Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators

Lei Zhang; Ruiqiang Ji; Yonghui Tian; Lin Yang; Ping Zhou; Yangyang Lu; Weiwei Zhu; Yuliang Liu; Lianxi Jia; Qing Fang; Mingbin Yu

doi:10.1364/OE.19.006524

Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators

Lei Zhang, Ruiqiang Ji, Yonghui Tian, Lin Yang, Ping Zhou, Yangyang Lu, Weiwei Zhu, Yuliang Liu, Lianxi Jia, Qing Fang, and Mingbin Yu

Optics Express
Vol. 19,
Issue 7,
pp. 6524-6540
(2011)
•https://doi.org/10.1364/OE.19.006524

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Lei Zhang, Ruiqiang Ji, Yonghui Tian, Lin Yang, Ping Zhou, Yangyang Lu, Weiwei Zhu, Yuliang Liu, Lianxi Jia, Qing Fang, and Mingbin Yu, "Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators," Opt. Express 19, 6524-6540 (2011)

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Abstract

We report the simultaneous implementation of the XOR and XNOR operations at two ports of a directed logic circuit based on two cascaded microring resonators (MRRs), which are both modulated through thermo-optic effect. Two electrical modulating signals applied to the MRRs represent the two operands of each logic operation. Simultaneous bitwise XOR and XNOR operations at 10 kbit/s are demonstrated in two different operating modes. We show that such a circuit can be readily realized using the plasma dispersion effect or the electric field effects, indicating its potential for high-speed operation. We further employ the scattering matrix method to analyze the spectral characteristics of the fabricated circuit, which can be regarded as a Mach-Zehnder interferometer (MZI) in whole. The two MRRs in the circuit act as wavelength-dependent splitting and combining units of the MZI. The degradation of the spectra observed in the experiment is found to be related to the length difference between the MZI’s two arms. The evolution of the spectra with this length difference is presented.

