Abstract

We investigate mode multistability, i.e. coexistence of direction bistability and wavelength bi/multistability in microring lasers (MRLs) theoretically and numerically. We derive the expressions for conditions required for mode multistable operation in microring lasers based on a nonlinear multimode model with nonlinear effects stemming from carrier density pulsation, carrier heating and spectral hole burning included. We find theoretically that lasing mode can be selected from the multistable modes by external optical injection through gain saturation, and removal of the external optical injection will not affect the stability of the established lasing mode. Numerical results on all-optical multistate flip-flop function demonstrate that switching between multistable modes can be induced by trigger signals with each states self-sustained after the removal of the trigger signals in a 50µm-radius microring laser.

©2013 Optical Society of America

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  1. K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6(4), 248–252 (2012).
    [Crossref]
  2. Q. Xu and M. Lipson, “All-optical logic based on silicon micro-ring resonators,” Opt. Express 15(3), 924–929 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-15-3-924 .
    [Crossref] [PubMed]
  3. 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).
    [Crossref]
  4. M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
    [Crossref] [PubMed]
  5. M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003).
    [Crossref]
  6. Z. Wang, G. Yuan, X. Cai, G. Verschaffelt, J. Dancka, Y. Liu, and S. Yu, “Error-free 10Gb/s all-optical switching based on a bidirectional SRL with miniaturized retro-reflector cavity,” IEEE Photon. Technol. Lett. 22(24), 1805–1807 (2010).
    [Crossref]
  7. L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. J. Geluk, T. D. Vries, P. Regreny, D. 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).
    [Crossref]
  8. D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010).
    [Crossref]
  9. C. Born, S. Yu, M. Sorel, and P. J. R. Laybourn, “Controllable and stable mode selection in a semiconductor ring laser by injection locking,” in CLEO Proceedings, paper CWK4, (2003).
  10. Z. Wang, G. Yuan, G. Verschaffelt, J. Danckaert, and S. Yu, “Storing 2 bits of information in a novel single semiconductor micro-ring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008).
    [Crossref]
  11. G. Yuan and S. Yu, “Bistability and switching properties of semiconductor ring lasers with external optical Injection,” IEEE J. Quantum Electron. 44(1), 41–48 (2008).
    [Crossref]
  12. G. Yuan and Z. Wang, “Theoretical and numerical investigations of wavelength bi/multistability in semiconductor ring lasers,” IEEE J. Quantum Electron. 47(11), 1375–1382 (2011).
    [Crossref]
  13. A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Longitudinal mode multistability in ring and Fabry-Pérot lasers: the effect of spatial hole burning,” Opt. Express 19(4), 3284–3289 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-19-4-3284 .
    [Crossref] [PubMed]
  14. C. Born, G. Yuan, Z. Wang, and S. Yu, “Nonlinear gain in semiconductor ring lasers,” IEEE J. Quantum Electron. 44(11), 1055–1064 (2008).
    [Crossref]

2012 (1)

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

2011 (2)

2010 (4)

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).
[Crossref]

Z. Wang, G. Yuan, X. Cai, G. Verschaffelt, J. Dancka, Y. Liu, and S. Yu, “Error-free 10Gb/s all-optical switching based on a bidirectional SRL with miniaturized retro-reflector cavity,” IEEE Photon. Technol. Lett. 22(24), 1805–1807 (2010).
[Crossref]

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. J. Geluk, T. D. Vries, P. Regreny, D. 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).
[Crossref]

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010).
[Crossref]

2008 (3)

Z. Wang, G. Yuan, G. Verschaffelt, J. Danckaert, and S. Yu, “Storing 2 bits of information in a novel single semiconductor micro-ring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008).
[Crossref]

G. Yuan and S. Yu, “Bistability and switching properties of semiconductor ring lasers with external optical Injection,” IEEE J. Quantum Electron. 44(1), 41–48 (2008).
[Crossref]

C. Born, G. Yuan, Z. Wang, and S. Yu, “Nonlinear gain in semiconductor ring lasers,” IEEE J. Quantum Electron. 44(11), 1055–1064 (2008).
[Crossref]

2007 (1)

2004 (1)

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[Crossref] [PubMed]

2003 (1)

M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003).
[Crossref]

Baets, R.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. J. Geluk, T. D. Vries, P. Regreny, D. 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).
[Crossref]

Balle, S.

