Abstract

We design scalable all-optical logic gates that operate with the same input and output wavelength. We demonstrated the operation by using coupled mode equations, and investigated the impact of input power fluctuations and fabrication errors. We found that a wavelength fluctuation 0.3 times greater than the resonant wavelength width will degrade the operation of the system. Stronger coupling increases the wavelength tolerance. As regards coupling coefficient fluctuation, we found that the system is error-free when the fabrication precision is better than ± 5 nm. This study provides information on the required input power stability and tolerable fabrication errors of a scalable system, which moves the numerical study closer to practical realization.

© 2014 Optical Society of America

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    [CrossRef]

2012 (4)

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[CrossRef]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[CrossRef] [PubMed]

A. Abbasi, M. Noshad, R. Ranjbar, R. Kheradmand, “Ultra compact and fast All Optical Flip Flop design in photonic crystal platform,” Opt. Commun. 285(24), 5073–5078 (2012).
[CrossRef]

W. Yoshiki, T. Tanabe, “Analysis of bistable memory in silica toroid microcavity,” JOSA B 29(12), 3335–3343 (2012).
[CrossRef]

2011 (4)

2010 (2)

M. Pöllinger, A. Rauschenbeutel, “All-optical signal processing at ultra-low powers in bottle microresonators using the Kerr effect,” Opt. Express 18(17), 17764–17775 (2010).
[CrossRef] [PubMed]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

2009 (2)

2007 (3)

T. Tanabe, K. Yamada, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90(3), 031115 (2007).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics 1(1), 49–52 (2007).
[CrossRef]

F. Xia, L. Sekaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

2006 (1)

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[CrossRef]

2005 (4)

T.-J. Wang, Y.-H. Huang, H.-L. Chen, “Resonant-wavelength tuning of microring filters by oxygen plasma treatment,” Photonics Technol. Lett. IEEE 17(3), 582–584 (2005).
[CrossRef]

Y. Liu, T. Chang, A. E. Craig, “Coupled mode theory for modeling microring resonators,” Opt. Eng. 44(8), 084601 (2005).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13(7), 2678–2687 (2005).
[CrossRef] [PubMed]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett. 30(19), 2575–2577 (2005).
[CrossRef] [PubMed]

2004 (3)

A. R. Cowan, G. W. Rieger, J. F. Young, “Nonlinear transmission of 1.5 microm pulses through single-mode silicon-on-insulator waveguide structures,” Opt. Express 12(8), 1611–1621 (2004).
[CrossRef] [PubMed]

G. Rieger, K. Virk, J. Young, “Nonlinear propagation of ultrafast 1.5 μm pulses in high-index-contrast silicon-on-insulator waveguides,” Appl. Phys. Lett. 84(6), 900–902 (2004).
[CrossRef]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004).
[CrossRef] [PubMed]

2003 (3)

Y. Akahane, T. Asano, B. S. Song, S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

V. R. Almeida, R. R. Panepucci, M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003).
[CrossRef] [PubMed]

2002 (1)

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

1999 (1)

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” Quantum Electron. IEEE J. 35(9), 1322–1331 (1999).
[CrossRef]

1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Abbasi, A.

A. Abbasi, M. Noshad, R. Ranjbar, R. Kheradmand, “Ultra compact and fast All Optical Flip Flop design in photonic crystal platform,” Opt. Commun. 285(24), 5073–5078 (2012).
[CrossRef]

Akahane, Y.

Y. Akahane, T. Asano, B. S. Song, S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004).
[CrossRef] [PubMed]

V. R. Almeida, R. R. Panepucci, M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003).
[CrossRef] [PubMed]

Andalib, P.

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

Asano, T.

Y. Akahane, T. Asano, B. S. Song, S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004).
[CrossRef] [PubMed]

Chang, T.

Y. Liu, T. Chang, A. E. Craig, “Coupled mode theory for modeling microring resonators,” Opt. Eng. 44(8), 084601 (2005).
[CrossRef]

Chen, C. J.

Chen, H.-L.

T.-J. Wang, Y.-H. Huang, H.-L. Chen, “Resonant-wavelength tuning of microring filters by oxygen plasma treatment,” Photonics Technol. Lett. IEEE 17(3), 582–584 (2005).
[CrossRef]

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Cowan, A. R.

