Abstract

We experimentally demonstrate a reproducible broadband optical noise-like signal generation scheme whereby dispersion induced phase modulation to intensity modulation conversion and an electro-optic nonlinear transform are utilized to post process a binary random sequence. A flat spectrum and a symmetrical distribution of the generated analog noise-like signal can be observed. Moreover, Gaussian-like probability distribution function can be obtained by using the central limit theorem. The influences of the digital input and the analog parameters on complexity performance of the generated analogue noise are discussed in detail. Finally, the impact of key parameters on the reproducibility of the system is discussed. The proposed scheme could be a more controllable way to generate broadband optical noise-like signal, and has potential to be applied in various real world applications.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (1)

2016 (3)

G. Kaddoum, “Design and performance analysis of a multiuser OFDM based differential chaos shift keying communication system,” IEEE Trans. Commun. 64(1), 249–260 (2016).

X. Jiang, D. Liu, M. Cheng, L. Deng, S. Fu, M. Zhang, M. Tang, and P. Shum, “High-frequency reverse-time chaos generation using an optical matched filter,” Opt. Lett. 41(6), 1157–1160 (2016).
[PubMed]

C. H. Cheng, Y. C. Chen, and F. Y. Lin, “Generation of uncorrelated multichannel chaos by electrical heterodyning for multiple-input–multiple-output chaos radar application,” IEEE Photonics J. 8(1), 1–14 (2016).

2015 (2)

T. Yao, D. Zhu, D. Ben, and S. Pan, “Distributed MIMO chaotic radar based on wavelength-division multiplexing technology,” Opt. Lett. 40(8), 1631–1634 (2015).
[PubMed]

A. Wang, B. Wang, L. Li, Y. Wang, and K. A. Shore, “Optical heterodyne generation of high-dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 1–10 (2015).

2014 (1)

2013 (2)

B. Wu, Z. Wang, Y. Tian, M. P. Fok, B. J. Shastri, D. R. Kanoff, and P. R. Prucnal, “Optical steganography based on amplified spontaneous emission noise,” Opt. Express 21(2), 2065–2071 (2013).
[PubMed]

A. Wang, Y. Wang, Y. Yang, M. Zhang, H. Xu, and B. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).

2012 (8)

J. J. Suárez-Vargas, B. A. Márquez, and J. A. González, “Highly complex optical signal generation using electro-optical systems with non-linear, non-invertible transmission functions,” Appl. Phys. Lett. 101(7), 071115 (2012).

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

L. Zhang, X. Xin, B. Liu, and J. Yu, “Physical-enhanced secure strategy in an OFDM-PON,” Opt. Express 20(3), 2255–2265 (2012).
[PubMed]

P. H. Chen, M. C. Shastry, C. P. Lai, and R. M. Narayanan, “A portable real-time digital noise radar system for through-the-wall imaging,” IEEE Trans. Geosci. Remote Sens. 50(10), 4123–4134 (2012).

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

A. Wang, N. Wang, Y. Yang, B. Wang, M. Zhang, and Y. Wang, “Precise fault location in WDM-PON by utilizing wavelength tunable chaotic laser,” J. Lightwave Technol. 30(21), 3420–3426 (2012).

L. Zhang, X. Xin, B. Liu, and X. Yin, “Physical secure enhancement in optical OFDMA-PON based on two-dimensional scrambling,” Opt. Express 20(26), B32–B37 (2012).
[PubMed]

C. Fu, J. J. Chen, H. Zou, W. H. Meng, Y. F. Zhan, and Y. W. Yu, “A chaos-based digital image encryption scheme with an improved diffusion strategy,” Opt. Express 20(3), 2363–2378 (2012).
[PubMed]

2011 (1)

M. Zhang, T. Liu, P. Li, A. Wang, J. Zhang, and Y. Wang, “Generation of broadband chaotic laser using dual-wavelength optically injected Fabry–Pérot laser diode with optical feedback,” IEEE Photonics Technol. Lett. 23(24), 1872–1874 (2011).

