Abstract

We experimentally show that a random optical pulse train can be generated by modulating a bistable semiconductor ring laser. When the ring laser is switched from the monostable to the bistable regime, it randomly selects one of two different stable unidirectional lasing modes, clockwise or counterclockwise modes. Non-deterministic random pulse sequences are generated by driving the switch parameter, the injection current, with a periodic pulse signal. The origin of the nondeterministic randomness is the amplified spontaneous emission noise coupled to the counter-propagating lasing modes. The statistical randomness properties are optimized by adjusting the relative strength of amplified spontaneous emission noise sources for the two lasing modes. It is also shown that it is possible to generate optical pulse sequences which pass a standard suite of statistical randomness tests.

© 2011 OSA

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    [CrossRef]
  2. M. Sorel, P. J. R. Laybourn, A. Scirè, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillation in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
    [CrossRef]
  3. M. Sorel, G. Giuliani, A. Scirè, R. Miglierina, S. Donati, and P. J. R. Laybourn, “Operating regimes of GaAs-AlGaAs semiconductor ring lasers,” IEEE J. Quantum Electron. 39, 1187–1195 (2003).
    [CrossRef]
  4. W. Coomans, S. Beri, G. Van der Sande, L. Gelens, and J. Danckaert, “Optical injection in semiconductor ring lasers,” Phys. Rev. A 81, 033802 (2010).
    [CrossRef]
  5. M. F. Booth, A. Schremer, and J. M. Ballantyne, “Spatial beam switching and bistability in a diode ring laser,” Appl. Phys. Lett. 76, 1095–1097 (2000).
    [CrossRef]
  6. G. Mezösi, M. J. Strain, S. Fürst, Z. Wang, S. Yu, and M. Sorel, “Unidirectional Bistability in AlGaInAs Microring and Microdisk Semiconductor Lasers,” IEEE Photon. Technol. Lett. 21, 88–90 (2009).
    [CrossRef]
  7. A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Bichromatic emission and multimode dynamics in bidirectional ring lasers,” Phys. Rev. A 81, 043817 (2010).
    [CrossRef]
  8. M. T. Hill, H. J. S. Dorren, T. Vries, X. J. M. Leijtens, J. H. Besten, B. Smalbrugge, Y.-S. Oel, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
    [CrossRef] [PubMed]
  9. L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4, 182–187 (2010).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  23. B. Li, M. I. Memon, G. Mezosi, G. Yuan, Z. Wang, M. Sorel, and S. Yu, “All-Optical Response of Semiconductor Ring Laser to Dual-Optical Injections,” IEEE Photon. Technol. Lett. 20, 770–772 (2008).
    [CrossRef]
  24. M. Choi, T. Tanaka, S. Sunada, and T. Harayama, “Linewidth properties of active-passive coupled monolithic InGaAs semiconductor ring lasers,” Appl. Phys. Lett. 94, 231110 (2009).
    [CrossRef]
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2010 (7)

W. Coomans, S. Beri, G. Van der Sande, L. Gelens, and J. Danckaert, “Optical injection in semiconductor ring lasers,” Phys. Rev. A 81, 033802 (2010).
[CrossRef]

A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Bichromatic emission and multimode dynamics in bidirectional ring lasers,” Phys. Rev. A 81, 043817 (2010).
[CrossRef]

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

B. Qi, Y-M. Chi, H-K. Lo, and L. Qian, “High-speed quantum random number generation by measuring phase noise of a single-mode laser,” Opt. Lett. 35, 312–314 (2010).
[CrossRef] [PubMed]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4, 58–61 (2010).
[CrossRef]

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18, 18763–18768 (2010).
[CrossRef] [PubMed]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18, 5512–5524 (2010).
[CrossRef] [PubMed]

2009 (6)

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef] [PubMed]

L. Gelens, G. Van der Sande, S. Beri, and J. Danckaert, “Phase-space approach to directional switching in semiconductor ring lasers,” Phys. Rev. E 79, 016213 (2009).
[CrossRef]

M. Choi, T. Tanaka, S. Sunada, and T. Harayama, “Linewidth properties of active-passive coupled monolithic InGaAs semiconductor ring lasers,” Appl. Phys. Lett. 94, 231110 (2009).
[CrossRef]

B. Li, M. I. Memon, G. Mezosi, Z. Wang, M. Sorel, and S. Yu, “All-optical Digital Logic Gates using Bistable Semiconductor Ring Lasers,” J. Opt. Commun. 30, 190–194 (2009).
[CrossRef]

A. Trita, M. J. Latorre Vidal, M. Zanola, G. Mezosi, J. Javaloyes, M. Sorel, F. Bragheri, I. Cristiani, A. Scirè, S. Balle, and G. Giuliani, “All-Optical Set-Reset Flip-Flop based on Semiconductor Ring Laser: Ultrafast Response and Error-Free Bit-Error-Rate Operation,” in International Conference on Photonics in Switching (IEEE, 2009), pp. 1–2.
[CrossRef]

