Abstract

In this manuscript, we experimentally and numerically investigate the chaotic dynamics of the state-of-polarization in a nonlinear optical fiber due to the cross-interaction between an incident signal and its intense backward replica generated at the fiber-end through an amplified reflective delayed loop. Thanks to the cross-polarization interaction between the two-delayed counter-propagating waves, the output polarization exhibits fast temporal chaotic dynamics, which enable a powerful scrambling process with moving speeds up to 600-krad/s. The performance of this all-optical scrambler was then evaluated on a 10-Gbit/s On/Off Keying telecom signal achieving an error-free transmission. We also describe how these temporal and chaotic polarization fluctuations can be exploited as an all-optical random number generator. To this aim, a billion-bit sequence was experimentally generated and successfully confronted to the dieharder benchmarking statistic tools. Our experimental analysis are supported by numerical simulations based on the resolution of counter-propagating coupled nonlinear propagation equations that confirm the observed behaviors.

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

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  33. Dataset 1: Results of the dieharder tests for the experimental 1-billion bit sequence generated from polarization chaos https://doi.org/10.6084/m9.figshare.5725807 .

2017 (3)

L. Keuninckx, M. C. Soriano, I. Fischer, C. R. Mirasso, R. M. Nguimdo, and G. Van der Sande, “Encryption key distribution via chaos synchronization,” Sci. Rep. 7, 43428 (2017).
[Crossref] [PubMed]

C. Wu, B. Bai, Y. Liu, X. Zhang, M. Yang, Y. Cao, J. Wang, S. Zhang, H. Zhou, X. Shi, X. Ma, J. G. Ren, J. Zhang, C. Z. Peng, J. Fan, Q. Zhang, and J. W. Pan, “Random Number Generation with Cosmic Photons,” Phys. Rev. Lett. 118(14), 140402 (2017).
[Crossref] [PubMed]

M. Guasoni, J. Garnier, B. Rumpf, D. Sugny, J. Fatome, F. Amrani, G. Millot, and A. Picozzi, “Incoherent Fermi-Pasta-Ulam recurrences and unconstrained thermalization mediated by strong phase-correlations,” Phys. Rev. X 7(1), 011025 (2017).
[Crossref]

2016 (2)

M. Guasoni, P. Y. Bony, M. Gilles, A. Picozzi, and J. Fatome, “Fast and Chaotic Fiber-Based Nonlinear Polarization Scrambler,” IEEE J. Sel. Top. Quantum Electron. 22(2), 88 (2016).
[Crossref]

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6(1), 22381 (2016).
[Crossref] [PubMed]

2015 (1)

T. Lunghi, J. B. Brask, C. C. W. Lim, Q. Lavigne, J. Bowles, A. Martin, H. Zbinden, and N. Brunner, “Self-testing quantum random number generator,” Phys. Rev. Lett. 114(15), 150501 (2015).
[Crossref] [PubMed]

2014 (2)

P.-Y. Bony, M. Guasoni, P. Morin, D. Sugny, A. Picozzi, H. R. Jauslin, S. Pitois, and J. Fatome, “Temporal spying and concealing process in fibre-optic data transmission systems through polarization bypass,” Nat. Commun. 5, 4678 (2014).
[Crossref] [PubMed]

B. Sanguinetti, A. Martin, H. Zbinden, and N. Gisin, “Quantum random number generation on a mobile phone,” Phys. Rev. X 4(3), 031056 (2014).
[Crossref]

2013 (2)

2012 (3)

2011 (3)

2010 (4)

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

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

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]

L. Larger and J. M. Dudley, “Nonlinear dynamics: Optoelectronic chaos,” Nature 465(7294), 41–42 (2010).
[Crossref] [PubMed]

2009 (2)

D. Sussillo and L. F. Abbott, “Generating coherent patterns of activity from chaotic neural networks,” Neuron 63(4), 544–557 (2009).
[Crossref] [PubMed]

P. Boffi, M. Ferrario, L. Marazzi, P. Martelli, P. Parolari, A. Righetti, R. Siano, and M. Martinelli, “Stable 100-Gb/s POLMUX-DQPSK transmission with automatic polarization stabilization,” IEEE Photonics Technol. Lett. 21(11), 745–747 (2009).
[Crossref]

2008 (1)

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. K. Lizé, R. Gomma, R. Kashyap, L. Palmer, and A. E. Willner, “Fast all-fiber polarization scrambling using re-entrant Lefèvre controller,” Opt. Commun. 279(1), 50–52 (2007).
[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]

1996 (1)

F. Heismann, “Compact electro-optic polarization scramblers for optically amplified lightwave systems,” J. Lightwave Technol. 14(8), 1801–1814 (1996).
[Crossref]

1994 (1)

F. Bruyere, O. Audouin, V. Letellier, G. Bassier, and P. Marmier, “Demonstration of an optimal polarization scrambler for long-haul optical amplifier systems,” IEEE Photonics Technol. Lett. 6(9), 1153–1155 (1994).
[Crossref]

1993 (1)

M. T. Rosenstein, J. J. Collins, and C. J. A. De Luca, “Practical method for calculating largest Lyapunov exponents from small data sets,” Physica D 65(1-2), 117–134 (1993).
[Crossref]

1989 (1)

W. H. J. Aarts and G. Khoe, “New endless polarization control method using three fiber squeezers,” J. Lightwave Technol. 7(7), 1033–1043 (1989).
[Crossref]

Aarts, W. H. J.