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J. Hardy and J. Shamir, “Optics inspired logic architecture,” Opt. Express 15(1), 150–165 (2007).
[Crossref] [PubMed]
H. J. Caulfield, R. A. Soref, and C. S. Vikram, “Universal reconfigurable optical logic with silicon-on-insulator resonant structures,” Photonics Nanostruct. Fund. Appl. 5(1), 14–20 (2007).
[Crossref]
H. J. Caulfield and S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics 4(5), 261–263 (2010).
[Crossref]
V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8(3), 705–713 (2002).
[Crossref]
X. Zhang, Y. Wang, J. Q. Sun, D. M. Liu, and D. X. Huang, “All-optical AND gate at 10 Gbit/s based on cascaded single-port-couple SOAs,” Opt. Express 12(3), 361–366 (2004).
[Crossref] [PubMed]
Q. F. Xu and M. Lipson, “All-optical logic based on silicon micro-ring resonators,” Opt. Express 15(3), 924–929 (2007).
[Crossref] [PubMed]
M. P. Fok and P. R. Prucnal, “All-optical XOR gate with optical feedback using highly Ge-doped nonlinear fiber and a terahertz optical asymmetric demultiplexer,” Appl. Opt. 50(2), 237–241 (2011).
[Crossref] [PubMed]
L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35(10), 1620–1622 (2010).
[Crossref] [PubMed]
T. Fukazawa, T. Hirano, F. Ohno, and T. Baba, “Low loss intersection of Si photonic wire waveguides,” Jpn. J. Appl. Phys. 43(2), 646–647 (2004).
[Crossref]
N. Sherwood-Droz, H. Wang, L. Chen, B. G. Lee, A. Biberman, K. Bergman, and M. Lipson, “Optical 4x4 hitless slicon router for optical networks-on-chip (NoC),” Opt. Express 16(20), 15915–15922 (2008).
[Crossref] [PubMed]
M. M. Geng, L. X. Jia, L. Zhang, L. Yang, P. Chen, T. Wang, and Y. L. Liu, “Four-channel reconfigurable optical add-drop multiplexer based on photonic wire waveguide,” Opt. Express 17(7), 5502–5516 (2009).
[Crossref] [PubMed]
R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]
G. T. Reed and A. P. Knights, Silicon Photonics: an Introduction (Wiley, West Sussex, 2004), Chap. 4.
G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]
Q. F. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, “12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulators,” Opt. Express 15(2), 430–436 (2007).
[Crossref] [PubMed]
A. S. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15(2), 660–668 (2007).
[Crossref] [PubMed]
P. Dong, R. Shafiiha, S. Liao, H. Liang, N.-N. Feng, D. Feng, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Wavelength-tunable silicon microring modulator,” Opt. Express 18(11), 10941–10946 (2010).
[Crossref] [PubMed]
M. Hochberg, T. Baehr-Jones, G. Wang, M. Shearn, K. Harvard, J. Luo, B. Chen, Z. Shi, R. Lawson, P. Sullivan, A. K. Jen, L. Dalton, and A. Scherer, “Terahertz all-optical modulation in a silicon-polymer hybrid system,” Nat. Mater. 5(9), 703–709 (2006).
[Crossref] [PubMed]
J. Takayesu, M. Hochberg, T. Baehr-Jones, E. Chan, G. Wang, P. Sullivan, Y. Liao, J. Davies, L. Dalton, A. Scherer, and W. Krug, “A hybrid electrooptic microring resonator-based 1×4×1 ROADM for wafer scale optical interconnects,” J. Lightwave Technol. 27(4), 440–448 (2009).
[Crossref]
C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[Crossref]
J. F. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2(7), 433–437 (2008).
[Crossref]
A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[Crossref]
A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002).
[Crossref]
J. Heebner, R. Grover, and T. A. Ibrahim, Optical Microresonators: Theory, Fabrication, and Applications (Springer, London, 2008), Chap. 3.
C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: a Signal Processing Approach (Wiley, New York, 1999), Chap. 3.
J. B. Feng, Q. Q. Li, and Z. P. Zhou, “Single ring interferometer configuration with doubled free-spectral range,” IEEE Photon. Technol. Lett. 23(2), 79–81 (2011).
[Crossref]
U. Fano, “Effects of Configuration Interaction on Intensities and Phase Shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[Crossref]
S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002).
[Crossref]
M. E. Solmaz, Y. F. Zhou, and C. K. Madsen, “Modeling Asymmetric Resonances Using an Optical Filter Approach,” J. Lightwave Technol. 28(20), 2951–2955 (2010).
[Crossref]

2011 (2)

M. P. Fok and P. R. Prucnal, “All-optical XOR gate with optical feedback using highly Ge-doped nonlinear fiber and a terahertz optical asymmetric demultiplexer,” Appl. Opt. 50(2), 237–241 (2011).
[Crossref] [PubMed]

J. B. Feng, Q. Q. Li, and Z. P. Zhou, “Single ring interferometer configuration with doubled free-spectral range,” IEEE Photon. Technol. Lett. 23(2), 79–81 (2011).
[Crossref]

2010 (5)

M. E. Solmaz, Y. F. Zhou, and C. K. Madsen, “Modeling Asymmetric Resonances Using an Optical Filter Approach,” J. Lightwave Technol. 28(20), 2951–2955 (2010).
[Crossref]

P. Dong, R. Shafiiha, S. Liao, H. Liang, N.-N. Feng, D. Feng, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Wavelength-tunable silicon microring modulator,” Opt. Express 18(11), 10941–10946 (2010).
[Crossref] [PubMed]

L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35(10), 1620–1622 (2010).
[Crossref] [PubMed]

H. J. Caulfield and S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics 4(5), 261–263 (2010).
[Crossref]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

2009 (3)

M. M. Geng, L. X. Jia, L. Zhang, L. Yang, P. Chen, T. Wang, and Y. L. Liu, “Four-channel reconfigurable optical add-drop multiplexer based on photonic wire waveguide,” Opt. Express 17(7), 5502–5516 (2009).
[Crossref] [PubMed]

