Abstract

In this work, we report the design of topological filter and all-optical logic gates based on two-dimensional photonic crystals with robust edge states. All major logic gates, including OR, AND, NOT, NOR, XOR, XNOR, and NAND, are suitably designed by using the linear interference approach. Moreover, numerical simulations show that our designed all-optical logic devices can always work well even if significant disorders exist. It is expected that such robust and compact logic devices have potential applications in future photonic integrated circuits.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (7)

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

M. I. Shalaev, W. Walasik, A. Xu, Y. Tsukernik, and N. M. Litchinitser, “Robust topologically protected transport in photonic crystals at telecommunication wavelengths,” Nat. Nanotechnol. 14(1), 31–34 (2019).
[Crossref]

Y. Yang, Z. Gao, H. Xue, L. Zhang, M. He, Z. Yang, R. Singh, Y. Chong, B. Zhang, and H. Chen, “Realization of a three-dimensional photonic topological insulator,” Nature 565(7741), 622–626 (2019).
[Crossref]

W. Zhang and X. Zhang, “Backscattering-Immune computing of spatial differentiation by nonreciprocal plasmonics,” Phys. Rev. Appl. 11(5), 054033 (2019).
[Crossref]

X. T. He, E. T. Liang, J. J. Yuan, H. Y. Qiu, X. D. Chen, F. L. Zhao, and J. W. Dong, “A silicon-on-insulator slab for topological valley transport,” Nat. Commun. 10(1), 872 (2019).
[Crossref]

S. Peng, N. J. Schilder, X. Ni, J. van de Groep, M. L. Brongersma, A. Alù, A. B. Khanikaev, H. A. Atwater, and A. Polman, “Probing the Band Structure of Topological Silicon Photonic Lattices in the Visible Spectrum,” Phys. Rev. Lett. 122(11), 117401 (2019).
[Crossref]

L. Zhang and S. Xiao, “Design of terahertz reconfigurable devices by locally controlling topological phases of square gyro-electric rod arrays,” Opt. Mater. Express 9(2), 544–554 (2019).
[Crossref]

2018 (11)

V. Jandieri, R. Khomeriki, and D. Erni, “Realization of True All-Optical AND Logic Gate based on the Nonlinear Coupled Air-hole Type Photonic Crystal Waveguide,” Opt. Express 26(16), 19845–19853 (2018).
[Crossref]

Y. Yang and Z. H. Hang, “Topological whispering gallery modes in two-dimensional photonic crystal cavities,” Opt. Express 26(16), 21235–21241 (2018).
[Crossref]

M. H. Rezaei and A. Zarifkar, “Dielectric-loaded graphene-based plasmonic multilogic gate using a multimode interference splitter,” Appl. Opt. 57(35), 10109–10116 (2018).
[Crossref]

Y. Yang, Y. F. Xu, T. Xu, H. X. Wang, J. H. Jiang, X. Hu, and Z. H. Hang, “Visualization of a unidirectional electromagnetic waveguide using topological photonic crystals made of dielectric materials,” Phys. Rev. Lett. 120(21), 217401 (2018).
[Crossref]

Y. Yang, H. Jiang, and Z. H. Hang, “Topological valley transport in two-dimensional honeycomb photonic crystals,” Sci. Rep. 8(1), 1588 (2018).
[Crossref]

M. I. Shalaev, S. Desnavi, W. Walasik, and N. M. Litchinitser, “Reconfigurable topological photonic crystal,” New J. Phys. 20(2), 023040 (2018).
[Crossref]

F. Liu, H. Y. Deng, and K. Wakabayashi, “Topological photonic crystals with zero Berry curvature,” Phys. Rev. B 97(3), 035442 (2018).
[Crossref]

M. A. Gorlach, X. Ni, D. A. Smirnova, D. Korobkin, D. Zhirihin, A. P. Slobozhanyuk, P. A. Belov, A. Alù, and A. B. Khanikaev, “Far-field probing of leaky topological states in all-dielectric metasurfaces,” Nat. Commun. 9(1), 909 (2018).
[Crossref]

M. H. Rezaei, A. Zarifkar, M. Miri, and O. Materials, “Ultra-compact electro-optical graphene-based plasmonic multi-logic gate with high extinction ratio,” Opt. Mater. 84, 572–578 (2018).
[Crossref]