Craig, A. E.

Y. Liu, T. Chang, A. E. Craig, “Coupled mode theory for modeling microring resonators,” Opt. Eng. 44(8), 084601 (2005).
[CrossRef]

Fan, L.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[CrossRef] [PubMed]

Fan, S.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” Quantum Electron. IEEE J. 35(9), 1322–1331 (1999).
[CrossRef]

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Foster, M. A.

J. S. Levy, M. A. Foster, A. L. Gaeta, M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19(12), 11415–11421 (2011).
[CrossRef] [PubMed]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

Fukuda, H.

T. Tanabe, K. Yamada, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90(3), 031115 (2007).
[CrossRef]

Gaeta, A. L.

J. S. Levy, M. A. Foster, A. L. Gaeta, M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19(12), 11415–11421 (2011).
[CrossRef] [PubMed]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

Gondarenko, A.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

A. Gondarenko, J. S. Levy, M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express 17(14), 11366–11370 (2009).
[CrossRef] [PubMed]

Granpayeh, N.

Gu, T.

Haus, H. A.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” Quantum Electron. IEEE J. 35(9), 1322–1331 (1999).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Huang, Y.-H.

T.-J. Wang, Y.-H. Huang, H.-L. Chen, “Resonant-wavelength tuning of microring filters by oxygen plasma treatment,” Photonics Technol. Lett. IEEE 17(3), 582–584 (2005).
[CrossRef]

Inokawa, H.

T. Tanabe, K. Yamada, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90(3), 031115 (2007).
[CrossRef]

Itabashi, S.

T. Tanabe, K. Yamada, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90(3), 031115 (2007).
[CrossRef]

Joannopoulos, J. D.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” Quantum Electron. IEEE J. 35(9), 1322–1331 (1999).
[CrossRef]

Kawaguchi, Y.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[CrossRef]

Khan, M. J.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” Quantum Electron. IEEE J. 35(9), 1322–1331 (1999).
[CrossRef]

Kheradmand, R.

A. Abbasi, M. Noshad, R. Ranjbar, R. Kheradmand, “Ultra compact and fast All Optical Flip Flop design in photonic crystal platform,” Opt. Commun. 285(24), 5073–5078 (2012).
[CrossRef]

Kippenberg, T. J.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

Kira, G.

Kuramochi, E.

M. Notomi, A. Shinya, K. Nozaki, T. Tanabe, S. Matsuo, E. Kuramochi, T. Sato, H. Taniyama, H. Sumikura, “Low-power nanophotonic devices based on photonic crystals towards dense photonic network on chip,” IET Circuits Devices Syst. 5(2), 84–93 (2011).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics 1(1), 49–52 (2007).
[CrossRef]

T. Tanabe, K. Yamada, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90(3), 031115 (2007).
[CrossRef]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13(7), 2678–2687 (2005).
[CrossRef] [PubMed]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett. 30(19), 2575–2577 (2005).
[CrossRef] [PubMed]

H. Takesue, N. Matsuda, E. Kuramochi, W. J. Munro, M. Notomi, “An on-chip coupled resonator optical waveguide single-photon buffer,” Nat. Commun.4,2725(2013).

Kwong, D.-L.

Laine, J.-P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Levy, J. S.

Li, Z.-Y.

Lipson, M.

J. S. Levy, M. A. Foster, A. L. Gaeta, M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express 19(12), 11415–11421 (2011).
[CrossRef] [PubMed]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

A. Gondarenko, J. S. Levy, M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express 17(14), 11366–11370 (2009).
[CrossRef] [PubMed]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004).
[CrossRef] [PubMed]

V. R. Almeida, R. R. Panepucci, M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003).
[CrossRef] [PubMed]

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Liu, Y.

Lo, G.-Q.

Manolatou, C.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” Quantum Electron. IEEE J. 35(9), 1322–1331 (1999).
[CrossRef]

Mao, Q.-H.

Matsuda, N.

H. Takesue, N. Matsuda, E. Kuramochi, W. J. Munro, M. Notomi, “An on-chip coupled resonator optical waveguide single-photon buffer,” Nat. Commun.4,2725(2013).