W. H. J. Aarts and G. Khoe, “New endless polarization control method using three fiber squeezers,” J. Lightwave Technol. 7(7), 1033–1043 (1989).
[Crossref]

Abbott, L. F.

D. Sussillo and L. F. Abbott, “Generating coherent patterns of activity from chaotic neural networks,” Neuron 63(4), 544–557 (2009).
[Crossref] [PubMed]

Akrout, A.

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6(1), 22381 (2016).
[Crossref] [PubMed]

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]

Amrani, F.

M. Guasoni, J. Garnier, B. Rumpf, D. Sugny, J. Fatome, F. Amrani, G. Millot, and A. Picozzi, “Incoherent Fermi-Pasta-Ulam recurrences and unconstrained thermalization mediated by strong phase-correlations,” Phys. Rev. X 7(1), 011025 (2017).
[Crossref]

Andersen, U. L.

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

Argyris, A.

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]

Assémat, E.

Audouin, O.

F. Bruyere, O. Audouin, V. Letellier, G. Bassier, and P. Marmier, “Demonstration of an optimal polarization scrambler for long-haul optical amplifier systems,” IEEE Photonics Technol. Lett. 6(9), 1153–1155 (1994).
[Crossref]

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]

Bai, B.

C. Wu, B. Bai, Y. Liu, X. Zhang, M. Yang, Y. Cao, J. Wang, S. Zhang, H. Zhou, X. Shi, X. Ma, J. G. Ren, J. Zhang, C. Z. Peng, J. Fan, Q. Zhang, and J. W. Pan, “Random Number Generation with Cosmic Photons,” Phys. Rev. Lett. 118(14), 140402 (2017).
[Crossref] [PubMed]

Bassier, G.

F. Bruyere, O. Audouin, V. Letellier, G. Bassier, and P. Marmier, “Demonstration of an optimal polarization scrambler for long-haul optical amplifier systems,” IEEE Photonics Technol. Lett. 6(9), 1153–1155 (1994).
[Crossref]

Blow, K. J.

Boffi, P.

P. Boffi, M. Ferrario, L. Marazzi, P. Martelli, P. Parolari, A. Righetti, R. Siano, and M. Martinelli, “Stable 100-Gb/s POLMUX-DQPSK transmission with automatic polarization stabilization,” IEEE Photonics Technol. Lett. 21(11), 745–747 (2009).
[Crossref]

Bony, P. Y.

M. Guasoni, P. Y. Bony, M. Gilles, A. Picozzi, and J. Fatome, “Fast and Chaotic Fiber-Based Nonlinear Polarization Scrambler,” IEEE J. Sel. Top. Quantum Electron. 22(2), 88 (2016).
[Crossref]

Bony, P.-Y.

P.-Y. Bony, M. Guasoni, P. Morin, D. Sugny, A. Picozzi, H. R. Jauslin, S. Pitois, and J. Fatome, “Temporal spying and concealing process in fibre-optic data transmission systems through polarization bypass,” Nat. Commun. 5, 4678 (2014).
[Crossref] [PubMed]

P.-Y. Bony, M. Guasoni, E. Assémat, S. Pitois, D. Sugny, A. Picozzi, H. R. Jauslin, and J. Fatome, “Optical flip-flop memory and data packet switching operation based on polarization bistability in a telecomunication optical fiber,” J. Opt. Soc. Am. B 30(8), 2318–2325 (2013).
[Crossref]

Bowles, J.

T. Lunghi, J. B. Brask, C. C. W. Lim, Q. Lavigne, J. Bowles, A. Martin, H. Zbinden, and N. Brunner, “Self-testing quantum random number generator,” Phys. Rev. Lett. 114(15), 150501 (2015).
[Crossref] [PubMed]

Brask, J. B.

T. Lunghi, J. B. Brask, C. C. W. Lim, Q. Lavigne, J. Bowles, A. Martin, H. Zbinden, and N. Brunner, “Self-testing quantum random number generator,” Phys. Rev. Lett. 114(15), 150501 (2015).
[Crossref] [PubMed]

Brunner, N.

T. Lunghi, J. B. Brask, C. C. W. Lim, Q. Lavigne, J. Bowles, A. Martin, H. Zbinden, and N. Brunner, “Self-testing quantum random number generator,” Phys. Rev. Lett. 114(15), 150501 (2015).
[Crossref] [PubMed]

Bruyere, F.

