Abstract

Variable-polarization optical feedback (VPOF) induced unpredictability enhancement in a vertical-cavity surface-emitting laser (VCSEL) is investigated numerically based on the spin-flip model. The chaotic unpredictability is evaluated quantitatively via an information-theory-based quantifier, the permutation entropy (PE). The role of polarizer angle on the chaotic unpredictability is focused on. The influences of feedback strengths, feedback delays, and injection currents are also considered. A critical polarizer angle, at which the PE reaches its maximum, is existed for relatively high feedback strength and injection current. The representations on Poincaré sphere are further given to provide physical insight into the unpredictability enhancement. Besides, larger feedback strength leads to lower critical polarizer angle, while larger injection current contributes to higher critical polarizer angle. These results show that, by selecting critical polarizer angles, the unpredictability of chaotic signals of VCSELs with VPOF can be enhanced significantly, which is extremely useful for VCSELs-based chaotic communication systems.

© 2011 IEEE

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  26. M. T. Martin, A. Plastino, O. A. Rosso, "Statistical complexity and disequilibrium," Phys. Lett. A 311, 126-132 (2003).
  27. O. A. Rosso, H. A. Larrondo, M. T. Martin, A. Plastino, M. A. Fuentes, "Distinguishing noise from chaos," Phys. Rev. Lett. 99, 154102_1-154102_4 (2007).
  28. O. A. Rosso, R. Vicente, C. R. Mirasso, "Encryption test of pseudo- aleatory messages embedded on chaotic laser signals: an information theory approach," Phys. Lett. A 372, 1018-1023 (2008).
  29. M. C. Soriano, L. Zunino, O. A. Rosso, C. R. Mirasso, "Quantifying complexity of the chaotic regime of a semiconductor laser subject to feedback via information theory measures," Proc. SPIE (2010) pp. 77202G_1-77202G_10.
  30. M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, 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, 252-261 (2011).
  31. J. Tiana-Alsina, M. C. Torrent, O. A. Rosso, C. Masoller, J. Garcia-Ojalvo, "Quantifying the statistical complexity of low-frequency fluctuations in semiconductor lasers with optical feedback," Phys. Rev. A 82, 013819_1-013819_6 (2010).
  32. S. Y. Xiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, N. Jiang, K. H. Wen, "Quantifying chaotic unpredictability of vertical-cavity surface-emitting lasers with polarized optical feedback via permutation entropy," IEEE J. Sel. Topics Quantum Electron. (to be published).
  33. S. Xiang, W. Pan, L. Yan, B. Luo, X. Zou, N. Jiang, K. Wen, "Influence of polarization-mode-competition on chaotic unpredictability of vertical-cavity surface-emitting lasers with polarization-rotated optical feedback," Opt. Lett. 36, 310-312 (2011).
  34. Y. Cao, W. Tung, J. B. Gao, V. A. Protopopescu, L. M. Hively, "Detecting dynamical changes in time series using the permutation entropy," Phys. Rev. E 70, 046217_1-046217_7 (2004).
  35. S. Ramanujan, G. P. Agrawal, J. M. Chwalek, H. Winful, "Elliptical polarization emission from GaAlAs laser diodes in an external cavity configuration," IEEE J. Quantum Electron. 32, 213-221 (1996).
  36. L. Chrostowski, B. Faraji, W. Hofmann, M. C. Amann, S. Wieczorek, W. W. Chow, "40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 $\mu$m VCSELs," IEEE J. Sel. Topics Quantum Electron. 13, 1200-1208 (2007).
  37. C. Masoller, N. B. Abraham, "Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback," Phys. Rev. A 59, 3021-3031 (1999).

2011 (2)

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, 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, 252-261 (2011).

S. Xiang, W. Pan, L. Yan, B. Luo, X. Zou, N. Jiang, K. Wen, "Influence of polarization-mode-competition on chaotic unpredictability of vertical-cavity surface-emitting lasers with polarization-rotated optical feedback," Opt. Lett. 36, 310-312 (2011).

