Numerical characterization of time delay signature in chaotic vertical-cavity surface-emitting lasers with optical feedback

Abstract We have discussed numerically the characterization of time delay (TD) signature in a chaotic vertical-cavity surface-emitting laser (VCSEL) subject to optical feedback, where the results for polarization-preserved optical feedback (PPOF) and polarization-rotated optical feedback (PROF) are presented comparatively. It is found that, when the feedback strength is moderate, TD signature can be retrieved successfully by analyzing the total intensity, intensities of x-linearly polarized (x-LP) mode, and y-LP mode in a VCSEL with PPOF; while for PROF case, the intensity amplitude peaks in autocorrelation function (ACF)/delayed mutual information (DMI) of the two orthogonal LP modes are located at multiple values of TD. Furthermore, the influence of the feedback strength and time delay has been investigated. The results show that, a further increase of the feedback strength (roughly>40 ns−1) leads to the successful identification of the TD signature in the two LP mode intensities of VCSELs with PROF. It is also observed that the estimation of TD depends significantly on the value of the spin–flip relaxation rate (γs). For low relaxation rates the TD signature could be much easier to be revealed by the two LP modes than that for large values of relaxation rate in VCSELs with PROF. Finally the influence of injection current and the device linear anisotropies is investigated, and the results of TD estimation are confirmed by calculating permutation entropy (PE).

[1]  K. Shore,et al.  Experimental study of polarization switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation. , 2005, Optics letters.

[2]  Alexandre Locquet,et al.  Influence of polarization mode competition on the synchronization of two unidirectionally coupled vertical-cavity surface-emitting lasers. , 2007, Optics letters.

[3]  Wei Pan,et al.  Quantifying Information Flow between Two Chaotic Semiconductor Lasers Using Symbolic Transfer Entropy , 2012 .

[4]  Jan Danckaert,et al.  Polarization message encoding through vectorial chaos synchronization in vertical-cavity surface-emitting lasers. , 2003, Physical review letters.

[5]  M. Lee,et al.  Dynamical characterisation of laser diode subject to double optical feedback for chaotic optical communications , 2005 .

[6]  B. Pompe,et al.  Permutation entropy: a natural complexity measure for time series. , 2002, Physical review letters.

[7]  Ingo Fischer,et al.  Estimation of delay times from a delayed optical feedback laser experiment , 1998 .

[8]  Anatoly S. Karavaev,et al.  Reconstruction of time-delayed feedback systems from time series , 2005 .

[9]  K. Shore,et al.  Experimental demonstration of VCSEL-based chaotic optical communications , 2004, IEEE Photonics Technology Letters.

[10]  K. Shore,et al.  Suppression of polarization switching in vertical-cavity surface-emitting lasers by use of optical feedback. , 2004, Optics letters.

[11]  Wei Pan,et al.  Conceal time-delay signature of chaotic vertical-cavity surface-emitting lasers by variable-polarization optical feedback , 2011 .

[12]  M. Sciamanna,et al.  Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Bin Luo,et al.  Analysis of nonlinear dynamics and detecting messages embedded in chaotic carriers using sample entropy algorithm , 2011 .

[14]  S. Giovannoni,et al.  Molecular diversity and ecology of microbial plankton , 2005, Nature.

[15]  S. Ortín,et al.  Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction , 2005 .

[16]  S. Ortin,et al.  Time-Delay Identification in a Chaotic Semiconductor Laser With Optical Feedback: A Dynamical Point of View , 2009, IEEE Journal of Quantum Electronics.

[17]  Neal B. Abraham,et al.  Polarization properties of vertical-cavity surface-emitting lasers , 1997 .

[18]  Roy,et al.  Communication with chaotic lasers , 1998, Science.

[19]  C. Masoller,et al.  Influence of optical feedback on the polarization switching of vertical-cavity surface-emitting lasers , 2005, IEEE Journal of Quantum Electronics.

[20]  D. Rontani,et al.  Multiplexed encryption using chaotic systems with multiple stochastic-delayed feedbacks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Zheng-Mao Wu,et al.  Evolution of time delay signature of chaos generated in a mutually delay-coupled semiconductor lasers system. , 2012, Optics express.

