Abstract

A novel electro-optic chaos source is proposed on the basis of the reverse-time chaos theory and an analog-digital hybrid feedback loop. The analog output of the system can be determined by the numeric states of shift registers, which makes the system robust and easy to control. The dynamical properties as well as the complexity dependence on the feedback parameters are investigated in detail. The correlation characteristics of the system are also studied. Two improving strategies which were established in digital field and analog field are proposed to conceal the time-delay signature. The proposed scheme has the potential to be used in radar and optical secure communication systems.

© 2016 Optical Society of America

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References

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2016 (6)

C. Xue, N. Jiang, Y. Lv, C. Wang, G. Li, S. Lin, and K. Qiu, “Security-enhanced chaos communication with time-delay signature suppression and phase encryption,” Opt. Lett. 41(16), 3690–3693 (2016).
[Crossref] [PubMed]

Y. K. Chembo, M. Jacquot, J. M. Dudley, and L. Larger, “Ikeda-like chaos on a dynamically filtered supercontinuum light source,” Phys. Rev. A 94(2), 023847 (2016).
[Crossref]

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).
[Crossref] [PubMed]

N. J. Corron, R. M. Cooper, and J. N. Blakely, “Analytically Solvable Chaotic Oscillator Based on a First-Order Filter,” Chaos 26(2), 023104 (2016).
[Crossref] [PubMed]

N. J. Corron, R. M. Cooper, and J. N. Blakely, “Entropy rates of low-significance bits sampled from chaotic physical systems,” Physica D 332, 34–40 (2016).
[Crossref]

T. Katayama, D. Hayashi, and H. Kawaguchi, “All-Optical Shift Register Using Polarization Bistable VCSEL Array,” IEEE Photonics Technol. Lett. 20(19), 2062–2065 (2016).
[Crossref]

2015 (5)

Y. Deng, H. Hu, N. Xiong, W. Xiong, and L. Liu, “A general hybrid model for chaos robust synchronization and degradation reduction,” Inf. Sci. 305, 146–164 (2015).
[Crossref]

B. Wu, B. J. Shastri, P. Mittal, A. N. Tait, and P. R. Prucnal, “Optical signal processing and stealth transmission for privacy,” IEEE J. Sel. Top. Signal Process. 9(7), 1185–1194 (2015).

J. H. Talla Mbé, A. F. Talla, G. R. G. Chengui, A. Coillet, L. Larger, P. Woafo, and Y. K. Chembo, “Mixed-mode oscillations in slow-fast delayed optoelectronic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(1), 012902 (2015).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

M. Cheng, L. Deng, X. Gao, H. Li, M. Tang, S. Fu, P. Shum, and D. Liu, “Security-Enhanced OFDM-PON Using Hybrid Chaotic System,” IEEE Photonics Technol. Lett. 27(3), 326–329 (2015).
[Crossref]

2014 (1)

2013 (1)

2012 (5)

2011 (2)

E. Lazzeri, G. Berrettini, G. Meloni, A. Bogoni, and L. Potì, “All-Optical N-Bits Shift Register Exploiting a Ring Buffer Based on Semiconductor Optical Amplifier,” IEEE Photonics Technol. Lett. 23(1), 45–47 (2011).
[Crossref]

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett. 107(3), 034103 (2011).
[Crossref] [PubMed]

2010 (5)

2009 (2)

J. P. Toomey, D. M. Kane, A. Davidović, and E. H. Huntington, “Hybrid electronic/optical synchronized chaos communication system,” Opt. Express 17(9), 7556–7561 (2009).
[Crossref] [PubMed]

M. Peil, M. Jacquot, Y. K. Chembo, L. Larger, and T. Erneux, “Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026208 (2009).
[Crossref] [PubMed]

2007 (1)

2006 (1)

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

2005 (3)

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

Y. Horio, T. Ikeguchi, and K. Aihara, “A mixed analog/digital chaotic neuro-computer system for quadratic assignment problems,” Neural Netw. 18(5-6), 505–513 (2005).
[Crossref] [PubMed]