2010 (3)

J. Tiana-Alsina, M. C. Torrent, O. A. Rosso, C. Masoller, J. Garcia-Ojalvo, "Quantifying the statistical complexity of low-frequency fluctuations in semiconductor lasers with optical feedback," Phys. Rev. A 82, 013819_1-013819_6 (2010).

S. Xiang, W. Pan, L. Yan, B. Luo, N. Jiang, K. Wen, X. Zou, L. Yang, "Polarization degree of vertical-cavity surface-emitting lasers subject to optical feedback with controllable polarization.," J. Opt. Soc. Amer. B. 27, 476-483 (2010).

N. Jiang, W. Pan, L. Yan, B. Luo, W. Zhang, S. Xiang, L. Yang, D. Zheng, "Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser," J. Lightw. Technol. 28, 1978-1986 (2010).

2009 (2)

Y. Hong, M. W. Lee, J. Paul, P. S. Spencer, K. A. Shore, "GHz bandwidth message transmission using chaotic vertical-cavity surface- emitting lasers," J. Lightw. Technol. 27, 5099-5105 (2009).

J. Liu, Z. M. Wu, 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. Exp. 17, 12619-12626 (2009).

2008 (3)

Y. Hong, M. W. Lee, J. Paul, P. S. Spencer, K. A. Shore, "Enhanced chaos synchronization in unidirectionally coupled vertical-cavity surface- emitting semiconductor lasers with polarization-preserved injection," Opt. Lett. 33, 587-589 (2008).

W. L. Zhang, W. Pan, B. Luo, X. H. Zuo, M. Y. Wang, "Polarization switching and hysteresis of VCSELs with time-varying optical injection," IEEE J. Sel. Topics Quantum Electron. 14, 889-894 (2008).

O. A. Rosso, R. Vicente, C. R. Mirasso, "Encryption test of pseudo- aleatory messages embedded on chaotic laser signals: an information theory approach," Phys. Lett. A 372, 1018-1023 (2008).

2007 (4)

L. Chrostowski, B. Faraji, W. Hofmann, M. C. Amann, S. Wieczorek, W. W. Chow, "40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 $\mu$m VCSELs," IEEE J. Sel. Topics Quantum Electron. 13, 1200-1208 (2007).

M. Sciamanna, I. Gatare, A. Locquet, K. Panajotov, "Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection," Phys. Rev. E. 75, 056213_1-056213_10 (2007).

I. Gatare, M. Sciamanna, A. Locquet, K. Panajotov, "Influence of polarization mode competition on the synchronization of two unidirectionally coupled vertical-cavity surface-emitting lasers," Opt. Lett. 32, 1629-1631 (2007).

O. A. Rosso, H. A. Larrondo, M. T. Martin, A. Plastino, M. A. Fuentes, "Distinguishing noise from chaos," Phys. Rev. Lett. 99, 154102_1-154102_4 (2007).

2006 (1)

2005 (4)

R. Ju, P. S. Spencer, K. A. Shore, "Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface- emitting lasers," IEEE J. Quantum Electron. 41, 1461-1467 (2005).

R. Vicente, J. Daudén, P. Colet, R. Toral, "Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop," IEEE J. Quantum Electron. 41, 541-548 (2005).

C. Masoller, M. S. Torre, "Influence of optical feedback on the polarization switching of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 41, 483-489 (2005).

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, "Chaos-based communications at high bit rates using commercial fiberoptic links," Nature 437, 343-346 (2005).

2004 (1)

Y. Cao, W. Tung, J. B. Gao, V. A. Protopopescu, L. M. Hively, "Detecting dynamical changes in time series using the permutation entropy," Phys. Rev. E 70, 046217_1-046217_7 (2004).