J. Takayesu, M. Hochberg, T. Baehr-Jones, E. Chan, G. Wang, P. Sullivan, Y. Liao, J. Davies, L. Dalton, A. Scherer, and W. Krug, “A hybrid electrooptic microring resonator-based 1×4×1 ROADM for wafer scale optical interconnects,” J. Lightwave Technol. 27(4), 440–448 (2009).
[Crossref]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[Crossref]

2008 (2)

J. F. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-integrated, ultralow-energy GeSi electro-absorption modulators,” Nat. Photonics 2(7), 433–437 (2008).
[Crossref]

N. Sherwood-Droz, H. Wang, L. Chen, B. G. Lee, A. Biberman, K. Bergman, and M. Lipson, “Optical 4x4 hitless slicon router for optical networks-on-chip (NoC),” Opt. Express 16(20), 15915–15922 (2008).
[Crossref] [PubMed]

2007 (5)

Q. F. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, “12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulators,” Opt. Express 15(2), 430–436 (2007).
[Crossref] [PubMed]

A. S. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15(2), 660–668 (2007).
[Crossref] [PubMed]

J. Hardy and J. Shamir, “Optics inspired logic architecture,” Opt. Express 15(1), 150–165 (2007).
[Crossref] [PubMed]

H. J. Caulfield, R. A. Soref, and C. S. Vikram, “Universal reconfigurable optical logic with silicon-on-insulator resonant structures,” Photonics Nanostruct. Fund. Appl. 5(1), 14–20 (2007).
[Crossref]

Q. F. Xu and M. Lipson, “All-optical logic based on silicon micro-ring resonators,” Opt. Express 15(3), 924–929 (2007).
[Crossref] [PubMed]

2006 (1)

M. Hochberg, T. Baehr-Jones, G. Wang, M. Shearn, K. Harvard, J. Luo, B. Chen, Z. Shi, R. Lawson, P. Sullivan, A. K. Jen, L. Dalton, and A. Scherer, “Terahertz all-optical modulation in a silicon-polymer hybrid system,” Nat. Mater. 5(9), 703–709 (2006).
[Crossref] [PubMed]

2004 (2)

X. Zhang, Y. Wang, J. Q. Sun, D. M. Liu, and D. X. Huang, “All-optical AND gate at 10 Gbit/s based on cascaded single-port-couple SOAs,” Opt. Express 12(3), 361–366 (2004).
[Crossref] [PubMed]

T. Fukazawa, T. Hirano, F. Ohno, and T. Baba, “Low loss intersection of Si photonic wire waveguides,” Jpn. J. Appl. Phys. 43(2), 646–647 (2004).
[Crossref]

2002 (3)

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover, and P.-T. Ho, “Optical signal processing using nonlinear semiconductor microring resonators,” IEEE J. Sel. Top. Quantum Electron. 8(3), 705–713 (2002).
[Crossref]

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002).
[Crossref]

S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002).
[Crossref]

2000 (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[Crossref]

1987 (1)

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

1961 (1)

U. Fano, “Effects of Configuration Interaction on Intensities and Phase Shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[Crossref]

Absil, P. P.

Asghari, M.

Baba, T.

T. Fukazawa, T. Hirano, F. Ohno, and T. Baba, “Low loss intersection of Si photonic wire waveguides,” Jpn. J. Appl. Phys. 43(2), 646–647 (2004).
[Crossref]

Baehr-Jones, T.

Baets, R.

Beals, M.

Bennett, B. R.

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Bergman, K.

Bernardis, S.

Biaggio, I.

Biberman, A.

Bogaerts, W.

Caulfield, H. J.

H. J. Caulfield and S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics 4(5), 261–263 (2010).
[Crossref]

Chan, E.

Chen, B.

Chen, L.

Chen, P.

Cheng, J.

Chetrit, Y.

Ciftcioglu, B.

Dalton, L.

Davies, J.

Diederich, F.

Dolev, S.

H. J. Caulfield and S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics 4(5), 261–263 (2010).
[Crossref]

Dong, P.

Dumon, P.

Esembeson, B.

Fan, S.

S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002).
[Crossref]

Fang, Q.

Fano, U.

