (2012) 1–5. [30] E. Shokati, N. Granpayeh, M. Danaeifar, Wideband and multi-frequency infrared cloaking of spherical objects by using the graphene-based metasurface, Appl. Opt. 56 (2017) 3053–3058. [31] S. Asgari, A. Dolatabady, N. Granpayeh, Tunable midinfrared wavelength selective structures based on resonator with antisymmetric parallel graphene pair, Opt. Eng . 56 (2017) 067102–067102. [32] F.H.L. Koppens, D.E. Chang, F.J.G. De Abajo, Graphene Plasmonics : A Platform for Strong LightÀMatter, Nano Lett. 11 (2011) 3370–3377. [33] R.R. Nair, P. Blake, A.N. Grigorenko, K.S. Novoselov, T.J. Booth, T. Stauber, N.M. Peres, A.. Geim, Fine structure constant defines visual transparency of graphene, Sci. 320 (2008) 1308–1308. [34] B. Sensale-Rodriguez, R. Yan, M.M. Kelly, T. Fang, K. Tahy, W.S. Hwang, D. Jena, L. Liu, H.. Xing, Broadband graphene terahertz modulators enabled by intraband transitions, Nat. Commun. 3 (2012) 780. [35] W. Gao, J. Shu, K. Reichel, D.V. Nickel, X. He, G. Shi, R. Vajtai, P.M. Ajayan, J. Kono, D.M. Mittleman, Q. Xu, High-Contrast Terahertz Wave Modulation by Gated Graphene Enhanced by Extraordinary Transmission through Ring Apertures, Nano Lett. 14 (2014) 1242–1248. [36] M. Mittendorff, S. Winnerl, J. Kamann, J. Eroms, D. Weiss, H. Schneider, M. Helm, Ultrafast graphene-based broadband THz detector, Appl. Phys. Lett. 103 (2013) 021113. [37] F. Xia, T. Mueller, Y.M. Lin, A. Valdes-Garcia, Ultrafast graphene photodetector, Nat. Nanotechnol. 4 (2009) 839–843. [38] Y. Huang, S. Zhong, Y. Shen, L. Yao, Y. Yu, D. Cui, Graphene/Insulator Stack Based Ultrasensitive Terahertz Sensor With Surface Plasmon Resonance, IEEE Photonics J. 9 (2017) 1–11. [39] B. Xiao, M. Gu, S. Xiao, Broadband, wide-angle and tunable terahertz absorber based on cross-shaped graphene arrays., Appl. Opt. 56 (2017) 5458–5462.
Jo
urn al P
re-
pro
of
[22]
Journal Pre-proof
H. Xiong, Y.N. Jiang, C. Yang, X.P. Zeng, Frequency-tunable terahertz absorber with wire-based metamaterial and graphene, J. Appl. Phys. 51 (2017) 015102. [41] R. Filter, M. Farhat, M. Steglich, R. Alaee, C. Rockstuhl, F. Lederer, Tunable graphene antennas for selective enhancement of THz-emission, Opt. Express. 21 (2013) 3737– 3745. [42] M. Dragoman, A.A. Muller, D. Dragoman, F. Coccetti, R. Plana, Terahertz antenna based on graphene, J. Appl. Phys. 107 (2010) 104313. [43] J.S. Gómez-Díaz, J. Perruisseau-Carrier, Graphene-based plasmonic switches at near infrared frequencies, Opt. Express. 21 (2013) 15490–15504. [44] R. Sordan, F. Traversi, V. Russo, Logic gates with a single graphene transistor, Appl. Phys. Lett. 94 (2009) 128–130. [45] X.B. Li, W.B. Lu, J. Wang, J. Hu, Z.G. Liu, B.H. Huang, H. Chen, Edge mode graphene plasmons based all-optical logic gates, Photonics Nanostructures - Fundam. Appl. 33 (2019) 66–69. [46] S. Afzal, V. Ahmadi, M. Ebnali-Heidari, All-optical tunable photonic crystal nor gate based on the nonlinear Kerr effect in a silicon nanocavity, J. Opt. Soc. Am. B. 30 (2013) 2535. [47] M. Ghadrdan, M.A. Mansouri-Birjandi, Concurrent implementation of all-optical halfadder and AND & XOR logic gates based on nonlinear photonic crystal, Opt. Quantum Electron. 