Abstract

We generate random bit sequences from chaotic temporal waveforms by using photonic integrated circuits (PICs) with different external cavity lengths. We investigate the condition for generating random bits at different sampling rates of single-bit generation method with the PICs. We succeed in generating certified random bit sequences by using the PIC with 3, 4, 5, or 10-mm-long external cavity, whereas random bits cannot pass all the statistical tests of randomness when the PIC with 1 or 2 mm-long external cavity is used.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2014 (1)

X. Fang, B. Wetzel, J.-M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Cir. Syst. I 61(3), 888–901 (2014).

2013 (7)

H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[CrossRef] [PubMed]

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

P. Li, Y. Wang, A. Wang, B. Wang, “Fast and tunable all-optical physical random number generator based on direct quantization of chaotic self-pulsations in two-section semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600208 (2013).
[CrossRef]

T. Yamazaki, A. Uchida, “Performance of random number generators using noise-based superluminescent diode and chaos-based semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600309 (2013).
[CrossRef]

X.-Z. Li, S.-C. Chan, “Heterodyne random bit generation using an optically injected semiconductor laser in chaos,” IEEE J. Quantum Electron. 49(10), 829–838 (2013).
[CrossRef]

N. Oliver, M. C. Soriano, D. W. Sukow, I. Fischer, “Fast random bit generation using a chaotic laser: approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[CrossRef]

J.-G. Wu, L.-J. Zhao, Z.-M. Wu, D. Lu, X. Tang, Z.-Q. Zhong, G.-Q. Xia, “Direct generation of broadband chaos by a monolithic integrated semiconductor laser chip,” Opt. Express 21(20), 23358–23364 (2013).
[CrossRef] [PubMed]

2012 (9)

F.-Y. Lin, Y.-K. Chao, T.-C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. Quantum Electron. 48(8), 1010–1014 (2012).
[CrossRef]

P. Li, Y. C. Wang, A. B. Wang, L. Z. Yang, M. J. Zhang, J. Z. Zhang, “Direct generation of all-optical random numbers from optical pulse amplitude chaos,” Opt. Express 20(4), 4297–4308 (2012).
[CrossRef] [PubMed]

J. Zhang, Y. Wang, M. Liu, L. Xue, P. Li, A. Wang, M. Zhang, “A robust random number generator based on differential comparison of chaotic laser signals,” Opt. Express 20(7), 7496–7506 (2012).
[CrossRef] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[CrossRef]

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[CrossRef] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (2012).
[CrossRef] [PubMed]

J. Zhang, Y. Wang, L. Xue, J. Hou, B. Zhang, A. Wang, M. Zhang, “Delay line length selection in generating fast random numbers with a chaotic laser,” Appl. Opt. 51(11), 1709–1714 (2012).
[CrossRef] [PubMed]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, 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. Argyris, E. Pikasis, S. Deligiannidis, D. Syvridis, “Sub-Tb/s physical random bit generators based on direct detection of amplified spontaneous emission signals,” J. Lightwave Technol. 30(9), 1329–1334 (2012).
[CrossRef]

2011 (6)

2010 (6)

2009 (3)

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[CrossRef] [PubMed]

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

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

2008 (5)

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

T. E. Murphy, R. Roy, “The world’s fastest dice,” Nat. Photonics 2(12), 714–715 (2008).
[CrossRef]

V. Z. Tronciu, C. R. Mirasso, P. Colet, “Chaos-based communications using semiconductor lasers subject to feedback from an integrated double cavity,” J. Phys. At. Mol. Opt. Phys. 41(15), 155401 (2008).
[CrossRef]

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[CrossRef] [PubMed]

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Lett. 93(3), 031109 (2008).
[CrossRef]

2007 (2)

M. Stipčević, B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78(4), 045104 (2007).
[CrossRef] [PubMed]

M. Yousefi, Y. Barbarin, S. Beri, E. A. Bente, M. K. Smit, R. Nötzel, D. Lenstra, “New role for nonlinear dynamics and chaos in integrated semiconductor laser technology,” Phys. Rev. Lett. 98(4), 044101 (2007).
[CrossRef] [PubMed]

2005 (1)

H.-J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

2004 (1)

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H.-J. Wünsche, F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1), 016206 (2004).
[CrossRef] [PubMed]

2003 (1)

F. Y. Lin, J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221(1-3), 173–180 (2003).
[CrossRef]

Aida, H.

