Abstract

The photon statistics and bunching of a semiconductor laser with external optical feedback are investigated experimentally and theoretically. In a chaotic regime, the photon number distribution is measured and undergoes a transition from Bose-Einstein distribution to Poisson distribution with increasing the mean photon number. The second order degree of coherence decreases gradually from 2 to 1. Based on Hanbury Brown-Twiss scheme, pronounced photon bunching is observed experimentally for various injection currents and feedback strengths, which indicates the randomness of the associated emission light. Near-threshold injection currents and strong feedback strengths modify exactly the laser performance to be more bunched. The macroscopic chaotic dynamics is confirmed simultaneously by high-speed analog detection. The theoretical results qualitatively agree with the experimental results. It is potentially useful to extract randomness and achieve desired entropy source for random number generator and imaging science by quantifying the control parameters.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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  44. Y. Li, G. Li, Y. C. Zhang, X. Y. Wang, J. Zhang, J. M. Wang, and T. C. Zhang, “Effects of counting rate and resolution time on a measurement of the intensity correlation function,” Phys. Rev. A 76(1), 013829 (2007).
    [Crossref]
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    [Crossref]

2016 (4)

V. H. Schultheiss, S. Batz, and U. Peschel, “Hanbury Brown and Twiss measurements in curved space,” Nat. Photonics 10(2), 106–110 (2016).
[Crossref]

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10(3), 167–170 (2016).
[Crossref]

O. S. Magaña-Loaiza, M. Mirhosseini, R. M. Cross, S. M. Hashemi Rafsanjani, and R. W. Boyd, “Hanbury Brown and Twiss interferometry with twisted light,” Sci. Adv. 2(4), e1501143 (2016).
[Crossref] [PubMed]

W. E. Hayenga, H. Garcia-Gracia, H. Hodaei, C. Reimer, R. Morandotti, P. LiKamWa, and M. Khajavikhan, “Second-order coherence properties of metallic nanolasers,” Optica 3(11), 1187–1193 (2016).
[Crossref]

2015 (3)

A. M. Hagerstrom, T. E. Murphy, and R. Roy, “Harvesting entropy and quantifying the transition from noise to chaos in a photon-counting feedback loop,” PNAS 112(30), 9258–9263 (2015).
[Crossref] [PubMed]

H. E. Kondakci, A. F. Abouraddy, and B. E. A. Saleh, “A photonic thermalization gap in disordered lattices,” Nat. Physics 11(11), 930–935 (2015).
[Crossref]

M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
[Crossref]

2014 (4)

J. P. Toomey and D. M. Kane, “Mapping the dynamic complexity of a semiconductor laser with optical feedback using permutation entropy,” Opt. Express 22(2), 1713–1725 (2014).
[Crossref] [PubMed]

X. Porte, M. C. Soriano, and I. Fischer, “Similarity properties in the dynamics of delayed-feedback semiconductor lasers,” Phys. Rev. A 89(2), 023822 (2014).
[Crossref]

N. Li, B. Kim, A. Locquet, D. Choi, W. Pan, and D. S. Citrin, “Statistics of the optical intensity of a chaotic external-cavity DFB laser,” Opt. Lett. 39(20), 5949–5952 (2014).
[Crossref] [PubMed]

F. Schulze, B. Lingnau, S. M. Hein, A. Carmele, E. Schöll, K. Lüdge, and A. Knorr, “Feedback-induced steady-state light bunching above the lasing threshold,” Phys. Rev. A 89(4), 041801 (2014).
[Crossref]

2013 (3)

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85(1), 421–470 (2013).
[Crossref]

A. B. Wang, P. Li, J. G. Zhang, J. Z. Zhang, L. Li, and Y. C. Wang, “4.5 Gbps high-speed real-time physical random bit generator,” Opt. Express 21(17), 20452–20462 (2013).
[Crossref] [PubMed]

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Communications 4(4), 1364 (2013).
[Crossref]

2012 (3)

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

Y. Q. Guo, G. Li, Y. F. Zhang, P. F. Zhang, J. M. Wang, and T. C. Zhang, “Efficient fluorescence detection of a single neutral atom with low background in a microscopic optical dipole trap,” Sci. China: Phys. Mech. Astron. 55(9), 1523–1528 (2012).