2010 (1)

2009 (1)

2008 (1)

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

2006 (3)

D. U. Lee, J. D. Villasenor, W. Luk, and H. W. Philip, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659–671 (2006).

D. U. Lee, J. D. Villasenor, W. Luk, and P. H. W. Leong, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659–671 (2006).

N. J. Corron, S. T. Hayes, S. D. Pethel, and J. N. Blakely, “Chaos without nonlinear dynamics,” Phys. Rev. Lett. 97(2), 024101 (2006).
[PubMed]

2005 (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).
[PubMed]

Y. C. Kouomou, P. Colet, L. Larger, and N. Gastaud, “Chaotic breathers in delayed electro-optical systems,” Phys. Rev. Lett. 95(20), 203903 (2005).
[PubMed]

2004 (2)

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

Y. Cao, W. W. Tung, J. B. Gao, V. A. Protopopescu, and L. M. Hively, “Detecting dynamical changes in time series using the permutation entropy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4 Pt 2), 046217 (2004).
[PubMed]

1997 (2)

B. Jung, H. P. Lenhof, P. Müller, and C. Rüb, “Langevin dynamics simulations of macromolecules on parallel computers,” Macromol. Theory Simul. 6(2), 507–521 (1997).

A. Brace, D. Gatarek, and M. Musiela, “The market model of interest rate dynamics,” Math. Finance 7(2), 127–155 (1997).

1991 (1)

S. M. Pincus, “Approximate entropy as a measure of system complexity,” Proc. Natl. Acad. Sci. U.S.A. 88(6), 2297–2301 (1991).
[PubMed]

1980 (1)

J. R. Dormand and P. J. Prince, “A family of embedded Runge-Kutta formulae,” J. Comput. Appl. Math. 6(1), 19–26 (1980).

1975 (1)

G. H. Tomlinson and P. Galvin, “Elimination of skewing in the amplitude distributions of long m sequences subjected to low-pass filtering,” Electron. Lett. 11(4), 77–78 (1975).

1963 (1)

E. N. Lorenz, “Deterministic nonperiodic flow,” J. Atmos. Sci. 20(2), 130–141 (1963).

1962 (1)

R. Gallager, “Low-density parity-check codes,” IEEE Trans. Inf. Theory 8(1), 21–28 (1962).

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).
[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).
[PubMed]

Ben, D.

Blakely, J. N.

N. J. Corron, S. T. Hayes, S. D. Pethel, and J. N. Blakely, “Chaos without nonlinear dynamics,” Phys. Rev. Lett. 97(2), 024101 (2006).
[PubMed]

Brace, A.

A. Brace, D. Gatarek, and M. Musiela, “The market model of interest rate dynamics,” Math. Finance 7(2), 127–155 (1997).

Cao, Y.

Y. Cao, W. W. Tung, J. B. Gao, V. A. Protopopescu, and L. M. Hively, “Detecting dynamical changes in time series using the permutation entropy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4 Pt 2), 046217 (2004).
[PubMed]

Chang, M. P.

Chao, Y. K.

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

Chen, J. J.

Chen, P. H.

P. H. Chen, M. C. Shastry, C. P. Lai, and R. M. Narayanan, “A portable real-time digital noise radar system for through-the-wall imaging,” IEEE Trans. Geosci. Remote Sens. 50(10), 4123–4134 (2012).

Chen, Y. C.

C. H. Cheng, Y. C. Chen, and F. Y. Lin, “Generation of uncorrelated multichannel chaos by electrical heterodyning for multiple-input–multiple-output chaos radar application,” IEEE Photonics J. 8(1), 1–14 (2016).

Cheng, C. H.

C. H. Cheng, Y. C. Chen, and F. Y. Lin, “Generation of uncorrelated multichannel chaos by electrical heterodyning for multiple-input–multiple-output chaos radar application,” IEEE Photonics J. 8(1), 1–14 (2016).

Cheng, M.

Chi, H.