G. Mezösi, M. J. Strain, S. Fürst, Z. Wang, S. Yu, and M. Sorel, “Unidirectional Bistability in AlGaInAs Microring and Microdisk Semiconductor Lasers,” IEEE Photon. Technol. Lett. 21, 88–90 (2009).
[CrossRef]

2008 (4)

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Scirè, G. Mezosi, M. Sorel, and J. Danckaert, “Topological Insight into the Non-Arrhenius Mode Hopping of Semiconductor Ring Lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

L. Gelens, S. Beri, G. Van der Sande, J. Danckaert, N. Calabretta, H. J. S. Dorren, R. Nötzel, E. A. J. M. Bente, and M. K. Smit, “Optical injection in semiconductor ring lasers: backfire dynamics,” Opt. Express 16, 10968–10974 (2008).
[CrossRef] [PubMed]

B. Li, M. I. Memon, G. Mezosi, G. Yuan, Z. Wang, M. Sorel, and S. Yu, “All-Optical Response of Semiconductor Ring Laser to Dual-Optical Injections,” IEEE Photon. Technol. Lett. 20, 770–772 (2008).
[CrossRef]

2007 (2)

T. Pérez, A. Scirè, G. Van der Sande, P. Colet, and C. R. Mirasso, “Bistability and all-optical switching in semiconductor ring lasers,” Opt. Express 15, 12941–12948 (2007).
[CrossRef] [PubMed]

V. N. Chizhevsky, D. B. Horoshko, D. I. Pustakhod, and S. Ya. Kilin, “Bistable vertical cavity laser as a truly random number generator,” in CLEO/Europe and IQEC 2007 Conference Digest (Optical Society of America, 2007), paper CB-29.

2004 (1)

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

2003 (1)

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

2002 (2)

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, “Unidirectional bistability in semiconductor waveguide ring lasers,” Appl. Phys. Lett. 80, 3051–3053 (2002).
[CrossRef]

M. Sorel, P. J. R. Laybourn, A. Scirè, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillation in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[CrossRef]

2000 (1)

M. F. Booth, A. Schremer, and J. M. Ballantyne, “Spatial beam switching and bistability in a diode ring laser,” Appl. Phys. Lett. 76, 1095–1097 (2000).
[CrossRef]

Aida, H.

Amano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Argyris, A.

Aviad, Y.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4, 58–61 (2010).
[CrossRef]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef] [PubMed]

Baets, R.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Ballantyne, J. M.

M. F. Booth, A. Schremer, and J. M. Ballantyne, “Spatial beam switching and bistability in a diode ring laser,” Appl. Phys. Lett. 76, 1095–1097 (2000).
[CrossRef]

Balle, S.

A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Bichromatic emission and multimode dynamics in bidirectional ring lasers,” Phys. Rev. A 81, 043817 (2010).
[CrossRef]

A. Trita, M. J. Latorre Vidal, M. Zanola, G. Mezosi, J. Javaloyes, M. Sorel, F. Bragheri, I. Cristiani, A. Scirè, S. Balle, and G. Giuliani, “All-Optical Set-Reset Flip-Flop based on Semiconductor Ring Laser: Ultrafast Response and Error-Free Bit-Error-Rate Operation,” in International Conference on Photonics in Switching (IEEE, 2009), pp. 1–2.
[CrossRef]

M. Sorel, P. J. R. Laybourn, A. Scirè, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillation in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[CrossRef]

Bente, E. A. J. M.

Beri, S.

W. Coomans, S. Beri, G. Van der Sande, L. Gelens, and J. Danckaert, “Optical injection in semiconductor ring lasers,” Phys. Rev. A 81, 033802 (2010).
[CrossRef]

L. Gelens, G. Van der Sande, S. Beri, and J. Danckaert, “Phase-space approach to directional switching in semiconductor ring lasers,” Phys. Rev. E 79, 016213 (2009).
[CrossRef]

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Scirè, G. Mezosi, M. Sorel, and J. Danckaert, “Topological Insight into the Non-Arrhenius Mode Hopping of Semiconductor Ring Lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

L. Gelens, S. Beri, G. Van der Sande, J. Danckaert, N. Calabretta, H. J. S. Dorren, R. Nötzel, E. A. J. M. Bente, and M. K. Smit, “Optical injection in semiconductor ring lasers: backfire dynamics,” Opt. Express 16, 10968–10974 (2008).
[CrossRef] [PubMed]

Besten, J. H.

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

Binsma, H.

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

Bogris, A.

Booth, M. F.

M. F. Booth, A. Schremer, and J. M. Ballantyne, “Spatial beam switching and bistability in a diode ring laser,” Appl. Phys. Lett. 76, 1095–1097 (2000).
[CrossRef]

Bragheri, F.