F. Bruyere, O. Audouin, V. Letellier, G. Bassier, and P. Marmier, “Demonstration of an optimal polarization scrambler for long-haul optical amplifier systems,” IEEE Photonics Technol. Lett. 6(9), 1153–1155 (1994).
[Crossref]

Cao, Y.

C. Wu, B. Bai, Y. Liu, X. Zhang, M. Yang, Y. Cao, J. Wang, S. Zhang, H. Zhou, X. Shi, X. Ma, J. G. Ren, J. Zhang, C. Z. Peng, J. Fan, Q. Zhang, and J. W. Pan, “Random Number Generation with Cosmic Photons,” Phys. Rev. Lett. 118(14), 140402 (2017).
[Crossref] [PubMed]

Chu, W. S.

Cohen, A. B.

Cohen, E.

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]

Colet, P.

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]

Collins, J. J.

M. T. Rosenstein, J. J. Collins, and C. J. A. De Luca, “Practical method for calculating largest Lyapunov exponents from small data sets,” Physica D 65(1-2), 117–134 (1993).
[Crossref]

Davis, P.

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]

De Luca, C. J. A.

M. T. Rosenstein, J. J. Collins, and C. J. A. De Luca, “Practical method for calculating largest Lyapunov exponents from small data sets,” Physica D 65(1-2), 117–134 (1993).
[Crossref]

Dong, R.

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

Dudley, J. M.

Duport, F.

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6(1), 22381 (2016).
[Crossref] [PubMed]

Fan, J.

C. Wu, B. Bai, Y. Liu, X. Zhang, M. Yang, Y. Cao, J. Wang, S. Zhang, H. Zhou, X. Shi, X. Ma, J. G. Ren, J. Zhang, C. Z. Peng, J. Fan, Q. Zhang, and J. W. Pan, “Random Number Generation with Cosmic Photons,” Phys. Rev. Lett. 118(14), 140402 (2017).
[Crossref] [PubMed]

Fatome, J.

M. Guasoni, J. Garnier, B. Rumpf, D. Sugny, J. Fatome, F. Amrani, G. Millot, and A. Picozzi, “Incoherent Fermi-Pasta-Ulam recurrences and unconstrained thermalization mediated by strong phase-correlations,” Phys. Rev. X 7(1), 011025 (2017).
[Crossref]

M. Guasoni, P. Y. Bony, M. Gilles, A. Picozzi, and J. Fatome, “Fast and Chaotic Fiber-Based Nonlinear Polarization Scrambler,” IEEE J. Sel. Top. Quantum Electron. 22(2), 88 (2016).
[Crossref]

P.-Y. Bony, M. Guasoni, P. Morin, D. Sugny, A. Picozzi, H. R. Jauslin, S. Pitois, and J. Fatome, “Temporal spying and concealing process in fibre-optic data transmission systems through polarization bypass,” Nat. Commun. 5, 4678 (2014).
[Crossref] [PubMed]

P.-Y. Bony, M. Guasoni, E. Assémat, S. Pitois, D. Sugny, A. Picozzi, H. R. Jauslin, and J. Fatome, “Optical flip-flop memory and data packet switching operation based on polarization bistability in a telecomunication optical fiber,” J. Opt. Soc. Am. B 30(8), 2318–2325 (2013).
[Crossref]

J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber Omnipolarizer,” Sci. Rep. 2(1), 938 (2012).
[Crossref] [PubMed]

Ferrario, M.

P. Boffi, M. Ferrario, L. Marazzi, P. Martelli, P. Parolari, A. Righetti, R. Siano, and M. Martinelli, “Stable 100-Gb/s POLMUX-DQPSK transmission with automatic polarization stabilization,” IEEE Photonics Technol. Lett. 21(11), 745–747 (2009).
[Crossref]

Fischer, I.

L. Keuninckx, M. C. Soriano, I. Fischer, C. R. Mirasso, R. M. Nguimdo, and G. Van der Sande, “Encryption key distribution via chaos synchronization,” Sci. Rep. 7, 43428 (2017).
[Crossref] [PubMed]

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Kozlov, V. V.

J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber Omnipolarizer,” Sci. Rep. 2(1), 938 (2012).
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B. Wetzel, K. J. Blow, S. K. Turitsyn, G. Millot, L. Larger, and J. M. Dudley, “Random walks and random numbers from supercontinuum generation,” Opt. Express 20(10), 11143–11152 (2012).
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F. Bruyere, O. Audouin, V. Letellier, G. Bassier, and P. Marmier, “Demonstration of an optimal polarization scrambler for long-haul optical amplifier systems,” IEEE Photonics Technol. Lett. 6(9), 1153–1155 (1994).
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Leuchs, G.

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

Z. Li, J. Mo, Y. Wang, and C. Lu, “Experimental evaluation of the effect of polarization scrambling speed on the performance of PMD mitigation using FEC,” in Optical Fiber Commun. Conference (2004).

