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]
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  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]
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    [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).
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    [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 (5)

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]

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)

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]

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]

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 (1)

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]

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]

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.

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]

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]

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.

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.

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, 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]

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.

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]

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.

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.

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.

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, 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]

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]

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]

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.

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.

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]

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.

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.

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]

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, 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]

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.

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.

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.

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]

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]

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