Abstract

A system framework is proposed and analyzed for generating polarization-resolved wideband unpredictability-enhanced chaotic signals based on a slave vertical-cavity surface-emitting laser (S-VCSEL) driven by an injected optical chaos signal from a master VCSEL (M-VCSEL) under optical feedback. After calculating the time series outputs from the M-VCSEL under optical feedback and the S-VCSEL under chaotic optical injection by using the spin-flip model (SFM), the unpredictability degree (UD) is evaluated by permutation entropy (PE), and the bandwidth of the polarization-resolved outputs from the M-VCSEL and S-VCSEL are numerically investigated. The results show that, under suitable parameters, both the bandwidth and UD of two polarization components (PCs) outputs from the S-VCSEL can be enhanced significantly compared with that of the driving chaotic signals output from the M-VCSEL. By simulating the influences of the feedback and injection parameters on the bandwidth and UD of the polarization-resolved outputs from S-VCSEL, related operating parameters can be optimized.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  39. Z. Q. Zhong, Z. M. Wu, J. G. Wu, and G. Q. Xia, “Time-delay signature suppression of polarization-resolved chaos outputs from two mutually coupled VCSELs,” IEEE Photon. J. 5(2), 1500409 (2013).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  43. M. Virte, K. Panajotov, and M. Sciamanna, “Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87(1), 013834 (2013).
    [Crossref]
  44. Y. Hong, P. S. Spencer, and K. A. Shore, “Wideband chaos with time-delay concealment in vertical-cavity surface-emitting lasers with optical feedback and injection,” IEEE J. Quantum Electron. 50(4), 236–242 (2014).
    [Crossref]
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    [Crossref]
  47. M. S. Baptista, E. J. Ngamga, P. R. F. Pinto, M. Brito, and J. Kurths, “Kolmogorov–Sinai entropy from recurrence times,” Phys. Lett. A 374(9), 1135–1140 (2010).
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    [Crossref] [PubMed]

2015 (1)

2014 (2)

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

Y. Hong, P. S. Spencer, and K. A. Shore, “Wideband chaos with time-delay concealment in vertical-cavity surface-emitting lasers with optical feedback and injection,” IEEE J. Quantum Electron. 50(4), 236–242 (2014).
[Crossref]

2013 (2)

Z. Q. Zhong, Z. M. Wu, J. G. Wu, and G. Q. Xia, “Time-delay signature suppression of polarization-resolved chaos outputs from two mutually coupled VCSELs,” IEEE Photon. J. 5(2), 1500409 (2013).
[Crossref]

M. Virte, K. Panajotov, and M. Sciamanna, “Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87(1), 013834 (2013).
[Crossref]

2012 (6)

D. W. Sukow, T. Gilfillan, B. Pope, M. S. Torre, A. Gavrielides, and C. Masoller, “Square-wave switching in vertical-cavity surface-emitting lasers with polarization-rotated optical feedback: Experiments and simulations,” Phys. Rev. A 86(3), 033818 (2012).
[Crossref]

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2012).
[Crossref]

S. Y. Xiang, W. Pan, N. Q. Li, B. Luo, L. S. Yan, X. H. Zou, L. Y. Zhang, and P. H. Mu, “Randomness-Enhanced Chaotic Source With Dual-Path Injection from a Single Master Laser,” IEEE Photon. Technol. Lett. 24(19), 1753–1756 (2012).
[Crossref]

S. Y. Xiang, W. Pan, B. Luo, L. S. Yan, X. H. Zou, N. Q. Li, and H. N. Zhu, “Wideband unpredictability-enhanced chaotic semiconductor lasers with dual-chaotic optical injections,” IEEE J. Quantum Electron. 48(8), 1069–1076 (2012).
[Crossref]

S. T. Kingni, J. H. Talla Mbé, and P. Woafo, “Nonlinear dynamics in VCSELs driven by a sinusoidally modulated current and Rössler oscillator,” Eur. Phys. J. Plus 127(5), 46–55 (2012).
[Crossref]

S. Priyadarshi, I. Pierce, Y. Hong, and K. A. Shore, “Optimal operating conditions for external cavity semiconductor laser optical chaos communication system,” Semicond. Sci. Technol. 27(9), 094002 (2012).
[Crossref]

2011 (2)

L. Zunino, O. A. Rosso, and M. C. Soriano, “Characterizing the hyperchaotic dynamics of a semiconductor laser subject to optical feedback via permutation entropy,” IEEE J. Sel. Top. Quantum Electron. 17(5), 1250–1257 (2011).
[Crossref]

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, “Time scales of a chaotic semiconductor laser with optical feedback under the lens of a permutation information analysis,” IEEE J. Quantum Electron. 47(2), 252–261 (2011).
[Crossref]

2010 (6)