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6(6), 355–359 (2012).
[Crossref] [PubMed]

2011 (3)

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation,” Opt. Lett. 36(23), 4632–4634 (2011).
[Crossref] [PubMed]

F. Albert, C. Hopfmann, S. Reitzenstein, C. Schneider, S. Höfling, L. Worschech, M. Kamp, W. Kinzel, A. Forchel, and I. Kanter, “Observing chaos for quantum-dot microlasers with external feedback,” Nat. Communications 2(1), 366 (2011).
[Crossref]

S. Heiligenthal, T. Dahms, S. Yanchuk, T. Jüngling, V. Flunkert, I. Kanter, E. Schöll, and W. Kinzel, “Strong and Weak Chaos in Nonlinear Networks with Time-Delayed Couplings,” Phys. Rev. Lett. 107(23), 234102 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (3)

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102 (2009).
[Crossref] [PubMed]

H. R. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics 3(12), 696–705 (2009).
[Crossref]

K. Banaszek, R. Demkowicz-Dobrzański, and I. A. Walmsley, “Quantum states made to measure,” Nat. Photonics 3(12), 673–676 (2009).
[Crossref]

2008 (2)

Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photon. Technol. Lett. 20(19), 1636–1638 (2008).
[Crossref]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

2007 (1)

Y. Li, G. Li, Y. C. Zhang, X. Y. Wang, J. Zhang, J. M. Wang, and T. C. Zhang, “Effects of counting rate and resolution time on a measurement of the intensity correlation function,” Phys. Rev. A 76(1), 013829 (2007).
[Crossref]

2006 (1)

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, “Low-frequency fluctuations in vertical cavity lasers: experiments versus Lang-Kobayashi dynamics,” Phys. Rev. A 74(6), 063801 (2006).
[Crossref]

2005 (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

2004 (1)

F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron. 40(6), 815–820 (2004).
[Crossref]

1999 (2)

T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, “Statistical properties of low-frequency fluctuations during single-mode operation in distributed-feedback lasers: experiments and modeling,” Opt. Lett. 24(18), 1275–1277 (1999).
[Crossref]

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl-AbiChedia, and W. Elsasser, “Picosecond intensity statistics of semiconductor lasers operating in the low-frequency fluctuation regime,” Phys. Rev. A 60(1), 667–673 (1999).
[Crossref]

1996 (2)

L. Davidovich, “Sub-Poissonian processes in quantum optics,” Rev. Mod. Phys. 68(1), 127–173 (1996).
[Crossref]

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsässer, E. Göbel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers,” Phys. Rev. Lett. 76(2), 220–223 (1996).
[Crossref] [PubMed]

1994 (1)

T. Sano, “Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50(3), 2719–2726 (1994).
[Crossref] [PubMed]

1989 (1)

J. Sacher, W. Elsässer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224–2227 (1989).
[Crossref] [PubMed]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[Crossref]

1977 (1)

H. J. Kimble, M. Dagenais, and L. Mandel, “Photon antibunching in resonance fluorescence,” Phys. Rev. Lett. 39(11), 691–695 (1977).
[Crossref]

1969 (1)

R. F. Broom, “Self modulation at gigahertz frequencies of a diode laser coupled to an external cavity,” Electron. Lett. 5(23), 571–572 (1969).
[Crossref]

1965 (1)

F. T. Arecchi, “Measurement of the statistical distribution of Gaussian and laser sources,” Phys. Rev. Lett. 15(24), 912–916 (1965).
[Crossref]

1963 (1)

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130(6), 2529–2539 (1963).
[Crossref]

1956 (1)

R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177(4497), 27–29 (1956).
[Crossref]

Abouraddy, A. F.

H. E. Kondakci, A. F. Abouraddy, and B. E. A. Saleh, “A photonic thermalization gap in disordered lattices,” Nat. Physics 11(11), 930–935 (2015).
[Crossref]

Aida, H.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

Albert, F.

