Design of an Ultra-Compact and High-Contrast Ratio All-Optical NOR Gate

Design of an Ultra-Compact and High-Contrast Ratio All-Optical NOR Gate | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Design of an Ultra-Compact and High-Contrast Ratio All-Optical NOR Gate Fariborz Parandin, Naser Mahtabi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-788185/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 02 Nov, 2021 Read the published version in Optical and Quantum Electronics → Version 1 posted 6 You are reading this latest preprint version Abstract In this research, an all-optical NOR gate is designed and simulated based on two-dimensional photonic crystals. A square lattice has been used to design this structure. This logic gate has two main inputs, a bias input and an output. Because the output of the NOR gate must be “1” for zero inputs, a bias input is required. One of the characteristics of this structure is its small size for use in optical integrated circuits. Also, in order to reduce the detection error in the output, it has been tried that the outputs have a suitable distance in two “0” and “1” logical states. The use of a small number and simple point defects makes the design of this gate easier. The simulation results show that the proposed structure is suitable for working at a wavelength of 1.55µm. Also, the amount of optical power at the output is high in the “1” logical mode and low in the “0” logical mode. This indicates that this structure has a reliable output for detecting logical values. In this paper, a photonic crystal structure is proposed to realize the NOR logic gate, which is small in size and uses simple linear and point defects. The use of very few point defects has made the design simpler and thus easier to build this gate. Due to these characteristics, this structure can be suitable for optically integrated circuits. Electrical Engineering Electronic Materials and Devices Optical Materials and Devices Atomic and Molecular Physics Photonic crystals PBG Line defect Point defect. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction Photonic crystals are alternating structures of dielectric material whose refractive index changes alternately in one, two, or three dimensions. Depending on the dielectric material, the shape of the structure, the radius of the rods, and the lattice constant, each structure prevents the propagation of a specific wavelength called the photonic band gap (PBG). The PBG property is used to design a variety of optical devices and logic gates [ 1 – 3 ]. The simplicity of the designed gates, high speed, and small dimensions are important features of photonic crystals. The invention of the transistor had revolutionized the electronics industry in the past, paving the way for the design of integrated circuits and the development of electronic devices, which transformed human life. In recent years, photonic crystals have also revolutionized the optical device industry and are widely used in the design of optical fibers, amplifiers, filters, sensors and, biosensors [ 4 , 5 ]. In the digital field, logic gates (AND, OR, NOT, NAND, NOR, etc.) can be designed based on photonic crystals, and many papers have been published in this field [ 6 – 28 ]. Structures in the field of optical adders and subtractors using photonic crystals have also been reported [ 29 – 35 ]. Decoders and encoders based on photonic crystals have also been designed so far [ 36 – 44 ]. One of the important goals of photonic crystals is to design all-optical processors that, in addition to their small size, dramatically increase the speed of information processing. A high quality logic gate can play an effective role in the design of a processor. One of the indicators of the quality of the logic gate is the closeness of the output power in logic “1” to the amount of input power in the “on” state, and also the closeness of the output of logic “0” to the amount of zero power. In other words, more distance between the output power values in the two modes of logic “1” and “0” is one of the design goals. It can be said that the greater power distance, the less possibility of detection error at the output. In this paper, we have tried to design an all-optical NOR gate based on photonic crystals that has a distance between the power values of “0” and “1” logic states, and also has small dimensions. Reducing the dimensions of the gate can make this gate usable in optically integrated circuits. Also, the simplicity of the proposed gate structure is another design goal. The simpler the designed gate, the easier it will be to build. Simpler defects can be used to have a simple structure. Also, not using ring resonators makes the design simple. If changing the radius of the rods in a structure is used as a point defect, the number of defects should be tried to be small. In the proposed optical gate, only one of the rods has changed radius and the two rods have moved slightly. Also, no ring resonator is used in this design, so the design of this optical gate is very simple and will be suitable for use in optical integrated circuits. The proposed NOR gate is designed to work at a wavelength of 1.55µm. The reason for choosing this wavelength is that it is used in current fiber optic communications. Therefore, the initial structure must be chosen so that this wavelength is in the range of PBG. In this way, light waves with this wavelength do not pass through the periodic structure, and by creating waveguide paths, it will be possible for light to propagate in the desired paths. To design the NOR optical gate, three input paths and one output path have been used. In addition to the two main inputs, additional input is required. Given that in the optical NOR gate, the output must be equal to “1” for “0” inputs, so we need an additional input called “Bias”. The bias input is considered “on” for all input modes. 2. All-optical Nor Gate To design an all-optical NOR gate, a photonic crystal structure with a square lattice is first selected. This structure consists of Si rods placed in the air. Si rods have a cylindrical cross section. The refractive index of the rods is 3.48 at the wavelength of 1.55µm and the refractive index of the air is equal to 1. The number of rods is considered to be 17×19. The lattice constant, which is the distance between the centers of the rods, is equal to 0.56µm, and the radius of the bars is considered to be 0.112µm. The results of the band structure for the alternating structure are shown in Fig. 1 . The resulting band structure diagram shows that a PBG is generated at the normalized wavelength. The wavelength equivalent to this normalized range is 1.35< λ < 2.00. Given that the PBG range has a wavelength of 1.55µm, this structure is suitable for the mentioned wavelengths. Now to reach the desired NOR gate, paths for inputs and output must be selected. Linear defects are used to propagate light in these directions. In this structure, to avoid the complexity of the structure and the simplicity of the design, very few point defects have been used. Figure 2 shows the defect paths to achieve the final structure of the all-optical NOR logic gate. Figure 2 shows that the two inputs A and B are located on the left