S. Zhang, Z. Li, Y. Liu, G. Khoe, and H. Dorren, “Optical shift register based on an optical flip-flop memory with a single active element,” Opt. Express 13(24), 9708–9713 (2005).
[Crossref] [PubMed]

2004 (1)

Y. C. Kouomou, P. Colet, N. Gastaud, and L. Larger, “Effect of parameter mismatch on the synchronization of chaotic semiconductor lasers with electro-optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(5), 056226 (2004).
[Crossref] [PubMed]

1998 (1)

R. Hegger, M. J. Bunner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett. 81(3), 558–561 (1998).
[Crossref]

Aihara, K.

Y. Horio, T. Ikeguchi, and K. Aihara, “A mixed analog/digital chaotic neuro-computer system for quadratic assignment problems,” Neural Netw. 18(5-6), 505–513 (2005).
[Crossref] [PubMed]

Argyris, A.

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

A. Argyris, D. Kanakidis, and D. Syvridis, “Noise dependence of high bit-rate optical chaotic communication back-to-back systems,” in Optical Fiber Communication Conference (Optical Society of America, 2003), MF79.
[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]

Ben, D.

Berrettini, G.

E. Lazzeri, G. Berrettini, G. Meloni, A. Bogoni, and L. Potì, “All-Optical N-Bits Shift Register Exploiting a Ring Buffer Based on Semiconductor Optical Amplifier,” IEEE Photonics Technol. Lett. 23(1), 45–47 (2011).
[Crossref]

Blakely, J. N.

N. J. Corron, R. M. Cooper, and J. N. Blakely, “Entropy rates of low-significance bits sampled from chaotic physical systems,” Physica D 332, 34–40 (2016).
[Crossref]

N. J. Corron, R. M. Cooper, and J. N. Blakely, “Analytically Solvable Chaotic Oscillator Based on a First-Order Filter,” Chaos 26(2), 023104 (2016).
[Crossref] [PubMed]

N. J. Corron, J. N. Blakely, and M. T. Stahl, “A matched filter for chaos,” Chaos 20(2), 023123 (2010).
[Crossref] [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).
[Crossref] [PubMed]

J. N. Blakely, M. S. Milosavljevic, and N. J. Corron, “Timing variation in an analytically solvable chaotic system,” Physica D (to be published).

Bogoni, A.

E. Lazzeri, G. Berrettini, G. Meloni, A. Bogoni, and L. Potì, “All-Optical N-Bits Shift Register Exploiting a Ring Buffer Based on Semiconductor Optical Amplifier,” IEEE Photonics Technol. Lett. 23(1), 45–47 (2011).
[Crossref]

Bogris, A.

Bolk, J.

Bunner, M. J.

R. Hegger, M. J. Bunner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett. 81(3), 558–561 (1998).
[Crossref]

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).
[Crossref]

Chembo, Y. K.

Y. K. Chembo, M. Jacquot, J. M. Dudley, and L. Larger, “Ikeda-like chaos on a dynamically filtered supercontinuum light source,” Phys. Rev. A 94(2), 023847 (2016).
[Crossref]

J. H. Talla Mbé, A. F. Talla, G. R. G. Chengui, A. Coillet, L. Larger, P. Woafo, and Y. K. Chembo, “Mixed-mode oscillations in slow-fast delayed optoelectronic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(1), 012902 (2015).
[Crossref] [PubMed]

R. M. Nguimdo, R. Lavrov, P. Colet, M. Jacquot, Y. K. Chembo, and L. Larger, “Effect of fiber dispersion on broadband chaos communications implemented by electro-optic nonlinear delay phase dynamics,” J. Lightwave Technol. 28(18), 2688–2696 (2010).
[Crossref]

M. Peil, M. Jacquot, Y. K. Chembo, L. Larger, and T. Erneux, “Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026208 (2009).
[Crossref] [PubMed]

Cheng, 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).
[Crossref] [PubMed]

M. Cheng, L. Deng, X. Gao, H. Li, M. Tang, S. Fu, P. Shum, and D. Liu, “Security-Enhanced OFDM-PON Using Hybrid Chaotic System,” IEEE Photonics Technol. Lett. 27(3), 326–329 (2015).
[Crossref]

Chengui, G. R. G.