Akizawa, Y.

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[CrossRef]

Y. Akizawa, R. Takahashi, T. Yamazaki, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Yoshimura, K. Arai, P. Davis, (in preparation).

Amano, K.

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[CrossRef] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

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

Andersen, U. L.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[CrossRef]

Aoyama, K.

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[CrossRef] [PubMed]

Arai, K.

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[CrossRef]

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[CrossRef] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (2012).
[CrossRef] [PubMed]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[CrossRef] [PubMed]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express 19(8), 7439–7450 (2011).
[CrossRef] [PubMed]

Y. Akizawa, R. Takahashi, T. Yamazaki, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Yoshimura, K. Arai, P. Davis, (in preparation).

Argyris, A.

Aviad, Y.

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

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

Bahi, J. M.

X. Fang, B. Wetzel, J.-M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Cir. Syst. I 61(3), 888–901 (2014).

Barbarin, Y.

M. Yousefi, Y. Barbarin, S. Beri, E. A. Bente, M. K. Smit, R. Nötzel, D. Lenstra, “New role for nonlinear dynamics and chaos in integrated semiconductor laser technology,” Phys. Rev. Lett. 98(4), 044101 (2007).
[CrossRef] [PubMed]

Bauer, S.

H.-J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H.-J. Wünsche, F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1), 016206 (2004).
[CrossRef] [PubMed]

Bente, E. A.

M. Yousefi, Y. Barbarin, S. Beri, E. A. Bente, M. K. Smit, R. Nötzel, D. Lenstra, “New role for nonlinear dynamics and chaos in integrated semiconductor laser technology,” Phys. Rev. Lett. 98(4), 044101 (2007).
[CrossRef] [PubMed]

Beri, S.

M. Yousefi, Y. Barbarin, S. Beri, E. A. Bente, M. K. Smit, R. Nötzel, D. Lenstra, “New role for nonlinear dynamics and chaos in integrated semiconductor laser technology,” Phys. Rev. Lett. 98(4), 044101 (2007).
[CrossRef] [PubMed]

Bogris, A.

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

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[CrossRef] [PubMed]

Brox, O.

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H.-J. Wünsche, F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1), 016206 (2004).
[CrossRef] [PubMed]

Chan, S.-C.

X.-Z. Li, S.-C. Chan, “Heterodyne random bit generation using an optically injected semiconductor laser in chaos,” IEEE J. Quantum Electron. 49(10), 829–838 (2013).
[CrossRef]

Chao, Y.-K.

F.-Y. Lin, Y.-K. Chao, T.-C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. Quantum Electron. 48(8), 1010–1014 (2012).
[CrossRef]

Chi, Y.-M.

Chlouverakis, K. E.

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[CrossRef] [PubMed]

Cohen, A. B.

Cohen, E.

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

Colet, P.

V. Z. Tronciu, C. R. Mirasso, P. Colet, “Chaos-based communications using semiconductor lasers subject to feedback from an integrated double cavity,” J. Phys. At. Mol. Opt. Phys. 41(15), 155401 (2008).
[CrossRef]

Davis, P.

H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[CrossRef] [PubMed]

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

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (2012).
[CrossRef] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[CrossRef]

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[CrossRef] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[CrossRef]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[CrossRef] [PubMed]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express 19(8), 7439–7450 (2011).
[CrossRef] [PubMed]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[CrossRef] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[CrossRef] [PubMed]

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

Y. Akizawa, R. Takahashi, T. Yamazaki, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Yoshimura, K. Arai, P. Davis, (in preparation).

Deligiannidis, S.

Dong, R.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[CrossRef]

Dudley, J. M.

X. Fang, B. Wetzel, J.-M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Cir. Syst. I 61(3), 888–901 (2014).

Dynes, J. F.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Lett. 93(3), 031109 (2008).
[CrossRef]

Elsässer, W.

H.-J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

Erzgräber, H.

H.-J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

Fang, X.

X. Fang, B. Wetzel, J.-M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Cir. Syst. I 61(3), 888–901 (2014).

Fischer, I.

N. Oliver, M. C. Soriano, D. W. Sukow, I. Fischer, “Fast random bit generation using a chaotic laser: approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[CrossRef]

N. Oliver, M. C. Soriano, D. W. Sukow, 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]

H.-J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

Gabriel, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[CrossRef]

Guyeux, C.