Colet, P.

Y. C. Kouomou, P. Colet, L. Larger, and N. Gastaud, “Chaotic breathers in delayed electro-optical systems,” Phys. Rev. Lett. 95(20), 203903 (2005).
[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).
[PubMed]

Corron, N. J.

N. J. Corron, S. T. Hayes, S. D. Pethel, and J. N. Blakely, “Chaos without nonlinear dynamics,” Phys. Rev. Lett. 97(2), 024101 (2006).
[PubMed]

Davis, R. H.

P. D. Roberts and R. H. Davis, “Statistical properties of smoothed maximal-length linear binary sequences, ” Proc. IEE113(1), 190–196 (1966).

Deng, L.

Dormand, J. R.

J. R. Dormand and P. J. Prince, “A family of embedded Runge-Kutta formulae,” J. Comput. Appl. Math. 6(1), 19–26 (1980).

Fischer, I.

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).
[PubMed]

Fok, M. P.

Fu, C.

Fu, S.

Gallager, R.

R. Gallager, “Low-density parity-check codes,” IEEE Trans. Inf. Theory 8(1), 21–28 (1962).

Galvin, P.

G. H. Tomlinson and P. Galvin, “Elimination of skewing in the amplitude distributions of long m sequences subjected to low-pass filtering,” Electron. Lett. 11(4), 77–78 (1975).

Gao, J. B.

Y. Cao, W. W. Tung, J. B. Gao, V. A. Protopopescu, and L. M. Hively, “Detecting dynamical changes in time series using the permutation entropy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4 Pt 2), 046217 (2004).
[PubMed]

García-Ojalvo, J.

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).
[PubMed]

Gastaud, N.

Y. C. Kouomou, P. Colet, L. Larger, and N. Gastaud, “Chaotic breathers in delayed electro-optical systems,” Phys. Rev. Lett. 95(20), 203903 (2005).
[PubMed]

Gatarek, D.

A. Brace, D. Gatarek, and M. Musiela, “The market model of interest rate dynamics,” Math. Finance 7(2), 127–155 (1997).

González, J. A.

J. J. Suárez-Vargas, B. A. Márquez, and J. A. González, “Highly complex optical signal generation using electro-optical systems with non-linear, non-invertible transmission functions,” Appl. Phys. Lett. 101(7), 071115 (2012).

Hayes, S. T.

N. J. Corron, S. T. Hayes, S. D. Pethel, and J. N. Blakely, “Chaos without nonlinear dynamics,” Phys. Rev. Lett. 97(2), 024101 (2006).
[PubMed]

Hively, L. M.

Y. Cao, W. W. Tung, J. B. Gao, V. A. Protopopescu, and L. M. Hively, “Detecting dynamical changes in time series using the permutation entropy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4 Pt 2), 046217 (2004).
[PubMed]

Jiang, X.

Jung, B.

B. Jung, H. P. Lenhof, P. Müller, and C. Rüb, “Langevin dynamics simulations of macromolecules on parallel computers,” Macromol. Theory Simul. 6(2), 507–521 (1997).

Kaddoum, G.

G. Kaddoum, “Design and performance analysis of a multiuser OFDM based differential chaos shift keying communication system,” IEEE Trans. Commun. 64(1), 249–260 (2016).

Kanoff, D. R.

Kouomou, Y. C.

Y. C. Kouomou, P. Colet, L. Larger, and N. Gastaud, “Chaotic breathers in delayed electro-optical systems,” Phys. Rev. Lett. 95(20), 203903 (2005).
[PubMed]

Lai, C. P.

P. H. Chen, M. C. Shastry, C. P. Lai, and R. M. Narayanan, “A portable real-time digital noise radar system for through-the-wall imaging,” IEEE Trans. Geosci. Remote Sens. 50(10), 4123–4134 (2012).

Larger, L.

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).
[PubMed]

Y. C. Kouomou, P. Colet, L. Larger, and N. Gastaud, “Chaotic breathers in delayed electro-optical systems,” Phys. Rev. Lett. 95(20), 203903 (2005).
[PubMed]

Lee, D. U.