J. H. Talla Mbé, A. F. Talla, G. R. G. Chengui, A. Coillet, L. Larger, P. Woafo, and Y. K. Chembo, “Mixed-mode oscillations in slow-fast delayed optoelectronic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(1), 012902 (2015).
[Crossref] [PubMed]

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]

Coillet, A.

J. H. Talla Mbé, A. F. Talla, G. R. G. Chengui, A. Coillet, L. Larger, P. Woafo, and Y. K. Chembo, “Mixed-mode oscillations in slow-fast delayed optoelectronic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(1), 012902 (2015).
[Crossref] [PubMed]

Colet, P.

R. M. Nguimdo and P. Colet, “Electro-optic phase chaos systems with an internal variable and a digital key,” Opt. Express 20(23), 25333–25344 (2012).
[Crossref] [PubMed]

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett. 107(3), 034103 (2011).
[Crossref] [PubMed]

R. M. Nguimdo, R. Lavrov, P. Colet, M. Jacquot, Y. K. Chembo, and L. Larger, “Effect of fiber dispersion on broadband chaos communications implemented by electro-optic nonlinear delay phase dynamics,” J. Lightwave Technol. 28(18), 2688–2696 (2010).
[Crossref]

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

Y. C. Kouomou, P. Colet, N. Gastaud, and L. Larger, “Effect of parameter mismatch on the synchronization of chaotic semiconductor lasers with electro-optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(5), 056226 (2004).
[Crossref] [PubMed]

Cooper, R. M.

N. J. Corron, R. M. Cooper, and J. N. Blakely, “Entropy rates of low-significance bits sampled from chaotic physical systems,” Physica D 332, 34–40 (2016).
[Crossref]

N. J. Corron, R. M. Cooper, and J. N. Blakely, “Analytically Solvable Chaotic Oscillator Based on a First-Order Filter,” Chaos 26(2), 023104 (2016).
[Crossref] [PubMed]

Corron, N. J.

N. J. Corron, R. M. Cooper, and J. N. Blakely, “Analytically Solvable Chaotic Oscillator Based on a First-Order Filter,” Chaos 26(2), 023104 (2016).
[Crossref] [PubMed]

N. J. Corron, R. M. Cooper, and J. N. Blakely, “Entropy rates of low-significance bits sampled from chaotic physical systems,” Physica D 332, 34–40 (2016).
[Crossref]

N. J. Corron, J. N. Blakely, and M. T. Stahl, “A matched filter for chaos,” Chaos 20(2), 023123 (2010).
[Crossref] [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).
[Crossref] [PubMed]

J. N. Blakely, M. S. Milosavljevic, and N. J. Corron, “Timing variation in an analytically solvable chaotic system,” Physica D (to be published).

Danckaert, J.

Davidovic, A.

Deligiannidis, S.

Deng, L.

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).
[Crossref] [PubMed]

M. Cheng, L. Deng, X. Gao, H. Li, M. Tang, S. Fu, P. Shum, and D. Liu, “Security-Enhanced OFDM-PON Using Hybrid Chaotic System,” IEEE Photonics Technol. Lett. 27(3), 326–329 (2015).
[Crossref]

Deng, Y.

Y. Deng, H. Hu, N. Xiong, W. Xiong, and L. Liu, “A general hybrid model for chaos robust synchronization and degradation reduction,” Inf. Sci. 305, 146–164 (2015).
[Crossref]

Dorren, H.

Dudley, J. M.

Y. K. Chembo, M. Jacquot, J. M. Dudley, and L. Larger, “Ikeda-like chaos on a dynamically filtered supercontinuum light source,” Phys. Rev. A 94(2), 023847 (2016).
[Crossref]

Erneux, T.

M. Peil, M. Jacquot, Y. K. Chembo, L. Larger, and T. Erneux, “Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026208 (2009).
[Crossref] [PubMed]

Figueiredo, J. M.

Fu, S.