Binsma, H.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[Crossref] [PubMed]

Born, C.

C. Born, G. Yuan, Z. Wang, and S. Yu, “Nonlinear gain in semiconductor ring lasers,” IEEE J. Quantum Electron. 44(11), 1055–1064 (2008).
[Crossref]

Bowers, J. E.

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010).
[Crossref]

Cai, X.

Z. Wang, G. Yuan, X. Cai, G. Verschaffelt, J. Dancka, Y. Liu, and S. Yu, “Error-free 10Gb/s all-optical switching based on a bidirectional SRL with miniaturized retro-reflector cavity,” IEEE Photon. Technol. Lett. 22(24), 1805–1807 (2010).
[Crossref]

Dancka, J.

Z. Wang, G. Yuan, X. Cai, G. Verschaffelt, J. Dancka, Y. Liu, and S. Yu, “Error-free 10Gb/s all-optical switching based on a bidirectional SRL with miniaturized retro-reflector cavity,” IEEE Photon. Technol. Lett. 22(24), 1805–1807 (2010).
[Crossref]

Danckaert, J.

Z. Wang, G. Yuan, G. Verschaffelt, J. Danckaert, and S. Yu, “Storing 2 bits of information in a novel single semiconductor micro-ring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008).
[Crossref]

De Vries, T.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[Crossref] [PubMed]

Den Besten, J. H.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[Crossref] [PubMed]

Donati, S.

M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003).
[Crossref]

Dorren, H. J. S.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[Crossref] [PubMed]

Geluk, E. J.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. J. Geluk, T. D. Vries, P. Regreny, D. 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).
[Crossref]

Giuliani, G.

M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003).
[Crossref]

Hill, M. T.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[Crossref] [PubMed]

Huybrechts, K.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. J. Geluk, T. D. Vries, P. Regreny, D. 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).
[Crossref]

Javaloyes, J.

Kawaguchi, Y.

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

Khoe, G. D.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[Crossref] [PubMed]

Kumar, R.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. J. Geluk, T. D. Vries, P. Regreny, D. 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).
[Crossref]

Laybourn, P. J. R.

M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003).
[Crossref]

Leijtens, X. J. M.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[Crossref] [PubMed]

Liang, D.

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010).
[Crossref]

Lipson, M.

Liu, L.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. J. Geluk, T. D. Vries, P. Regreny, D. 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).
[Crossref]

Liu, Y.

Z. Wang, G. Yuan, X. Cai, G. Verschaffelt, J. Dancka, Y. Liu, and S. Yu, “Error-free 10Gb/s all-optical switching based on a bidirectional SRL with miniaturized retro-reflector cavity,” IEEE Photon. Technol. Lett. 22(24), 1805–1807 (2010).
[Crossref]

Matsuo, S.

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

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).
[Crossref]

Miglierina, R.

M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003).
[Crossref]

Morthier, G.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. J. Geluk, T. D. Vries, P. Regreny, D. 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).
[Crossref]

Notomi, M.

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

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).
[Crossref]

Nozaki, K.

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

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).
[Crossref]

Oei, Y. S.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[Crossref] [PubMed]

Pérez-Serrano, A.

Regreny, P.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. J. Geluk, T. D. Vries, P. Regreny, D. 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).
[Crossref]

Roelkens, G.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. J. Geluk, T. D. Vries, P. Regreny, D. 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).
[Crossref]

Sato, T.

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

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).
[Crossref]

Scire, A.

M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003).
[Crossref]

Segawa, T.

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

Shinya, A.

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

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).
[Crossref]

Smalbrugge, B.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[Crossref] [PubMed]

Smit, M. K.

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[Crossref] [PubMed]

Sorel, M.

M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003).
[Crossref]

Spuesens, T.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. J. Geluk, T. D. Vries, P. Regreny, D. 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).
[Crossref]

Suzaki, Y.

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

Tanabe, T.

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).
[Crossref]

Taniyama, H.

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).
[Crossref]

Thourhout, D.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. J. Geluk, T. D. Vries, P. Regreny, D. 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).
[Crossref]

Verschaffelt, G.