2003 (3)

M. T. Martin, A. Plastino, O. A. Rosso, "Statistical complexity and disequilibrium," Phys. Lett. A 311, 126-132 (2003).

A. Scire, J. Mulet, C. R. Mirasso, J. Danckaert, M. S. Miguel, "Polarization message encoding through vectorial chaos synchronization in vertical-cavity surface-emitting lasers," Phys. Rev. Lett. 90, 113901-1-113901-4 (2003).

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, M. Blondel, "Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers," Opt. Lett. 28, 1543-1545 (2003).

2002 (3)

J. Ohtsubo, "Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback," IEEE J. Quantum Electron. 38, 1141-1154 (2002).

J. M. Liu, H. F. Chen, S. Tang, "Synchronized chaotic optical communications at high bit rates," IEEE J. Quantum Electron. 38, 1184-1196 (2002).

C. Bandt, B. Pompe, "Permutation entropy: A natural complexity measure for time series," Phys. Rev. Lett. 88, 174102_1-174102_4 (2002).

1999 (1)

C. Masoller, N. B. Abraham, "Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback," Phys. Rev. A 59, 3021-3031 (1999).

1998 (1)

V. Ahlers, U. Parlitz, W. Lauterborn, "Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers," Phys. Rev. E. 58, 7208-7213 (1998).

1997 (1)

J. Martin-Regalado, F. Prati, M. S. Miguel, N. B. Abraham, "Polarization properties of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 33, 765-783 (1997).

1996 (1)

S. Ramanujan, G. P. Agrawal, J. M. Chwalek, H. Winful, "Elliptical polarization emission from GaAlAs laser diodes in an external cavity configuration," IEEE J. Quantum Electron. 32, 213-221 (1996).

1995 (2)

R. López-Ruiz, H. L. Mancini, X. Calbet, "A statistical measure of complexity," Phys. Lett. A 209, 321-326 (1995).

M. S. Miguel, Q. Feng, J. V. Moloney, "Light polarization dynamics in surface-emitting semiconductor lasers," Phys. Rev. A 52, 1728-1739 (1995).

1993 (1)

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, M. W. Focht, "Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 2999-3001 (1993).

1990 (1)

L. M. Pecora, T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990).

1982 (1)

J. D. Farmer, "Chaotic attractors of an infinite-dimensional dynamical system," Physica D 4, 366-393 (1982).

Appl. Phys. Lett. (1)

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, M. W. Focht, "Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 2999-3001 (1993).

IEEE J. Quantum Electron. (8)

J. Ohtsubo, "Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback," IEEE J. Quantum Electron. 38, 1141-1154 (2002).

J. M. Liu, H. F. Chen, S. Tang, "Synchronized chaotic optical communications at high bit rates," IEEE J. Quantum Electron. 38, 1184-1196 (2002).

C. Masoller, M. S. Torre, "Influence of optical feedback on the polarization switching of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 41, 483-489 (2005).

J. Martin-Regalado, F. Prati, M. S. Miguel, N. B. Abraham, "Polarization properties of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 33, 765-783 (1997).

R. Ju, P. S. Spencer, K. A. Shore, "Polarization-preserved and polarization-rotated synchronization of chaotic vertical-cavity surface- emitting lasers," IEEE J. Quantum Electron. 41, 1461-1467 (2005).

R. Vicente, J. Daudén, P. Colet, R. Toral, "Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop," IEEE J. Quantum Electron. 41, 541-548 (2005).

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, 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, 252-261 (2011).

S. Ramanujan, G. P. Agrawal, J. M. Chwalek, H. Winful, "Elliptical polarization emission from GaAlAs laser diodes in an external cavity configuration," IEEE J. Quantum Electron. 32, 213-221 (1996).

IEEE J. Sel. Topics Quantum Electron. (3)

L. Chrostowski, B. Faraji, W. Hofmann, M. C. Amann, S. Wieczorek, W. W. Chow, "40 GHz bandwidth and 64 GHz resonance frequency in injection-locked 1.55 $\mu$m VCSELs," IEEE J. Sel. Topics Quantum Electron. 13, 1200-1208 (2007).