side of the structure. Using two linear defects named W1 and W2, the light propagation path is created in these inputs. There is also a bias input in the middle of the main inputs. The bias input has a phase difference of 180 o compared to the two main inputs. A vertical linear defect is also selected to connect all inputs. Finally, the output path is created with a linear defect along the bias input. A rod is selected at the beginning of the output path as a point defect, whose radius is half the radius of the other rods and is shown in the figure by R 1 . Also, two rods at the top and bottom of the vertical path are moved 0.4a to the corners. These rods are shown in Fig. 2 in green. As can be seen, the number of point defects in this structure is very small and this makes the structure less complex during implementation. Figure 3 shows a diagram of the distribution of optical power in defect paths. Figure 3 (a) shows the power distribution for the zero inputs (A = B = 0). In this case, since the bias input is always on, the power generated from this source is directed to the output path, and most of the power is transferred to the output. In this case, a small amount of light power is emitted to the main inputs and will cause power dissipation. Figure 3 (b, c) shows the optical power distribution for unequal inputs (A ≠ B). These two figures show that when only one of the main inputs is on, the emitted waves from it have a destructive interference with the emitted waves from the bias input at the point of collision. Therefore the power distribution is very small and the amount of power at the output will be very low. When both inputs are on, the light waves emitted from them also interfere with the bias source at the point of collision, resulting in a reduction in the amplitude of the wave. That is, the interference of the waves will be destructive. Figure 3 (d) shows the power distribution diagram for this mode. To analyze the simulation results quantitatively, optical power simulation has been performed for the optical NOR gate for different input modes. In these graphs, normalized quantities are used to better compare the results. This means that the power of the bias source is considered as the basis and the power calculated at the output is considered relative to the power of this source. Output power values are calculated for all four input modes. Case 1 (A = B = 0) : In the case where both input sources are off, the bias source is on and provides the power needed to activate the output. Figure 4 shows the normalized power diagram in this case. According to Fig. 4 , it can be seen that the optical power at the output is equal to 0.68. In other words, 68% of the optical power of the bias source is transmitted to the output. This power can be considered as logic “1”. Cases 2 and 3. (A = 0, B = 1, and A = 1, B = 0) : When only one of the inputs is on, due to the selection of point defects as well as the path length of the input waveguides and also the phase difference of the bias source, the light waves at the collision point weaken each other and the power propagated to the output is very low. Figure 5 shows the normalized power diagram for these two modes. Due to the symmetry of the circuit for inputs A and B, the power diagram in the outputs will be the same for these two modes of input. Figure 5 shows that the normalized output power, in this case, is 0.07. In other words, only 7% of the optical power of the input source is transmitted to the output. This small value can be considered as a logical “0”. Case 4 (A = B = 1) : If both input sources are on, the waves generated by the input sources and the bias source will overlap at the point of collision, resulting in signal attenuation and a very small amount of power being emitted to the output. The simulation results show that the amount of power emitted to the output, in this case, is equal to 0.07. This amount of power is very low and is equivalent to a logical “0”. Figure 6 shows the normalized power diagram for this mode. The only point defect that has changed radius is a rod with radius R 1 . Now we want to get the optimal value of the radius of this rod so that the output power for the logical “1” and the logical “0” is in the best position. The best situation will be when the logical “1” has high power and the logical “0” has low power. Figure 7 shows the simulation results for the output optical power at different input modes for different values of R 1 . As shown in Fig. 7 , for low values of R 1 , the output power in logic “1” is close to the bias source power and the output has a strong “1”. In this case, the output value in logical “0” modes is close to 0.2. As R 1 increases, the amount of power in logic “1” decreases, but in this case, the value of “0” also decreases. Table 1 shows the output normalized power for radius changes R 1 . Table 1 Normalized optical power for different values of R1 R1 Outputs AB = 00 A ≠ B AB = 11 CR( dB) 20nm 1.00 0.19 0.20 7.0 40nm 0.90 0.14 0.14 8.0 50nm 0.77 0.10 0.10 8.9 55nm 0.68 0.07 0.07 9.9 60nm 0.60 0.06 0.06 10 65nm 0.53 0.05 0.05 10.2 According to Table 1 , it can be said that with increasing radius R 1 , although the value of logical “0” decreases, the value of logical “1” also decreases. For R 1 values from 50nm to 60nm, the power is acceptable in the logical “1” mode and the value of logic “0” is greatly reduced and therefore the contrast ratio (CR) value is increased. For example, when R 1 = 55nm, the normalized output power in logical “1” mode is equal to 0.68 and its value in logic “0” is equal to 0.07. The value of CR, in this case, is equal to CR = 9.9dB. With further increase of R 1 , the amount of optical power in the logical “1” mode is reduced and is not desirable. 3. Conclusion In this paper, an all-optical NOR logic gate is designed based on two-dimensional photon crystals with a square lattice. Optical power is used to define the logical values of “0” and “1”. In this way, high optical power is considered as logic “1” and very low optical power is considered as logic “0”. For the desired gate, two inputs are considered as main inputs and one as bias input. To use the proposed structure in optically integrated circuits, the size of the gate has been reduced as much as possible. Also, in the design of this gate, very simple defects have been used so that it can be built easily. The simulation results show that this logic gate has high optical power for logic “1” and low optical power for logic “0”. Therefore, the distance between the upper and lower logic values is large and the detection error at the output will be low. 4. Declarations Acknowledgment: This paper was written with the support of Kermanshah Branch, Islamic Azad University. 