F. Parandin, M. R. Malmir, M. Naseri, and A. Zahedi, “Reconfigurable all-optical NOT, XOR, and NOR logic gates based on two dimensional photonic crystals,” Superlattices Microstruct. 113, 737–744 (2018).
[Crossref]

S. Stützer, Y. Plotnik, Y. Lumer, P. Titum, N. H. Lindner, M. Segev, M. C. Rechtsman, and A. Szameit, “Photonic topological Anderson insulators,” Nature 560(7719), 461–465 (2018).
[Crossref]

2017 (4)

X. Wu, J. Tian, and R. Yang, “A type of all-optical logic gate based on graphene surface plasmon polaritons,” Opt. Commun. 403, 185–192 (2017).
[Crossref]

Z. Chai, X. Hu, F. Wang, C. Li, Y. Ao, Y. Wu, Y. Wu, K. Shi, H. Yang, and Q. Gong, “Ultrafast on-Chip Remotely-Triggered All-Optical Switching Based on Epsilon-Near-Zero Nanocomposites,” Laser Photonics Rev. 11(5), 1700042 (2017).
[Crossref]

G. Siroki, P. A. Huidobro, and V. Giannini, “Topological photonics: From crystals to particles,” Phys. Rev. B 96(4), 041408 (2017).
[Crossref]

Y. Zhi, X. C. Yu, Q. Gong, L. Yang, and Y. F. Xiao, “Single nanoparticle detection using optical microcavities,” Adv. Mater. 29(12), 1604920 (2017).
[Crossref]

2016 (8)

D. Leykam and Y. D. Chong, “Edge solitons in nonlinear-photonic topological insulators,” Phys. Rev. Lett. 117(14), 143901 (2016).
[Crossref]

F. Mehdizadeh and M. Soroosh, “Designing of all optical NOR gate based on photonic crystal,” Indian J. Pure Appl. Phys. 54(01), 35–39 (2016).

S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016).
[Crossref]

T. Ma and G. Shvets, “All-Si valley-Hall photonic topological insulator,” New J. Phys. 18(2), 025012 (2016).
[Crossref]

R. Fan, X. Yang, X. Meng, and X. Sun, “2D photonic crystal logic gates based on self-collimated effect,” J. Phys. D: Appl. Phys. 49(32), 325104 (2016).
[Crossref]

C. He, X. C. Sun, X. P. Liu, M. H. Lu, Y. Chen, L. Feng, and Y. F. Chen, “Photonic topological insulator with broken time-reversal symmetry,” Proc. Natl. Acad. Sci. 113(18), 4924–4928 (2016).
[Crossref]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological states in photonic systems,” Nat. Phys. 12(7), 626–629 (2016).
[Crossref]

L. Xu, H. X. Wang, Y. D. Xu, H. Y. Chen, and J. H. Jiang, “Accidental degeneracy in photonic bands and topological phase transitions in two-dimensional core-shell dielectric photonic crystals,” Opt. Express 24(16), 18059–18071 (2016).
[Crossref]

2015 (6)

S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large Chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
[Crossref]

P. Rani, Y. Kalra, and R. K. Sinha, “Design of all optical logic gates in photonic crystal waveguides,” Optik 126(9–10), 950–955 (2015).
[Crossref]

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2014 (5)

A. E. Willner, S. Khaleghi, M. R. Chitgarha, and O. F. Yilmaz, “All-optical signal processing,” J. Lightwave Technol. 32(4), 660–680 (2014).
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L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
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C. Tang, X. Dou, Y. Lin, H. Yin, B. Wu, and Q. Zhao, “Design of all-optical logic gates avoiding external phase shifters in a two-dimensional photonic crystal based on multi-mode interference for BPSK signals,” Opt. Commun. 316, 49–55 (2014).
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H. Alipour-Banaei, S. Serajmohammadi, and F. Mehdizadeh, “All optical NOR and NAND gate based on nonlinear photonic crystal ring resonators,” Optik 125(19), 5701–5704 (2014).
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J. R. R. Sousa, A. C. Ferreira, G. S. Batista, C. S. Sobrinho, A. M. Bastos, M. L. Lyra, and A. S. B. Sombra, “Generation of logic gates based on a photonic crystal fiber Michelson interferometer,” Opt. Commun. 322, 143–149 (2014).
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2013 (5)