U. Fano, “Effects of Configuration Interaction on Intensities and Phase Shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[Crossref]

Feng, D.

Feng, J. B.

J. B. Feng, Q. Q. Li, and Z. P. Zhou, “Single ring interferometer configuration with doubled free-spectral range,” IEEE Photon. Technol. Lett. 23(2), 79–81 (2011).
[Crossref]

Feng, N.-N.

Fok, M. P.

Freude, W.

Fukazawa, T.

T. Fukazawa, T. Hirano, F. Ohno, and T. Baba, “Low loss intersection of Si photonic wire waveguides,” Jpn. J. Appl. Phys. 43(2), 646–647 (2004).
[Crossref]

Gardes, F. Y.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Geng, M. M.

Grover, R.

Hardy, J.

J. Hardy and J. Shamir, “Optics inspired logic architecture,” Opt. Express 15(1), 150–165 (2007).
[Crossref] [PubMed]

Harvard, K.

Hirano, T.

T. Fukazawa, T. Hirano, F. Ohno, and T. Baba, “Low loss intersection of Si photonic wire waveguides,” Jpn. J. Appl. Phys. 43(2), 646–647 (2004).
[Crossref]

Ho, P.-T.

Hochberg, M.

Huang, D. X.

X. Zhang, Y. Wang, J. Q. Sun, D. M. Liu, and D. X. Huang, “All-optical AND gate at 10 Gbit/s based on cascaded single-port-couple SOAs,” Opt. Express 12(3), 361–366 (2004).
[Crossref] [PubMed]

Ibrahim, T. A.

Izhaky, N.

Jen, A. K.

Ji, R. Q.

Jia, L. X.

Jiang, Z. Y.

Johnson, F. G.

Kimerling, L. C.

Koos, C.

Krishnamoorthy, A. V.

Krug, W.

Lawson, R.

Lee, B. G.

Leuthold, J.

Li, G.

Li, Q. Q.

J. B. Feng, Q. Q. Li, and Z. P. Zhou, “Single ring interferometer configuration with doubled free-spectral range,” IEEE Photon. Technol. Lett. 23(2), 79–81 (2011).
[Crossref]

Liang, H.

Liao, L.

Liao, S.

Liao, Y.

Lipson, M.

Q. F. Xu and M. Lipson, “All-optical logic based on silicon micro-ring resonators,” Opt. Express 15(3), 924–929 (2007).
[Crossref] [PubMed]

Liu, A. S.

Liu, D. M.

X. Zhang, Y. Wang, J. Q. Sun, D. M. Liu, and D. X. Huang, “All-optical AND gate at 10 Gbit/s based on cascaded single-port-couple SOAs,” Opt. Express 12(3), 361–366 (2004).
[Crossref] [PubMed]

Liu, J. F.

Liu, Y. L.

Lu, Y. Y.

Luo, J.

Madsen, C. K.

M. E. Solmaz, Y. F. Zhou, and C. K. Madsen, “Modeling Asymmetric Resonances Using an Optical Filter Approach,” J. Lightwave Technol. 28(20), 2951–2955 (2010).
[Crossref]

Manipatruni, S.

Mashanovich, G.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Michel, J.

Michinobu, T.

Nguyen, H.

Ohno, F.

T. Fukazawa, T. Hirano, F. Ohno, and T. Baba, “Low loss intersection of Si photonic wire waveguides,” Jpn. J. Appl. Phys. 43(2), 646–647 (2004).
[Crossref]

Paniccia, M.

Pomerene, A.

Prucnal, P. R.

Reed, G. T.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Rubin, D.

Scherer, A.

Schmidt, B.

Shafiiha, R.

Shakya, J.

Shamir, J.

J. Hardy and J. Shamir, “Optics inspired logic architecture,” Opt. Express 15(1), 150–165 (2007).
[Crossref] [PubMed]

Shearn, M.

Sherwood-Droz, N.

Shi, Z.

Solmaz, M. E.