5. References [1] J.D. Joannopoulos, R.D. Meade, J.N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton University Press, Princeton, 1995 [2] E. Yablonovitch, Photonic crystals: semiconductors of light. Sci Am. 285(6):47-55., Sci. Am. 2001 [3] S. John, Strong localization of photons in certain disordered dielectric superlattices, Phys. Rev. Lett. 58, 2486–2489 (1987) [4] S. Olyaee, A. Naraghi, V. Ahmadi, High sensitivity evanescent-field gas sensor based on modified photonic crystal fiber for gas condensate and air pollution monitoring, Optik - International Journal for Light and Electron Optics, 125(1), 596-600, 2014 [5] S. Olyaee, F. Taghipour, Design of new square-lattice photonic crystal fibers for optical communication applications, Int. J. Physical Sci., 6(18), 4405-4411, 2011 [6] A. Farmani, A. Mir, M. Irannejad, 2D-FDTD simulation of ultra-compact multifunctional logic gates with nonlinear photonic crystal, Journal of the Optical Society of America B, 36(4), 811-818, 2019 [7] F. Parandin, M. Moayed, Designing and simulation of 3-input majority gate based on two-dimensional photonic crystals, Optik, 216, 164930, 2020 [8] H. Sharifi, S. M. Hamidi, K. Navi, A new design procedure for all-optical photonic crystal logic gates and functions based on threshold logic, Optics Communications, 370, 231-238, 2016 [9] A. Salimzadeh, H. Alipour-Banaei, An all optical 8 to 3 encoder based on photonic crystal OR-gate ring resonators, Optics Communications, 410(1), 793-798, 2018 [10] A. Mohebzadeh-Bahabady, S. Olyaee , All-optical NOT and XOR logic gates using photonic crystal nano-resonator and based on an interference effect, IET Optoelectronics, 12(4), 191-195, 2018 [11] M.M. Gupta, S. Medhekar, All-optical NOT and AND gates using counter propagating beams innonlinear Mach–Zehnder interferometer made of photonic crystal waveguides, Optik, 127, 1221-1228, 2016 [12] K. Goudarzi, A. Mir, I. Chaharmahali, D. Goudarzi, All-optical XOR and OR logic gates based on line and point defects in 2-D photonic crystal, Optics &Laser Technology, 78, 139-142, 2016 [13] H.M.E. Hussein, T.A. Ali, N.H. Rafat, New designs of a complete set of Photonic Crystals logic gates, Optics Communications, 411, 175-181, 2018 [14] P. Andalib, N. Granpayeh, All-optical ultra-compact photonic crystal AND gate based on nonlinear ring resonators. J. Opt. Soc. Am B 26, 10-16, 2009 [15] H. Saghaei, A. Zahedi, R. Karimzadeh, F. Parandin, Line defects on photonic crystals for the design of all-optical power splitters and digital logic gates, Superlattices and Microstructures, 110, 133-138, 2017 [16] S. Olyaee, M. Seifouri, A. Mohebzadeh-Bahabady, M. Sardari, Realization of all-optical NOT and XOR logic gates based on interference effect with high contrast ratio and ultra-compacted size, Opt Quant Electron, 50, 385, 2018 [17] W.P. Lin, Y.F. Hsu, H.L. Kuo, Design of Optical Nor Logic Gates Using Two Dimension Photonic Crystals. Journal of Modern Physics, 2(3), 144-147, 2013 [18] J. Bao, J. Xiao, L. Fan, X. Li, Y. Hai, T. Zhang, C. Yang, All-optical NOR and NAND gates based on photonic crystal ring resonator, Optics Communications, 329, 109-112, 2014 [19] H. Alipour-Banaei, S. Serajmohammadi, F. Mehdizadeh, All optical NOR and NAND gate based on nonlinear photonic crystalring resonators, Optik, 125, 5701-5704, 2014 [20] Mehdizadeh, Farhad, and Mohammad Soroosh, Designing of all optical NOR gate based on photonic crystal, Indian Journal of Pure & Applied Physics (IJPAP) 54.01, 35-39, 2016 [21] F. Parandin, M.M. Karkhanehchi, Terahertz all-optical NOR and AND logic gates based on 2D photonic crystals, Superlattices and Microstructures , 101, 253-260, 2017 [22] A. Kumar, S. Medhekar, All optical NOT and NOR gates using interference in the structures based on 2D linear photonic crystal ring resonator, Optik, 179, 237-243, 2019 [23] E. Shaik, N. Rangaswamy, Realization of all-optical NAND and NOR logic functions with photonic crystal based NOT, OR and AND gates using De Morgan’s theorem. J. Opt. 47, 8–21, 2018 [24] F. Parandin, M.R. Malmir, M. Naseri, A. Zahedi, Reconfigurable all-optical NOT, XOR, and NOR logic gates based on two dimensional photonic crystals, Superlattices and Microstructures 113, 737-744, 2018 [25] A. Kumar, S. Medhekar, All optical NOR and NAND gates using four circular cavities created in 2D nonlinear photonic crystal. Optics & Laser Technology, 123, 105910, 2020 [26] D.G.S. Rao, S. Swarnakar, S. Kumar, Performance analysis of all-optical NAND, NOR, and XNOR logic gates using photonic crystal waveguide for optical computing applications, Opt. Eng. 59(5), 057101, 2020 [27] A. Mohebzadeh-Bahabady, S. Olyaee, Investigation of response time of small footprint photonic crystal AND logic gate. Optoelectron. Lett. 16, 477–480, 2020 https://doi.org/10.1007/s11801-020-0056-4 [28] E. Veisi, M. Seifouri,S. Olyaee, A novel design of all-optical high speed and ultra-compact photonic crystal AND logic gate based on the Kerr effect. Appl. Phys. B 127, 70, 2021 [29] M. Seifouri, S. Olyaee, M. Sardari, A. Mohebzadeh-Bahabady, Ultra-fast and compact all-optical half adder using 2D photonic crystals, IET Optoelectronics, 13(3), 139-143, 2019 [30] M.M. Karkhanehchi, F. Parandin, A. Zahedi, Design of an all optical half-adder based on 2D photonic crystals. Photon Netw Commun 33, 159-165, 2017 [31] M.H. Sani,A.A. Tabrizi, H. Saghaei, et al. An ultrafast all-optical half adder using nonlinear ring resonators in photonic crystal microstructure. Opt Quant Electron 52, 107, 2020 [32] M. Abdollahi, F. Parandin, A novel structure for realization of an all-optical, one-bit half-adder based on 2D photonic crystals. J Comput Electron 18, 1416-1422, 2019 [33] F. Parandin, M.R. Malmir, M. Naseri, All-optical half-subtractor with low-time delay based on two-dimensional photonic crystals, Superlattices and Microstructures 109 , 437-441, 2017 [34] M. Ghadrdan, M.A. Mansouri-Birjandi, Concurrent implementation of all-optical half-adder and AND & XOR logic gates based on nonlinear photonic crystal, Opt Quant Electron, 45, 1027-1036, 2013 [35] F. Parandin, M.R. Malmir, Reconfigurable all optical half adder and optical XOR and AND logic gates based on 2D photonic crystals. Opt Quant Electron 52, 56, 2020 [36] S. Naghizade , H. Saghaei , A novel design of all-optical 4 to 2 encoder with multiple defects in silica-based photonic crystal fiber, Optik, 222, 165419, 2020 [37] F. Parandin, High contrast ratio all-optical 4 × 2 encoder based on two-dimensional photonic crystals, Optics & Laser Technology, 113, 447-452, 2019 [38] T. A. Moniem, All optical active high decoder using integrated 2D square lattice photonic crystals, Journal of Modern Optics, Volume 62, Issue 19, 1643-1649, 2015 [39] F. Parandin, M. M. Karkhanehchi, M. Naseri, A. Zahedi, Design of a high bitrate optical decoder based on photonic crystals, Journal of Computational Electronics, 17, 830-836, 2018 [40] A. Zahedi, F. Parandin, M.M. Karkhanehchi, H. Habibi-Shams, S. Rajamand, Design and Simulation of Optical 4-Channel Demultiplexer Using Photonic Crystals, Journal of Optical Communications, 40(1), 17-20, 2017 [41] F. Parandin, R. Kamarian, M. Jomour, A novel design of all optical half-subtractor using a square lattice photonic crystals. Opt Quant Electron 53, 114, 2021 [42] S. Olyaee, "Ultra-fast and compact all-optical encoder based on photonic crystal nano-resonator without using nonlinear materials", Phot. Lett. Pol., 11(1), 10-12, 2019 [43] F. Parandin, Ultra-compact terahertz all-optical logic comparator on GaAs photonic crystal platform, Optics & Laser Technology, 144, 107399, 2021 [44] F. Parandin, R. Kamarian, and M. Jomour, Optical 1-bit comparator based on two-dimensional photonic crystals, Appl. Opt. 60, 2275-2280 (2021) Cite Share Download PDF Status: Published Journal Publication published 02 Nov, 2021 Read the published version in Optical and Quantum Electronics → Version 1 posted Editorial decision: Minor revisions 22 Sep, 2021 Reviews received at journal 11 Aug, 2021 Reviewers invited by journal 11 Aug, 2021 Editor invited by journal 09 Aug, 2021 Editor assigned by journal 06 Aug, 2021 First submitted to journal 05 Aug, 2021 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-788185","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":45336099,"identity":"0409822a-b932-469c-aff2-679d3aad4087","order_by":0,"name":"Fariborz 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A=B=1","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-788185/v1/c568c42caa689b8bd58e4e4f.png"},{"id":12422599,"identity":"d9631308-c865-48d3-9f91-70dad61f881d","added_by":"auto","created_at":"2021-08-13 20:52:19","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":9375,"visible":true,"origin":"","legend":"Output normalized power for A=B=0","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-788185/v1/6c27a9ebfbce6e8fca715fde.png"},{"id":12422608,"identity":"3e07338c-9fbc-4058-9b5f-c14f42405899","added_by":"auto","created_at":"2021-08-13 20:55:18","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":10095,"visible":true,"origin":"","legend":"Output normalized power for A=0, B=1 and A=1, B=0","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-788185/v1/69faa695073a34dbbb1aa754.png"},{"id":12422464,"identity":"a70e8ff8-896e-4c02-86a7-609a1895a001","added_by":"auto","created_at":"2021-08-13 20:49:19","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":9204,"visible":true,"origin":"","legend":"Output normalized power for A=B=1","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-788185/v1/e33f945e1e6e7167c68df95e.png"},{"id":12422463,"identity":"5d9b24b7-0985-4c26-96d0-3735af59b581","added_by":"auto","created_at":"2021-08-13 20:49:18","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":11157,"visible":true,"origin":"","legend":"Output normalized power for different values of R1","description":"","filename":"Onlinefloatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-788185/v1/900d963ca8b9bd281ba6289b.png"},{"id":16038974,"identity":"79e9b434-7e36-495d-b435-b6ccf8605045","added_by":"auto","created_at":"2021-11-30 19:58:30","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":353383,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-788185/v1/d0e43118-1c8e-48a8-9a5a-589f5390661e.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eDesign of an Ultra-Compact and High-Contrast Ratio All-Optical NOR Gate\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003ePhotonic crystals are alternating structures of dielectric material whose refractive index changes alternately in one, two, or three dimensions. Depending on the dielectric material, the shape of the structure, the radius of the rods, and the lattice constant, each structure prevents the propagation of a specific wavelength called the photonic band gap (PBG). The PBG property is used to design a variety of optical devices and logic gates [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe simplicity of the designed gates, high speed, and small dimensions are important features of photonic crystals. The invention of the transistor had revolutionized the electronics industry in the past, paving the way for the design of integrated circuits and the development of electronic devices, which transformed human life. In recent years, photonic crystals have also revolutionized the optical device industry and are widely used in the design of optical fibers, amplifiers, filters, sensors and, biosensors [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn the digital field, logic gates (AND, OR, NOT, NAND, NOR, etc.) can be designed based on photonic crystals, and many papers have been published in this field [\u003cspan additionalcitationids=\"CR7 CR8 CR9 CR10 CR11 CR12 CR13 CR14 CR15 CR16 CR17 CR18 CR19 CR20 CR21 CR22 CR23 CR24 CR25 CR26 CR27\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. Structures in the field of optical adders and subtractors using photonic crystals have also been reported [\u003cspan additionalcitationids=\"CR30 CR31 CR32 CR33 CR34\" citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. Decoders and encoders based on photonic crystals have also been designed so far [\u003cspan additionalcitationids=\"CR37 CR38 CR39 CR40 CR41 CR42 CR43\" citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eOne of the important goals of photonic crystals is to design all-optical processors that, in addition to their small size, dramatically increase the speed of information processing. A high quality logic gate can play an effective role in the design of a processor. One of the indicators of the quality of the logic gate is the closeness of the output power in logic \u0026ldquo;1\u0026rdquo; to the amount of input power in the \u0026ldquo;on\u0026rdquo; state, and also the closeness of the output of logic \u0026ldquo;0\u0026rdquo; to the amount of zero power. In other words, more distance between the output power values in the two modes of logic \u0026ldquo;1\u0026rdquo; and \u0026ldquo;0\u0026rdquo; is one of the design goals. It can be said that the greater power distance, the less possibility of detection error at the output.\u003c/p\u003e \u003cp\u003eIn this paper, we have tried to design an all-optical NOR gate based on photonic crystals that has a distance between the power values of \u0026ldquo;0\u0026rdquo; and \u0026ldquo;1\u0026rdquo; logic states, and also has small dimensions. Reducing the dimensions of the gate can make this gate usable in optically integrated circuits. Also, the simplicity of the proposed gate structure is another design goal. The simpler the designed gate, the easier it will be to build. Simpler defects can be used to have a simple structure. Also, not using ring resonators makes the design simple. If changing the radius of the rods in a structure is used as a point defect, the number of defects should be tried to be small.\u003c/p\u003e \u003cp\u003eIn the proposed optical gate, only one of the rods has changed radius and the two rods have moved slightly. Also, no ring resonator is used in this design, so the design of this optical gate is very simple and will be suitable for use in optical integrated circuits.\u003c/p\u003e \u003cp\u003eThe proposed NOR gate is designed to work at a wavelength of 1.55\u0026micro;m. The reason for choosing this wavelength is that it is used in current fiber optic communications. Therefore, the initial structure must be chosen so that this wavelength is in the range of PBG. In this way, light waves with this wavelength do not pass through the periodic structure, and by creating waveguide paths, it will be possible for light to propagate in the desired paths.\u003c/p\u003e \u003cp\u003eTo design the NOR optical gate, three input paths and one output path have been used. In addition to the two main inputs, additional input is required. Given that in the optical NOR gate, the output must be equal to \u0026ldquo;1\u0026rdquo; for \u0026ldquo;0\u0026rdquo; inputs, so we need an additional input called \u0026ldquo;Bias\u0026rdquo;. The bias input is considered \u0026ldquo;on\u0026rdquo; for all input modes.