X. Fang, B. Wetzel, J.-M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Cir. Syst. I 61(3), 888–901 (2014).

Hamacher, M.

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[CrossRef] [PubMed]

Harayama, T.

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

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (2012).
[CrossRef] [PubMed]

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[CrossRef] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[CrossRef]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express 19(8), 7439–7450 (2011).
[CrossRef] [PubMed]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[CrossRef] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[CrossRef]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[CrossRef] [PubMed]

Y. Akizawa, R. Takahashi, T. Yamazaki, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Yoshimura, K. Arai, P. Davis, (in preparation).

Henneberger, F.

H.-J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H.-J. Wünsche, F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1), 016206 (2004).
[CrossRef] [PubMed]

Hirano, K.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[CrossRef] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[CrossRef] [PubMed]

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

Honjo, T.

Hou, J.

Ikeguchi, T.

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[CrossRef] [PubMed]

Inoue, M.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

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

Kakesu, I.

Kanno, K.

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[CrossRef] [PubMed]

Kanter, I.

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

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

Koizumi, H.

Korneyev, N.

H.-J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

Kreissl, J.

H.-J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H.-J. Wünsche, F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1), 016206 (2004).
[CrossRef] [PubMed]

Kurashige, T.

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

Larger, L.

X. Fang, B. Wetzel, J.-M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Cir. Syst. I 61(3), 888–901 (2014).

Lenstra, D.

M. Yousefi, Y. Barbarin, S. Beri, E. A. Bente, M. K. Smit, R. Nötzel, D. Lenstra, “New role for nonlinear dynamics and chaos in integrated semiconductor laser technology,” Phys. Rev. Lett. 98(4), 044101 (2007).
[CrossRef] [PubMed]

Leuchs, G.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[CrossRef]

Li, L.

Li, P.

Li, X.

Li, X.-Z.

X.-Z. Li, S.-C. Chan, “Heterodyne random bit generation using an optically injected semiconductor laser in chaos,” IEEE J. Quantum Electron. 49(10), 829–838 (2013).
[CrossRef]

Lin, F. Y.

F. Y. Lin, J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221(1-3), 173–180 (2003).
[CrossRef]

Lin, F.-Y.

F.-Y. Lin, Y.-K. Chao, T.-C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. Quantum Electron. 48(8), 1010–1014 (2012).
[CrossRef]

Liu, J. M.

F. Y. Lin, J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221(1-3), 173–180 (2003).
[CrossRef]

Liu, M.

Lo, H.-K.

Lu, D.

Marquardt, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[CrossRef]

Mauerer, W.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[CrossRef]

Merolla, J.-M.

X. Fang, B. Wetzel, J.-M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Cir. Syst. I 61(3), 888–901 (2014).

Mikami, T.

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[CrossRef] [PubMed]

Mirasso, C. R.

V. Z. Tronciu, C. R. Mirasso, P. Colet, “Chaos-based communications using semiconductor lasers subject to feedback from an integrated double cavity,” J. Phys. At. Mol. Opt. Phys. 41(15), 155401 (2008).
[CrossRef]

Morikatsu, S.

Muramatsu, J.

H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[CrossRef] [PubMed]

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

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (2012).
[CrossRef] [PubMed]

Murphy, T. E.

Naito, S.

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

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

Nötzel, R.

M. Yousefi, Y. Barbarin, S. Beri, E. A. Bente, M. K. Smit, R. Nötzel, D. Lenstra, “New role for nonlinear dynamics and chaos in integrated semiconductor laser technology,” Phys. Rev. Lett. 98(4), 044101 (2007).
[CrossRef] [PubMed]

Nozawa, T.

Okumura, H.

Oliver, N.

N. Oliver, M. C. Soriano, D. W. Sukow, I. Fischer, “Fast random bit generation using a chaotic laser: approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[CrossRef]

N. Oliver, M. C. Soriano, D. W. Sukow, 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]

Oowada, I.

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

Peil, M.

H.-J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

Pikasis, E.

Qi, B.

Qian, L.

Radziunas, M.

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H.-J. Wünsche, F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1), 016206 (2004).
[CrossRef] [PubMed]

Reidler, I.

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

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

Rogina, B. M.

M. Stipčević, B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78(4), 045104 (2007).
[CrossRef] [PubMed]

Rosenbluh, M.

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

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

Roy, R.

Salevan, J. C.

Sartorius, B.