A. Trita, M. J. Latorre Vidal, M. Zanola, G. Mezosi, J. Javaloyes, M. Sorel, F. Bragheri, I. Cristiani, A. Scirè, S. Balle, and G. Giuliani, “All-Optical Set-Reset Flip-Flop based on Semiconductor Ring Laser: Ultrafast Response and Error-Free Bit-Error-Rate Operation,” in International Conference on Photonics in Switching (IEEE, 2009), pp. 1–2.
[CrossRef]

Calabretta, N.

Chi, Y-M.

Chizhevsky, V. N.

V. N. Chizhevsky, D. B. Horoshko, D. I. Pustakhod, and S. Ya. Kilin, “Bistable vertical cavity laser as a truly random number generator,” in CLEO/Europe and IQEC 2007 Conference Digest (Optical Society of America, 2007), paper CB-29.

Choi, M.

M. Choi, T. Tanaka, S. Sunada, and T. Harayama, “Linewidth properties of active-passive coupled monolithic InGaAs semiconductor ring lasers,” Appl. Phys. Lett. 94, 231110 (2009).
[CrossRef]

Cohen, E.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4, 58–61 (2010).
[CrossRef]

Colet, P.

Coomans, W.

W. Coomans, S. Beri, G. Van der Sande, L. Gelens, and J. Danckaert, “Optical injection in semiconductor ring lasers,” Phys. Rev. A 81, 033802 (2010).
[CrossRef]

Cristiani, I.

A. Trita, M. J. Latorre Vidal, M. Zanola, G. Mezosi, J. Javaloyes, M. Sorel, F. Bragheri, I. Cristiani, A. Scirè, S. Balle, and G. Giuliani, “All-Optical Set-Reset Flip-Flop based on Semiconductor Ring Laser: Ultrafast Response and Error-Free Bit-Error-Rate Operation,” in International Conference on Photonics in Switching (IEEE, 2009), pp. 1–2.
[CrossRef]

Danckaert, J.

W. Coomans, S. Beri, G. Van der Sande, L. Gelens, and J. Danckaert, “Optical injection in semiconductor ring lasers,” Phys. Rev. A 81, 033802 (2010).
[CrossRef]

L. Gelens, G. Van der Sande, S. Beri, and J. Danckaert, “Phase-space approach to directional switching in semiconductor ring lasers,” Phys. Rev. E 79, 016213 (2009).
[CrossRef]

L. Gelens, S. Beri, G. Van der Sande, J. Danckaert, N. Calabretta, H. J. S. Dorren, R. Nötzel, E. A. J. M. Bente, and M. K. Smit, “Optical injection in semiconductor ring lasers: backfire dynamics,” Opt. Express 16, 10968–10974 (2008).
[CrossRef] [PubMed]

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Scirè, G. Mezosi, M. Sorel, and J. Danckaert, “Topological Insight into the Non-Arrhenius Mode Hopping of Semiconductor Ring Lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

Davis, P.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18, 5512–5524 (2010).
[CrossRef] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Deligiannidis, S.

Donati, S.

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

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, “Unidirectional bistability in semiconductor waveguide ring lasers,” Appl. Phys. Lett. 80, 3051–3053 (2002).
[CrossRef]

M. Sorel, P. J. R. Laybourn, A. Scirè, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillation in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[CrossRef]

Dorren, H. J. S.

L. Gelens, S. Beri, G. Van der Sande, J. Danckaert, N. Calabretta, H. J. S. Dorren, R. Nötzel, E. A. J. M. Bente, and M. K. Smit, “Optical injection in semiconductor ring lasers: backfire dynamics,” Opt. Express 16, 10968–10974 (2008).
[CrossRef] [PubMed]

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

Fürst, S.

G. Mezösi, M. J. Strain, S. Fürst, Z. Wang, S. Yu, and M. Sorel, “Unidirectional Bistability in AlGaInAs Microring and Microdisk Semiconductor Lasers,” IEEE Photon. Technol. Lett. 21, 88–90 (2009).
[CrossRef]

Gelens, L.

W. Coomans, S. Beri, G. Van der Sande, L. Gelens, and J. Danckaert, “Optical injection in semiconductor ring lasers,” Phys. Rev. A 81, 033802 (2010).
[CrossRef]

L. Gelens, G. Van der Sande, S. Beri, and J. Danckaert, “Phase-space approach to directional switching in semiconductor ring lasers,” Phys. Rev. E 79, 016213 (2009).
[CrossRef]

L. Gelens, S. Beri, G. Van der Sande, J. Danckaert, N. Calabretta, H. J. S. Dorren, R. Nötzel, E. A. J. M. Bente, and M. K. Smit, “Optical injection in semiconductor ring lasers: backfire dynamics,” Opt. Express 16, 10968–10974 (2008).
[CrossRef] [PubMed]

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Scirè, G. Mezosi, M. Sorel, and J. Danckaert, “Topological Insight into the Non-Arrhenius Mode Hopping of Semiconductor Ring Lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

Geluk, E.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Giuliani, G.