M. E. Solmaz, Y. F. Zhou, and C. K. Madsen, “Modeling Asymmetric Resonances Using an Optical Filter Approach,” J. Lightwave Technol. 28(20), 2951–2955 (2010).
[Crossref]

Soref, R. A.

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Sullivan, P.

Sun, J. Q.

X. Zhang, Y. Wang, J. Q. Sun, D. M. Liu, and D. X. Huang, “All-optical AND gate at 10 Gbit/s based on cascaded single-port-couple SOAs,” Opt. Express 12(3), 361–366 (2004).
[Crossref] [PubMed]

Sun, R.

Takayesu, J.

Thomson, D. J.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Tian, Y. H.

Vallaitis, T.

Van, V.

Vikram, C. S.

Vorreau, P.

Wang, G.

Wang, H.

Wang, T.

Wang, Y.

X. Zhang, Y. Wang, J. Q. Sun, D. M. Liu, and D. X. Huang, “All-optical AND gate at 10 Gbit/s based on cascaded single-port-couple SOAs,” Opt. Express 12(3), 361–366 (2004).
[Crossref] [PubMed]

Xu, Q. F.

Q. F. Xu and M. Lipson, “All-optical logic based on silicon micro-ring resonators,” Opt. Express 15(3), 924–929 (2007).
[Crossref] [PubMed]

Yang, L.

Yariv, A.

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002).
[Crossref]

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[Crossref]

Yu, M. B.

Zhang, L.

Zhang, X.

X. Zhang, Y. Wang, J. Q. Sun, D. M. Liu, and D. X. Huang, “All-optical AND gate at 10 Gbit/s based on cascaded single-port-couple SOAs,” Opt. Express 12(3), 361–366 (2004).
[Crossref] [PubMed]

Zheng, X.

Zhou, P.

Zhou, Y. F.

M. E. Solmaz, Y. F. Zhou, and C. K. Madsen, “Modeling Asymmetric Resonances Using an Optical Filter Approach,” J. Lightwave Technol. 28(20), 2951–2955 (2010).
[Crossref]

Zhou, Z. P.

J. B. Feng, Q. Q. Li, and Z. P. Zhou, “Single ring interferometer configuration with doubled free-spectral range,” IEEE Photon. Technol. Lett. 23(2), 79–81 (2011).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80(6), 908–910 (2002).
[Crossref]

Electron. Lett. (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000).
[Crossref]

IEEE J. Quantum Electron. (1)

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

IEEE Photon. Technol. Lett. (2)

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14(4), 483–485 (2002).
[Crossref]

J. B. Feng, Q. Q. Li, and Z. P. Zhou, “Single ring interferometer configuration with doubled free-spectral range,” IEEE Photon. Technol. Lett. 23(2), 79–81 (2011).
[Crossref]

J. Lightwave Technol. (2)

M. E. Solmaz, Y. F. Zhou, and C. K. Madsen, “Modeling Asymmetric Resonances Using an Optical Filter Approach,” J. Lightwave Technol. 28(20), 2951–2955 (2010).
[Crossref]

Jpn. J. Appl. Phys. (1)

T. Fukazawa, T. Hirano, F. Ohno, and T. Baba, “Low loss intersection of Si photonic wire waveguides,” Jpn. J. Appl. Phys. 43(2), 646–647 (2004).
[Crossref]

Nat. Mater. (1)

Nat. Photonics (4)

H. J. Caulfield and S. Dolev, “Why future supercomputing requires optics,” Nat. Photonics 4(5), 261–263 (2010).
[Crossref]

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Opt. Express (8)

X. Zhang, Y. Wang, J. Q. Sun, D. M. Liu, and D. X. Huang, “All-optical AND gate at 10 Gbit/s based on cascaded single-port-couple SOAs,” Opt. Express 12(3), 361–366 (2004).
[Crossref] [PubMed]

Q. F. Xu and M. Lipson, “All-optical logic based on silicon micro-ring resonators,” Opt. Express 15(3), 924–929 (2007).
[Crossref] [PubMed]

J. Hardy and J. Shamir, “Optics inspired logic architecture,” Opt. Express 15(1), 150–165 (2007).
[Crossref] [PubMed]

Opt. Lett. (1)

Photonics Nanostruct. Fund. Appl. (1)

Phys. Rev. (1)

U. Fano, “Effects of Configuration Interaction on Intensities and Phase Shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[Crossref]

Other (3)

J. Heebner, R. Grover, and T. A. Ibrahim, Optical Microresonators: Theory, Fabrication, and Applications (Springer, London, 2008), Chap. 3.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: a Signal Processing Approach (Wiley, New York, 1999), Chap. 3.