\u003c/p\u003e"},{"header":"2. All-optical Nor Gate","content":"\u003cp\u003eTo design an all-optical NOR gate, a photonic crystal structure with a square lattice is first selected. This structure consists of Si rods placed in the air. Si rods have a cylindrical cross section. The refractive index of the rods is 3.48 at the wavelength of 1.55\u0026micro;m and the refractive index of the air is equal to 1. The number of rods is considered to be 17\u0026times;19. The lattice constant, which is the distance between the centers of the rods, is equal to 0.56\u0026micro;m, and the radius of the bars is considered to be 0.112\u0026micro;m.\u003c/p\u003e\n\u003cp\u003eThe results of the band structure for the alternating structure are shown in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. The resulting band structure diagram shows that a PBG is generated at the normalized wavelength. The wavelength equivalent to this normalized range is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e1.35\u0026lt; \u003cspan style=\"color: rgb(29, 28, 29); font-family: Slack-Lato, appleLogo, sans-serif; font-size: 15px; font-style: normal; font-variant-ligatures: common-ligatures; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(248, 248, 248); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;\"\u003e\u0026lambda; \u0026lt; 2.00.\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eGiven that the PBG range has a wavelength of 1.55\u0026micro;m, this structure is suitable for the mentioned wavelengths. Now to reach the desired NOR gate, paths for inputs and output must be selected. Linear defects are used to propagate light in these directions. In this structure, to avoid the complexity of the structure and the simplicity of the design, very few point defects have been used. Figure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e shows the defect paths to achieve the final structure of the all-optical NOR logic gate.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e shows that the two inputs A and B are located on the left side of the structure. Using two linear defects named W1 and W2, the light propagation path is created in these inputs. There is also a bias input in the middle of the main inputs. The bias input has a phase difference of 180\u003csup\u003eo\u003c/sup\u003e compared to the two main inputs. A vertical linear defect is also selected to connect all inputs. Finally, the output path is created with a linear defect along the bias input. A rod is selected at the beginning of the output path as a point defect, whose radius is half the radius of the other rods and is shown in the figure by R\u003csub\u003e1\u003c/sub\u003e. Also, two rods at the top and bottom of the vertical path are moved 0.4a to the corners. These rods are shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e in green. As can be seen, the number of point defects in this structure is very small and this makes the structure less complex during implementation.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e shows a diagram of the distribution of optical power in defect paths. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e (a) shows the power distribution for the zero inputs (A\u0026thinsp;=\u0026thinsp;B\u0026thinsp;=\u0026thinsp;0). In this case, since the bias input is always on, the power generated from this source is directed to the output path, and most of the power is transferred to the output. In this case, a small amount of light power is emitted to the main inputs and will cause power dissipation.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e (b, c) shows the optical power distribution for unequal inputs (A\u0026thinsp;\u0026ne;\u0026thinsp;B). These two figures show that when only one of the main inputs is on, the emitted waves from it have a destructive interference with the emitted waves from the bias input at the point of collision. Therefore the power distribution is very small and the amount of power at the output will be very low.\u003c/p\u003e\n\u003cp\u003eWhen both inputs are on, the light waves emitted from them also interfere with the bias source at the point of collision, resulting in a reduction in the amplitude of the wave. That is, the interference of the waves will be destructive. Figure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e (d) shows the power distribution diagram for this mode.\u003c/p\u003e\n\u003cp\u003eTo analyze the simulation results quantitatively, optical power simulation has been performed for the optical NOR gate for different input modes. In these graphs, normalized quantities are used to better compare the results. This means that the power of the bias source is considered as the basis and the power calculated at the output is considered relative to the power of this source. Output power values are calculated for all four input modes.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCase 1\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e(A\u0026thinsp;=\u0026thinsp;B\u0026thinsp;=\u0026thinsp;0)\u003c/strong\u003e: In the case where both input sources are off, the bias source is on and provides the power needed to activate the output. Figure \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e shows the normalized power diagram in this case. According to Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e, it can be seen that the optical power at the output is equal to 0.68. In other words, 68% of the optical power of the bias source is transmitted to the output. This power can be considered as logic \u0026ldquo;1\u0026rdquo;.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCases 2\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eand 3. (A\u0026thinsp;=\u0026thinsp;0, B\u0026thinsp;=\u0026thinsp;1, and A\u0026thinsp;=\u0026thinsp;1, B\u0026thinsp;=\u0026thinsp;0)\u003c/strong\u003e: When only one of the inputs is on, due to the selection of point defects as well as the path length of the input waveguides and also the phase difference of the bias source, the light waves at the collision point weaken each other and the power propagated to the output is very low. Figure \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e shows the normalized power diagram for these two modes. Due to the symmetry of the circuit for inputs A and B, the power diagram in the outputs will be the same for these two modes of input. Figure \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e shows that the normalized output power, in this case, is 0.07. In other words, only 7% of the optical power of the input source is transmitted to the output. This small value can be considered as a logical \u0026ldquo;0\u0026rdquo;.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCase 4\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e(A\u0026thinsp;=\u0026thinsp;B\u0026thinsp;=\u0026thinsp;1)\u003c/strong\u003e: If both input sources are on, the waves generated by the input sources and the bias source will overlap at the point of collision, resulting in signal attenuation and a very small amount of power being emitted to the output. The simulation results show that the amount of power emitted to the output, in this case, is equal to 0.07. This amount of power is very low and is equivalent to a logical \u0026ldquo;0\u0026rdquo;. Figure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e shows the normalized power diagram for this mode.