A. Trita, M. J. Latorre Vidal, M. Zanola, G. Mezosi, J. Javaloyes, M. Sorel, F. Bragheri, I. Cristiani, A. Scirè, S. Balle, and G. Giuliani, “All-Optical Set-Reset Flip-Flop based on Semiconductor Ring Laser: Ultrafast Response and Error-Free Bit-Error-Rate Operation,” in International Conference on Photonics in Switching (IEEE, 2009), pp. 1–2.
[CrossRef]

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

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, “Unidirectional bistability in semiconductor waveguide ring lasers,” Appl. Phys. Lett. 80, 3051–3053 (2002).
[CrossRef]

M. Sorel, P. J. R. Laybourn, A. Scirè, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillation in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[CrossRef]

Harayama, T.

Hill, M. T.

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

Hirano, K.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18, 5512–5524 (2010).
[CrossRef] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Horoshko, D. B.

V. N. Chizhevsky, D. B. Horoshko, D. I. Pustakhod, and S. Ya. Kilin, “Bistable vertical cavity laser as a truly random number generator,” in CLEO/Europe and IQEC 2007 Conference Digest (Optical Society of America, 2007), paper CB-29.

Huybrechts, K.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Inoue, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Javaloyes, J.

A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Bichromatic emission and multimode dynamics in bidirectional ring lasers,” Phys. Rev. A 81, 043817 (2010).
[CrossRef]

A. Trita, M. J. Latorre Vidal, M. Zanola, G. Mezosi, J. Javaloyes, M. Sorel, F. Bragheri, I. Cristiani, A. Scirè, S. Balle, and G. Giuliani, “All-Optical Set-Reset Flip-Flop based on Semiconductor Ring Laser: Ultrafast Response and Error-Free Bit-Error-Rate Operation,” in International Conference on Photonics in Switching (IEEE, 2009), pp. 1–2.
[CrossRef]

Kanter, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4, 58–61 (2010).
[CrossRef]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef] [PubMed]

Karashige, T.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Khoe, G.-D.

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

Kumar, R.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Latorre Vidal, M. J.

A. Trita, M. J. Latorre Vidal, M. Zanola, G. Mezosi, J. Javaloyes, M. Sorel, F. Bragheri, I. Cristiani, A. Scirè, S. Balle, and G. Giuliani, “All-Optical Set-Reset Flip-Flop based on Semiconductor Ring Laser: Ultrafast Response and Error-Free Bit-Error-Rate Operation,” in International Conference on Photonics in Switching (IEEE, 2009), pp. 1–2.
[CrossRef]

Laybourn, P. J. R.

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

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, “Unidirectional bistability in semiconductor waveguide ring lasers,” Appl. Phys. Lett. 80, 3051–3053 (2002).
[CrossRef]

M. Sorel, P. J. R. Laybourn, A. Scirè, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillation in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[CrossRef]

Leijtens, X. J. M.

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

Li, B.

B. Li, M. I. Memon, G. Mezosi, Z. Wang, M. Sorel, and S. Yu, “All-optical Digital Logic Gates using Bistable Semiconductor Ring Lasers,” J. Opt. Commun. 30, 190–194 (2009).
[CrossRef]

B. Li, M. I. Memon, G. Mezosi, G. Yuan, Z. Wang, M. Sorel, and S. Yu, “All-Optical Response of Semiconductor Ring Laser to Dual-Optical Injections,” IEEE Photon. Technol. Lett. 20, 770–772 (2008).
[CrossRef]

Liu, L.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Lo, H-K.

Memon, M. I.

B. Li, M. I. Memon, G. Mezosi, Z. Wang, M. Sorel, and S. Yu, “All-optical Digital Logic Gates using Bistable Semiconductor Ring Lasers,” J. Opt. Commun. 30, 190–194 (2009).
[CrossRef]

B. Li, M. I. Memon, G. Mezosi, G. Yuan, Z. Wang, M. Sorel, and S. Yu, “All-Optical Response of Semiconductor Ring Laser to Dual-Optical Injections,” IEEE Photon. Technol. Lett. 20, 770–772 (2008).
[CrossRef]

Mestre, M.

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Scirè, G. Mezosi, M. Sorel, and J. Danckaert, “Topological Insight into the Non-Arrhenius Mode Hopping of Semiconductor Ring Lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

Mezosi, G.