D. U. Lee, J. D. Villasenor, W. Luk, and H. W. Philip, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659–671 (2006).

D. U. Lee, J. D. Villasenor, W. Luk, and P. H. W. Leong, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659–671 (2006).

Lenhof, H. P.

B. Jung, H. P. Lenhof, P. Müller, and C. Rüb, “Langevin dynamics simulations of macromolecules on parallel computers,” Macromol. Theory Simul. 6(2), 507–521 (1997).

Leong, P. H. W.

D. U. Lee, J. D. Villasenor, W. Luk, and P. H. W. Leong, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659–671 (2006).

Li, L.

A. Wang, B. Wang, L. Li, Y. Wang, and K. A. Shore, “Optical heterodyne generation of high-dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 1–10 (2015).

Li, P.

Li, X.

Lin, F. Y.

C. H. Cheng, Y. C. Chen, and F. Y. Lin, “Generation of uncorrelated multichannel chaos by electrical heterodyning for multiple-input–multiple-output chaos radar application,” IEEE Photonics J. 8(1), 1–14 (2016).

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

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

Liu, B.

Liu, D.

Liu, J. M.

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

Liu, M.

Liu, T.

M. Zhang, T. Liu, P. Li, A. Wang, J. Zhang, and Y. Wang, “Generation of broadband chaotic laser using dual-wavelength optically injected Fabry–Pérot laser diode with optical feedback,” IEEE Photonics Technol. Lett. 23(24), 1872–1874 (2011).

Lorenz, E. N.

E. N. Lorenz, “Deterministic nonperiodic flow,” J. Atmos. Sci. 20(2), 130–141 (1963).

Luk, W.

D. U. Lee, J. D. Villasenor, W. Luk, and P. H. W. Leong, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659–671 (2006).

D. U. Lee, J. D. Villasenor, W. Luk, and H. W. Philip, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659–671 (2006).

Márquez, B. A.

J. J. Suárez-Vargas, B. A. Márquez, and J. A. González, “Highly complex optical signal generation using electro-optical systems with non-linear, non-invertible transmission functions,” Appl. Phys. Lett. 101(7), 071115 (2012).

Meng, W. H.

Mirasso, C. R.

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).
[PubMed]

Müller, P.

B. Jung, H. P. Lenhof, P. Müller, and C. Rüb, “Langevin dynamics simulations of macromolecules on parallel computers,” Macromol. Theory Simul. 6(2), 507–521 (1997).

Murphy, T. E.

Musiela, M.

A. Brace, D. Gatarek, and M. Musiela, “The market model of interest rate dynamics,” Math. Finance 7(2), 127–155 (1997).

Narayanan, R. M.

P. H. Chen, M. C. Shastry, C. P. Lai, and R. M. Narayanan, “A portable real-time digital noise radar system for through-the-wall imaging,” IEEE Trans. Geosci. Remote Sens. 50(10), 4123–4134 (2012).

Pan, S.

Pesquera, L.

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).
[PubMed]

Pethel, S. D.

N. J. Corron, S. T. Hayes, S. D. Pethel, and J. N. Blakely, “Chaos without nonlinear dynamics,” Phys. Rev. Lett. 97(2), 024101 (2006).
[PubMed]

Philip, H. W.

D. U. Lee, J. D. Villasenor, W. Luk, and H. W. Philip, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659–671 (2006).

Pincus, S. M.

S. M. Pincus, “Approximate entropy as a measure of system complexity,” Proc. Natl. Acad. Sci. U.S.A. 88(6), 2297–2301 (1991).
[PubMed]

Prince, P. J.

J. R. Dormand and P. J. Prince, “A family of embedded Runge-Kutta formulae,” J. Comput. Appl. Math. 6(1), 19–26 (1980).

Protopopescu, V. A.