Matsuo, S.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[CrossRef]

M. Notomi, A. Shinya, K. Nozaki, T. Tanabe, S. Matsuo, E. Kuramochi, T. Sato, H. Taniyama, H. Sumikura, “Low-power nanophotonic devices based on photonic crystals towards dense photonic network on chip,” IET Circuits Devices Syst. 5(2), 84–93 (2011).
[CrossRef]

McMillan, J. F.

Meng, Z.-M.

Mitsugi, S.

Munro, W. J.

H. Takesue, N. Matsuda, E. Kuramochi, W. J. Munro, M. Notomi, “An on-chip coupled resonator optical waveguide single-photon buffer,” Nat. Commun.4,2725(2013).

Nishiguchi, K.

T. Tanabe, K. Yamada, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90(3), 031115 (2007).
[CrossRef]

Niu, B.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[CrossRef] [PubMed]

Noda, S.

Y. Akahane, T. Asano, B. S. Song, S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Noshad, M.

A. Abbasi, M. Noshad, R. Ranjbar, R. Kheradmand, “Ultra compact and fast All Optical Flip Flop design in photonic crystal platform,” Opt. Commun. 285(24), 5073–5078 (2012).
[CrossRef]

Notomi, M.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[CrossRef]

M. Notomi, A. Shinya, K. Nozaki, T. Tanabe, S. Matsuo, E. Kuramochi, T. Sato, H. Taniyama, H. Sumikura, “Low-power nanophotonic devices based on photonic crystals towards dense photonic network on chip,” IET Circuits Devices Syst. 5(2), 84–93 (2011).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics 1(1), 49–52 (2007).
[CrossRef]

T. Tanabe, K. Yamada, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90(3), 031115 (2007).
[CrossRef]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13(7), 2678–2687 (2005).
[CrossRef] [PubMed]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett. 30(19), 2575–2577 (2005).
[CrossRef] [PubMed]

H. Takesue, N. Matsuda, E. Kuramochi, W. J. Munro, M. Notomi, “An on-chip coupled resonator optical waveguide single-photon buffer,” Nat. Commun.4,2725(2013).

Nozaki, K.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[CrossRef]

M. Notomi, A. Shinya, K. Nozaki, T. Tanabe, S. Matsuo, E. Kuramochi, T. Sato, H. Taniyama, H. Sumikura, “Low-power nanophotonic devices based on photonic crystals towards dense photonic network on chip,” IET Circuits Devices Syst. 5(2), 84–93 (2011).
[CrossRef]

Panepucci, R. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004).
[CrossRef] [PubMed]

V. R. Almeida, R. R. Panepucci, M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003).
[CrossRef] [PubMed]

Pöllinger, M.

Qi, M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[CrossRef] [PubMed]

Qin, F.

Ranjbar, R.

A. Abbasi, M. Noshad, R. Ranjbar, R. Kheradmand, “Ultra compact and fast All Optical Flip Flop design in photonic crystal platform,” Opt. Commun. 285(24), 5073–5078 (2012).
[CrossRef]

Rauschenbeutel, A.

Rieger, G.

G. Rieger, K. Virk, J. Young, “Nonlinear propagation of ultrafast 1.5 μm pulses in high-index-contrast silicon-on-insulator waveguides,” Appl. Phys. Lett. 84(6), 900–902 (2004).
[CrossRef]

Rieger, G. W.

Sato, T.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[CrossRef]

M. Notomi, A. Shinya, K. Nozaki, T. Tanabe, S. Matsuo, E. Kuramochi, T. Sato, H. Taniyama, H. Sumikura, “Low-power nanophotonic devices based on photonic crystals towards dense photonic network on chip,” IET Circuits Devices Syst. 5(2), 84–93 (2011).
[CrossRef]

Segawa, T.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[CrossRef]

Sekaric, L.

F. Xia, L. Sekaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Shen, H.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[CrossRef] [PubMed]

Shinojima, H.