B. Li, M. I. Memon, G. Mezosi, Z. Wang, M. Sorel, and S. Yu, “All-optical Digital Logic Gates using Bistable Semiconductor Ring Lasers,” J. Opt. Commun. 30, 190–194 (2009).
[CrossRef]

A. Trita, M. J. Latorre Vidal, M. Zanola, G. Mezosi, J. Javaloyes, M. Sorel, F. Bragheri, I. Cristiani, A. Scirè, S. Balle, and G. Giuliani, “All-Optical Set-Reset Flip-Flop based on Semiconductor Ring Laser: Ultrafast Response and Error-Free Bit-Error-Rate Operation,” in International Conference on Photonics in Switching (IEEE, 2009), pp. 1–2.
[CrossRef]

B. Li, M. I. Memon, G. Mezosi, G. Yuan, Z. Wang, M. Sorel, and S. Yu, “All-Optical Response of Semiconductor Ring Laser to Dual-Optical Injections,” IEEE Photon. Technol. Lett. 20, 770–772 (2008).
[CrossRef]

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Scirè, G. Mezosi, M. Sorel, and J. Danckaert, “Topological Insight into the Non-Arrhenius Mode Hopping of Semiconductor Ring Lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

Mezösi, G.

G. Mezösi, M. J. Strain, S. Fürst, Z. Wang, S. Yu, and M. Sorel, “Unidirectional Bistability in AlGaInAs Microring and Microdisk Semiconductor Lasers,” IEEE Photon. Technol. Lett. 21, 88–90 (2009).
[CrossRef]

Miglierina, R.

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

M. Sorel, P. J. R. Laybourn, A. Scirè, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillation in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[CrossRef]

Mirasso, C. R.

Morikatsu, S.

Morthier, G.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Naito, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Nötzel, R.

Oel, Y.-S.

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

Okumura, H.

Oowada, I.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Pérez, T.

Pérez-Serrano, A.

A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Bichromatic emission and multimode dynamics in bidirectional ring lasers,” Phys. Rev. A 81, 043817 (2010).
[CrossRef]

Pikasis, E.

Pustakhod, D. I.

V. N. Chizhevsky, D. B. Horoshko, D. I. Pustakhod, and S. Ya. Kilin, “Bistable vertical cavity laser as a truly random number generator,” in CLEO/Europe and IQEC 2007 Conference Digest (Optical Society of America, 2007), paper CB-29.

Qi, B.

Qian, L.

Regreny, P.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Reidler, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4, 58–61 (2010).
[CrossRef]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef] [PubMed]

Roelkens, G.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Rosenbluh, M.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4, 58–61 (2010).
[CrossRef]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef] [PubMed]

Schremer, A.

M. F. Booth, A. Schremer, and J. M. Ballantyne, “Spatial beam switching and bistability in a diode ring laser,” Appl. Phys. Lett. 76, 1095–1097 (2000).
[CrossRef]

Scirè, A.

A. Trita, M. J. Latorre Vidal, M. Zanola, G. Mezosi, J. Javaloyes, M. Sorel, F. Bragheri, I. Cristiani, A. Scirè, S. Balle, and G. Giuliani, “All-Optical Set-Reset Flip-Flop based on Semiconductor Ring Laser: Ultrafast Response and Error-Free Bit-Error-Rate Operation,” in International Conference on Photonics in Switching (IEEE, 2009), pp. 1–2.
[CrossRef]

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Scirè, G. Mezosi, M. Sorel, and J. Danckaert, “Topological Insight into the Non-Arrhenius Mode Hopping of Semiconductor Ring Lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

T. Pérez, A. Scirè, G. Van der Sande, P. Colet, and C. R. Mirasso, “Bistability and all-optical switching in semiconductor ring lasers,” Opt. Express 15, 12941–12948 (2007).
[CrossRef] [PubMed]

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

M. Sorel, P. J. R. Laybourn, A. Scirè, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillation in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[CrossRef]

Shiki, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Smalbrugge, B.

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

Smit, M. K.

L. Gelens, S. Beri, G. Van der Sande, J. Danckaert, N. Calabretta, H. J. S. Dorren, R. Nötzel, E. A. J. M. Bente, and M. K. Smit, “Optical injection in semiconductor ring lasers: backfire dynamics,” Opt. Express 16, 10968–10974 (2008).
[CrossRef] [PubMed]

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

Someya, H.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Sorel, M.