F. Albert, C. Hopfmann, S. Reitzenstein, C. Schneider, S. Höfling, L. Worschech, M. Kamp, W. Kinzel, A. Forchel, and I. Kanter, “Observing chaos for quantum-dot microlasers with external feedback,” Nat. Communications 2(1), 366 (2011).
[Crossref]

Amano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Annovazzi-Lodi, V.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Arecchi, F. T.

F. T. Arecchi, “Measurement of the statistical distribution of Gaussian and laser sources,” Phys. Rev. Lett. 15(24), 912–916 (1965).
[Crossref]

Argyris, A.

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

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Aviad, Y.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 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(2), 024102 (2009).
[Crossref] [PubMed]

Banaszek, K.

K. Banaszek, R. Demkowicz-Dobrzański, and I. A. Walmsley, “Quantum states made to measure,” Nat. Photonics 3(12), 673–676 (2009).
[Crossref]

Barbier, M.

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10(3), 167–170 (2016).
[Crossref]

Barland, S.

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, “Low-frequency fluctuations in vertical cavity lasers: experiments versus Lang-Kobayashi dynamics,” Phys. Rev. A 74(6), 063801 (2006).
[Crossref]

Batz, S.

V. H. Schultheiss, S. Batz, and U. Peschel, “Hanbury Brown and Twiss measurements in curved space,” Nat. Photonics 10(2), 106–110 (2016).
[Crossref]

Bogris, A.

Boyd, R. W.

O. S. Magaña-Loaiza, M. Mirhosseini, R. M. Cross, S. M. Hashemi Rafsanjani, and R. W. Boyd, “Hanbury Brown and Twiss interferometry with twisted light,” Sci. Adv. 2(4), e1501143 (2016).
[Crossref] [PubMed]

Broom, R. F.

R. F. Broom, “Self modulation at gigahertz frequencies of a diode laser coupled to an external cavity,” Electron. Lett. 5(23), 571–572 (1969).
[Crossref]

Brunner, D.

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Communications 4(4), 1364 (2013).
[Crossref]

Cao, H.

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6(6), 355–359 (2012).
[Crossref] [PubMed]

Carmele, A.

F. Schulze, B. Lingnau, S. M. Hein, A. Carmele, E. Schöll, K. Lüdge, and A. Knorr, “Feedback-induced steady-state light bunching above the lasing threshold,” Phys. Rev. A 89(4), 041801 (2014).
[Crossref]

Choi, D.

Choma, M. A.

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6(6), 355–359 (2012).
[Crossref] [PubMed]

Citrin, D. S.

Cohen, E.

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F. Albert, C. Hopfmann, S. Reitzenstein, C. Schneider, S. Höfling, L. Worschech, M. Kamp, W. Kinzel, A. Forchel, and I. Kanter, “Observing chaos for quantum-dot microlasers with external feedback,” Nat. Communications 2(1), 366 (2011).
[Crossref]

Rosenbluh, M.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 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(2), 024102 (2009).
[Crossref] [PubMed]

Roy, R.

A. M. Hagerstrom, T. E. Murphy, and R. Roy, “Harvesting entropy and quantifying the transition from noise to chaos in a photon-counting feedback loop,” PNAS 112(30), 9258–9263 (2015).
[Crossref] [PubMed]

Ryczkowski, P.

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10(3), 167–170 (2016).
[Crossref]

Sacher, J.

J. Sacher, W. Elsässer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224–2227 (1989).
[Crossref] [PubMed]

Saleh, B. E. A.

H. E. Kondakci, A. F. Abouraddy, and B. E. A. Saleh, “A photonic thermalization gap in disordered lattices,” Nat. Physics 11(11), 930–935 (2015).
[Crossref]

Sano, T.

T. Sano, “Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50(3), 2719–2726 (1994).
[Crossref] [PubMed]

Schneider, C.

F. Albert, C. Hopfmann, S. Reitzenstein, C. Schneider, S. Höfling, L. Worschech, M. Kamp, W. Kinzel, A. Forchel, and I. Kanter, “Observing chaos for quantum-dot microlasers with external feedback,” Nat. Communications 2(1), 366 (2011).
[Crossref]

Schöll, E.