Z. Wang, G. Yuan, X. Cai, G. Verschaffelt, J. Dancka, Y. Liu, and S. Yu, “Error-free 10Gb/s all-optical switching based on a bidirectional SRL with miniaturized retro-reflector cavity,” IEEE Photon. Technol. Lett. 22(24), 1805–1807 (2010).
[Crossref]

Z. Wang, G. Yuan, G. Verschaffelt, J. Danckaert, and S. Yu, “Storing 2 bits of information in a novel single semiconductor micro-ring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008).
[Crossref]

Vries, T. D.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. J. Geluk, T. D. Vries, P. Regreny, D. 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).
[Crossref]

Wang, Z.

G. Yuan and Z. Wang, “Theoretical and numerical investigations of wavelength bi/multistability in semiconductor ring lasers,” IEEE J. Quantum Electron. 47(11), 1375–1382 (2011).
[Crossref]

Z. Wang, G. Yuan, X. Cai, G. Verschaffelt, J. Dancka, Y. Liu, and S. Yu, “Error-free 10Gb/s all-optical switching based on a bidirectional SRL with miniaturized retro-reflector cavity,” IEEE Photon. Technol. Lett. 22(24), 1805–1807 (2010).
[Crossref]

Z. Wang, G. Yuan, G. Verschaffelt, J. Danckaert, and S. Yu, “Storing 2 bits of information in a novel single semiconductor micro-ring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008).
[Crossref]

C. Born, G. Yuan, Z. Wang, and S. Yu, “Nonlinear gain in semiconductor ring lasers,” IEEE J. Quantum Electron. 44(11), 1055–1064 (2008).
[Crossref]

Xu, Q.

Yu, S.

Z. Wang, G. Yuan, X. Cai, G. Verschaffelt, J. Dancka, Y. Liu, and S. Yu, “Error-free 10Gb/s all-optical switching based on a bidirectional SRL with miniaturized retro-reflector cavity,” IEEE Photon. Technol. Lett. 22(24), 1805–1807 (2010).
[Crossref]

C. Born, G. Yuan, Z. Wang, and S. Yu, “Nonlinear gain in semiconductor ring lasers,” IEEE J. Quantum Electron. 44(11), 1055–1064 (2008).
[Crossref]

Z. Wang, G. Yuan, G. Verschaffelt, J. Danckaert, and S. Yu, “Storing 2 bits of information in a novel single semiconductor micro-ring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008).
[Crossref]

G. Yuan and S. Yu, “Bistability and switching properties of semiconductor ring lasers with external optical Injection,” IEEE J. Quantum Electron. 44(1), 41–48 (2008).
[Crossref]

Yuan, G.

G. Yuan and Z. Wang, “Theoretical and numerical investigations of wavelength bi/multistability in semiconductor ring lasers,” IEEE J. Quantum Electron. 47(11), 1375–1382 (2011).
[Crossref]

Z. Wang, G. Yuan, X. Cai, G. Verschaffelt, J. Dancka, Y. Liu, and S. Yu, “Error-free 10Gb/s all-optical switching based on a bidirectional SRL with miniaturized retro-reflector cavity,” IEEE Photon. Technol. Lett. 22(24), 1805–1807 (2010).
[Crossref]

G. Yuan and S. Yu, “Bistability and switching properties of semiconductor ring lasers with external optical Injection,” IEEE J. Quantum Electron. 44(1), 41–48 (2008).
[Crossref]

Z. Wang, G. Yuan, G. Verschaffelt, J. Danckaert, and S. Yu, “Storing 2 bits of information in a novel single semiconductor micro-ring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008).
[Crossref]

C. Born, G. Yuan, Z. Wang, and S. Yu, “Nonlinear gain in semiconductor ring lasers,” IEEE J. Quantum Electron. 44(11), 1055–1064 (2008).
[Crossref]

IEEE J. Quantum Electron. (4)

M. Sorel, G. Giuliani, A. Scire, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model,” IEEE J. Quantum Electron. 39(10), 1187–1195 (2003).
[Crossref]

G. Yuan and S. Yu, “Bistability and switching properties of semiconductor ring lasers with external optical Injection,” IEEE J. Quantum Electron. 44(1), 41–48 (2008).
[Crossref]

G. Yuan and Z. Wang, “Theoretical and numerical investigations of wavelength bi/multistability in semiconductor ring lasers,” IEEE J. Quantum Electron. 47(11), 1375–1382 (2011).
[Crossref]

C. Born, G. Yuan, Z. Wang, and S. Yu, “Nonlinear gain in semiconductor ring lasers,” IEEE J. Quantum Electron. 44(11), 1055–1064 (2008).
[Crossref]