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).
[Crossref] [PubMed]

M. Cheng, L. Deng, X. Gao, H. Li, M. Tang, S. Fu, P. Shum, and D. Liu, “Security-Enhanced OFDM-PON Using Hybrid Chaotic System,” IEEE Photonics Technol. Lett. 27(3), 326–329 (2015).
[Crossref]

Gao, X.

M. Cheng, L. Deng, X. Gao, H. Li, M. Tang, S. Fu, P. Shum, and D. Liu, “Security-Enhanced OFDM-PON Using Hybrid Chaotic System,” IEEE Photonics Technol. Lett. 27(3), 326–329 (2015).
[Crossref]

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).
[Crossref] [PubMed]

Y. C. Kouomou, P. Colet, N. Gastaud, and L. Larger, “Effect of parameter mismatch on the synchronization of chaotic semiconductor lasers with electro-optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(5), 056226 (2004).
[Crossref] [PubMed]

Giaquinta, A.

R. Hegger, M. J. Bunner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett. 81(3), 558–561 (1998).
[Crossref]

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).
[Crossref]

Hayashi, D.

T. Katayama, D. Hayashi, and H. Kawaguchi, “All-Optical Shift Register Using Polarization Bistable VCSEL Array,” IEEE Photonics Technol. Lett. 20(19), 2062–2065 (2016).
[Crossref]

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).
[Crossref] [PubMed]

Hegger, R.

R. Hegger, M. J. Bunner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett. 81(3), 558–561 (1998).
[Crossref]

Horio, Y.

Y. Horio, T. Ikeguchi, and K. Aihara, “A mixed analog/digital chaotic neuro-computer system for quadratic assignment problems,” Neural Netw. 18(5-6), 505–513 (2005).
[Crossref] [PubMed]

Hu, H.

Y. Deng, H. Hu, N. Xiong, W. Xiong, and L. Liu, “A general hybrid model for chaos robust synchronization and degradation reduction,” Inf. Sci. 305, 146–164 (2015).
[Crossref]

Huntington, E. H.

Ikeguchi, T.

Y. Horio, T. Ikeguchi, and K. Aihara, “A mixed analog/digital chaotic neuro-computer system for quadratic assignment problems,” Neural Netw. 18(5-6), 505–513 (2005).
[Crossref] [PubMed]

Jacquot, M.

Y. K. Chembo, M. Jacquot, J. M. Dudley, and L. Larger, “Ikeda-like chaos on a dynamically filtered supercontinuum light source,” Phys. Rev. A 94(2), 023847 (2016).
[Crossref]

R. M. Nguimdo, R. Lavrov, P. Colet, M. Jacquot, Y. K. Chembo, and L. Larger, “Effect of fiber dispersion on broadband chaos communications implemented by electro-optic nonlinear delay phase dynamics,” J. Lightwave Technol. 28(18), 2688–2696 (2010).
[Crossref]

M. Peil, M. Jacquot, Y. K. Chembo, L. Larger, and T. Erneux, “Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026208 (2009).
[Crossref] [PubMed]

Javaloyes, J.

Jiang, N.

Jiang, X.

Kanakidis, D.

A. Argyris, D. Kanakidis, and D. Syvridis, “Noise dependence of high bit-rate optical chaotic communication back-to-back systems,” in Optical Fiber Communication Conference (Optical Society of America, 2003), MF79.
[Crossref]

Kane, D. M.

Kanter, I.

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]

Kantz, H.

R. Hegger, M. J. Bunner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett. 81(3), 558–561 (1998).
[Crossref]

Katayama, T.

T. Katayama, D. Hayashi, and H. Kawaguchi, “All-Optical Shift Register Using Polarization Bistable VCSEL Array,” IEEE Photonics Technol. Lett. 20(19), 2062–2065 (2016).
[Crossref]

Kawaguchi, H.

T. Katayama, D. Hayashi, and H. Kawaguchi, “All-Optical Shift Register Using Polarization Bistable VCSEL Array,” IEEE Photonics Technol. Lett. 20(19), 2062–2065 (2016).
[Crossref]

Khoe, G.