F. Schulze, B. Lingnau, S. M. Hein, A. Carmele, E. Schöll, K. Lüdge, and A. Knorr, “Feedback-induced steady-state light bunching above the lasing threshold,” Phys. Rev. A 89(4), 041801 (2014).
[Crossref]

S. Heiligenthal, T. Dahms, S. Yanchuk, T. Jüngling, V. Flunkert, I. Kanter, E. Schöll, and W. Kinzel, “Strong and Weak Chaos in Nonlinear Networks with Time-Delayed Couplings,” Phys. Rev. Lett. 107(23), 234102 (2011).
[Crossref] [PubMed]

Schultheiss, V. H.

V. H. Schultheiss, S. Batz, and U. Peschel, “Hanbury Brown and Twiss measurements in curved space,” Nat. Photonics 10(2), 106–110 (2016).
[Crossref]

Schulze, F.

F. Schulze, B. Lingnau, S. M. Hein, A. Carmele, E. Schöll, K. Lüdge, and A. Knorr, “Feedback-induced steady-state light bunching above the lasing threshold,” Phys. Rev. A 89(4), 041801 (2014).
[Crossref]

Sciamanna, M.

M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
[Crossref]

Shiki, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Shore, K. A.

M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
[Crossref]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Someya, H.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Soriano, M. C.

X. Porte, M. C. Soriano, and I. Fischer, “Similarity properties in the dynamics of delayed-feedback semiconductor lasers,” Phys. Rev. A 89(2), 023822 (2014).
[Crossref]

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85(1), 421–470 (2013).
[Crossref]

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Communications 4(4), 1364 (2013).
[Crossref]

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation,” Opt. Lett. 36(23), 4632–4634 (2011).
[Crossref] [PubMed]

Sukow, D. W.

N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation,” Opt. Lett. 36(23), 4632–4634 (2011).
[Crossref] [PubMed]

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl-AbiChedia, and W. Elsasser, “Picosecond intensity statistics of semiconductor lasers operating in the low-frequency fluctuation regime,” Phys. Rev. A 60(1), 667–673 (1999).
[Crossref]

Syvridis, D.

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

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

Toomey, J. P.

Torcini, A.

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, “Low-frequency fluctuations in vertical cavity lasers: experiments versus Lang-Kobayashi dynamics,” Phys. Rev. A 74(6), 063801 (2006).
[Crossref]

Twiss, R. Q.

R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177(4497), 27–29 (1956).
[Crossref]

Uchida, A.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

van Tartwijk, G. H. M.

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsässer, E. Göbel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers,” Phys. Rev. Lett. 76(2), 220–223 (1996).
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Walmsley, I. A.

K. Banaszek, R. Demkowicz-Dobrzański, and I. A. Walmsley, “Quantum states made to measure,” Nat. Photonics 3(12), 673–676 (2009).
[Crossref]

Wang, A. B.

A. B. Wang, P. Li, J. G. Zhang, J. Z. Zhang, L. Li, and Y. C. Wang, “4.5 Gbps high-speed real-time physical random bit generator,” Opt. Express 21(17), 20452–20462 (2013).
[Crossref] [PubMed]

Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photon. Technol. Lett. 20(19), 1636–1638 (2008).
[Crossref]

Wang, B. J.

Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photon. Technol. Lett. 20(19), 1636–1638 (2008).
[Crossref]

Wang, J. M.

Y. Q. Guo, G. Li, Y. F. Zhang, P. F. Zhang, J. M. Wang, and T. C. Zhang, “Efficient fluorescence detection of a single neutral atom with low background in a microscopic optical dipole trap,” Sci. China: Phys. Mech. Astron. 55(9), 1523–1528 (2012).

Y. Li, G. Li, Y. C. Zhang, X. Y. Wang, J. Zhang, J. M. Wang, and T. C. Zhang, “Effects of counting rate and resolution time on a measurement of the intensity correlation function,” Phys. Rev. A 76(1), 013829 (2007).
[Crossref]

Wang, X. Y.