L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, “Permutation-information-theory approach to unveil delay dynamics from time-series analysis,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(4), 046212 (2010).
[Crossref] [PubMed]

M. S. Baptista, E. J. Ngamga, P. R. F. Pinto, M. Brito, and J. Kurths, “Kolmogorov–Sinai entropy from recurrence times,” Phys. Lett. A 374(9), 1135–1140 (2010).
[Crossref]

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

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

J. P. Toomey, D. M. Kane, M. W. Lee, and K. A. Shore, “Nonlinear dynamics of semiconductor lasers with feedback and modulation,” Opt. Express 18(16), 16955–16972 (2010).
[Crossref] [PubMed]

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]

2009 (7)

A. B. Wang, Y. C. Wang, and J. F. Wang, “Route to broadband chaos in a chaotic laser diode subject to optical injection,” Opt. Lett. 34(8), 1144–1146 (2009).
[Crossref] [PubMed]

J. Liu, Z. M. Wu, and G. Q. Xia, “Dual-channel chaos synchronization and communication based on unidirectionally coupled VCSELs with polarization-rotated optical feedback and polarization-rotated optical injection,” Opt. Express 17(15), 12619–12626 (2009).
[Crossref] [PubMed]

H. Someya, I. Oowada, H. Okumura, T. Kida, and A. Uchida, “Synchronization of bandwidth-enhanced chaos in semiconductor lasers with optical feedback and injection,” Opt. Express 17(22), 19536–19543 (2009).
[Crossref] [PubMed]

J. G. Wu, G. Q. Xia, and Z. M. Wu, “Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback,” Opt. Express 17(22), 20124–20133 (2009).
[Crossref] [PubMed]

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

S. L. Yan, “Bifurcation and locking in a multi-quantum-well laser subjected to external injection,” Opt. Commun. 282(17), 3558–3564 (2009).
[Crossref]

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view,” IEEE J. Quantum Electron. 45(7), 879–891 (2009).
[Crossref]

2008 (3)

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20(19), 1633–1635 (2008).
[Crossref]

J. Paul, C. Masoller, P. Mandel, Y. Hong, P. S. Spencer, and K. A. Shore, “Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarization switching of vertical-cavity surface-emitting lasers,” Phys. Rev. A 77(4), 043803 (2008).
[Crossref]

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

2007 (1)

C. Masoller, M. S. Torre, and K. A. Shore, “Polarization dynamics of current-modulated vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 43(11), 1074–1082 (2007).
[Crossref]

2006 (1)

2005 (3)

J. Paul, M. W. Lee, and K. A. Shore, “3.5-GHz signal transmission in an all-optical chaotic communication scheme using 1550-nm diode lasers,” IEEE Photon. Technol. Lett. 17(4), 920–922 (2005).
[Crossref]

R. Vicente, J. Daudén, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron. 41(4), 541–548 (2005).
[Crossref]

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

2004 (1)

F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10(5), 991–997 (2004).
[Crossref]

2003 (1)

2002 (2)

C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett. 88(17), 174102 (2002).
[Crossref] [PubMed]

J. Ohtsubo, “Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. Quantum Electron. 38(9), 1141–1154 (2002).
[Crossref]

2001 (1)

J. García-Ojalvo and R. Roy, “Spatiotemporal communication with synchronized optical chaos,” Phys. Rev. Lett. 86(22), 5204–5207 (2001).
[Crossref] [PubMed]

2000 (1)

K. Iga, “Surface-emitting laser—its birth and generation of new optoelectronics field,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1201–1215 (2000).
[Crossref]

1999 (1)

J. Huisman and F. J. Weissing, “Biodiversity of plankton by species oscillations and chaos,” Nature 402(6760), 407–410 (1999).
[Crossref]

1998 (3)

J. Shukla, “Predictability in the midst of chaos: A scientific basis for climate forecasting,” Science 282(5389), 728–731 (1998).
[Crossref] [PubMed]

K. M. Short and A. T. Parker, “Unmasking a hyperchaotic communication scheme,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(1), 1159–1162 (1998).
[Crossref]

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

1997 (1)

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[Crossref]

1995 (1)

L. Chen and K. Aihara, “Chaotic simulated annealing by a neural network model with transient chaos,” Neural Netw. 8(6), 915–930 (1995).
[Crossref]

1993 (2)

K. M. Cuomo and A. V. Oppenheim, “Circuit implementation of synchronized chaos with applications to communications,” Phys. Rev. Lett. 71(1), 65–68 (1993).
[Crossref] [PubMed]

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

Abraham, N. B.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, “Polarization properties of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 33(5), 765–783 (1997).
[Crossref]

Aida, H.

Aihara, K.