G. T. Reed and A. P. Knights, Silicon Photonics: an Introduction (Wiley, West Sussex, 2004), Chap. 4.

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Fig. 1

(a) Schematic and (b) micrograph of the XOR/XNOR directed logic circuit based on two cascaded microring resonators (CW: continuous wave, EPT: electrical pulse train, OPT: optical pulse train, MRR: microring resonator).

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Fig. 2

Response spectra obtained at (a-d) the drop port and (e-h) the through port of the device. Voltages applied to MRR₁ and MRR₂ are both 0 V in (a) and (e), 3.13 V and 0 V in (b) and (f), 0 V and 2.15 V in (c) and (g), and 3.13 V and 2.15 V in (d) and (h). The dashed arrow indicates the location of the working wavelength λ _w1.

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Fig. 3

Signals applied to two MRRs and detected at the drop and through ports in the first operating mode. Signals applied to (a) MRR₁ and (b) MRR₂. Results of (c) XNOR operation result at the drop port and (d) XOR operation result at the through port.

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Fig. 4

Response spectra obtained at (a-d) the drop port and (e-h) the through port of the device. Voltages applied to MRR₁ and MRR₂ are 0.8 V and 0 V in (a) and (e), 3.07 V and 0 V in (b) and (f), 0.8 V and 2.15 V in (c) and (g), and 3.07 V and 2.15 V in (d) and (h). The dashed arrow indicates the location of the working wavelength λ _w2.

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Fig. 5

Signals applied to two MRRs and detected at the drop and through ports in the second operating mode. Signals applied to (a) MRR₁ and (b) MRR₂. Result of (c) XNOR operation result at the drop port and (d) XOR operation result at the through port.

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Fig. 6

Response spectra obtained at (a-d) the drop port and (e-h) the through port when the device operates in the first mode. No voltages are applied in (a) and (e), MRR₁ is tuned to λ_w1 in (b) and (f), MRR₂ is tuned to λ_w1 in (c) and (g), and both MRRs are tuned to λ_w1 in (d) and (h).

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Fig. 7

Scattering matrix model of the circuit (Z₁~Z₄: coupling regions, S₁~S₂: straight waveguides, R₁~R₂: ring waveguides).

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Fig. 8

Response spectra obtained in simulations at (a-d) the drop port and (e-h) the through port when the device operates in the first mode. No voltages are applied in (a) and (e), MRR₁ is tuned to λ_w1 in (b) and (f), MRR₂ is tuned to λ_w1 in (c) and (g), and both MRRs are tuned to λ_w1 in (d) and (h).

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Fig. 9

Amplitudes of the two constituent parts of E _v3 (E_v _3- _v ₂ and E_v _3- _p ₂) as functions of the wavelength.

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Fig. 10

Amplitude of the electric field E _v3 and the phase difference of its two constituent parts (E_v _3- _v ₂ and E_v _3- _p ₂) when the length difference of S₁ and S₂ is (a) odd multiples of half the perimeter of the ring waveguides (p = 1), (b) even multiples of half the perimeter of the ring waveguides (p = 0).

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Fig. 11

The spectra obtained at (a-c) the drop port and (d-f) the through port when the length differences between S₁ and S₂ are C/8, C/4, and 3C/8. C represents the ring waveguide’s perimeter.