T. Tanabe, K. Yamada, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90(3), 031115 (2007).
[CrossRef]

Shinya, A.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[CrossRef]

M. Notomi, A. Shinya, K. Nozaki, T. Tanabe, S. Matsuo, E. Kuramochi, T. Sato, H. Taniyama, H. Sumikura, “Low-power nanophotonic devices based on photonic crystals towards dense photonic network on chip,” IET Circuits Devices Syst. 5(2), 84–93 (2011).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics 1(1), 49–52 (2007).
[CrossRef]

T. Tanabe, K. Yamada, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90(3), 031115 (2007).
[CrossRef]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13(7), 2678–2687 (2005).
[CrossRef] [PubMed]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett. 30(19), 2575–2577 (2005).
[CrossRef] [PubMed]

Song, B. S.

Y. Akahane, T. Asano, B. S. Song, S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Spillane, S. M.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

Sumikura, H.

M. Notomi, A. Shinya, K. Nozaki, T. Tanabe, S. Matsuo, E. Kuramochi, T. Sato, H. Taniyama, H. Sumikura, “Low-power nanophotonic devices based on photonic crystals towards dense photonic network on chip,” IET Circuits Devices Syst. 5(2), 84–93 (2011).
[CrossRef]

Suzaki, Y.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[CrossRef]

Takahashi, R.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[CrossRef]

Takesue, H.

H. Takesue, N. Matsuda, E. Kuramochi, W. J. Munro, M. Notomi, “An on-chip coupled resonator optical waveguide single-photon buffer,” Nat. Commun.4,2725(2013).

Tanabe, T.

W. Yoshiki, T. Tanabe, “Analysis of bistable memory in silica toroid microcavity,” JOSA B 29(12), 3335–3343 (2012).
[CrossRef]

M. Notomi, A. Shinya, K. Nozaki, T. Tanabe, S. Matsuo, E. Kuramochi, T. Sato, H. Taniyama, H. Sumikura, “Low-power nanophotonic devices based on photonic crystals towards dense photonic network on chip,” IET Circuits Devices Syst. 5(2), 84–93 (2011).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics 1(1), 49–52 (2007).
[CrossRef]

T. Tanabe, K. Yamada, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90(3), 031115 (2007).
[CrossRef]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13(7), 2678–2687 (2005).
[CrossRef] [PubMed]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett. 30(19), 2575–2577 (2005).
[CrossRef] [PubMed]

W. Yoshiki, T. Tanabe, “Add-drop system for Kerr bistable memory in silicon nitride microrings,” Opt. Express. submitted. (arXiv:1308.6042).

Taniyama, H.

M. Notomi, A. Shinya, K. Nozaki, T. Tanabe, S. Matsuo, E. Kuramochi, T. Sato, H. Taniyama, H. Sumikura, “Low-power nanophotonic devices based on photonic crystals towards dense photonic network on chip,” IET Circuits Devices Syst. 5(2), 84–93 (2011).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics 1(1), 49–52 (2007).
[CrossRef]

Tsuchizawa, T.

T. Tanabe, K. Yamada, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90(3), 031115 (2007).
[CrossRef]

Turner-Foster, A. C.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

Vahala, K. J.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

Varghese, L. T.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[CrossRef] [PubMed]

Villeneuve, P. R.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” Quantum Electron. IEEE J. 35(9), 1322–1331 (1999).
[CrossRef]

Virk, K.

G. Rieger, K. Virk, J. Young, “Nonlinear propagation of ultrafast 1.5 μm pulses in high-index-contrast silicon-on-insulator waveguides,” Appl. Phys. Lett. 84(6), 900–902 (2004).
[CrossRef]

Vlasov, Y.

F. Xia, L. Sekaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Wang, J.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[CrossRef] [PubMed]

Wang, T.-J.

T.-J. Wang, Y.-H. Huang, H.-L. Chen, “Resonant-wavelength tuning of microring filters by oxygen plasma treatment,” Photonics Technol. Lett. IEEE 17(3), 582–584 (2005).
[CrossRef]

Watanabe, T.

T. Tanabe, K. Yamada, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90(3), 031115 (2007).
[CrossRef]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[CrossRef]

Weiner, A. M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[CrossRef] [PubMed]

Wong, C. W.

Xia, F.

F. Xia, L. Sekaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Xuan, Y.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[CrossRef] [PubMed]

Yamada, K.

T. Tanabe, K. Yamada, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90(3), 031115 (2007).
[CrossRef]

Yariv, A.

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

Yoshiki, W.