\u003c/p\u003e\n\u003cp\u003eThe only point defect that has changed radius is a rod with radius R\u003csub\u003e1\u003c/sub\u003e. Now we want to get the optimal value of the radius of this rod so that the output power for the logical \u0026ldquo;1\u0026rdquo; and the logical \u0026ldquo;0\u0026rdquo; is in the best position. The best situation will be when the logical \u0026ldquo;1\u0026rdquo; has high power and the logical \u0026ldquo;0\u0026rdquo; has low power. Figure \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e shows the simulation results for the output optical power at different input modes for different values of R\u003csub\u003e1\u003c/sub\u003e.\u003c/p\u003e\n\u003cp\u003eAs shown in Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e, for low values of R\u003csub\u003e1\u003c/sub\u003e, the output power in logic \u0026ldquo;1\u0026rdquo; is close to the bias source power and the output has a strong \u0026ldquo;1\u0026rdquo;. In this case, the output value in logical \u0026ldquo;0\u0026rdquo; modes is close to 0.2. As R\u003csub\u003e1\u003c/sub\u003e increases, the amount of power in logic \u0026ldquo;1\u0026rdquo; decreases, but in this case, the value of \u0026ldquo;0\u0026rdquo; also decreases. Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e shows the output normalized power for radius changes R\u003csub\u003e1\u003c/sub\u003e.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable border=\"1\" id=\"Tab1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eNormalized optical power for different values of R1\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eR1\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"4\"\u003e\n \u003cp\u003eOutputs\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAB\u0026thinsp;=\u0026thinsp;00\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eA\u0026thinsp;\u0026ne;\u0026thinsp;B\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAB\u0026thinsp;=\u0026thinsp;11\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCR(\u003cstrong\u003edB)\u003c/strong\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e20nm\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e1.00\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.19\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.20\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e7.0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e40nm\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.90\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.14\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.14\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e8.0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e50nm\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.77\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.10\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.10\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e8.9\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e55nm\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.68\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.07\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.07\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e9.9\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e60nm\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.60\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.06\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.06\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e10\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e65nm\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.53\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.05\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.05\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e10.2\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003eAccording to Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, it can be said that with increasing radius R\u003csub\u003e1\u003c/sub\u003e, although the value of logical \u0026ldquo;0\u0026rdquo; decreases, the value of logical \u0026ldquo;1\u0026rdquo; also decreases. For R\u003csub\u003e1\u003c/sub\u003e values from 50nm to 60nm, the power is acceptable in the logical \u0026ldquo;1\u0026rdquo; mode and the value of logic \u0026ldquo;0\u0026rdquo; is greatly reduced and therefore the contrast ratio (CR) value is increased. For example, when R\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;55nm, the normalized output power in logical \u0026ldquo;1\u0026rdquo; mode is equal to 0.68 and its value in logic \u0026ldquo;0\u0026rdquo; is equal to 0.07. The value of CR, in this case, is equal to CR\u0026thinsp;=\u0026thinsp;9.9dB. With further increase of R\u003csub\u003e1\u003c/sub\u003e, the amount of optical power in the logical \u0026ldquo;1\u0026rdquo; mode is reduced and is not desirable.\u003c/p\u003e"},{"header":"3. Conclusion","content":"\u003cp\u003eIn this paper, an all-optical NOR logic gate is designed based on two-dimensional photon crystals with a square lattice. Optical power is used to define the logical values of \u0026ldquo;0\u0026rdquo; and \u0026ldquo;1\u0026rdquo;. In this way, high optical power is considered as logic \u0026ldquo;1\u0026rdquo; and very low optical power is considered as logic \u0026ldquo;0\u0026rdquo;. For the desired gate, two inputs are considered as main inputs and one as bias input. To use the proposed structure in optically integrated circuits, the size of the gate has been reduced as much as possible. Also, in the design of this gate, very simple defects have been used so that it can be built easily. The simulation results show that this logic gate has high optical power for logic \u0026ldquo;1\u0026rdquo; and low optical power for logic \u0026ldquo;0\u0026rdquo;. Therefore, the distance between the upper and lower logic values is large and the detection error at the output will be low.\u003c/p\u003e"},{"header":"4. Declarations","content":"\u003ch2\u003eAcknowledgment:\u003c/h2\u003e \u003cp\u003eThis paper was written with the support of Kermanshah Branch, Islamic Azad University.