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T. Lunghi, J. B. Brask, C. C. W. Lim, Q. Lavigne, J. Bowles, A. Martin, H. Zbinden, and N. Brunner, “Self-testing quantum random number generator,” Phys. Rev. Lett. 114(15), 150501 (2015).
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C. Wu, B. Bai, Y. Liu, X. Zhang, M. Yang, Y. Cao, J. Wang, S. Zhang, H. Zhou, X. Shi, X. Ma, J. G. Ren, J. Zhang, C. Z. Peng, J. Fan, Q. Zhang, and J. W. Pan, “Random Number Generation with Cosmic Photons,” Phys. Rev. Lett. 118(14), 140402 (2017).
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Y. K. Lizé, R. Gomma, R. Kashyap, L. Palmer, and A. E. Willner, “Fast all-fiber polarization scrambling using re-entrant Lefèvre controller,” Opt. Commun. 279(1), 50–52 (2007).
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Z. Li, J. Mo, Y. Wang, and C. Lu, “Experimental evaluation of the effect of polarization scrambling speed on the performance of PMD mitigation using FEC,” in Optical Fiber Commun. Conference (2004).

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T. Lunghi, J. B. Brask, C. C. W. Lim, Q. Lavigne, J. Bowles, A. Martin, H. Zbinden, and N. Brunner, “Self-testing quantum random number generator,” Phys. Rev. Lett. 114(15), 150501 (2015).
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C. Wu, B. Bai, Y. Liu, X. Zhang, M. Yang, Y. Cao, J. Wang, S. Zhang, H. Zhou, X. Shi, X. Ma, J. G. Ren, J. Zhang, C. Z. Peng, J. Fan, Q. Zhang, and J. W. Pan, “Random Number Generation with Cosmic Photons,” Phys. Rev. Lett. 118(14), 140402 (2017).
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F. Bruyere, O. Audouin, V. Letellier, G. Bassier, and P. Marmier, “Demonstration of an optimal polarization scrambler for long-haul optical amplifier systems,” IEEE Photonics Technol. Lett. 6(9), 1153–1155 (1994).
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C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
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P. Boffi, M. Ferrario, L. Marazzi, P. Martelli, P. Parolari, A. Righetti, R. Siano, and M. Martinelli, “Stable 100-Gb/s POLMUX-DQPSK transmission with automatic polarization stabilization,” IEEE Photonics Technol. Lett. 21(11), 745–747 (2009).
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T. Lunghi, J. B. Brask, C. C. W. Lim, Q. Lavigne, J. Bowles, A. Martin, H. Zbinden, and N. Brunner, “Self-testing quantum random number generator,” Phys. Rev. Lett. 114(15), 150501 (2015).
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P. Boffi, M. Ferrario, L. Marazzi, P. Martelli, P. Parolari, A. Righetti, R. Siano, and M. Martinelli, “Stable 100-Gb/s POLMUX-DQPSK transmission with automatic polarization stabilization,” IEEE Photonics Technol. Lett. 21(11), 745–747 (2009).
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F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6(1), 22381 (2016).
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Mauerer, W.

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
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M. Guasoni, J. Garnier, B. Rumpf, D. Sugny, J. Fatome, F. Amrani, G. Millot, and A. Picozzi, “Incoherent Fermi-Pasta-Ulam recurrences and unconstrained thermalization mediated by strong phase-correlations,” Phys. Rev. X 7(1), 011025 (2017).
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J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber Omnipolarizer,” Sci. Rep. 2(1), 938 (2012).
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Mirasso, C. R.

L. Keuninckx, M. C. Soriano, I. Fischer, C. R. Mirasso, R. M. Nguimdo, and G. Van der Sande, “Encryption key distribution via chaos synchronization,” Sci. Rep. 7, 43428 (2017).
[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]

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R. Noé, B. Koch, D. Sandel, and V. Mirvoda, “100-krad/s endless polarisation tracking with miniaturised module card,” Electron. Lett. 47(14), 813–814 (2011).
[Crossref]

Mo, J.

Z. Li, J. Mo, Y. Wang, and C. Lu, “Experimental evaluation of the effect of polarization scrambling speed on the performance of PMD mitigation using FEC,” in Optical Fiber Commun. Conference (2004).

Morin, P.

P.-Y. Bony, M. Guasoni, P. Morin, D. Sugny, A. Picozzi, H. R. Jauslin, S. Pitois, and J. Fatome, “Temporal spying and concealing process in fibre-optic data transmission systems through polarization bypass,” Nat. Commun. 5, 4678 (2014).
[Crossref] [PubMed]

J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber Omnipolarizer,” Sci. Rep. 2(1), 938 (2012).
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Naito, 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]

Nguimdo, R. M.