Y. Li, G. Li, Y. C. Zhang, X. Y. Wang, J. Zhang, J. M. Wang, and T. C. Zhang, “Effects of counting rate and resolution time on a measurement of the intensity correlation function,” Phys. Rev. A 76(1), 013829 (2007).
[Crossref]

Wang, Y. C.

A. B. Wang, P. Li, J. G. Zhang, J. Z. Zhang, L. Li, and Y. C. Wang, “4.5 Gbps high-speed real-time physical random bit generator,” Opt. Express 21(17), 20452–20462 (2013).
[Crossref] [PubMed]

Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photon. Technol. Lett. 20(19), 1636–1638 (2008).
[Crossref]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995).
[Crossref]

Worschech, L.

F. Albert, C. Hopfmann, S. Reitzenstein, C. Schneider, S. Höfling, L. Worschech, M. Kamp, W. Kinzel, A. Forchel, and I. Kanter, “Observing chaos for quantum-dot microlasers with external feedback,” Nat. Communications 2(1), 366 (2011).
[Crossref]

Yanchuk, S.

S. Heiligenthal, T. Dahms, S. Yanchuk, T. Jüngling, V. Flunkert, I. Kanter, E. Schöll, and W. Kinzel, “Strong and Weak Chaos in Nonlinear Networks with Time-Delayed Couplings,” Phys. Rev. Lett. 107(23), 234102 (2011).
[Crossref] [PubMed]

Yoshimori, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Yoshimura, K.

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Zhang, J.

Y. Li, G. Li, Y. C. Zhang, X. Y. Wang, J. Zhang, J. M. Wang, and T. C. Zhang, “Effects of counting rate and resolution time on a measurement of the intensity correlation function,” Phys. Rev. A 76(1), 013829 (2007).
[Crossref]

Zhang, J. G.

Zhang, J. Z.

Zhang, P. F.

Y. Q. Guo, G. Li, Y. F. Zhang, P. F. Zhang, J. M. Wang, and T. C. Zhang, “Efficient fluorescence detection of a single neutral atom with low background in a microscopic optical dipole trap,” Sci. China: Phys. Mech. Astron. 55(9), 1523–1528 (2012).

Zhang, T. C.

Y. Q. Guo, G. Li, Y. F. Zhang, P. F. Zhang, J. M. Wang, and T. C. Zhang, “Efficient fluorescence detection of a single neutral atom with low background in a microscopic optical dipole trap,” Sci. China: Phys. Mech. Astron. 55(9), 1523–1528 (2012).

Y. Li, G. Li, Y. C. Zhang, X. Y. Wang, J. Zhang, J. M. Wang, and T. C. Zhang, “Effects of counting rate and resolution time on a measurement of the intensity correlation function,” Phys. Rev. A 76(1), 013829 (2007).
[Crossref]

Zhang, Y. C.

Y. Li, G. Li, Y. C. Zhang, X. Y. Wang, J. Zhang, J. M. Wang, and T. C. Zhang, “Effects of counting rate and resolution time on a measurement of the intensity correlation function,” Phys. Rev. A 76(1), 013829 (2007).
[Crossref]

Zhang, Y. F.

Y. Q. Guo, G. Li, Y. F. Zhang, P. F. Zhang, J. M. Wang, and T. C. Zhang, “Efficient fluorescence detection of a single neutral atom with low background in a microscopic optical dipole trap,” Sci. China: Phys. Mech. Astron. 55(9), 1523–1528 (2012).

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Y. C. Wang, B. J. Wang, and A. B. Wang, “Chaotic correlation optical time domain reflectometer utilizing laser diode,” IEEE Photon. Technol. Lett. 20(19), 1636–1638 (2008).
[Crossref]

Nat. Communications (2)

D. Brunner, M. C. Soriano, C. R. Mirasso, and I. Fischer, “Parallel photonic information processing at gigabyte per second data rates using transient states,” Nat. Communications 4(4), 1364 (2013).
[Crossref]

F. Albert, C. Hopfmann, S. Reitzenstein, C. Schneider, S. Höfling, L. Worschech, M. Kamp, W. Kinzel, A. Forchel, and I. Kanter, “Observing chaos for quantum-dot microlasers with external feedback,” Nat. Communications 2(1), 366 (2011).
[Crossref]