L. Chen and K. Aihara, “Chaotic simulated annealing by a neural network model with transient chaos,” Neural Netw. 8(6), 915–930 (1995).
[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, 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, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008).
[Crossref] [PubMed]

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

Aviad, Y.

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

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

Bandt, C.

C. Bandt and B. Pompe, “Permutation entropy: a natural complexity measure for time series,” Phys. Rev. Lett. 88(17), 174102 (2002).
[Crossref] [PubMed]

Baptista, M. S.

M. S. Baptista, E. J. Ngamga, P. R. F. Pinto, M. Brito, and J. Kurths, “Kolmogorov–Sinai entropy from recurrence times,” Phys. Lett. A 374(9), 1135–1140 (2010).
[Crossref]

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

Brito, M.

M. S. Baptista, E. J. Ngamga, P. R. F. Pinto, M. Brito, and J. Kurths, “Kolmogorov–Sinai entropy from recurrence times,” Phys. Lett. A 374(9), 1135–1140 (2010).
[Crossref]

Bünner, M. J.

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Y. Hong, P. S. Spencer, and K. A. Shore, “Wideband chaos with time-delay concealment in vertical-cavity surface-emitting lasers with optical feedback and injection,” IEEE J. Quantum Electron. 50(4), 236–242 (2014).
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S. Y. Xiang, W. Pan, N. Q. Li, B. Luo, L. S. Yan, X. H. Zou, L. Y. Zhang, and P. H. Mu, “Randomness-Enhanced Chaotic Source With Dual-Path Injection from a Single Master Laser,” IEEE Photon. Technol. Lett. 24(19), 1753–1756 (2012).
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Figures (8)

Fig. 1
Fig. 1 Schematic diagram of a VCSELs-based chaotic system for generating polarization-resolved wideband unpredictability-enhanced chaotic signals. M-VCSEL: master vertical-cavity surface-emitting laser; S-VCSEL: slave vertical-cavity surface-emitting laser; M: mirror; VA: variable attenuator; ISO: optical isolator.
Fig. 2
Fig. 2 P-I curves (a), time series (b1, b2), and corresponding optical spectra (c1, c2) of polarization-resolved outputs from a solitary VCSEL under u = 2.7
Fig. 3
Fig. 3 Time series (the first row) of polarization-resolved chaos outputs and corresponding power spectra (the second row) with kf = 15 ns−1, τf = 3 ns, η = 50 ns−1 and Δv = 20 GHz.
Fig. 4
Fig. 4 Bandwidths of X-PC and Y-PC of S-VCSEL as a function of the injection strength η under kf = 15 ns−1 and τf = 3 ns for different frequency detuning.
Fig. 5
Fig. 5 Evolution maps of bandwidths of the polarization-resolved outputs from S-VCSEL in the parameter space of injection strength η and frequency detuning Δv under τf = 3 ns and kf = 15 ns−1.
Fig. 6
Fig. 6 PE of the polarization-resolved outputs from M-VCSEL and S-VCSEL as functions of feedback strength kf (the first row) and feedback delay time τf (the second row) with Δν = 0 GHz and η = 15 ns−1.
Fig. 7
Fig. 7 Evolution maps of PE of the polarization-resolved outputs from M-VCSEL (the first row) and S-VCSEL (the second row) under Δν = 0 GHz and η = 15 ns−1 in the parameter space of delay time τ and feedback strength kf, where different colors represent different values of PE.
Fig. 8
Fig. 8 Evolution maps of PE of the polarization-resolved outputs from S-VCSEL in the parameter space of injection strength η and frequency detuning Δν with τf = 3 ns for kf = 15 ns−1 (the first row), kf = 30 ns−1 (the second row) and kf = 45 ns−1 (the third row).

Equations (7)

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d E x,y M dt = k M (1+i α M )[( N M 1) E x,y M ±i n M E y,x M ]( γ a M +i γ p M ) E x,y M + k f E x,y M (t τ f ) e i2π v M τ f + β sp ξ x,y M
d E x,y S dt = k S (1+i α S )[( N S 1) E x,y S ±i n S E y,x S ]( γ a S +i γ p S ) E x,y S +η E x,y M (t τ η ) e i2π v M τ η +i2πΔvt + β sp ξ x,y S
d N M,S dt = γ e M,S [ N M,S (1+| E x M,S | 2 +| E y M,S | 2 ) u M,S +i n M,S ( E y M,S E x M,S E x M,S E y M,S )]
d n M,S dt = γ s M,S n M,S γ e M,S [ n M,S (| E x M,S | 2 +| E y M,S | 2 )+i N M,S ( E y M,S E x M,S E x M,S E y M,S )]
p(π)= #{m| mND,( S m+1 ,, S m+D ) hastypeπ} ND+1
h[p]= p(π) logp(π)
H[p]= h[p] h max = p(π) logp(π) log(D!)

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