M. Ghadrdan and M. A. Mansouri-Birjandi, “Concurrent implementation of all-optical half-adder and AND and XOR logic gates based on nonlinear photonic crystal,” Opt. Quantum Electron. 45(10), 1027–1036 (2013).
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2012 (1)

K. Fang, Z. Yu, and S. Fan, “Realizing effective magnetic field for photons by controlling the phase of dynamic modulation,” Nat. Photonics 6(11), 782–787 (2012).
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2011 (3)

Y. Ishizaka, Y. Kawaguchi, K. Saitoh, and M. Koshiba, “Design of ultra compact all-optical XOR and AND logic gates with low power consumption,” Opt. Commun. 284(14), 3528–3533 (2011).
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D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Hübner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
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Y. Liu, F. Qin, Z. M. Meng, F. Zhou, Q. H. Mao, and Z. Y. Li, “All-optical logic gates based on two-dimensional low-refractive-index nonlinear photonic crystal slabs,” Opt. Express 19(3), 1945–1953 (2011).
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2010 (5)

T. T. Kim, S. G. Lee, H. Y. Park, J. E. Kim, and C. S. Kee, “Asymmetric Mach-Zehnder filter based on self-collimation phenomenon in two-dimensional photonic crystals,” Opt. Express 18(6), 5384–5389 (2010).
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L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. J. Geluk, T. Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4(3), 182–187 (2010).
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K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4(7), 477–483 (2010).
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2009 (2)

2008 (5)

Q. Liu, Z. Ouyang, C. J. Wu, C. P. Liu, and J. C. Wang, “All-optical half adder based on cross structures in two-dimensional photonic crystals,” Opt. Express 16(23), 18992–19000 (2008).
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2007 (4)

D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007).
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2005 (1)

2004 (1)

Q. Wang, G. Zhu, H. Chen, J. Jaques, J. Leuthold, A. B. Piccirilli, and N. K. Dutta, “Study of all-optical XOR using Mach-Zehnder interferometer and differential scheme,” IEEE J. Quantum Electron. 40(6), 703–710 (2004).
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2002 (1)

J. H. Kim, Y. M. Jhon, Y. T. Byun, S. Lee, D. H. Woo, and S. H. Kim, “All-optical XOR gate using semiconductor optical amplifiers without additional input beam,” IEEE Photonics Technol. Lett. 14(10), 1436–1438 (2002).
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2000 (2)

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1999 (1)

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
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F. Parandin, M. R. Malmir, M. Naseri, and A. Zahedi, “Reconfigurable all-optical NOT, XOR, and NOR logic gates based on two dimensional photonic crystals,” Superlattices Microstruct. 113, 737–744 (2018).
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Figures (10)