G. Mezösi, M. J. Strain, S. Fürst, Z. Wang, S. Yu, and M. Sorel, “Unidirectional Bistability in AlGaInAs Microring and Microdisk Semiconductor Lasers,” IEEE Photon. Technol. Lett. 21, 88–90 (2009).
[CrossRef]

A. Trita, M. J. Latorre Vidal, M. Zanola, G. Mezosi, J. Javaloyes, M. Sorel, F. Bragheri, I. Cristiani, A. Scirè, S. Balle, and G. Giuliani, “All-Optical Set-Reset Flip-Flop based on Semiconductor Ring Laser: Ultrafast Response and Error-Free Bit-Error-Rate Operation,” in International Conference on Photonics in Switching (IEEE, 2009), pp. 1–2.
[CrossRef]

B. Li, M. I. Memon, G. Mezosi, Z. Wang, M. Sorel, and S. Yu, “All-optical Digital Logic Gates using Bistable Semiconductor Ring Lasers,” J. Opt. Commun. 30, 190–194 (2009).
[CrossRef]

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Scirè, G. Mezosi, M. Sorel, and J. Danckaert, “Topological Insight into the Non-Arrhenius Mode Hopping of Semiconductor Ring Lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

B. Li, M. I. Memon, G. Mezosi, G. Yuan, Z. Wang, M. Sorel, and S. Yu, “All-Optical Response of Semiconductor Ring Laser to Dual-Optical Injections,” IEEE Photon. Technol. Lett. 20, 770–772 (2008).
[CrossRef]

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

M. Sorel, P. J. R. Laybourn, A. Scirè, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillation in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[CrossRef]

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, “Unidirectional bistability in semiconductor waveguide ring lasers,” Appl. Phys. Lett. 80, 3051–3053 (2002).
[CrossRef]

Spuesens, T.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Strain, M. J.

G. Mezösi, M. J. Strain, S. Fürst, Z. Wang, S. Yu, and M. Sorel, “Unidirectional Bistability in AlGaInAs Microring and Microdisk Semiconductor Lasers,” IEEE Photon. Technol. Lett. 21, 88–90 (2009).
[CrossRef]

Sunada, S.

M. Choi, T. Tanaka, S. Sunada, and T. Harayama, “Linewidth properties of active-passive coupled monolithic InGaAs semiconductor ring lasers,” Appl. Phys. Lett. 94, 231110 (2009).
[CrossRef]

Syvridis, D.

Tanaka, T.

M. Choi, T. Tanaka, S. Sunada, and T. Harayama, “Linewidth properties of active-passive coupled monolithic InGaAs semiconductor ring lasers,” Appl. Phys. Lett. 94, 231110 (2009).
[CrossRef]

Thourhout, D. V.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Trita, A.

A. Trita, M. J. Latorre Vidal, M. Zanola, G. Mezosi, J. Javaloyes, M. Sorel, F. Bragheri, I. Cristiani, A. Scirè, S. Balle, and G. Giuliani, “All-Optical Set-Reset Flip-Flop based on Semiconductor Ring Laser: Ultrafast Response and Error-Free Bit-Error-Rate Operation,” in International Conference on Photonics in Switching (IEEE, 2009), pp. 1–2.
[CrossRef]

Uchida, A.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18, 5512–5524 (2010).
[CrossRef] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Van der Sande, G.

W. Coomans, S. Beri, G. Van der Sande, L. Gelens, and J. Danckaert, “Optical injection in semiconductor ring lasers,” Phys. Rev. A 81, 033802 (2010).
[CrossRef]

L. Gelens, G. Van der Sande, S. Beri, and J. Danckaert, “Phase-space approach to directional switching in semiconductor ring lasers,” Phys. Rev. E 79, 016213 (2009).
[CrossRef]

L. Gelens, S. Beri, G. Van der Sande, J. Danckaert, N. Calabretta, H. J. S. Dorren, R. Nötzel, E. A. J. M. Bente, and M. K. Smit, “Optical injection in semiconductor ring lasers: backfire dynamics,” Opt. Express 16, 10968–10974 (2008).
[CrossRef] [PubMed]

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Scirè, G. Mezosi, M. Sorel, and J. Danckaert, “Topological Insight into the Non-Arrhenius Mode Hopping of Semiconductor Ring Lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

T. Pérez, A. Scirè, G. Van der Sande, P. Colet, and C. R. Mirasso, “Bistability and all-optical switching in semiconductor ring lasers,” Opt. Express 15, 12941–12948 (2007).
[CrossRef] [PubMed]

Verschaffelt, G.

S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Scirè, G. Mezosi, M. Sorel, and J. Danckaert, “Topological Insight into the Non-Arrhenius Mode Hopping of Semiconductor Ring Lasers,” Phys. Rev. Lett. 101, 093903 (2008).
[CrossRef] [PubMed]

Vries, T.

L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

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

Wang, Z.

G. Mezösi, M. J. Strain, S. Fürst, Z. Wang, S. Yu, and M. Sorel, “Unidirectional Bistability in AlGaInAs Microring and Microdisk Semiconductor Lasers,” IEEE Photon. Technol. Lett. 21, 88–90 (2009).
[CrossRef]

B. Li, M. I. Memon, G. Mezosi, Z. Wang, M. Sorel, and S. Yu, “All-optical Digital Logic Gates using Bistable Semiconductor Ring Lasers,” J. Opt. Commun. 30, 190–194 (2009).
[CrossRef]

B. Li, M. I. Memon, G. Mezosi, G. Yuan, Z. Wang, M. Sorel, and S. Yu, “All-Optical Response of Semiconductor Ring Laser to Dual-Optical Injections,” IEEE Photon. Technol. Lett. 20, 770–772 (2008).
[CrossRef]

Ya. Kilin, S.