Kitayama, K.-I.

Kong, F.

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).
[Crossref] [PubMed]

Y. C. Kouomou, P. Colet, N. Gastaud, and L. Larger, “Effect of parameter mismatch on the synchronization of chaotic semiconductor lasers with electro-optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(5), 056226 (2004).
[Crossref] [PubMed]

Larger, L.

Y. K. Chembo, M. Jacquot, J. M. Dudley, and L. Larger, “Ikeda-like chaos on a dynamically filtered supercontinuum light source,” Phys. Rev. A 94(2), 023847 (2016).
[Crossref]

J. H. Talla Mbé, A. F. Talla, G. R. G. Chengui, A. Coillet, L. Larger, P. Woafo, and Y. K. Chembo, “Mixed-mode oscillations in slow-fast delayed optoelectronic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(1), 012902 (2015).
[Crossref] [PubMed]

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett. 107(3), 034103 (2011).
[Crossref] [PubMed]

R. M. Nguimdo, R. Lavrov, P. Colet, M. Jacquot, Y. K. Chembo, and L. Larger, “Effect of fiber dispersion on broadband chaos communications implemented by electro-optic nonlinear delay phase dynamics,” J. Lightwave Technol. 28(18), 2688–2696 (2010).
[Crossref]

M. Peil, M. Jacquot, Y. K. Chembo, L. Larger, and T. Erneux, “Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026208 (2009).
[Crossref] [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).
[Crossref] [PubMed]

Y. C. Kouomou, P. Colet, N. Gastaud, and L. Larger, “Effect of parameter mismatch on the synchronization of chaotic semiconductor lasers with electro-optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(5), 056226 (2004).
[Crossref] [PubMed]

Lavrov, R.

Lazzeri, E.

E. Lazzeri, G. Berrettini, G. Meloni, A. Bogoni, and L. Potì, “All-Optical N-Bits Shift Register Exploiting a Ring Buffer Based on Semiconductor Optical Amplifier,” IEEE Photonics Technol. Lett. 23(1), 45–47 (2011).
[Crossref]

Leijtens, X.

Li, G.

Li, H.

M. Cheng, L. Deng, X. Gao, H. Li, M. Tang, S. Fu, P. Shum, and D. Liu, “Security-Enhanced OFDM-PON Using Hybrid Chaotic System,” IEEE Photonics Technol. Lett. 27(3), 326–329 (2015).
[Crossref]

Li, N.

Li, P.

Li, W.

Li, Z.

Lin, F. Y.

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).
[Crossref]

Lin, S.

Liu, D.

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).
[Crossref] [PubMed]

M. Cheng, L. Deng, X. Gao, H. Li, M. Tang, S. Fu, P. Shum, and D. Liu, “Security-Enhanced OFDM-PON Using Hybrid Chaotic System,” IEEE Photonics Technol. Lett. 27(3), 326–329 (2015).
[Crossref]

Liu, L.

Y. Deng, H. Hu, N. Xiong, W. Xiong, and L. Liu, “A general hybrid model for chaos robust synchronization and degradation reduction,” Inf. Sci. 305, 146–164 (2015).
[Crossref]

Liu, M.

Liu, Y.

Luo, B.

Lv, Y.

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).
[Crossref]

Meloni, G.

E. Lazzeri, G. Berrettini, G. Meloni, A. Bogoni, and L. Potì, “All-Optical N-Bits Shift Register Exploiting a Ring Buffer Based on Semiconductor Optical Amplifier,” IEEE Photonics Technol. Lett. 23(1), 45–47 (2011).
[Crossref]

Milosavljevic, M. S.

J. N. Blakely, M. S. Milosavljevic, and N. J. Corron, “Timing variation in an analytically solvable chaotic system,” Physica D (to be published).

Mittal, P.

B. Wu, B. J. Shastri, P. Mittal, A. N. Tait, and P. R. Prucnal, “Optical signal processing and stealth transmission for privacy,” IEEE J. Sel. Top. Signal Process. 9(7), 1185–1194 (2015).