W. Yoshiki, T. Tanabe, “Analysis of bistable memory in silica toroid microcavity,” JOSA B 29(12), 3335–3343 (2012).
[CrossRef]

W. Yoshiki, T. Tanabe, “Add-drop system for Kerr bistable memory in silicon nitride microrings,” Opt. Express. submitted. (arXiv:1308.6042).

Young, J.

G. Rieger, K. Virk, J. Young, “Nonlinear propagation of ultrafast 1.5 μm pulses in high-index-contrast silicon-on-insulator waveguides,” Appl. Phys. Lett. 84(6), 900–902 (2004).
[CrossRef]

Young, J. F.

Yu, M.

Zheng, J.

Zhou, F.

Appl. Phys. Lett. (3)

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[CrossRef]

G. Rieger, K. Virk, J. Young, “Nonlinear propagation of ultrafast 1.5 μm pulses in high-index-contrast silicon-on-insulator waveguides,” Appl. Phys. Lett. 84(6), 900–902 (2004).
[CrossRef]

T. Tanabe, K. Yamada, K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett. 90(3), 031115 (2007).
[CrossRef]

IET Circuits Devices Syst. (1)

M. Notomi, A. Shinya, K. Nozaki, T. Tanabe, S. Matsuo, E. Kuramochi, T. Sato, H. Taniyama, H. Sumikura, “Low-power nanophotonic devices based on photonic crystals towards dense photonic network on chip,” IET Circuits Devices Syst. 5(2), 84–93 (2011).
[CrossRef]

J. Lightwave Technol. (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

J. Opt. Soc. Am. B (1)

JOSA B (1)

W. Yoshiki, T. Tanabe, “Analysis of bistable memory in silica toroid microcavity,” JOSA B 29(12), 3335–3343 (2012).
[CrossRef]

Nat. Photonics (4)

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics 1(1), 49–52 (2007).
[CrossRef]

F. Xia, L. Sekaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
[CrossRef]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

Nature (3)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B. S. Song, S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

A. Abbasi, M. Noshad, R. Ranjbar, R. Kheradmand, “Ultra compact and fast All Optical Flip Flop design in photonic crystal platform,” Opt. Commun. 285(24), 5073–5078 (2012).
[CrossRef]

Opt. Eng. (1)

Y. Liu, T. Chang, A. E. Craig, “Coupled mode theory for modeling microring resonators,” Opt. Eng. 44(8), 084601 (2005).
[CrossRef]

Opt. Express (7)

Opt. Lett. (2)

Photonics Technol. Lett. IEEE (2)

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

T.-J. Wang, Y.-H. Huang, H.-L. Chen, “Resonant-wavelength tuning of microring filters by oxygen plasma treatment,” Photonics Technol. Lett. IEEE 17(3), 582–584 (2005).
[CrossRef]

Quantum Electron. IEEE J. (1)

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” Quantum Electron. IEEE J. 35(9), 1322–1331 (1999).
[CrossRef]

Science (1)

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[CrossRef] [PubMed]

Other (5)

M. Noshad, A. Abbasi, R. Ranjbar, and R. Kheradmand, “Novel all-optical logic gates based on photonic crystal structure,” in Journal of Physics: Conference Series350 (2012).

M. W. Lee, C. Grillet, S. Tomljenovic-Hanic, D. Moss, B. J. Eggleton, X. Gai, S. Madden, D. Y. Choi, D. Bulla, and B. Luther-Davies, “High-Q Photonic Crystal Chalcogenide Cavities by Photosensitive Post Processing,” in in Advances in Optical Sciences Congress, OSA Technical Digest (CD) (Optical Society of America, 2009), paper PDPC2 (2009).

W. Yoshiki, T. Tanabe, “Add-drop system for Kerr bistable memory in silicon nitride microrings,” Opt. Express. submitted. (arXiv:1308.6042).

H. Takesue, N. Matsuda, E. Kuramochi, W. J. Munro, M. Notomi, “An on-chip coupled resonator optical waveguide single-photon buffer,” Nat. Commun.4,2725(2013).

A. K. Erdamar, M. M. van Leest, S. J. Picken, and J. Caro, “Thermal tuning of a silicon photonic crystal cavity infilled with an elastomer,” in SPIE NanoScience + Engineering8095 (2011).