V. N. Chizhevsky, D. B. Horoshko, D. I. Pustakhod, and S. Ya. Kilin, “Bistable vertical cavity laser as a truly random number generator,” in CLEO/Europe and IQEC 2007 Conference Digest (Optical Society of America, 2007), paper CB-29.

Yamazaki, T.

Yoshimori, S.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18, 5512–5524 (2010).
[CrossRef] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Yoshimura, K.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18, 5512–5524 (2010).
[CrossRef] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Yu, S.

B. Li, M. I. Memon, G. Mezosi, Z. Wang, M. Sorel, and S. Yu, “All-optical Digital Logic Gates using Bistable Semiconductor Ring Lasers,” J. Opt. Commun. 30, 190–194 (2009).
[CrossRef]

G. Mezösi, M. J. Strain, S. Fürst, Z. Wang, S. Yu, and M. Sorel, “Unidirectional Bistability in AlGaInAs Microring and Microdisk Semiconductor Lasers,” IEEE Photon. Technol. Lett. 21, 88–90 (2009).
[CrossRef]

B. Li, M. I. Memon, G. Mezosi, G. Yuan, Z. Wang, M. Sorel, and S. Yu, “All-Optical Response of Semiconductor Ring Laser to Dual-Optical Injections,” IEEE Photon. Technol. Lett. 20, 770–772 (2008).
[CrossRef]

Yuan, G.

B. Li, M. I. Memon, G. Mezosi, G. Yuan, Z. Wang, M. Sorel, and S. Yu, “All-Optical Response of Semiconductor Ring Laser to Dual-Optical Injections,” IEEE Photon. Technol. Lett. 20, 770–772 (2008).
[CrossRef]

Zanola, M.

A. Trita, M. J. Latorre Vidal, M. Zanola, G. Mezosi, J. Javaloyes, M. Sorel, F. Bragheri, I. Cristiani, A. Scirè, S. Balle, and G. Giuliani, “All-Optical Set-Reset Flip-Flop based on Semiconductor Ring Laser: Ultrafast Response and Error-Free Bit-Error-Rate Operation,” in International Conference on Photonics in Switching (IEEE, 2009), pp. 1–2.
[CrossRef]

Appl. Phys. Lett. (3)

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, “Unidirectional bistability in semiconductor waveguide ring lasers,” Appl. Phys. Lett. 80, 3051–3053 (2002).
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M. F. Booth, A. Schremer, and J. M. Ballantyne, “Spatial beam switching and bistability in a diode ring laser,” Appl. Phys. Lett. 76, 1095–1097 (2000).
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M. Choi, T. Tanaka, S. Sunada, and T. Harayama, “Linewidth properties of active-passive coupled monolithic InGaAs semiconductor ring lasers,” Appl. Phys. Lett. 94, 231110 (2009).
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IEEE J. Quantum Electron. (1)

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

IEEE Photon. Technol. Lett. (2)

G. Mezösi, M. J. Strain, S. Fürst, Z. Wang, S. Yu, and M. Sorel, “Unidirectional Bistability in AlGaInAs Microring and Microdisk Semiconductor Lasers,” IEEE Photon. Technol. Lett. 21, 88–90 (2009).
[CrossRef]

B. Li, M. I. Memon, G. Mezosi, G. Yuan, Z. Wang, M. Sorel, and S. Yu, “All-Optical Response of Semiconductor Ring Laser to Dual-Optical Injections,” IEEE Photon. Technol. Lett. 20, 770–772 (2008).
[CrossRef]

J. Opt. Commun. (1)

B. Li, M. I. Memon, G. Mezosi, Z. Wang, M. Sorel, and S. Yu, “All-optical Digital Logic Gates using Bistable Semiconductor Ring Lasers,” J. Opt. Commun. 30, 190–194 (2009).
[CrossRef]

Nat. Photonics (3)

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Karashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4, 58–61 (2010).
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L. Liu, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. Vries, P. Regreny, D. V. Thourhout, R. Baets, and G. Morthier, “An ultra-small, low-power, all-optical flip-flop memory on a silicon chip,” Nat. Photonics 4, 182–187 (2010).
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Nature (1)

M. T. Hill, H. J. S. Dorren, T. Vries, X. J. M. Leijtens, J. H. Besten, B. Smalbrugge, Y.-S. Oel, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
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Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. A (2)