Miyoshi, Y.

Namiki, S.

Nguimdo, R. M.

Pan, S.

Pan, W.

Peil, M.

M. Peil, M. Jacquot, Y. K. Chembo, L. Larger, and T. Erneux, “Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026208 (2009).
[Crossref] [PubMed]

Pesquera, L.

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett. 107(3), 034103 (2011).
[Crossref] [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).
[Crossref] [PubMed]

Pikasis, E.

Potì, L.

E. Lazzeri, G. Berrettini, G. Meloni, A. Bogoni, and L. Potì, “All-Optical N-Bits Shift Register Exploiting a Ring Buffer Based on Semiconductor Optical Amplifier,” IEEE Photonics Technol. Lett. 23(1), 45–47 (2011).
[Crossref]

Prucnal, P. R.

B. Wu, B. J. Shastri, P. Mittal, A. N. Tait, and P. R. Prucnal, “Optical signal processing and stealth transmission for privacy,” IEEE J. Sel. Top. Signal Process. 9(7), 1185–1194 (2015).

Qiu, K.

Reidler, I.

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]

Romeira, B.

Rosenbluh, M.

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

Shastri, B. J.

B. Wu, B. J. Shastri, P. Mittal, A. N. Tait, and P. R. Prucnal, “Optical signal processing and stealth transmission for privacy,” IEEE J. Sel. Top. Signal Process. 9(7), 1185–1194 (2015).

Shum, P.

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).
[Crossref] [PubMed]

M. Cheng, L. Deng, X. Gao, H. Li, M. Tang, S. Fu, P. Shum, and D. Liu, “Security-Enhanced OFDM-PON Using Hybrid Chaotic System,” IEEE Photonics Technol. Lett. 27(3), 326–329 (2015).
[Crossref]

Stahl, M. T.

N. J. Corron, J. N. Blakely, and M. T. Stahl, “A matched filter for chaos,” Chaos 20(2), 023123 (2010).
[Crossref] [PubMed]

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).
[Crossref]

Syvridis, D.

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

A. Argyris, D. Kanakidis, and D. Syvridis, “Noise dependence of high bit-rate optical chaotic communication back-to-back systems,” in Optical Fiber Communication Conference (Optical Society of America, 2003), MF79.
[Crossref]

Tait, A. N.

B. Wu, B. J. Shastri, P. Mittal, A. N. Tait, and P. R. Prucnal, “Optical signal processing and stealth transmission for privacy,” IEEE J. Sel. Top. Signal Process. 9(7), 1185–1194 (2015).

Takagi, S.

Talla, A. F.

J. H. Talla Mbé, A. F. Talla, G. R. G. Chengui, A. Coillet, L. Larger, P. Woafo, and Y. K. Chembo, “Mixed-mode oscillations in slow-fast delayed optoelectronic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(1), 012902 (2015).
[Crossref] [PubMed]

Talla Mbé, J. H.

J. H. Talla Mbé, A. F. Talla, G. R. G. Chengui, A. Coillet, L. Larger, P. Woafo, and Y. K. Chembo, “Mixed-mode oscillations in slow-fast delayed optoelectronic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(1), 012902 (2015).
[Crossref] [PubMed]

Tang, 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).
[Crossref] [PubMed]

M. Cheng, L. Deng, X. Gao, H. Li, M. Tang, S. Fu, P. Shum, and D. Liu, “Security-Enhanced OFDM-PON Using Hybrid Chaotic System,” IEEE Photonics Technol. Lett. 27(3), 326–329 (2015).
[Crossref]

Toomey, J. P.

Valley, G. C.

Van der Sande, G.

Verschaffelt, G.

Wang, A.

Wang, C.

Wang, Y.

Woafo, P.

J. H. Talla Mbé, A. F. Talla, G. R. G. Chengui, A. Coillet, L. Larger, P. Woafo, and Y. K. Chembo, “Mixed-mode oscillations in slow-fast delayed optoelectronic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(1), 012902 (2015).
[Crossref] [PubMed]

Wu, B.