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Tables (1)

Table 1 Parameters adopted in the numerical simulation

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Equations (11)

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(\begin{matrix} E_{p 1} \\ E_{r 2} \end{matrix}) = (\begin{matrix} t & j k \\ j k & t \end{matrix}) (\begin{matrix} E_{in} \\ E_{r 1} \end{matrix}),

\begin{array}{l} E_{p 1} = \frac{t (1 - α exp(j θ))}{1- α t^{2} \exp (j θ)} \times E_{i n}, \\ E_{v 1} = \frac{- k^{2} α^{1 / 4} exp(j θ / 4)}{1- α t^{2} \exp (j θ)} \times E_{i n} . \end{array}

θ = β • 2 π R = 4 π^{2} n_{e f f} \frac{R}{λ},

\begin{array}{l} ϕ_{p 1} = \arctan [\frac{- α \sin (θ)}{1 - α \cos (θ)}] - \arctan [\frac{- α t^{2} \sin (θ)}{1 - α t^{2} \cos (θ)}], \\ ϕ_{v 1} = π + \frac{θ}{4} - \arctan [\frac{- α t^{2} \sin (θ)}{1 - α t^{2} \cos (θ)}], \end{array}

\begin{array}{l} | E_{p 1} | = {[\frac{t^{2} (1 + α^{2} - 2 α \cos (θ))}{1 + α^{2} t^{4} - 2 α t^{2} \cos (θ)}]}^{1 / 2}, \\ | E_{v 1} | = {[\frac{k^{4} α^{1 / 2}}{1 + α^{2} t^{4} - 2 α t^{2} \cos (θ)}]}^{1 / 2} . \end{array}

\begin{array}{l} | E_{v 3 - v 2} | = \frac{t^{2} (1 + α^{2} - 2 α \cos (θ))}{1 + α^{2} t^{4} - 2 α t^{2} \cos (θ)} \times α_{1}, \\ | E_{v 3 - p 2} | = \frac{k^{4} α^{1 / 2}}{1 + α^{2} t^{4} - 2 α t^{2} \cos (θ)} \times α_{2}, \end{array}

\begin{array}{l} φ_{v 3 - v 2} = 2 \arctan [\frac{- α \sin (θ)}{1 - α \cos (θ)}] - 2 \arctan [\frac{- α t^{2} \sin (θ)}{1 - α t^{2} \cos (θ)}] + θ_{1}, \\ φ_{v 3 - p 2} = \frac{θ}{2} - 2 \arctan [\frac{- α t^{2} \sin (θ)}{1 - α t^{2} \cos (θ)}] + θ_{2}, \end{array}

Δ φ_{v 3} = 2 \arctan [\frac{- α \sin (θ)}{1 - α \cos (θ)}] - \frac{θ}{2} + (θ_{1} - θ_{2}) .

Δ φ_{v 3} = 2 \arctan [\frac{- 1}{\frac{ε}{2} + \frac{(1 / α) - 1}{ε}}] + (p - 1) m π \approx {\begin{matrix} - π + (p - 1) m π, \begin{matrix}  \end{matrix} w h e n \begin{matrix}  \end{matrix} ε = \sqrt{2 [(1 / α) - 1]}, \\ π + (p - 1) m π, \begin{matrix}  \end{matrix} w h e n \begin{matrix}  \end{matrix} ε = - \sqrt{2 [(1 / α) - 1]} . \end{matrix}

| E_{v 3} | = | | E_{v 3 - v 2} | - | E_{v 3 - p 2} | |

| E_{v 3} | = | | E_{v 3 - v 2} | + | E_{v 3 - p 2} | |

Variables	Explanation	Values
R ₁	radius of the ring waveguide R₁	10.0308 μm
R ₂	radius of the ring waveguide R₂	10.0318 μm
Δn ₁	index increase of R₁ when actuated	0.00306
Δn ₂	index increase of R₂ when actuated	0.00280
k	cross-coupling coefficient of the field amplitude	0.250
t	self-coupling coefficient of the field amplitude	0.968
lc _s	loss coefficient in the straight waveguides	3 dB/cm
lc _r	loss coefficient in the ring waveguides	10 dB/cm
L ₁	length of the straight waveguide S₁	552.870 μm
L ₂	length of the straight waveguide S₂	554.420 μm
α _c	transmission factor of the crossing of S₁ and S₂	0.890