L. Keuninckx, M. C. Soriano, I. Fischer, C. R. Mirasso, R. M. Nguimdo, and G. Van der Sande, “Encryption key distribution via chaos synchronization,” Sci. Rep. 7, 43428 (2017).
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R. Noé, B. Koch, D. Sandel, and V. Mirvoda, “100-krad/s endless polarisation tracking with miniaturised module card,” Electron. Lett. 47(14), 813–814 (2011).
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Oh, M. C.

Oowada, I.

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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Y. K. Lizé, R. Gomma, R. Kashyap, L. Palmer, and A. E. Willner, “Fast all-fiber polarization scrambling using re-entrant Lefèvre controller,” Opt. Commun. 279(1), 50–52 (2007).
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C. Wu, B. Bai, Y. Liu, X. Zhang, M. Yang, Y. Cao, J. Wang, S. Zhang, H. Zhou, X. Shi, X. Ma, J. G. Ren, J. Zhang, C. Z. Peng, J. Fan, Q. Zhang, and J. W. Pan, “Random Number Generation with Cosmic Photons,” Phys. Rev. Lett. 118(14), 140402 (2017).
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M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
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Parolari, P.

P. Boffi, M. Ferrario, L. Marazzi, P. Martelli, P. Parolari, A. Righetti, R. Siano, and M. Martinelli, “Stable 100-Gb/s POLMUX-DQPSK transmission with automatic polarization stabilization,” IEEE Photonics Technol. Lett. 21(11), 745–747 (2009).
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C. Wu, B. Bai, Y. Liu, X. Zhang, M. Yang, Y. Cao, J. Wang, S. Zhang, H. Zhou, X. Shi, X. Ma, J. G. Ren, J. Zhang, C. Z. Peng, J. Fan, Q. Zhang, and J. W. Pan, “Random Number Generation with Cosmic Photons,” Phys. Rev. Lett. 118(14), 140402 (2017).
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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).
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M. Guasoni, J. Garnier, B. Rumpf, D. Sugny, J. Fatome, F. Amrani, G. Millot, and A. Picozzi, “Incoherent Fermi-Pasta-Ulam recurrences and unconstrained thermalization mediated by strong phase-correlations,” Phys. Rev. X 7(1), 011025 (2017).
[Crossref]

M. Guasoni, P. Y. Bony, M. Gilles, A. Picozzi, and J. Fatome, “Fast and Chaotic Fiber-Based Nonlinear Polarization Scrambler,” IEEE J. Sel. Top. Quantum Electron. 22(2), 88 (2016).
[Crossref]

P.-Y. Bony, M. Guasoni, P. Morin, D. Sugny, A. Picozzi, H. R. Jauslin, S. Pitois, and J. Fatome, “Temporal spying and concealing process in fibre-optic data transmission systems through polarization bypass,” Nat. Commun. 5, 4678 (2014).
[Crossref] [PubMed]

P.-Y. Bony, M. Guasoni, E. Assémat, S. Pitois, D. Sugny, A. Picozzi, H. R. Jauslin, and J. Fatome, “Optical flip-flop memory and data packet switching operation based on polarization bistability in a telecomunication optical fiber,” J. Opt. Soc. Am. B 30(8), 2318–2325 (2013).
[Crossref]

J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber Omnipolarizer,” Sci. Rep. 2(1), 938 (2012).
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P.-Y. Bony, M. Guasoni, P. Morin, D. Sugny, A. Picozzi, H. R. Jauslin, S. Pitois, and J. Fatome, “Temporal spying and concealing process in fibre-optic data transmission systems through polarization bypass,” Nat. Commun. 5, 4678 (2014).
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P.-Y. Bony, M. Guasoni, E. Assémat, S. Pitois, D. Sugny, A. Picozzi, H. R. Jauslin, and J. Fatome, “Optical flip-flop memory and data packet switching operation based on polarization bistability in a telecomunication optical fiber,” J. Opt. Soc. Am. B 30(8), 2318–2325 (2013).
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J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber Omnipolarizer,” Sci. Rep. 2(1), 938 (2012).
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I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
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C. Wu, B. Bai, Y. Liu, X. Zhang, M. Yang, Y. Cao, J. Wang, S. Zhang, H. Zhou, X. Shi, X. Ma, J. G. Ren, J. Zhang, C. Z. Peng, J. Fan, Q. Zhang, and J. W. Pan, “Random Number Generation with Cosmic Photons,” Phys. Rev. Lett. 118(14), 140402 (2017).
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P. Boffi, M. Ferrario, L. Marazzi, P. Martelli, P. Parolari, A. Righetti, R. Siano, and M. Martinelli, “Stable 100-Gb/s POLMUX-DQPSK transmission with automatic polarization stabilization,” IEEE Photonics Technol. Lett. 21(11), 745–747 (2009).
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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).
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M. T. Rosenstein, J. J. Collins, and C. J. A. De Luca, “Practical method for calculating largest Lyapunov exponents from small data sets,” Physica D 65(1-2), 117–134 (1993).
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Rumpf, B.