B. Wu, B. J. Shastri, P. Mittal, A. N. Tait, and P. R. Prucnal, “Optical signal processing and stealth transmission for privacy,” IEEE J. Sel. Top. Signal Process. 9(7), 1185–1194 (2015).

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).
[Crossref]

Xiang, S.

Xiong, N.

Y. Deng, H. Hu, N. Xiong, W. Xiong, and L. Liu, “A general hybrid model for chaos robust synchronization and degradation reduction,” Inf. Sci. 305, 146–164 (2015).
[Crossref]

Xiong, W.

Y. Deng, H. Hu, N. Xiong, W. Xiong, and L. Liu, “A general hybrid model for chaos robust synchronization and degradation reduction,” Inf. Sci. 305, 146–164 (2015).
[Crossref]

Xue, C.

Xue, L.

Yan, L.

Yao, J.

Yao, T.

Zhang, J.

Zhang, M.

Zhang, S.

Zhu, D.

Zou, X.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

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).
[Crossref]

Chaos (2)

N. J. Corron, J. N. Blakely, and M. T. Stahl, “A matched filter for chaos,” Chaos 20(2), 023123 (2010).
[Crossref] [PubMed]

N. J. Corron, R. M. Cooper, and J. N. Blakely, “Analytically Solvable Chaotic Oscillator Based on a First-Order Filter,” Chaos 26(2), 023104 (2016).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (1)

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).
[Crossref]

IEEE J. Sel. Top. Signal Process. (1)

B. Wu, B. J. Shastri, P. Mittal, A. N. Tait, and P. R. Prucnal, “Optical signal processing and stealth transmission for privacy,” IEEE J. Sel. Top. Signal Process. 9(7), 1185–1194 (2015).

IEEE Photonics Technol. Lett. (3)

M. Cheng, L. Deng, X. Gao, H. Li, M. Tang, S. Fu, P. Shum, and D. Liu, “Security-Enhanced OFDM-PON Using Hybrid Chaotic System,” IEEE Photonics Technol. Lett. 27(3), 326–329 (2015).
[Crossref]

T. Katayama, D. Hayashi, and H. Kawaguchi, “All-Optical Shift Register Using Polarization Bistable VCSEL Array,” IEEE Photonics Technol. Lett. 20(19), 2062–2065 (2016).
[Crossref]

E. Lazzeri, G. Berrettini, G. Meloni, A. Bogoni, and L. Potì, “All-Optical N-Bits Shift Register Exploiting a Ring Buffer Based on Semiconductor Optical Amplifier,” IEEE Photonics Technol. Lett. 23(1), 45–47 (2011).
[Crossref]

Inf. Sci. (1)

Y. Deng, H. Hu, N. Xiong, W. Xiong, and L. Liu, “A general hybrid model for chaos robust synchronization and degradation reduction,” Inf. Sci. 305, 146–164 (2015).
[Crossref]

J. Lightwave Technol. (3)

Nat. Photonics (1)

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]

Neural Netw. (1)

Y. Horio, T. Ikeguchi, and K. Aihara, “A mixed analog/digital chaotic neuro-computer system for quadratic assignment problems,” Neural Netw. 18(5-6), 505–513 (2005).
[Crossref] [PubMed]

Opt. Express (7)

Opt. Lett. (3)

Phys. Rev. A (1)

Y. K. Chembo, M. Jacquot, J. M. Dudley, and L. Larger, “Ikeda-like chaos on a dynamically filtered supercontinuum light source,” Phys. Rev. A 94(2), 023847 (2016).
[Crossref]

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

J. H. Talla Mbé, A. F. Talla, G. R. G. Chengui, A. Coillet, L. Larger, P. Woafo, and Y. K. Chembo, “Mixed-mode oscillations in slow-fast delayed optoelectronic systems,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(1), 012902 (2015).
[Crossref] [PubMed]

Y. C. Kouomou, P. Colet, N. Gastaud, and L. Larger, “Effect of parameter mismatch on the synchronization of chaotic semiconductor lasers with electro-optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(5), 056226 (2004).
[Crossref] [PubMed]