Y. Cao, W. W. Tung, J. B. Gao, V. A. Protopopescu, and L. M. Hively, “Detecting dynamical changes in time series using the permutation entropy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4 Pt 2), 046217 (2004).
[PubMed]

Prucnal, P. R.

Roberts, P. D.

P. D. Roberts and R. H. Davis, “Statistical properties of smoothed maximal-length linear binary sequences, ” Proc. IEE113(1), 190–196 (1966).

Roy, R.

Rüb, C.

B. Jung, H. P. Lenhof, P. Müller, and C. Rüb, “Langevin dynamics simulations of macromolecules on parallel computers,” Macromol. Theory Simul. 6(2), 507–521 (1997).

Salevan, J. C.

Shastri, B. J.

Shastry, M. C.

P. H. Chen, M. C. Shastry, C. P. Lai, and R. M. Narayanan, “A portable real-time digital noise radar system for through-the-wall imaging,” IEEE Trans. Geosci. Remote Sens. 50(10), 4123–4134 (2012).

Shore, K. A.

A. Wang, B. Wang, L. Li, Y. Wang, and K. A. Shore, “Optical heterodyne generation of high-dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 1–10 (2015).

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).
[PubMed]

Shum, P.

Suárez-Vargas, J. J.

J. J. Suárez-Vargas, B. A. Márquez, and J. A. González, “Highly complex optical signal generation using electro-optical systems with non-linear, non-invertible transmission functions,” Appl. Phys. Lett. 101(7), 071115 (2012).

Syvridis, D.

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).
[PubMed]

Tang, M.

Tian, Y.

Tomlinson, G. H.

G. H. Tomlinson and P. Galvin, “Elimination of skewing in the amplitude distributions of long m sequences subjected to low-pass filtering,” Electron. Lett. 11(4), 77–78 (1975).

Tung, W. W.

Y. Cao, W. W. Tung, J. B. Gao, V. A. Protopopescu, and L. M. Hively, “Detecting dynamical changes in time series using the permutation entropy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4 Pt 2), 046217 (2004).
[PubMed]

Villasenor, J. D.

D. U. Lee, J. D. Villasenor, W. Luk, and P. H. W. Leong, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659–671 (2006).

D. U. Lee, J. D. Villasenor, W. Luk, and H. W. Philip, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659–671 (2006).

Wang, A.

A. Wang, L. Wang, P. Li, and Y. Wang, “Minimal-post-processing 320-Gbps true random bit generation using physical white chaos,” Opt. Express 25(4), 3153–3164 (2017).
[PubMed]

A. Wang, B. Wang, L. Li, Y. Wang, and K. A. Shore, “Optical heterodyne generation of high-dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 1–10 (2015).

A. Wang, Y. Wang, Y. Yang, M. Zhang, H. Xu, and B. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).

A. Wang, N. Wang, Y. Yang, B. Wang, M. Zhang, and Y. Wang, “Precise fault location in WDM-PON by utilizing wavelength tunable chaotic laser,” J. Lightwave Technol. 30(21), 3420–3426 (2012).

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

M. Zhang, T. Liu, P. Li, A. Wang, J. Zhang, and Y. Wang, “Generation of broadband chaotic laser using dual-wavelength optically injected Fabry–Pérot laser diode with optical feedback,” IEEE Photonics Technol. Lett. 23(24), 1872–1874 (2011).

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

Wang, B.

A. Wang, B. Wang, L. Li, Y. Wang, and K. A. Shore, “Optical heterodyne generation of high-dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 1–10 (2015).

A. Wang, Y. Wang, Y. Yang, M. Zhang, H. Xu, and B. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).

A. Wang, N. Wang, Y. Yang, B. Wang, M. Zhang, and Y. Wang, “Precise fault location in WDM-PON by utilizing wavelength tunable chaotic laser,” J. Lightwave Technol. 30(21), 3420–3426 (2012).

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

Wang, L.

Wang, N.

Wang, Y.