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H.-J. Wünsche, F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1), 016206 (2004).
[CrossRef] [PubMed]

Sharpe, A. W.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Lett. 93(3), 031109 (2008).
[CrossRef]

Shields, A. J.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Lett. 93(3), 031109 (2008).
[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, P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Sieber, J.

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H.-J. Wünsche, F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1), 016206 (2004).
[CrossRef] [PubMed]

Smit, M. K.

M. Yousefi, Y. Barbarin, S. Beri, E. A. Bente, M. K. Smit, R. Nötzel, D. Lenstra, “New role for nonlinear dynamics and chaos in integrated semiconductor laser technology,” Phys. Rev. Lett. 98(4), 044101 (2007).
[CrossRef] [PubMed]

Someya, H.

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[CrossRef] [PubMed]

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

Soriano, M. C.

N. Oliver, M. C. Soriano, D. W. Sukow, I. Fischer, “Fast random bit generation using a chaotic laser: approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[CrossRef]

N. Oliver, M. C. Soriano, D. W. Sukow, 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]

Stipcevic, M.

M. Stipčević, B. M. Rogina, “Quantum random number generator based on photonic emission in semiconductors,” Rev. Sci. Instrum. 78(4), 045104 (2007).
[CrossRef] [PubMed]

Sukow, D. W.

N. Oliver, M. C. Soriano, D. W. Sukow, I. Fischer, “Fast random bit generation using a chaotic laser: approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[CrossRef]

N. Oliver, M. C. Soriano, D. W. Sukow, 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]

Sunada, S.

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[CrossRef]

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[CrossRef] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (2012).
[CrossRef] [PubMed]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express 19(8), 7439–7450 (2011).
[CrossRef] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[CrossRef]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[CrossRef] [PubMed]

Y. Akizawa, R. Takahashi, T. Yamazaki, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Yoshimura, K. Arai, P. Davis, (in preparation).

Sych, D.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[CrossRef]

Syvridis, D.

Takahashi, R.

Y. Akizawa, R. Takahashi, T. Yamazaki, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Yoshimura, K. Arai, P. Davis, (in preparation).

Tang, X.

Tokura, Y.

Tronciu, V. Z.

V. Z. Tronciu, C. R. Mirasso, P. Colet, “Chaos-based communications using semiconductor lasers subject to feedback from an integrated double cavity,” J. Phys. At. Mol. Opt. Phys. 41(15), 155401 (2008).
[CrossRef]

Tsuzuki, K.

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[CrossRef]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[CrossRef] [PubMed]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express 19(8), 7439–7450 (2011).
[CrossRef] [PubMed]

Y. Akizawa, R. Takahashi, T. Yamazaki, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Yoshimura, K. Arai, P. Davis, (in preparation).

Uchida, A.

H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[CrossRef] [PubMed]

T. Yamazaki, A. Uchida, “Performance of random number generators using noise-based superluminescent diode and chaos-based semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600309 (2013).
[CrossRef]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (2012).
[CrossRef] [PubMed]

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[CrossRef] [PubMed]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[CrossRef]

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

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express 19(8), 7439–7450 (2011).
[CrossRef] [PubMed]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[CrossRef] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[CrossRef]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[CrossRef] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[CrossRef] [PubMed]

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

Y. Akizawa, R. Takahashi, T. Yamazaki, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Yoshimura, K. Arai, P. Davis, (in preparation).

Ushakov, O.

H.-J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

Wang, A.

Wang, A. B.

Wang, B.

P. Li, Y. Wang, A. Wang, B. Wang, “Fast and tunable all-optical physical random number generator based on direct quantization of chaotic self-pulsations in two-section semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600208 (2013).
[CrossRef]

Wang, Y.

Wang, Y. C.

Wetzel, B.

X. Fang, B. Wetzel, J.-M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Cir. Syst. I 61(3), 888–901 (2014).

Wille, E.

H.-J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

Williams, C. R. S.

Wittmann, C.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[CrossRef]

Wu, J.-G.

Wu, T.-C.

F.-Y. Lin, Y.-K. Chao, T.-C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. Quantum Electron. 48(8), 1010–1014 (2012).
[CrossRef]

Wu, Z.-M.

Wünsche, H.-J.

H.-J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
[CrossRef] [PubMed]

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H.-J. Wünsche, F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1), 016206 (2004).
[CrossRef] [PubMed]

Xia, G.-Q.

Xue, L.

Yamazaki, T.