M. Guasoni, J. Garnier, B. Rumpf, D. Sugny, J. Fatome, F. Amrani, G. Millot, and A. Picozzi, “Incoherent Fermi-Pasta-Ulam recurrences and unconstrained thermalization mediated by strong phase-correlations,” Phys. Rev. X 7(1), 011025 (2017).
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Salevan, J. C.

Sandel, D.

R. Noé, B. Koch, D. Sandel, and V. Mirvoda, “100-krad/s endless polarisation tracking with miniaturised module card,” Electron. Lett. 47(14), 813–814 (2011).
[Crossref]

Sanguinetti, B.

B. Sanguinetti, A. Martin, H. Zbinden, and N. Gisin, “Quantum random number generation on a mobile phone,” Phys. Rev. X 4(3), 031056 (2014).
[Crossref]

Sciamanna, M.

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
[Crossref]

Shi, X.

C. Wu, B. Bai, Y. Liu, X. Zhang, M. Yang, Y. Cao, J. Wang, S. Zhang, H. Zhou, X. Shi, X. Ma, J. G. Ren, J. Zhang, C. Z. Peng, J. Fan, Q. Zhang, and J. W. Pan, “Random Number Generation with Cosmic Photons,” Phys. Rev. Lett. 118(14), 140402 (2017).
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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.

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]

Siano, R.

P. Boffi, M. Ferrario, L. Marazzi, P. Martelli, P. Parolari, A. Righetti, R. Siano, and M. Martinelli, “Stable 100-Gb/s POLMUX-DQPSK transmission with automatic polarization stabilization,” IEEE Photonics Technol. Lett. 21(11), 745–747 (2009).
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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, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

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L. Keuninckx, M. C. Soriano, I. Fischer, C. R. Mirasso, R. M. Nguimdo, and G. Van der Sande, “Encryption key distribution via chaos synchronization,” Sci. Rep. 7, 43428 (2017).
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M. Guasoni, J. Garnier, B. Rumpf, D. Sugny, J. Fatome, F. Amrani, G. Millot, and A. Picozzi, “Incoherent Fermi-Pasta-Ulam recurrences and unconstrained thermalization mediated by strong phase-correlations,” Phys. Rev. X 7(1), 011025 (2017).
[Crossref]

P.-Y. Bony, M. Guasoni, P. Morin, D. Sugny, A. Picozzi, H. R. Jauslin, S. Pitois, and J. Fatome, “Temporal spying and concealing process in fibre-optic data transmission systems through polarization bypass,” Nat. Commun. 5, 4678 (2014).
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P.-Y. Bony, M. Guasoni, E. Assémat, S. Pitois, D. Sugny, A. Picozzi, H. R. Jauslin, and J. Fatome, “Optical flip-flop memory and data packet switching operation based on polarization bistability in a telecomunication optical fiber,” J. Opt. Soc. Am. B 30(8), 2318–2325 (2013).
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J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber Omnipolarizer,” Sci. Rep. 2(1), 938 (2012).
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C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and 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. 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).
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M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
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Uchida, A.

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[Crossref]

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L. Keuninckx, M. C. Soriano, I. Fischer, C. R. Mirasso, R. M. Nguimdo, and G. Van der Sande, “Encryption key distribution via chaos synchronization,” Sci. Rep. 7, 43428 (2017).
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M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
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J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber Omnipolarizer,” Sci. Rep. 2(1), 938 (2012).
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Williams, C. R. S.

Willner, A. E.

Y. K. Lizé, R. Gomma, R. Kashyap, L. Palmer, and A. E. Willner, “Fast all-fiber polarization scrambling using re-entrant Lefèvre controller,” Opt. Commun. 279(1), 50–52 (2007).
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C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
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C. Wu, B. Bai, Y. Liu, X. Zhang, M. Yang, Y. Cao, J. Wang, S. Zhang, H. Zhou, X. Shi, X. Ma, J. G. Ren, J. Zhang, C. Z. Peng, J. Fan, Q. Zhang, and J. W. Pan, “Random Number Generation with Cosmic Photons,” Phys. Rev. Lett. 118(14), 140402 (2017).
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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, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[Crossref]

Yoshimura, 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).
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Zbinden, H.

T. Lunghi, J. B. Brask, C. C. W. Lim, Q. Lavigne, J. Bowles, A. Martin, H. Zbinden, and N. Brunner, “Self-testing quantum random number generator,” Phys. Rev. Lett. 114(15), 150501 (2015).
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B. Sanguinetti, A. Martin, H. Zbinden, and N. Gisin, “Quantum random number generation on a mobile phone,” Phys. Rev. X 4(3), 031056 (2014).
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Zhang, J.