IEEE Photon. Technol. Lett. (2)

Z. Wang, G. Yuan, G. Verschaffelt, J. Danckaert, and S. Yu, “Storing 2 bits of information in a novel single semiconductor micro-ring laser memory cell,” IEEE Photon. Technol. Lett. 20(14), 1228–1230 (2008).
[Crossref]

Z. Wang, G. Yuan, X. Cai, G. Verschaffelt, J. Dancka, Y. Liu, and S. Yu, “Error-free 10Gb/s all-optical switching based on a bidirectional SRL with miniaturized retro-reflector cavity,” IEEE Photon. Technol. Lett. 22(24), 1805–1807 (2010).
[Crossref]

Nat. Photonics (4)

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. J. Geluk, T. D. Vries, P. Regreny, D. 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).
[Crossref]

D. Liang and J. E. Bowers, “Recent progress in lasers on silicon,” Nat. Photonics 4(8), 511–517 (2010).
[Crossref]

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

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).
[Crossref]

Nature (1)

M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004).
[Crossref] [PubMed]

Opt. Express (2)

Other (1)

C. Born, S. Yu, M. Sorel, and P. J. R. Laybourn, “Controllable and stable mode selection in a semiconductor ring laser by injection locking,” in CLEO Proceedings, paper CWK4, (2003).

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Figures (8)

Fig. 1
Fig. 1 Illustration of modes Lp and Mq in both directions of a microring laser.

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Fig. 2
Fig. 2 Illustration of transient behaviour of the intensities of modes L and M in the phase plane. Dashed straight line for d S L / d S M = 0 , and dotted straight line for d S M / d S L = 0 .

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Fig. 3
Fig. 3 Illustration of transient behaviour of the intensities of modes in the CCW and CW directions in the phase plane. Dashed straight line for d S 1 / d S 2 = 0 , and dotted straight line for d S 2 / d S 1 = 0 .

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Fig. 4
Fig. 4 Illustration of transient behaviour of the intensities of modes L and M in the phase plane with appropriate external optical injections. Dashed line for d S L / d S M = 0 , and dotted line for d S M / d S L = 0 . (a) an external optical injection is added to mode L; (b) an external optical injection is added to mode M.

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Fig. 5
Fig. 5 Illustration of transient behaviour of the intensities of modes in the CCW and CW directions in the phase plane with appropriate external optical injections. Dashed line for d S 1 / d S 2 = 0 , and dotted line for d S 2 / d S 1 = 0 . (a) an external optical injection is added to the CCW direction of mode L or M; (b) an external optical injection is added to CW direction of mode L or M.

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Fig. 6
Fig. 6 Illustrations of the external trigger pulse signals. (a) external trigger pulse signals with 10ns pulse width and 20ns time slot; (b) zone A with 10 pulses included; (c) zone B with 15 pulses included.

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Fig. 7
Fig. 7 (a) Simulated switching dynamics between multistable modes. (a) switching induced by the trigger pulse stream shown in Fig. 6(b); (b) Switching induced by the trigger signals illustrated in Fig. 6(c).

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Fig. 8
Fig. 8 Optical spectra for CCW direction (a) and for CW direction (b) show the power of resonant modes at different self-sustained states after the removal of trigger signals in multistate flip-flop operations.

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Tables (1)

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Table 1 Main parameters

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Equations (21)