\u003c/p\u003e"},{"header":"5. References","content":"\u003cp dir=\"LTR\"\u003e[1] J.D. Joannopoulos, R.D. Meade, J.N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton University Press, Princeton, 1995\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[2] E. Yablonovitch, Photonic crystals: semiconductors of light. Sci Am. 285(6):47-55., Sci. Am. 2001\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[3] S. John, Strong localization of photons in certain disordered dielectric superlattices, Phys. Rev. Lett. 58, 2486\u0026ndash;2489 (1987)\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[4] S. Olyaee, A. Naraghi, V. Ahmadi, High sensitivity evanescent-field gas sensor based on modified photonic crystal fiber for gas condensate and air pollution monitoring, Optik - International Journal for Light and Electron Optics, 125(1), 596-600, 2014\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[5] S. Olyaee, F. Taghipour, Design of new square-lattice photonic crystal fibers for optical communication applications,\u0026nbsp;Int. J. Physical Sci., 6(18), 4405-4411, 2011\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[6] A. Farmani, A. Mir, M. Irannejad, 2D-FDTD simulation of ultra-compact multifunctional logic gates with nonlinear photonic crystal, Journal of the Optical Society of America B, 36(4), 811-818, 2019\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[7] F. Parandin, M. Moayed, Designing and simulation of 3-input majority gate based on two-dimensional photonic crystals, Optik, 216, 164930, 2020\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[8] H. Sharifi, S. M. Hamidi, K. Navi, A new design procedure for all-optical photonic crystal logic gates and functions based on threshold logic, Optics Communications, 370, 231-238, 2016\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[9] A. Salimzadeh, H. Alipour-Banaei, An all optical 8 to 3 encoder based on photonic crystal OR-gate ring resonators, Optics Communications, 410(1), 793-798, 2018\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[10] A. Mohebzadeh-Bahabady,\u0026nbsp;\u003ca href=\"https://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=%22First%20Name%22:%22Saeed%22\u0026searchWithin=%22Last%20Name%22:%22Olyaee%22\u0026newsearch=true\u0026sortType=newest\"\u003eS. Olyaee\u003c/a\u003e, All-optical NOT and XOR logic gates using photonic crystal nano-resonator and based on an interference effect, IET Optoelectronics, 12(4), 191-195, 2018\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[11] M.M. Gupta, S. Medhekar, All-optical NOT and AND gates using counter propagating beams innonlinear Mach\u0026ndash;Zehnder interferometer made of photonic crystal waveguides, Optik, 127, 1221-1228, 2016\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[12] K. Goudarzi, A. Mir, I. Chaharmahali, D. Goudarzi, \u0026nbsp;All-optical XOR and OR logic gates based on line and point defects in 2-D photonic crystal, Optics \u0026amp;Laser Technology, 78, 139-142, 2016\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[13] H.M.E. Hussein, T.A. Ali, N.H. Rafat, New designs of a complete set of Photonic Crystals logic gates, Optics Communications, 411, 175-181, 2018\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[14] P. Andalib, N. Granpayeh, All-optical ultra-compact photonic crystal AND gate based on nonlinear ring resonators. J. Opt. Soc. Am B 26, 10-16, 2009\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[15] H. Saghaei, A. Zahedi, R. Karimzadeh, F. Parandin, Line defects on photonic crystals for the design of all-optical power splitters and digital logic gates, Superlattices and Microstructures, 110, 133-138, 2017\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e\u0026nbsp;[16] S. Olyaee, M. Seifouri, A. Mohebzadeh-Bahabady, M. Sardari, Realization of all-optical NOT and XOR logic gates based on interference effect with high contrast ratio and ultra-compacted size, Opt Quant Electron, 50, 385, 2018\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[17] W.P. Lin, Y.F. Hsu, H.L. Kuo, Design of Optical Nor Logic Gates Using Two Dimension Photonic Crystals. Journal of Modern Physics, 2(3), 144-147, 2013\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[18] J. Bao, J. Xiao, L. Fan, X. Li, Y. Hai, T. Zhang, C. Yang, All-optical NOR and NAND gates based on photonic crystal ring resonator, Optics Communications, 329, 109-112, 2014\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[19] H. Alipour-Banaei, S. Serajmohammadi, F. Mehdizadeh, All optical NOR and NAND gate based on nonlinear photonic crystalring resonators, Optik, 125, 5701-5704, 2014\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[20] Mehdizadeh, Farhad, and Mohammad Soroosh, Designing of all optical NOR gate based on photonic crystal, Indian Journal of Pure \u0026amp; Applied Physics (IJPAP) 54.01, 35-39, 2016\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[21] F. Parandin, M.M. Karkhanehchi, Terahertz all-optical NOR and AND logic gates based on 2D photonic crystals,\u0026nbsp;\u003ca href=\"http://www.sciencedirect.com/science/journal/07496036\" title=\"Go to Superlattices and Microstructures on ScienceDirect\"\u003eSuperlattices and Microstructures\u003c/a\u003e, 101, 253-260, 2017\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[22] A. Kumar, S. Medhekar, All optical NOT and NOR gates using interference in the structures based on 2D linear photonic crystal ring resonator,\u0026nbsp;Optik,\u0026nbsp;179, 237-243, 2019\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[23] E. Shaik, N. Rangaswamy, Realization of all-optical NAND and NOR logic functions with photonic crystal based NOT, OR and AND gates using De Morgan\u0026rsquo;s theorem.\u0026nbsp;J. Opt.\u0026nbsp;47,\u0026nbsp;8\u0026ndash;21, 2018\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[24] F. Parandin, M.R. Malmir, M. Naseri, A. Zahedi, Reconfigurable all-optical NOT, XOR, and NOR logic gates based on two dimensional photonic crystals, Superlattices and Microstructures 113, 737-744, 2018\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[25] A. Kumar, S. Medhekar, All optical NOR and NAND gates using four circular cavities created in 2D nonlinear photonic crystal. Optics \u0026amp; Laser Technology, 123, 105910, 2020\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e\u0026nbsp;[26] D.G.S. Rao, S. Swarnakar, S. Kumar, Performance analysis of all-optical NAND, NOR, and XNOR logic gates using photonic crystal waveguide for optical computing applications, Opt. Eng. 59(5), 057101, 2020\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[27] A. Mohebzadeh-Bahabady, S. Olyaee, Investigation of response time of small footprint photonic crystal AND logic gate.\u0026nbsp;Optoelectron. Lett.\u0026nbsp;16,\u0026nbsp;477\u0026ndash;480, 2020 https://doi.org/10.1007/s11801-020-0056-4\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[28] E. Veisi, M. Seifouri,S. Olyaee, A novel design of all-optical high speed and ultra-compact photonic crystal AND logic gate based on the Kerr effect.\u0026nbsp;Appl. Phys. B\u0026nbsp;127,\u0026nbsp;70, 2021\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[29] M. Seifouri, S. Olyaee, M. Sardari, A. Mohebzadeh-Bahabady, Ultra-fast and compact all-optical half adder using 2D photonic crystals, IET Optoelectronics, 13(3), 139-143, 2019\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[30] M.M. Karkhanehchi, F. Parandin, A. Zahedi, Design of an all optical half-adder based on 2D photonic crystals. Photon Netw Commun 33, 159-165, 2017\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[31] M.H. Sani,A.A. Tabrizi, H. Saghaei, et al. An ultrafast all-optical half adder using nonlinear ring resonators in photonic crystal microstructure. Opt Quant Electron 52, 107, 2020\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[32] M. Abdollahi, F. Parandin, A novel structure for realization of an all-optical, one-bit half-adder based on 2D photonic crystals. J Comput Electron 18, 1416-1422, 2019\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[33] F. Parandin, M.R. Malmir, M. Naseri, All-optical half-subtractor with low-time delay based on two-dimensional photonic crystals, Superlattices and Microstructures\u0026nbsp;\u003ca href=\"file:///C%3A/Users/HN-PC/Desktop/papers/NOR-3/109\"\u003e109\u003c/a\u003e, 437-441, 2017\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[34] M. Ghadrdan, M.A. Mansouri-Birjandi, Concurrent implementation of all-optical half-adder and AND \u0026amp; XOR logic gates based on nonlinear photonic crystal, Opt Quant Electron, 45, 1027-1036, 2013\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[35] F. Parandin, M.R. Malmir, Reconfigurable all optical half adder and optical XOR and AND logic gates based on 2D photonic crystals. Opt Quant Electron 52, 56, 2020\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[36]\u0026nbsp;\u003ca href=\"https://www.sciencedirect.com/science/article/abs/pii/S0030402620312559#!