W. Coomans, S. Beri, G. Van der Sande, L. Gelens, and J. Danckaert, “Optical injection in semiconductor ring lasers,” Phys. Rev. A 81, 033802 (2010).
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A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Bichromatic emission and multimode dynamics in bidirectional ring lasers,” Phys. Rev. A 81, 043817 (2010).
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Phys. Rev. E (1)

L. Gelens, G. Van der Sande, S. Beri, and J. Danckaert, “Phase-space approach to directional switching in semiconductor ring lasers,” Phys. Rev. E 79, 016213 (2009).
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I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009).
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Other (3)

V. N. Chizhevsky, D. B. Horoshko, D. I. Pustakhod, and S. Ya. Kilin, “Bistable vertical cavity laser as a truly random number generator,” in CLEO/Europe and IQEC 2007 Conference Digest (Optical Society of America, 2007), paper CB-29.

A. Trita, M. J. Latorre Vidal, M. Zanola, G. Mezosi, J. Javaloyes, M. Sorel, F. Bragheri, I. Cristiani, A. Scirè, S. Balle, and G. Giuliani, “All-Optical Set-Reset Flip-Flop based on Semiconductor Ring Laser: Ultrafast Response and Error-Free Bit-Error-Rate Operation,” in International Conference on Photonics in Switching (IEEE, 2009), pp. 1–2.
[CrossRef]

G. Marsaglia, DIEHARD: A battery of tests of randomness (1996). http://stat.fsu.edu/geo .

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Figures (7)

Fig. 1
Fig. 1

(a) The phase space in a bidirectional regime. O; unstable fixed point corresponding to the non-lasing state, B; stable fixed point corresponding to the bidirectional lasing state. The line |E 1 | 2 = |E 2 | 2 is shown as a blue dotted line. In this regime, evolution from any initial state converges to the stable state B. (b) The phase space in a bistable regime. S; saddle fixed point corresponding to the bidirectional lasing state, UCW ( CCW ); stable fixed point corresponding to the CW (CCW) lasing state. Blue dotted line (line |E 1 | 2 = |E 2 | 2) represents the stable manifold of the saddle point S. Red and green curves represent two trajectories starting from an initial state (indicated by open circle) on the stable manifold with different noise instances. The trajectories are numerically calculated by using Eqs. (1) and (2) with the parameter values for our SRL devices, α = 3.5, 2s = c = 0.01, kd = 3.27 × 10−4, kc = 2.5 × 10−3, γ = 0.02, μ = 4.921, Cs = 5 × 10−6, τp = 40 ps, G 0 = 10−12 m3s−1, N 0 = 1.4 × 1024m−3.

Fig. 2
Fig. 2

A schematic of a SRL device with spontaneous emission noise sources B1 and B2.

Fig. 3
Fig. 3

(a) A schematic and (b) a photograph of the fabricated SRL device. The ring laser part consists of a semiconductor optical amplifier (SOA) and a passive waveguide. B1 and B2 are 50 μm-long SOAs used to enhance the amounts of spontaneous emission noises coupled to the CCW and CW modes, respectively. They are also used as the photodiodes to detect the CW and CCW output signals, when they are not used as the ASE noise sources.

Fig. 4
Fig. 4

L-I curves of the fabricated SRL device. The bidirectional and bistable regimes are observed for 52.6 mA < J < 70 mA and J > 81.3 mA, respectively. The mode-extinction ratio of the CW mode to the CCW mode is more than 16 dB for J > 117 mA.

Fig. 5
Fig. 5

(a) Time traces of the CW (red) and CCW (green) light intensities under the pulse-modulation of the injection current to the SRL. The upper panel represents the pulse current. J 0 and J 1 are respectively 55 mA and 117 mA. (b) The enlargement of the left figure (a).

Fig. 6
Fig. 6

(a) The bias current dependence of the statistical frequency of the appearance of the CW lasing mode. Dots and error bars respectively represent the mean value and three standard deviations. (b) An enlargement of the left figure (a).

Fig. 7
Fig. 7

The absolute values of the autocorrelation function of the random optical bit sequences of length N = 106 generated from the experiment.

Tables (1)

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Table 1 Typical Results of “Diehard” Statistical Test Suite a

Equations (3)

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dE 1 ( 2 ) dt = ( 1 + i α ) 2 [ N ( 1 s | E 1 ( 2 ) | 2 c | E 2 ( 1 ) | 2 ) 1 ] E 1 ( 2 ) ( k d + ik c ) E 2 ( 1 ) + D ξ 1 ( 2 ) ( t ) ,
dN dt = γ [ μ N N ( 1 s | E 1 | 2 c | E 2 | 2 ) | E 1 | 2 N ( 1 s | E 2 | 2 c | E 1 | 2 ) | E 2 | 2 ] ,
K 2 k d + Re K 2 + 4 α k c K 4 k c 2 = 0 ,

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