A. Wang, L. Wang, P. Li, and Y. Wang, “Minimal-post-processing 320-Gbps true random bit generation using physical white chaos,” Opt. Express 25(4), 3153–3164 (2017).
[PubMed]

A. Wang, B. Wang, L. Li, Y. Wang, and K. A. Shore, “Optical heterodyne generation of high-dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 1–10 (2015).

A. Wang, Y. Wang, Y. Yang, M. Zhang, H. Xu, and B. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).

A. Wang, N. Wang, Y. Yang, B. Wang, M. Zhang, and Y. Wang, “Precise fault location in WDM-PON by utilizing wavelength tunable chaotic laser,” J. Lightwave Technol. 30(21), 3420–3426 (2012).

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

M. Zhang, T. Liu, P. Li, A. Wang, J. Zhang, and Y. Wang, “Generation of broadband chaotic laser using dual-wavelength optically injected Fabry–Pérot laser diode with optical feedback,” IEEE Photonics Technol. Lett. 23(24), 1872–1874 (2011).

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

Wang, Z.

Williams, C. R. S.

Wu, B.

Wu, T. C.

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

Xin, X.

Xu, H.

A. Wang, Y. Wang, Y. Yang, M. Zhang, H. Xu, and B. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).

Xue, L.

Yang, Y.

A. Wang, Y. Wang, Y. Yang, M. Zhang, H. Xu, and B. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).

A. Wang, N. Wang, Y. Yang, B. Wang, M. Zhang, and Y. Wang, “Precise fault location in WDM-PON by utilizing wavelength tunable chaotic laser,” J. Lightwave Technol. 30(21), 3420–3426 (2012).

Yao, J.

Yao, T.

Yin, X.

Yu, J.

Yu, Y. W.

Zhan, Y. F.

Zhang, J.

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

M. Zhang, T. Liu, P. Li, A. Wang, J. Zhang, and Y. Wang, “Generation of broadband chaotic laser using dual-wavelength optically injected Fabry–Pérot laser diode with optical feedback,” IEEE Photonics Technol. Lett. 23(24), 1872–1874 (2011).

Zhang, L.

Zhang, M.

X. Jiang, D. Liu, M. Cheng, L. Deng, S. Fu, M. Zhang, M. Tang, and P. Shum, “High-frequency reverse-time chaos generation using an optical matched filter,” Opt. Lett. 41(6), 1157–1160 (2016).
[PubMed]

A. Wang, Y. Wang, Y. Yang, M. Zhang, H. Xu, and B. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).

A. Wang, N. Wang, Y. Yang, B. Wang, M. Zhang, and Y. Wang, “Precise fault location in WDM-PON by utilizing wavelength tunable chaotic laser,” J. Lightwave Technol. 30(21), 3420–3426 (2012).

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

M. Zhang, T. Liu, P. Li, A. Wang, J. Zhang, and Y. Wang, “Generation of broadband chaotic laser using dual-wavelength optically injected Fabry–Pérot laser diode with optical feedback,” IEEE Photonics Technol. Lett. 23(24), 1872–1874 (2011).

Zhu, D.

Zou, H.

Zou, X.

Appl. Phys. Lett. (2)

J. J. Suárez-Vargas, B. A. Márquez, and J. A. González, “Highly complex optical signal generation using electro-optical systems with non-linear, non-invertible transmission functions,” Appl. Phys. Lett. 101(7), 071115 (2012).

A. Wang, Y. Wang, Y. Yang, M. Zhang, H. Xu, and B. Wang, “Generation of flat-spectrum wideband chaos by fiber ring resonator,” Appl. Phys. Lett. 102(3), 031112 (2013).

Electron. Lett. (1)

G. H. Tomlinson and P. Galvin, “Elimination of skewing in the amplitude distributions of long m sequences subjected to low-pass filtering,” Electron. Lett. 11(4), 77–78 (1975).