\"\u003eS. Naghizade\u003c/a\u003e,\u0026nbsp;\u003ca href=\"https://www.sciencedirect.com/science/article/abs/pii/S0030402620312559#!\"\u003eH. Saghaei\u003c/a\u003e, A novel design of all-optical 4 to 2 encoder with multiple defects in silica-based photonic crystal fiber, Optik, 222, 165419, 2020\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[37] F. Parandin, High contrast ratio all-optical 4 \u0026times; 2 encoder based on two-dimensional photonic crystals, Optics \u0026amp; Laser Technology, 113, 447-452, 2019\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[38] T. A. Moniem, All optical active high decoder using integrated 2D square lattice photonic crystals, Journal of Modern Optics, Volume 62, Issue 19, 1643-1649, 2015\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e\u0026nbsp;[39] F. Parandin, M. M. Karkhanehchi, M. Naseri, A. Zahedi, Design of a high bitrate optical decoder based on photonic crystals, Journal of Computational Electronics, 17, 830-836, 2018\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e\u0026nbsp;[40] A. Zahedi, F. Parandin, M.M. \u0026nbsp;Karkhanehchi, H. Habibi-Shams, S. Rajamand, Design and Simulation of Optical 4-Channel Demultiplexer Using Photonic Crystals, Journal of Optical Communications, 40(1), 17-20, 2017\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[41] F. Parandin, R. Kamarian, M. Jomour, A novel design of all optical half-subtractor using a square lattice photonic crystals.\u0026nbsp;Opt Quant Electron\u0026nbsp;53,\u0026nbsp;114, 2021\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[42] S. Olyaee, \u0026quot;Ultra-fast and compact all-optical encoder based on photonic crystal nano-resonator without using nonlinear materials\u0026quot;, Phot. Lett. Pol., 11(1), 10-12, 2019\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[43] F. Parandin, Ultra-compact terahertz all-optical logic comparator on GaAs photonic crystal platform, Optics \u0026amp; Laser Technology, 144, 107399, 2021\u003c/p\u003e\n\u003cp dir=\"LTR\"\u003e[44] F. Parandin, R. Kamarian, and M. Jomour, Optical 1-bit comparator based on two-dimensional photonic crystals, Appl. Opt. 60, 2275-2280 (2021)\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"optical-and-quantum-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"oqel","sideBox":"Learn more about [Optical and Quantum Electronics](https://www.springer.com/journal/11082)","snPcode":"11082","submissionUrl":"https://submission.nature.com/new-submission/11082/3","title":"Optical and Quantum Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Photonic crystals, PBG, Line defect, Point defect.","lastPublishedDoi":"10.21203/rs.3.rs-788185/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-788185/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this research, an all-optical NOR gate is designed and simulated based on two-dimensional photonic crystals. A square lattice has been used to design this structure. This logic gate has two main inputs, a bias input and an output. Because the output of the NOR gate must be \u0026ldquo;1\u0026rdquo; for zero inputs, a bias input is required. One of the characteristics of this structure is its small size for use in optical integrated circuits. Also, in order to reduce the detection error in the output, it has been tried that the outputs have a suitable distance in two \u0026ldquo;0\u0026rdquo; and \u0026ldquo;1\u0026rdquo; logical states. The use of a small number and simple point defects makes the design of this gate easier. The simulation results show that the proposed structure is suitable for working at a wavelength of 1.55\u0026micro;m. Also, the amount of optical power at the output is high in the \u0026ldquo;1\u0026rdquo; logical mode and low in the \u0026ldquo;0\u0026rdquo; logical mode. This indicates that this structure has a reliable output for detecting logical values. In this paper, a photonic crystal structure is proposed to realize the NOR logic gate, which is small in size and uses simple linear and point defects. The use of very few point defects has made the design simpler and thus easier to build this gate. Due to these characteristics, this structure can be suitable for optically integrated circuits.\u003c/p\u003e","manuscriptTitle":"Design of an Ultra-Compact and High-Contrast Ratio All-Optical NOR Gate","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2021-08-13 20:49:17","doi":"10.21203/rs.3.rs-788185/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Minor revisions","date":"2021-09-22T09:02:17+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2021-08-11T13:24:42+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2021-08-11T12:56:25+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"Optical and Quantum Electronics","date":"2021-08-09T13:59:16+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2021-08-06T13:59:27+00:00","index":"","fulltext":""},{"type":"submitted","content":"Optical and Quantum Electronics","date":"2021-08-05T11:30:25+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"optical-and-quantum-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"oqel","sideBox":"Learn more about [Optical and Quantum Electronics](https://www.springer.com/journal/11082)","snPcode":"11082","submissionUrl":"https://submission.nature.com/new-submission/11082/3","title":"Optical and Quantum Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"8255066f-5643-4537-b242-430aa0300664","owner":[],"postedDate":"August 13th, 2021","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":6434771,"name":"Electrical Engineering"},{"id":6434772,"name":"Electronic Materials and Devices"},{"id":6434773,"name":"Optical Materials and Devices"},{"id":6434774,"name":"Atomic and Molecular Physics"}],"tags":[],"updatedAt":"2021-11-30T19:58:23+00:00","versionOfRecord":{"articleIdentity":"rs-788185","link":"https://doi.org/10.1007/s11082-021-03322-y","journal":{"identity":"optical-and-quantum-electronics","isVorOnly":false,"title":"Optical and Quantum Electronics"},"publishedOn":"2021-11-02 19:58:23","publishedOnDateReadable":"November 2nd, 2021"},"versionCreatedAt":"2021-08-13 20:49:17","video":"","vorDoi":"10.1007/s11082-021-03322-y","vorDoiUrl":"https://doi.org/10.1007/s11082-021-03322-y","workflowStages":[]},"version":"v1","identity":"rs-788185","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-788185","identity":"rs-788185","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}