45 (2013) 1027–1036. [48] J.W.M. Menezes, W.B. De Fraga, A.C. Ferreira, K.D.A. Saboia, A.F.G.F. Filho, G.F. Guimarães, J.R.R. Sousa, H.H.B. Rocha, A.S.B. Sombra, Logic gates based in two- and three-modes nonlinear optical fiber couplers, Opt. Quantum Electron. 39 (2007) 1191– 1206. [49] C.P. Singh, K.S. Bindra, Saturation and reverse saturable absorption in semiconductor doped glass and its application to parallel logic gates, Opt. Quantum Electron. 47 (2015) 3313–3321. [50] C.J. Wu, C.P. Liu, Z. Ouyang, Compact and low-power optical logic NOT gate based on photonic crystal waveguides without optical amplifiers and nonlinear materials, Appl. Opt. 51 (2012) 680. [51] X. Wu, J. Tian, R. Yang, A type of all-optical logic gate based on graphene surface plasmon polaritons, Opt. Commun. 403 (2017) 185–192. [52] K.J.A. Ooi, H.S. Chu, P. Bai, L.K. Ang, Electro-optical graphene plasmonic logic gates, Opt. Lett. 39 (2014) 2–5. [53] J. Dong, X. Zhang, D. Huang, A proposal for two-input arbitrary Boolean logic gates using single semiconductor optical amplifier by picosecond pulse injection, Opt. Express. 17 (2009) 7725. [54] X. Hu, J. Wang, High-speed gate-tunable terahertz coherent perfect absorption using a split-ring graphene, Opt. Lett. 40 (2015) 5538–5541. [55] V.P. Gusynin, S.G. Sharapov, J.P. Carbotte, Magneto-optical conductivity in graphene, J. Phys. Condens. Matter. 19 (2007) 026222. [56] L.A. Falkovsky, A.A. Varlamov, Space-time dispersion of graphene conductivity, Eur. Phys. J. B. 56 (2007) 281–284. [57] X. Fang, K.F. MacDonald, E. Plum, N.I. Zheludev, Coherent control of light-matter interactions in polarization standing waves, Sci. Rep. 6 (2016) 1–7. [58] H. Tao, C.M. Bingham, A.C. Strikwerda, D. Pilon, D. Shrekenhamer, N.I. Landy, K.
Jo
urn al P
re-
pro
of
[40]
Journal Pre-proof
of
pro
[62]
re-
[61]
urn al P
[60]
Jo
[59]
Fan, X. Zhang, W.J. Padilla, R.D. Averitt, Highly flexible wide angle of incidence terahertz metamaterial absorber : Design , fabrication , and characterization, Phys. Rev. B. 78(24) (2008) 2–5. H. Wang, X. Yu, X. Rong, All-optical AND, XOR, and NOT logic gates based on Ybranch photonic crystal waveguide, Opt. Eng. 54 (2015) 077101–077101. C. Qiu, W. Gao, R. Vajtai, P.M. Ajayan, J. Kono, Q. Xu, Efficient modulation of 1.55 μm radiation with gated graphene on a silicon microring resonator, Nano Lett. 14 (2014) 6811–6815. F. Parandin, M.M. Karkhanehchi, Terahertz all-optical NOR and AND logic gates based on 2D photonic crystals, Superlattices Microstruct. 101 (2017) 253–260. J. Gosciniak, D.T.H. Tan, graphene-based photonic modulators, Sci. Rep. 3 (2013) 1897.
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Highlights
of pro reurn al P
A novel method for designing all optical logic gates based on coherent perfect absorption and transmission principles. Some designs are proposed and the numerical results are discussed. The design structures are compact and simple to fabricate.
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