M. Peil, M. Jacquot, Y. K. Chembo, L. Larger, and T. Erneux, “Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026208 (2009).
[Crossref] [PubMed]

Phys. Rev. Lett. (4)

R. Hegger, M. J. Bunner, H. Kantz, and A. Giaquinta, “Identifying and modeling delay feedback systems,” Phys. Rev. Lett. 81(3), 558–561 (1998).
[Crossref]

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett. 107(3), 034103 (2011).
[Crossref] [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).
[Crossref] [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).
[Crossref] [PubMed]

Physica D (1)

N. J. Corron, R. M. Cooper, and J. N. Blakely, “Entropy rates of low-significance bits sampled from chaotic physical systems,” Physica D 332, 34–40 (2016).
[Crossref]

Other (3)

M. Boesgaard, M. Vesterager, T. Pedersen, J. Christiansen, and O. Scavenius, “Rabbit: A new high-performance stream cipher, ” In Fast Software Encryption, Thomas Johansson, ed. (Springer Berlin Heidelberg, 2003).

J. N. Blakely, M. S. Milosavljevic, and N. J. Corron, “Timing variation in an analytically solvable chaotic system,” Physica D (to be published).

A. Argyris, D. Kanakidis, and D. Syvridis, “Noise dependence of high bit-rate optical chaotic communication back-to-back systems,” in Optical Fiber Communication Conference (Optical Society of America, 2003), MF79.
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 (a) The principle of the scheme; (b) The system setup.
Fig. 2
Fig. 2 The dynamic behavior of waveforms. (a), (b), (c) and (d) correspond to G = 0.28, 0.4, 2 and 10 respectively using the ideal filter. (e), (f), (g), (h) show their details. (i), (j), (k) and (l) correspond to G = 0.25, 0.4, 1.8 and 10 using the experimnetal response.
Fig. 3
Fig. 3 The bifuraction of x3.
Fig. 4
Fig. 4 (a) corresponds to the attractor of x2 using the ideal filter; (b) and (c) correspond to the attractors of Fig. 2(h) and Fig. 2(l).
Fig. 5
Fig. 5 The frequency spectrums correspond to (a) Fig. 2(h); (b) Fig. 2(l).
Fig. 6
Fig. 6 The relationship between the complexity and G, N: (a) the LZC of x1; (b) the PE of x3.
Fig. 7
Fig. 7 The relationship between the complexity and B, N: (a) the LZC of x1; (b) the PE of x3.
Fig. 8
Fig. 8 The correlation of x3.
Fig. 9
Fig. 9 ACF of x3 for B = 1~6.
Fig. 10
Fig. 10 Two improving scheme: (a) digital method; (b) analog method.
Fig. 11
Fig. 11 The ACF of x3 using (a) the digital method and (b) the analog method.

Tables (1)

Tables Icon

Table 1 The measured complexity for B = 6~8

Equations (10)

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

E(t)=S(t)exp(jωt+ ϕ 0 )= E ˜ (t)exp(jωt+ ϕ 0 ),
S(t)=A x 1 (n),nTt(n+1)T, x 1 { 0,1 },
E ˜ (t)=S(t)=A x 1 (n),nTt(n+1)T.
d 2 x 2 (t) d t 2 +2β d x 2 (t) dt +( w 2 + β 2 ) x 2 (t)= E ˜ (t).
x 3 (t)= γ 2 P 2 cos 2 ( π γ 1 a 2 x 2 2 (t) V pi +φ)
G=( γ 1 a 2 x 2 2 (t) V pi ) pkpk .
x 1 (n)=f(g( x 3 (tτ)δ(tnT+T/2)) γ 2 P 2 )),n=1,2,3...
g(x)={ round(x 2 M ),x<1 1 2 M+1 2 M 1,x1 1 2 M+1 ,
f(x)=(x 2 1B )mod2,
ρ= ( y 1 (t) y 1 (t))( y 2 (t+Δt) y 2 (t)) ( y 1 (t) y 1 (t)) 2 ( y 2 (t+Δt) y 2 (t)) 2 ,

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