[22]  Romain Modeste Nguimdo,et al.  Digital key for chaos communication performing time delay concealment. , 2011, Physical review letters.

[23]  W. Pan,et al.  Variable-polarization optical feedback induced hysteresis of the polarization switching in vertical-cavity surface-emitting lasers , 2010 .

[24]  Junji Ohtsubo,et al.  Observation of the synchronization of chaos in mutually injected vertical-cavity surface-emitting semiconductor lasers. , 2003, Optics letters.

[25]  J. Ohtsubo.  Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback , 2002 .

[26]  S. Sivaprakasam,et al.  Message encoding and decoding using chaotic external-cavity diode lasers , 2000, IEEE Journal of Quantum Electronics.

[27]  Wei Pan,et al.  Chaotic optical cryptographic communication using a three-semiconductor-laser scheme , 2012 .

[28]  G. Agrawal,et al.  Elliptical polarization emission from GaAlAs laser diodes in an external cavity configuration , 1996 .

[29]  Silvano Donati,et al.  Chaos and locking in a semiconductor laser due to external injection , 1994 .

[30]  M. Lee,et al.  Enhanced chaos synchronization in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers with polarization-preserved injection. , 2008, Optics letters.

[31]  Zheng-Mao Wu,et al.  Dual-channel chaos synchronization and communication based on unidirectionally coupled VCSELs with polarization-rotated optical feedback and polarization-rotated optical injection. , 2009, Optics express.

[32]  Yanhua Hong,et al.  GHz Bandwidth Message Transmission Using Chaotic Vertical-Cavity Surface-Emitting Lasers , 2009, Journal of Lightwave Technology.

[33]  K. Shore,et al.  Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface-emitting lasers , 2005, IEEE Journal of Quantum Electronics.

[34]  Wei Pan,et al.  Chaos synchronization of unidirectionally injected vertical-cavity surface-emitting lasers with global and mode-selective coupling. , 2006, Optics express.

[35]  Holger Kantz,et al.  Identifying and Modeling Delay Feedback Systems. , 1998, chao-dyn/9907019.

[36]  Jiagui Wu,et al.  Suppression of time delay signatures of chaotic output in a semiconductor laser with double optical feedback. , 2009, Optics express.

[37]  Laurent Larger,et al.  Chaos-based communications at high bit rates using commercial fibre-optic links , 2005, Nature.

[38]  Cristina Masoller,et al.  Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback , 1999 .

[39]  R. Toral,et al.  Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop , 2005, IEEE Journal of Quantum Electronics.

[40]  M. Benedetti,et al.  Private Message Transmission by Common Driving of Two Chaotic Lasers , 2010, IEEE Journal of Quantum Electronics.

[41]  M. C. Soriano,et al.  Permutation-information-theory approach to unveil delay dynamics from time-series analysis. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  Wei Pan,et al.  On joint identification of the feedback parameters for hyperchaotic systems: An optimization-based approach , 2011 .

[43]  Wei Pan,et al.  Polarization degree of vertical-cavity surface-emitting lasers subject to optical feedback with controllable polarization , 2010 .

[44]  Wei Pan,et al.  Polarization Switching and Hysteresis of VCSELs With Time-Varying Optical Injection , 2008, IEEE Journal of Selected Topics in Quantum Electronics.

[45]  D S Citrin,et al.  Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback. , 2007, Optics letters.

[46]  W. Pan,et al.  Chaos synchronization communication using extremely unsymmetrical bidirectional injections. , 2008, Optics letters.

[47]  Romain Modeste Nguimdo,et al.  Role of the phase in the identification of delay time in semiconductor lasers with optical feedback. , 2011, Optics letters.

[48]  Laurent Larger,et al.  Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations , 2003 .

[49]  Xiaofeng Li,et al.  Mismatch robustness and security of chaotic optical communications based on injection-locking chaos synchronization , 2006, IEEE Journal of Quantum Electronics.