C. Wu, B. Bai, Y. Liu, X. Zhang, M. Yang, Y. Cao, J. Wang, S. Zhang, H. Zhou, X. Shi, X. Ma, J. G. Ren, J. Zhang, C. Z. Peng, J. Fan, Q. Zhang, and J. W. Pan, “Random Number Generation with Cosmic Photons,” Phys. Rev. Lett. 118(14), 140402 (2017).
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Zhang, Q.

C. Wu, B. Bai, Y. Liu, X. Zhang, M. Yang, Y. Cao, J. Wang, S. Zhang, H. Zhou, X. Shi, X. Ma, J. G. Ren, J. Zhang, C. Z. Peng, J. Fan, Q. Zhang, and J. W. Pan, “Random Number Generation with Cosmic Photons,” Phys. Rev. Lett. 118(14), 140402 (2017).
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Zhang, S.

C. Wu, B. Bai, Y. Liu, X. Zhang, M. Yang, Y. Cao, J. Wang, S. Zhang, H. Zhou, X. Shi, X. Ma, J. G. Ren, J. Zhang, C. Z. Peng, J. Fan, Q. Zhang, and J. W. Pan, “Random Number Generation with Cosmic Photons,” Phys. Rev. Lett. 118(14), 140402 (2017).
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Zhang, X.

C. Wu, B. Bai, Y. Liu, X. Zhang, M. Yang, Y. Cao, J. Wang, S. Zhang, H. Zhou, X. Shi, X. Ma, J. G. Ren, J. Zhang, C. Z. Peng, J. Fan, Q. Zhang, and J. W. Pan, “Random Number Generation with Cosmic Photons,” Phys. Rev. Lett. 118(14), 140402 (2017).
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Zhou, H.

C. Wu, B. Bai, Y. Liu, X. Zhang, M. Yang, Y. Cao, J. Wang, S. Zhang, H. Zhou, X. Shi, X. Ma, J. G. Ren, J. Zhang, C. Z. Peng, J. Fan, Q. Zhang, and J. W. Pan, “Random Number Generation with Cosmic Photons,” Phys. Rev. Lett. 118(14), 140402 (2017).
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M. Guasoni, P. Y. Bony, M. Gilles, A. Picozzi, and J. Fatome, “Fast and Chaotic Fiber-Based Nonlinear Polarization Scrambler,” IEEE J. Sel. Top. Quantum Electron. 22(2), 88 (2016).
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F. Bruyere, O. Audouin, V. Letellier, G. Bassier, and P. Marmier, “Demonstration of an optimal polarization scrambler for long-haul optical amplifier systems,” IEEE Photonics Technol. Lett. 6(9), 1153–1155 (1994).
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P.-Y. Bony, M. Guasoni, P. Morin, D. Sugny, A. Picozzi, H. R. Jauslin, S. Pitois, and J. Fatome, “Temporal spying and concealing process in fibre-optic data transmission systems through polarization bypass,” Nat. Commun. 5, 4678 (2014).
[Crossref] [PubMed]

Nat. Photonics (4)

C. Gabriel, C. Wittmann, D. Sych, R. Dong, W. Mauerer, U. L. Andersen, C. Marquardt, and G. Leuchs, “A generator for unique quantum random numbers based on vacuum states,” Nat. Photonics 4(10), 711–715 (2010).
[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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M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
[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).
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D. Sussillo and L. F. Abbott, “Generating coherent patterns of activity from chaotic neural networks,” Neuron 63(4), 544–557 (2009).
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Opt. Commun. (1)

Y. K. Lizé, R. Gomma, R. Kashyap, L. Palmer, and A. E. Willner, “Fast all-fiber polarization scrambling using re-entrant Lefèvre controller,” Opt. Commun. 279(1), 50–52 (2007).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. Lett. (2)

T. Lunghi, J. B. Brask, C. C. W. Lim, Q. Lavigne, J. Bowles, A. Martin, H. Zbinden, and N. Brunner, “Self-testing quantum random number generator,” Phys. Rev. Lett. 114(15), 150501 (2015).
[Crossref] [PubMed]

C. Wu, B. Bai, Y. Liu, X. Zhang, M. Yang, Y. Cao, J. Wang, S. Zhang, H. Zhou, X. Shi, X. Ma, J. G. Ren, J. Zhang, C. Z. Peng, J. Fan, Q. Zhang, and J. W. Pan, “Random Number Generation with Cosmic Photons,” Phys. Rev. Lett. 118(14), 140402 (2017).
[Crossref] [PubMed]

Phys. Rev. X (2)

B. Sanguinetti, A. Martin, H. Zbinden, and N. Gisin, “Quantum random number generation on a mobile phone,” Phys. Rev. X 4(3), 031056 (2014).
[Crossref]

M. Guasoni, J. Garnier, B. Rumpf, D. Sugny, J. Fatome, F. Amrani, G. Millot, and A. Picozzi, “Incoherent Fermi-Pasta-Ulam recurrences and unconstrained thermalization mediated by strong phase-correlations,” Phys. Rev. X 7(1), 011025 (2017).
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J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber Omnipolarizer,” Sci. Rep. 2(1), 938 (2012).
[Crossref] [PubMed]