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Figures (12)

Fig. 1
Fig. 1

Schematic illustration of an all-optical switch made of an add-drop microring resonator. The dotted line represents the transmittance spectrum of a cold cavity. The solid line is the transmittance when inputs are applied. A resonant shift occurs due to the optical Kerr effect. Two different wavelengths λ1, and λ2 are used for the operation. (a) λ1 will drop (high) when only λ1 is inputted (high). (b) λ2 will not drop (low) when only λ2 is inputted (high). (c) λ2 will drop (high) when both λ1 and λ2 are inputted (high). As a result, λ2 can be switched off and on by turning λ1 signal on and off.

Fig. 2
Fig. 2

Schematic dimension of add-drop system used for this calculation.

Fig. 3
Fig. 3

Reflection and radiation at tapered waveguide.

Fig. 4
Fig. 4

(a) Design of NAND gate. (b) Input and output versus time. The black, red, and green lines represent input 1, input 2, and output, respectively.

Fig. 5
Fig. 5

Input and output amplitudes of different logic gate versus time. (a) AND gate. (b) OR gate. (c) NOR gate. (d) NAND gate. The black squares are the output when the power of inputs 1 and 2 were changed together, the red circles are the output when only input 1 was changed (input 2 is fixed at 250 mW). The blue triangles are the output when only input 2 was changed (input 1 is fixed at 250 mW).

Fig. 6
Fig. 6

Error rate of NAND gate that have different resonant wavelength fluctuation. (a) Result for a NAND gate with optimized waveguide-cavity couplings. (b) Result for a NAND gate with strong waveguide-cavity couplings.

Fig. 7
Fig. 7

Error rate of a NAND gate when the gap distances fluctuate.

Fig. 8
Fig. 8

(a) Design of AND gate. (b) Input and output versus time. The black, red, and green lines represent input 1, input 2, and output, respectively.

Fig. 9
Fig. 9

(a) Design of OR gate. (b) Input and output versus time. The black, red, and green lines represent input1, input2, and output. The input amplitude is 250 mW.

Fig. 10
Fig. 10

(a) Design of NOR gate. (b) Input and output versus time. The black, red, and green lines represent input 1, input 2, and output, respectively. The input amplitude is 250 mW.

Fig. 11
Fig. 11

(a) Logic circuit chart of the cascade system. (b) The truth table. (c) Input and output versus time. The black, red, green, and blue lines represent the input1, input2, input3, and output, respectively.

Fig. 12
Fig. 12

Input and output waveforms. The black, red, green, and blue lines are the input1, input2, input3, and output, respectively.

Tables (2)

Tables Icon

Table 1 Maximum and minimum widths of resonant spectrum (FWHM) Smax, Smin, and the standard deviation σlim limit of each logic gate

Tables Icon

Table 2 The limit of the fabrication fluctuation (in standard deviation σ`lim) for different logic gate

Equations (15)

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k x = n 2 k 2 β 2
α= β 2 n 2 k 2
P= β 2ω μ 0 ( w+ 1 α )
κ( s )= ω ε 0 cos( k x w 2 ) 2P( k x 2 + α 2 ) ( n 2 n 0 2 )× πR α exp( αs ) ×[ αcos( k x w 2 )sinh( αw 2 )+ k x sin( k x w 2 )cosh( αw 2 ) ]
Q= 2 π 2 R n e λ 0 κ 2
τ coup = Q ω = πR n e c κ 2
da dt =[ j ω 0 1 2 ( 1 τ loss + 2 τ coup ) ]a+ 1 τ coup exp( jθ ) s in
s tr =exp( jβd )×[ s in 1 τ coup exp( jθ )a ]
s dr =exp( jβd )× 1 τ coup a
θ=4 π 2 n 0 R( 1 λ 0 1 λ )
Δ n kerr = 2 n 2 c n 0 ( U λ 1 +2 U λ 2 ) V
δλ= Δ n kerr n 0 λ 0
dN(t) dt = 2 λ 1 c β TPA h n 0 2 V 2 ( U λ 1 + U λ 2 ) 2 N(t) τ c
d U T (t) dt = E g N(t) τ c U T (t) τ T
Δ n c (t)=1.12× 10 16 U T (t)[8.8× 10 22 N(t)+8.8× 10 18 N (t) 0.8 ]

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