IEEE J. Quantum Electron. (2)

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

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

IEEE J. Sel. Top. Quantum Electron. (1)

A. Wang, B. Wang, L. Li, Y. Wang, and K. A. Shore, “Optical heterodyne generation of high-dimensional and broadband white chaos,” IEEE J. Sel. Top. Quantum Electron. 21(6), 1–10 (2015).

IEEE Photonics J. (1)

C. H. Cheng, Y. C. Chen, and F. Y. Lin, “Generation of uncorrelated multichannel chaos by electrical heterodyning for multiple-input–multiple-output chaos radar application,” IEEE Photonics J. 8(1), 1–14 (2016).

IEEE Photonics Technol. Lett. (2)

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

M. Zhang, T. Liu, P. Li, A. Wang, J. Zhang, and Y. Wang, “Generation of broadband chaotic laser using dual-wavelength optically injected Fabry–Pérot laser diode with optical feedback,” IEEE Photonics Technol. Lett. 23(24), 1872–1874 (2011).

IEEE Trans. Commun. (1)

G. Kaddoum, “Design and performance analysis of a multiuser OFDM based differential chaos shift keying communication system,” IEEE Trans. Commun. 64(1), 249–260 (2016).

IEEE Trans. Comput. (2)

D. U. Lee, J. D. Villasenor, W. Luk, and H. W. Philip, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659–671 (2006).

D. U. Lee, J. D. Villasenor, W. Luk, and P. H. W. Leong, “A hardware Gaussian noise generator using the Box-Muller method and its error analysis,” IEEE Trans. Comput. 55(6), 659–671 (2006).

IEEE Trans. Geosci. Remote Sens. (1)

P. H. Chen, M. C. Shastry, C. P. Lai, and R. M. Narayanan, “A portable real-time digital noise radar system for through-the-wall imaging,” IEEE Trans. Geosci. Remote Sens. 50(10), 4123–4134 (2012).

IEEE Trans. Inf. Theory (1)

R. Gallager, “Low-density parity-check codes,” IEEE Trans. Inf. Theory 8(1), 21–28 (1962).

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E. N. Lorenz, “Deterministic nonperiodic flow,” J. Atmos. Sci. 20(2), 130–141 (1963).

J. Comput. Appl. Math. (1)

J. R. Dormand and P. J. Prince, “A family of embedded Runge-Kutta formulae,” J. Comput. Appl. Math. 6(1), 19–26 (1980).

J. Lightwave Technol. (2)

Macromol. Theory Simul. (1)

B. Jung, H. P. Lenhof, P. Müller, and C. Rüb, “Langevin dynamics simulations of macromolecules on parallel computers,” Macromol. Theory Simul. 6(2), 507–521 (1997).

Math. Finance (1)

A. Brace, D. Gatarek, and M. Musiela, “The market model of interest rate dynamics,” Math. Finance 7(2), 127–155 (1997).

Nature (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).
[PubMed]

Opt. Express (8)

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).
[PubMed]

L. Zhang, X. Xin, B. Liu, and J. Yu, “Physical-enhanced secure strategy in an OFDM-PON,” Opt. Express 20(3), 2255–2265 (2012).
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C. Fu, J. J. Chen, H. Zou, W. H. Meng, Y. F. Zhan, and Y. W. Yu, “A chaos-based digital image encryption scheme with an improved diffusion strategy,” Opt. Express 20(3), 2363–2378 (2012).
[PubMed]

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

L. Zhang, X. Xin, B. Liu, and X. Yin, “Physical secure enhancement in optical OFDMA-PON based on two-dimensional scrambling,” Opt. Express 20(26), B32–B37 (2012).
[PubMed]

B. Wu, Z. Wang, Y. Tian, M. P. Fok, B. J. Shastri, D. R. Kanoff, and P. R. Prucnal, “Optical steganography based on amplified spontaneous emission noise,” Opt. Express 21(2), 2065–2071 (2013).
[PubMed]

B. Wu, M. P. Chang, B. J. Shastri, Z. Wang, and P. R. Prucnal, “Analog noise protected optical encryption with two-dimensional key space,” Opt. Express 22(12), 14568–14574 (2014).
[PubMed]