Fig. 1.
Fig. 1. Modes analysis of topological photonic crystal cavity. (a) The band structure of supercell sustaining edge state (the red points are edge modes; the black points are bulk modes). The inset plot the schematic drawing of unit cell and supercell. (b) Schematic of topological cavity (topological PhC1 outside, trivial PhC2 inside). (c) The topological cavity modes (the green points are standing modes; the red points are traveling modes). (d) The steady-state distribution of electric field in z direction of traveling mode and standing mode (red arrows are time-averaged Poynting vectors, black dashed lines are the boundaries between PhC1 and PhC2).
Fig. 2.
Fig. 2. Topological filter and modes analysis. (a) Schematic of topological filter. Numerical transmittivity of the traveling mode (b) and the standing mode (c). The steady-state distributions of the absolute value of electric field of (d) the traveling mode and (f) the standing mode at the resonant frequency and (e) the traveling mode at fhalf. (g) Phase difference of the traveling mode toward DR and T ports. Analytical transmittivity of (h) the traveling mode and (i) the standing mode.
Fig. 3.
Fig. 3. OR and XOR gates. Schematic diagrams of OR and XOR gates with logical inputs being (a) 00, (b) 01, (c) 10, and (d) 11. The steady-state distributions of the absolute value of electric field for logical inputs (e) 00, (f) 01, (g) 10, and (h) 11. The output normalized intensity with input states being 01, 10 and 11 from (i) the OR port and (j) the XOR port. (k) XOR extinction ratios between logic 0 (input 11) and 1 (input 01 or 10). 10/11 (01/11) represent the ER between inputs 10 (01) and 11.
Fig. 4.
Fig. 4. XNOR gate. (a) Scheme of the XNOR gate. Schematic diagrams and the steady-state distributions of the absolute value of electric field for logic inputs (b) 00, (d) 01, (f) 10, and (h) 11. (f) The output normalized intensity of the XNOR port close to fhalf. (g) XNOR extinction ratios between logic 0 (input 10, 01) and 1 (input 00, 11). 11/10 represent the ER between inputs 11 and 10, and so on.
Fig. 5.
Fig. 5. NAND gate. (a) Scheme of the NAND gate. Schematic diagrams and the steady-state distributions of the absolute value of electric field for logical inputs (b) 00, (d) 01, (f) 10, and (h) 11. (f) The output normalized intensity of the NAND port close to fhalf. (g) NAND extinction ratios between logic 0 (input 11) and 1 (inputs 00, 01, and 10). 00/11 represent the ER between inputs 00 and 11, and so on.
Fig. 6.
Fig. 6. NOR gate. (a) Scheme of the NOR gate. Interference analyzes and the steady-state distributions of the absolute value of electric field for logical inputs (b) 00, (c) 01, (d) 10, and (e) 11. (f) The output normalized intensity of the NOR port close to fhalf. (g) NOR extinction ratios between logic 1 (input 00) and 0 (inputs 01, 10, and 11). 00/01 represent the ER between inputs 00 and 01, and so on.
Fig. 7.
Fig. 7. AND gate. (a) Scheme of the AND gate. Schematic diagrams and the steady-state distributions of the absolute value of electric field for logical inputs (b) 00, (c) 01, (d) 10, and (e) 11. (f) The output normalized intensity of the AND port close to fhalf. (j) AND extinction ratios between logic 1 (input 11) and 0 (inputs 00, 01, and 10). 11/01 represent the ER between inputs 11 and 01, and so on.
Fig. 8.
Fig. 8. The NAND gate with a defect. The steady-state distributions of the absolute value of electric field with disturbance for inputs (a) 00, (b) 01, (c) 10, and (d) 11.
Fig. 9.
Fig. 9. XOR and OR gate with a defect. (a) Schematic of the topological cavity with defect. The steady-state distributions of the absolute value of electric field with cavity defect for inputs (b) 01, (c) 10, and (d) 11.
Fig. 10.
Fig. 10. XOR and OR gate used air-hole PhCs structure. (a) Schematic of the topological air-hole PhCs with the parameters (the yellow represents Si and the white represents air holes). (b) Schematic diagrams of OR and XOR gates. The steady-state distributions of the absolute value of electric field for inputs (c) 01, (d) 10, and (e) 11. (f) The normalized intensity of OR and XOR gates output. (g) The ER between XOR and OR gate at input state 11.

Tables (7)

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Table 1. Truth table of XOR and OR gates (wave function is shown in parentheses, positive and negative represent phases).

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Table 2. Truth table of the NOT gate.

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Table 3. Truth table of the XNOR gate.

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Table 4. Truth table of the NAND gate.

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Table 5. Truth table of the NOR gate.

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Table 6. Truth table of the AND gate.

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Table 7. Comparison table of main reported researches.

Equations (10)

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d a 0 d t = ( i f 0 κ R κ T κ D R κ D L ) a 0 + κ R S R i n ,
a 0 = κ R S R i n i ( f f 0 ) + κ R + κ T + κ D R + κ D L .
S R o u t = e i β d ( κ T a 0 ) ,
S T o u t = e i β d ( S R i n κ R a 0 ) ,
S D L o u t = e i β d ( κ D R a 0 ) ,
S D R o u t = e i β d ( κ D L a 0 ) ,
O R = 4 κ T κ R ( κ T + κ R + κ D L + κ D R ) 2 + 4 ( f f 0 ) 2 ,
O T = ( κ T + κ R + κ D L + κ D R ) 2 + 4 ( f f 0 ) 2 ( κ T + κ R + κ D L + κ D R ) 2 + 4 ( f f 0 ) 2 ,
O D R = 4 κ T κ D R ( κ T + κ R + κ D L + κ D R ) 2 + 4 ( f f 0 ) 2 ,
O D L = 4 κ T κ D L ( κ T + κ R + κ D L + κ D R ) 2 + 4 ( f f 0 ) 2 ,

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