Nat. Photonics (8)

V. H. Schultheiss, S. Batz, and U. Peschel, “Hanbury Brown and Twiss measurements in curved space,” Nat. Photonics 10(2), 106–110 (2016).
[Crossref]

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nat. Photonics 10(3), 167–170 (2016).
[Crossref]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[Crossref]

M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).
[Crossref]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
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H. R. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics 3(12), 696–705 (2009).
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K. Banaszek, R. Demkowicz-Dobrzański, and I. A. Walmsley, “Quantum states made to measure,” Nat. Photonics 3(12), 673–676 (2009).
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B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6(6), 355–359 (2012).
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Nat. Physics (1)

H. E. Kondakci, A. F. Abouraddy, and B. E. A. Saleh, “A photonic thermalization gap in disordered lattices,” Nat. Physics 11(11), 930–935 (2015).
[Crossref]

Nature (2)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, “Chaos-based communications at high bit rates using commercial fibre-optic links,” Nature 438(7066), 343–346 (2005).
[Crossref] [PubMed]

R. Hanbury Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177(4497), 27–29 (1956).
[Crossref]

Opt. Express (3)

Opt. Lett. (3)

Optica (1)

Phys. Rev. (1)

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130(6), 2529–2539 (1963).
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Phys. Rev. A (6)

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl-AbiChedia, and W. Elsasser, “Picosecond intensity statistics of semiconductor lasers operating in the low-frequency fluctuation regime,” Phys. Rev. A 60(1), 667–673 (1999).
[Crossref]

X. Porte, M. C. Soriano, and I. Fischer, “Similarity properties in the dynamics of delayed-feedback semiconductor lasers,” Phys. Rev. A 89(2), 023822 (2014).
[Crossref]

F. Schulze, B. Lingnau, S. M. Hein, A. Carmele, E. Schöll, K. Lüdge, and A. Knorr, “Feedback-induced steady-state light bunching above the lasing threshold,” Phys. Rev. A 89(4), 041801 (2014).
[Crossref]

T. Sano, “Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50(3), 2719–2726 (1994).
[Crossref] [PubMed]

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, “Low-frequency fluctuations in vertical cavity lasers: experiments versus Lang-Kobayashi dynamics,” Phys. Rev. A 74(6), 063801 (2006).
[Crossref]

Y. Li, G. Li, Y. C. Zhang, X. Y. Wang, J. Zhang, J. M. Wang, and T. C. Zhang, “Effects of counting rate and resolution time on a measurement of the intensity correlation function,” Phys. Rev. A 76(1), 013829 (2007).
[Crossref]

Phys. Rev. Lett. (7)

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
[Crossref] [PubMed]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103(2), 024102 (2009).
[Crossref] [PubMed]

S. Heiligenthal, T. Dahms, S. Yanchuk, T. Jüngling, V. Flunkert, I. Kanter, E. Schöll, and W. Kinzel, “Strong and Weak Chaos in Nonlinear Networks with Time-Delayed Couplings,” Phys. Rev. Lett. 107(23), 234102 (2011).
[Crossref] [PubMed]

I. Fischer, G. H. M. van Tartwijk, A. M. Levine, W. Elsässer, E. Göbel, and D. Lenstra, “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers,” Phys. Rev. Lett. 76(2), 220–223 (1996).
[Crossref] [PubMed]

J. Sacher, W. Elsässer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224–2227 (1989).
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PNAS (1)

A. M. Hagerstrom, T. E. Murphy, and R. Roy, “Harvesting entropy and quantifying the transition from noise to chaos in a photon-counting feedback loop,” PNAS 112(30), 9258–9263 (2015).
[Crossref] [PubMed]

Rev. Mod. Phys. (2)

L. Davidovich, “Sub-Poissonian processes in quantum optics,” Rev. Mod. Phys. 68(1), 127–173 (1996).
[Crossref]

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85(1), 421–470 (2013).
[Crossref]

Sci. Adv. (1)

O. S. Magaña-Loaiza, M. Mirhosseini, R. M. Cross, S. M. Hashemi Rafsanjani, and R. W. Boyd, “Hanbury Brown and Twiss interferometry with twisted light,” Sci. Adv. 2(4), e1501143 (2016).
[Crossref] [PubMed]

Sci. China: Phys. Mech. Astron. (1)

Y. Q. Guo, G. Li, Y. F. Zhang, P. F. Zhang, J. M. Wang, and T. C. Zhang, “Efficient fluorescence detection of a single neutral atom with low background in a microscopic optical dipole trap,” Sci. China: Phys. Mech. Astron. 55(9), 1523–1528 (2012).