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d Δ N d t = I − I t h e V c − Δ N τ N − 2 ε 0 n g n 0 ℏ ω p k v g ∑ a g a | E a | 2
E ( z , t ) = ∑ a E a ( t ) exp ( i k a z ) exp ( − i ω a t ) + c . c .
k a = { ω a n 0 c , + z d i r e c t i o n − ω a n 0 c , − z d i r e c t i o n
d E a d t = [ 0.5 v g Γ ( g a + Δ N d g d N ( 1 − i α N ) − 1 Γ v g τ p ) − i Δ ω a d i s ] E a ( t ) + i 0.5 v g ω a c n Γ ∑ b c d χ b c d 3 E b ( t ) E c * ( t ) E d ( t ) ζ a b c d + F a ( t )
χ b c d 3 = χ b c d C D P + χ b c d S H B + χ b c d C H
χ b c d C D P = − 2 ε 0 n n g ℏ ω p k ε C D P η c d C D P ( α C D P + i ) 1 ( 1 − i Ω τ C D P η c d C D P ) ( 1 − i Ω τ S H B η c d S H B ) χ p k 1 ' '
χ b c d C H = − 2 ε 0 n n g ℏ ω p k ε C H η c d C H ( α C H + i ) 1 ( 1 − i Ω τ C H η c d C H ) ( 1 − i Ω τ S H B η c d S H B ) χ p k 1 ' '
χ b c d S H B = − 2 ε 0 n n g ℏ ω p k ε S H B η c d S H B i ( 1 − i Ω τ S H B η c d S H B ) ( 1 − i ( ω a − ω c ) τ d p / 2 ) χ p k 1 ' '
ζ a b c d = 1 L ∫ 0 L exp [ i ( k a − k b + k c − k d ) z ] d z
g a = g p k [ 1 − ( ω a − ω p k Δ ω H G ) 2 ]
d E L p d t = [ 0.5 v g ( Γ g L p + Δ N Γ d g d N ( 1 − i α N ) − 1 v g τ p ) − i Δ ω L p d i s ] E L p ( t ) + F L p + i 0.5 v g ω p k c n Γ ∑ b c d χ b c d 3 E b ( t ) E c * ( t ) E d ( t ) ζ L p b c d
d E M q d t = [ 0.5 v g ( Γ g M q + Δ N Γ d g d N ( 1 − i α N ) − 1 v g τ p ) − i Δ ω M q d i s ] E M q ( t ) + F M q + i 0.5 v g ω p k c n Γ ∑ b c d χ b c d 3 E b ( t ) E c * ( t ) E d ( t ) ζ M q b c d
d S L , M d t = Γ v g ( g L , M + Δ N d g d N − 1 Γ v g τ p − ω p k c n χ L L L , M M M 3 ' ' S L , M − ω p k c n ( χ L M M , M L L 3 ' ' + χ M M L , L L M 3 ' ' ) S M , L ) S L , M
∑ b c d χ b c d 3 E b ( t ) E c * ( t ) E d ( t ) ζ L b c d = χ L L L 3 ζ L L L L | E L | 2 E L + ( χ L M M 3 ζ L L M M + χ M M L 3 ζ L M M L ) | E M | 2 E L ∑ b c d χ b c d 3 E b ( t ) E c * ( t ) E d ( t ) ζ M b c d = χ M M M 3 ζ M M M M | E M | 2 E M + ( χ M L L 3 ζ M M L L + χ L L M 3 ζ M L L M ) | E L | 2 E M
d S 1 , 2 d t = Γ v g ( g L , M + Δ N d g d N − 1 Γ v g τ p − ω p k c n χ 111 , 222 3 ' ' S 1 , 2 − ω p k c n ( χ 122 , 211 3 ' ' + χ 221 , 112 3 ' ' ) S 2 , 1 ) S 1 , 2
L l > L m > 0 ⇔ g L + Δ N d g d N − 1 Γ v g τ p χ L L L 3 ' ' > g M + Δ N d g d N − 1 Γ v g τ p χ M L L 3 ' ' + χ L L M 3 ' ' > 0
0 < M l < M m ⇔ 0 < g L + Δ N d g d N − 1 Γ v g τ p χ L M M 3 ' ' + χ M M L 3 ' ' < g M + Δ N d g d N − 1 Γ v g τ p χ M M M 3 ' '
C C W 1 > C C W 2 > 0 ⇔ 1 χ 111 3 ' ' > 1 χ 211 3 ' ' + χ 112 3 ' ' > 0
0 < C W 1 < C W 2 ⇔ 0 < 1 χ 122 3 ' ' + χ 221 3 ' ' < 1 χ 222 3 ' '
d S L , M d t = Γ v g ( g L , M + Δ N d g d N − 1 Γ v g τ p − ω p k c n χ L L L , M M M 3 ' ' S L , M − ω p k c n ( χ L M M , M L L 3 ' ' + χ M M L , L L M 3 ' ' ) S M , L ) S L , M + κ S L , M S i n j L , M
d S 1 , 2 d t = Γ v g ( g L , M + Δ N d g d N − 1 Γ v g τ p − ω p k c n χ 111 , 222 3 ' ' S 1 , 2 − ω p k c n ( χ 122 , 211 3 ' ' + χ 221 , 112 3 ' ' ) S 2 , 1 ) S 1 , 2 + κ S 1 , 2 S i n j 1 , 2

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