T. Yamazaki, A. Uchida, “Performance of random number generators using noise-based superluminescent diode and chaos-based semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600309 (2013).
[CrossRef]

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[CrossRef]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[CrossRef] [PubMed]

Y. Akizawa, R. Takahashi, T. Yamazaki, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Yoshimura, K. Arai, P. Davis, (in preparation).

Yang, L. Z.

Yoshimori, S.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[CrossRef] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

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

Yoshimura, K.

H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[CrossRef] [PubMed]

K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, 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. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Technol. Lett. 24(12), 1042–1044 (2012).
[CrossRef]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (2012).
[CrossRef] [PubMed]

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[CrossRef] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[CrossRef]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[CrossRef] [PubMed]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express 19(8), 7439–7450 (2011).
[CrossRef] [PubMed]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
[CrossRef] [PubMed]

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
[CrossRef]

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[CrossRef] [PubMed]

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

Y. Akizawa, R. Takahashi, T. Yamazaki, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Yoshimura, K. Arai, P. Davis, (in preparation).

Yousefi, M.

M. Yousefi, Y. Barbarin, S. Beri, E. A. Bente, M. K. Smit, R. Nötzel, D. Lenstra, “New role for nonlinear dynamics and chaos in integrated semiconductor laser technology,” Phys. Rev. Lett. 98(4), 044101 (2007).
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Yuan, Z. L.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Lett. 93(3), 031109 (2008).
[CrossRef]

Zhang, B.

Zhang, J.

Zhang, J. Z.

Zhang, M.

Zhang, M. J.

Zhang, Y.

Zhao, L.-J.

Zhong, Z.-Q.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Lett. 93(3), 031109 (2008).
[CrossRef]

Chin. Opt. Lett. (1)

IEEE J. Quantum Electron. (4)

K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45(11), 1367–1379 (2009).
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X.-Z. Li, S.-C. Chan, “Heterodyne random bit generation using an optically injected semiconductor laser in chaos,” IEEE J. Quantum Electron. 49(10), 829–838 (2013).
[CrossRef]

N. Oliver, M. C. Soriano, D. W. Sukow, I. Fischer, “Fast random bit generation using a chaotic laser: approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).
[CrossRef]

F.-Y. Lin, Y.-K. Chao, T.-C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. Quantum Electron. 48(8), 1010–1014 (2012).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

P. Li, Y. Wang, A. Wang, B. Wang, “Fast and tunable all-optical physical random number generator based on direct quantization of chaotic self-pulsations in two-section semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600208 (2013).
[CrossRef]

T. Yamazaki, A. Uchida, “Performance of random number generators using noise-based superluminescent diode and chaos-based semiconductor lasers,” IEEE J. Sel. Top. Quantum Electron. 19(4), 0600309 (2013).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Y. Akizawa, T. Yamazaki, A. Uchida, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Fast random number generation with bandwidth-enhanced chaotic semiconductor lasers at 8 × 50 Gb/s,” IEEE Photon. Technol. Lett. 24(12), 1042–1044 (2012).
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IEEE Trans. Cir. Syst. I (1)

X. Fang, B. Wetzel, J.-M. Merolla, J. M. Dudley, L. Larger, C. Guyeux, J. M. Bahi, “Noise and chaos contributions in fast random bit sequence generated from broadband optoelectronic entropy sources,” IEEE Trans. Cir. Syst. I 61(3), 888–901 (2014).

J. Lightwave Technol. (1)

J. Phys. At. Mol. Opt. Phys. (1)

V. Z. Tronciu, C. R. Mirasso, P. Colet, “Chaos-based communications using semiconductor lasers subject to feedback from an integrated double cavity,” J. Phys. At. Mol. Opt. Phys. 41(15), 155401 (2008).
[CrossRef]

Nat. Photonics (4)

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
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A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
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F. Y. Lin, J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221(1-3), 173–180 (2003).
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Opt. Express (11)

J.-G. Wu, L.-J. Zhao, Z.-M. Wu, D. Lu, X. Tang, Z.-Q. Zhong, G.-Q. Xia, “Direct generation of broadband chaos by a monolithic integrated semiconductor laser chip,” Opt. Express 21(20), 23358–23364 (2013).
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S. Sunada, T. Harayama, K. Arai, K. Yoshimura, P. Davis, K. Tsuzuki, A. Uchida, “Chaos laser chips with delayed optical feedback using a passive ring waveguide,” Opt. Express 19(7), 5713–5724 (2011).
[CrossRef] [PubMed]