Other (2)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995).
[Crossref]

A. Locquet, “Chaos-Based Secure Optical Communications Using Semiconductor Lasers,” in Handbook of Information and Communication Security, M. Stamp and P. Stavroulakis, eds. (Springer, 2010), pp. 451–478.
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Schematic illustration of the experimental setup. LD: distributed feedback laser diode; PC: polarization controller; TC: temperature controller; CS: current source; OC1, OC2 and OC3: optical coupler; VOA1, VOA2 and VOA3: variable optical attenuator; SMF: single mode fiber; BS: beam splitter; DSPD: dual-channel single photon detector; PD: Photodetector; OSC: oscilloscope; SA: spectrum analyzer.
Fig. 2
Fig. 2 Intensity time traces, photon number distribution and second-order degree of coherence for J = 1.5Jth with κ = 35 ns−1, κ = 50 ns−1, and κ = 65 ns −1. (a) Calculated emission intensity and (b) associated photon number distribution of a semiconductor laser with external optical feedback. The blue solid and black dotted curves are the Bose-Einstein and Poisson distributions. (c) The corresponding g(2)(τ) are obtained from emission intensity for various κ = 35 ns−1 (blue dotted curve), κ = 50 ns−1 (red dash-dotted curve), and κ = 65 ns−1 (black solid curve).
Fig. 3
Fig. 3 Characteristics of chaotic laser when J = 1.5Jth and η = 12.8%. (a) Measured time traces and (b) power spectrum of the chaotic laser. The inset in (a) is the time series in a shorter time interval.
Fig. 4
Fig. 4 The blue histograms are the measured photon number distribution P(nph), corresponding to g(2)(0) for the chaotic laser with different mean photon numbers 〈nph〉 at the input. The red solid and black dashed curves are the Bose-Einstein and Poisson fitting, respectively.
Fig. 5
Fig. 5 (a), (c) Theoretical and (b), (d) experimental results for g(2)(0) at five J (a), (b): 1.07Jth, 1.12Jth, 1.2Jth, 1.5Jth, and 2.0Jth; four κ(η) (c), (d): 5.5 ns−1 (3.1%), 7 ns−1 (6.3%), 11 ns−1 (12.5%), 20 ns−1 (25%).
Fig. 6
Fig. 6 Measured temporal waveform and RF spectrum of chaotic signals for three η, when (a) J = 1.07Jth, (b) J = 1.2Jth, and (c) J = 1.5Jth.
Fig. 7
Fig. 7 (a) Theoretical and (b) experimental results for h at various κ(η) and three J: 1.07Jth, 1.2Jth, and 1.5Jth.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

E ˙ ( t ) = 1 2 [ G ( t ) τ p 1 ) E ( t ) + κ E ( t τ e x t ) cos [ ϕ ( t ) ] ,
φ ˙ ( t ) = α 2 [ G ( t ) τ p 1 ] κ E ( t τ e x t ) E ( t ) 1 sin [ ϕ ( t ) ] ,
N ˙ ( t ) = J e N ( t ) τ N G ( t ) | E ( t ) | 2 ,
ϕ ( t ) = ω τ + φ ( t ) φ ( t τ e x t ) ,
g ( 2 ) ( τ ) = E * ( t ) E * ( t + τ ) E ( t + τ ) E ( t ) E * ( t ) E ( t ) 2 = t I ( t ) I ( t + τ ) d t ( t I ( t ) d t ) 2 = n p h ( t ) n p h ( t + τ ) n p h ( t ) 2 ,

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