F. Duport, A. Smerieri, A. Akrout, M. Haelterman, and S. Massar, “Fully analogue photonic reservoir computer,” Sci. Rep. 6(1), 22381 (2016).
[Crossref] [PubMed]

L. Keuninckx, M. C. Soriano, I. Fischer, C. R. Mirasso, R. M. Nguimdo, and G. Van der Sande, “Encryption key distribution via chaos synchronization,” Sci. Rep. 7, 43428 (2017).
[Crossref] [PubMed]

Other (4)

Z. Li, J. Mo, Y. Wang, and C. Lu, “Experimental evaluation of the effect of polarization scrambling speed on the performance of PMD mitigation using FEC,” in Optical Fiber Commun. Conference (2004).

J. Morosi, A. Akrout, A. Picozzi, M. Gilles, M. Guasoni, and J. Fatome, “Polarization Chaos in Nonlinear Optical Fibers Induced by a Reflective Delayed Loop,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2017), paper SM2M.3.
[Crossref]

http://www.phy.duke.edu/~rgb/General/dieharder.php

Dataset 1: Results of the dieharder tests for the experimental 1-billion bit sequence generated from polarization chaos https://doi.org/10.6084/m9.figshare.5725807 .

Supplementary Material (1)

NameDescription
» Dataset 1       Results of the dieharder tests

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Figures (8)

Fig. 1
Fig. 1 Principle of operation: The signal wave S is injected and interacts in the fiber of length L with its backward replica J generated by an amplified reflective delayed loop R (with gain g and a delay determined by the fiber length Ld).
Fig. 2
Fig. 2 Experimental setup. ASE: Amplified spontaneous noise emission, BPF: bandpass filter, Pol: Polarizer, PPG: Pulse pattern generator, MLFL: Mode-locked fiber laser, PM: Phase modulator, IM: Intensity modulator, EDFA: Erbium-doped fiber amplifier, CIR: Optical circulator, HNLF: highly nonlinear fiber, PC: polarization controller, SSMF: Standard single mode fiber, RBG: Random bit generation, BER: Bit-error-rate.
Fig. 3
Fig. 3 (a) Bifurcation diagram of the system: Projection of the experimentally measured output SOP in the S2-S3 plane (b-e) Poincaré sphere for different values of the reflective amplification factor g as well as corresponding RF spectrum of the S1 component: (b) g = 1, (c) g = 10, (d) g = 17 and (e) g = 53.
Fig. 4
Fig. 4 (Top line) DOP measured at the output of the system as a function of the amplification factor g for the 0-delay configuration (a) a 1-km long delay-line (b) and 5-km long delay-line (c), respectively. (Bottom line) Scrambling speed as a function of amplification factor g (same convention as for DOP measurements). The red solid-lines correspond to the experimental data averaged over 100 realizations, while the shaded areas represent respective fluctuations (standard deviation in grey and maximal excursion in ochre). The black circles correspond to the numerical simulation results averaged over 24 realizations.
Fig. 5
Fig. 5 (a) Scrambling speed (blue circles) and corresponding DOP (red triangles) as a function of fiber length used as delay-line within the reflective loop of the Omnipolarizer. The amplification factor g is kept constant to g = 53. Numerical simulations are displayed with blue stars and red crosses, respectively (b) Corresponding experimental Lyapunov coefficient L as a function of the fiber length inserted into the reflective loop. All measurements have been averaged over 100 realizations (c) Typical temporal evolution of the S1 parameter at maximum scrambling speed and 5 km of delay.
Fig. 6
Fig. 6 (a) Input Poincaré sphere of the 10-Gbit/s RZ signal (b) Output SOP in scrambling regime for g = 50 (c&d) Output eye-diagrams of the 10-Gbit/s signal recorded in pump OFF (c) and pump ON configuration (d) (e) BER measurements as a function of the average power incoming on the receiver, back-to-back configuration (blue circles), pump OFF (red dots) and pump ON: 29 dBm (yellow squares) and 30 dBm (purple diamonds).
Fig. 7
Fig. 7 (a) In blue, evolution of the S1 parameter over time. In red sampled values taken in correspondence of rising edges of an ad hoc defined clock (in black). (b) Random sequence generated after thresholding samples chosen in (a). In (c) and (d) autocorrelation and cross-correlation functions of different random sequences generated in experiments.
Fig. 8
Fig. 8 Dieharder benchmark tests results for the 109 experimental binary sequence generated from polarization chaos.

Equations (3)

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{ c 1 t S+ z S=γS( DJ )αS c 1 t  J z  J=γJ( DS )αJ
DOP= S 1 ( t ) 2 + S 2 ( t ) 2 + S 3 ( t ) 2 S 0 ( t )
V scr =2arcsin( 1 2 s (L,t) t )

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