S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express 19(8), 7439–7450 (2011).
[CrossRef] [PubMed]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18(6), 5512–5524 (2010).
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A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18(18), 18763–18768 (2010).
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P. Li, Y. C. Wang, A. B. Wang, L. Z. Yang, M. J. Zhang, J. Z. Zhang, “Direct generation of all-optical random numbers from optical pulse amplitude chaos,” Opt. Express 20(4), 4297–4308 (2012).
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J. Zhang, Y. Wang, M. Liu, L. Xue, P. Li, A. Wang, M. Zhang, “A robust random number generator based on differential comparison of chaotic laser signals,” Opt. Express 20(7), 7496–7506 (2012).
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A. Wang, P. Li, J. Zhang, J. Zhang, L. Li, Y. Wang, “4.5 Gbps high-speed real-time physical random bit generator,” Opt. Express 21(17), 20452–20462 (2013).
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H. Koizumi, S. Morikatsu, H. Aida, T. Nozawa, I. Kakesu, A. Uchida, K. Yoshimura, J. Muramatsu, P. Davis, “Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers,” Opt. Express 21(15), 17869–17893 (2013).
[CrossRef] [PubMed]

T. Honjo, A. Uchida, K. Amano, K. Hirano, H. Someya, H. Okumura, K. Yoshimura, P. Davis, Y. Tokura, “Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers,” Opt. Express 17(11), 9053–9061 (2009).
[CrossRef] [PubMed]

C. R. S. Williams, J. C. Salevan, X. Li, R. Roy, T. E. Murphy, “Fast physical random number generator using amplified spontaneous emission,” Opt. Express 18(23), 23584–23597 (2010).
[CrossRef] [PubMed]

Opt. Lett. (3)

Phys. Rev. A (1)

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83(3), 031803 (2011).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (3)

T. Mikami, K. Kanno, K. Aoyama, A. Uchida, T. Ikeguchi, T. Harayama, S. Sunada, K. Arai, K. Yoshimura, P. Davis, “Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(1), 016211 (2012).
[CrossRef] [PubMed]

T. Harayama, S. Sunada, K. Yoshimura, J. Muramatsu, K. Arai, A. Uchida, P. Davis, “Theory of fast nondeterministic physical random-bit generation with chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85(4), 046215 (2012).
[CrossRef] [PubMed]

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H.-J. Wünsche, F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(1), 016206 (2004).
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H.-J. Wünsche, S. Bauer, J. Kreissl, O. Ushakov, N. Korneyev, F. Henneberger, E. Wille, H. Erzgräber, M. Peil, W. Elsässer, I. Fischer, “Synchronization of delay-coupled oscillators: A study of semiconductor lasers,” Phys. Rev. Lett. 94(16), 163901 (2005).
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K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, A. Uchida, “Secure key distribution using correlated randomness in lasers driven by common random light,” Phys. Rev. Lett. 108(7), 070602 (2012).
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Rev. Sci. Instrum. (1)

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Other (4)

J. Ohtsubo, Semiconductor Lasers, Stability, Instability and Chaos, 3rd ed. (Springer-Verlag, 2013).

A. Uchida, Optical Communication with Chaotic Lasers, Applications of Nonlinear Dynamics and Synchronization, (Wiley-VCH, 2012).

Y. Akizawa, R. Takahashi, T. Yamazaki, A. Uchida, T. Harayama, K. Tsuzuki, S. Sunada, K. Yoshimura, K. Arai, P. Davis, (in preparation).

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, S. Vo, and L. E. Bassham III, National Institute of Standards and Technology, Special Publication 800–22, Revision 1a (2010).

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Figures (10)

Fig. 1
Fig. 1

(a) Schematics of the photonic integrated circuit (PIC). The PIC consists of a photodetector (PD), a distributed-feedback (DFB) semiconductor laser, two semiconductor optical amplifiers (SOA 1 and 2), a passive waveguide (PW), and an external mirror (M). The external cavity length is set to 1, 2, 3, 4, 5 or 10 mm. (b) Experimental setup for random bit generation.

Fig. 2
Fig. 2

Single-bit random-number generation method with 1-bit AD conversion and XOR operation.