A. Wang, L. Wang, P. Li, and Y. Wang, “Minimal-post-processing 320-Gbps true random bit generation using physical white chaos,” Opt. Express 25(4), 3153–3164 (2017).
[PubMed]

Opt. Lett. (2)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

Y. Cao, W. W. Tung, J. B. Gao, V. A. Protopopescu, and L. M. Hively, “Detecting dynamical changes in time series using the permutation entropy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4 Pt 2), 046217 (2004).
[PubMed]

Phys. Rev. Lett. (2)

Y. C. Kouomou, P. Colet, L. Larger, and N. Gastaud, “Chaotic breathers in delayed electro-optical systems,” Phys. Rev. Lett. 95(20), 203903 (2005).
[PubMed]

N. J. Corron, S. T. Hayes, S. D. Pethel, and J. N. Blakely, “Chaos without nonlinear dynamics,” Phys. Rev. Lett. 97(2), 024101 (2006).
[PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

S. M. Pincus, “Approximate entropy as a measure of system complexity,” Proc. Natl. Acad. Sci. U.S.A. 88(6), 2297–2301 (1991).
[PubMed]

Other (4)

D. E. Knuth, “Seminumerical Algorithms” in The Art of Computer Programming, 3rd ed. (Addison-Wesley, 1997).

Y. Fan, Z. Zilic, and M. Chiang, “A versatile high speed bit error rate testing scheme,” in Proceeding of IEEE International Symposium on Quality Electronic Design (IEEE 2004), pp. 395–400.

X. Jiang, M. Cheng, F. Luo, L. Deng, C. Ke, S. Fu, M. Tang, D. Liu, M. Zhang, and P. Shum, “Reproducible Broadband Optical Noise Generation Based on Phase Modulation to Intensity Modulation Conversion and a Nonlinear Transformation,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2017), paper Th2A.49.

P. D. Roberts and R. H. Davis, “Statistical properties of smoothed maximal-length linear binary sequences, ” Proc. IEE113(1), 190–196 (1966).

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Figures (10)

Fig. 1
Fig. 1 Experimental setup of the optical noise generator.
Fig. 2
Fig. 2 (a), (b), (c) are the experimental waveforms of x1, x2, x3.
Fig. 3
Fig. 3 (a), (b), (c) are the experimental spectrums of x1, x2, x3 and (d), (e), (f) are corresponding simulation results.
Fig. 4
Fig. 4 The ACF of x3.
Fig. 5
Fig. 5 The probability distribution of the amplitude of x3 .
Fig. 6
Fig. 6 (a)The output waveform of simulation result; (b) the corresponding PDF of (a).
Fig. 7
Fig. 7 The ACF of signal in Fig. 6(a).
Fig. 8
Fig. 8 (a) The relationship between the complexity of output noise and the order of input LFSR; (b) the relationship between the complexity of output noise and the strength of nonlinear effect.
Fig. 9
Fig. 9 The complexity of generated noise with M-ary input sequences.
Fig. 10
Fig. 10 (a) (b) reveal the effect of m and m1 on the system’s reproducibility.

Equations (7)

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

E ( t ) = P 0 exp [ j ( ω 0 t + φ 0 ) ] exp [ j m x 1 ] .
H ( ω ) = exp [ j d 2 ( ω ω 0 ) 2 ] ,
x 3 = γ P 1 cos 2 ( m 1 N ( x 2 ) + φ 0 ) .
ρ = ( y ( t ) y ( t ) ) ( y ( t + Δ t ) y ( t ) ) ( y ( t ) y ( t ) ) 2 ( y ( t + Δ t ) y ( t ) ) 2 ,
x 1 ( t ) = x 1 ( k ) , ( k 1 ) T < t k T
x 1 ( k ) = g ( y ( k / f ) ) , k = 1 , 2 , 3...
g ( z ) = { c e i l ( z M ) 1 , 0 < z 1 0 , z = 0 .

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