Fig. 3
Fig. 3

(a) Chaotic temporal waveform and (b) its RF spectrum generated from the PIC with 5-mm-long external cavity. The injection current of the DFB laser is IDFB = 39.00 mA (3.0 Ith, where Ith is the lasing threshold for the solitary DFB laser). The injection currents of the SOA1 and SOA2 are ISOA1 = 6.00 mA and ISOA2 = 5.00 mA, respectively.

Fig. 4
Fig. 4

(a) Number of passed NIST tests for generated random bit sequences as a function of the sampling time (i.e., the sampling rate). (b) Autocorrelation function (absolute value) of the chaotic temporal waveform as a function of the delay time and result of NIST tests for generated random bit sequences. Red circles: all the NIST tests are passed. Blue triangles: one or more NIST tests are failed. The dotted line indicates the autocorrelation value 1.3 × 10−2.

Fig. 5
Fig. 5

Chaotic temporal waveforms and corresponding RF spectra used for random bit generation. (a),(b) IDFB = 39.00 mA (3.0 Ith), ISOA1 = 6.00 mA, and ISOA2 = 5.00 mA. The same figures are used as Fig. 3 for comparison. (c),(d) IDFB = 70.00 mA (5.4 Ith), ISOA1 = 14.00 mA, and ISOA2 = 5.00 mA. The maximum rates of random bit generation with these temporal waveforms and RF spectra are (a),(b) 4.6 Gb/s and (c),(d) 1.0 Gb/s, respectively.

Fig. 6
Fig. 6

The maximum random bit generation rate as a function of the difference in the heights between the low frequency peak and the peak of the chaotic broadband spectrum component (Pchaos -PLFF).

Fig. 7
Fig. 7

Typical examples of chaotic temporal waveforms generated from PICs with external cavity lengths of (a) 1 mm, (b) 2 mm, (c) 3 mm, (d) 4 mm, (e) 5 mm, and (f) 10 mm. The injection current of the SOA 2 is fixed at ISOA2 = 5.00 mA for all the PICs. The injection currents of the DFB laser and SOA 1 are set as follows. (a) IDFB = 31.20 mA (2.6 Ith), ISOA1 = 2.30 mA. (b) IDFB = 21.60 mA (1.8 Ith), ISOA1 = 1.85 mA. (c) IDFB = 48.00 mA (4.0 Ith), ISOA1 = 15.30 mA. (d) IDFB = 38.40 mA (3.2 Ith), ISOA1 = 10.30 mA. (e) IDFB = 39.00 mA (3.0 Ith), ISOA1 = 6.00 mA. (f) IDFB = 39.00 mA (3.0 Ith), ISOA1 = 14.50 mA.

Fig. 8
Fig. 8

Typical examples of RF spectra generated from PICs with external cavity lengths of (a) 1 mm, (b) 2 mm, (c) 3 mm, (d) 4 mm, (e) 5 mm, and (f) 10 mm. Each figure corresponds to that in Fig. 7. The external cavity frequencies fext are (a) 35.7 GHz, (b) 17.8 GHz, (c) 11.9 GHz, (d) 8.9 GHz, (e) 7.1 GHz, and (f) 3.6 GHz, respectively.

Fig. 9
Fig. 9

Results of the NIST tests for different random bit generation rates and the PICs with different external cavity lengths. The red circles indicate that random bit sequences generated at the sampling rate and the corresponding PIC can pass all the NIST tests, whereas the blue triangles indicate that random bit sequences generated the sampling rate and the corresponding PIC fail one or more of the NIST tests. The sampling rate is changed from 1 to 6 GHz and selected at the condition for the local minima and maxima of the autocorrelation values at the corresponding delay times.

Fig. 10
Fig. 10

Multi-bit random number generation method [15].

Tables (3)

Tables Icon

Table 1 Result of NIST SP 800-22 for random bits generated from PIC with 5-mm-long external cavity at rate of 4.6 Gb/s. Significance level is set to α = 0.01. To pass the tests, the P-value of the uniformity of p-values should be larger than 0.0001, and the proportion of sequences satisfying p-value > α for 1000 samples of 1 Mbit data should be in the range of 0.99 ± 0.0094392 [45]. For tests which produce multiple P-values and proportions, the worst case is shown.

Tables Icon

Table 2 Standard bandwidth, effective bandwidth, and flatness of the RF spectra in Fig. 8 for the PICs with different external cavity lengths.

Tables Icon

Table 3 Result of NIST SP 800-22 for random bits generated from multi-bit random number generation method.

Equations (1)

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f ext = c 2nL

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