S. Y. Xiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, N. Jiang, K. H. Wen, "Quantifying chaotic unpredictability of vertical-cavity surface-emitting lasers with polarized optical feedback via permutation entropy," IEEE J. Sel. Topics Quantum Electron. (to be published).

W. L. Zhang, W. Pan, B. Luo, X. H. Zuo, M. Y. Wang, "Polarization switching and hysteresis of VCSELs with time-varying optical injection," IEEE J. Sel. Topics Quantum Electron. 14, 889-894 (2008).

J. Lightw. Technol. (2)

N. Jiang, W. Pan, L. Yan, B. Luo, W. Zhang, S. Xiang, L. Yang, D. Zheng, "Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser," J. Lightw. Technol. 28, 1978-1986 (2010).

Y. Hong, M. W. Lee, J. Paul, P. S. Spencer, K. A. Shore, "GHz bandwidth message transmission using chaotic vertical-cavity surface- emitting lasers," J. Lightw. Technol. 27, 5099-5105 (2009).

J. Opt. Soc. Amer. B. (1)

S. Xiang, W. Pan, L. Yan, B. Luo, N. Jiang, K. Wen, X. Zou, L. Yang, "Polarization degree of vertical-cavity surface-emitting lasers subject to optical feedback with controllable polarization.," J. Opt. Soc. Amer. B. 27, 476-483 (2010).

Nature (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, "Chaos-based communications at high bit rates using commercial fiberoptic links," Nature 437, 343-346 (2005).

Opt. Exp. (1)

J. Liu, Z. M. Wu, 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. Exp. 17, 12619-12626 (2009).

Opt. Lett. (5)

Phys. Lett. A (3)

R. López-Ruiz, H. L. Mancini, X. Calbet, "A statistical measure of complexity," Phys. Lett. A 209, 321-326 (1995).

M. T. Martin, A. Plastino, O. A. Rosso, "Statistical complexity and disequilibrium," Phys. Lett. A 311, 126-132 (2003).

O. A. Rosso, R. Vicente, C. R. Mirasso, "Encryption test of pseudo- aleatory messages embedded on chaotic laser signals: an information theory approach," Phys. Lett. A 372, 1018-1023 (2008).

Phys. Rev. A (3)

J. Tiana-Alsina, M. C. Torrent, O. A. Rosso, C. Masoller, J. Garcia-Ojalvo, "Quantifying the statistical complexity of low-frequency fluctuations in semiconductor lasers with optical feedback," Phys. Rev. A 82, 013819_1-013819_6 (2010).

C. Masoller, N. B. Abraham, "Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback," Phys. Rev. A 59, 3021-3031 (1999).

M. S. Miguel, Q. Feng, J. V. Moloney, "Light polarization dynamics in surface-emitting semiconductor lasers," Phys. Rev. A 52, 1728-1739 (1995).

Phys. Rev. E (1)

Y. Cao, W. Tung, J. B. Gao, V. A. Protopopescu, L. M. Hively, "Detecting dynamical changes in time series using the permutation entropy," Phys. Rev. E 70, 046217_1-046217_7 (2004).

Phys. Rev. E. (2)

V. Ahlers, U. Parlitz, W. Lauterborn, "Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers," Phys. Rev. E. 58, 7208-7213 (1998).

M. Sciamanna, I. Gatare, A. Locquet, K. Panajotov, "Polarization synchronization in unidirectionally coupled vertical-cavity surface-emitting lasers with orthogonal optical injection," Phys. Rev. E. 75, 056213_1-056213_10 (2007).

Phys. Rev. Lett. (4)

L. M. Pecora, T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990).

A. Scire, J. Mulet, C. R. Mirasso, J. Danckaert, M. S. Miguel, "Polarization message encoding through vectorial chaos synchronization in vertical-cavity surface-emitting lasers," Phys. Rev. Lett. 90, 113901-1-113901-4 (2003).

O. A. Rosso, H. A. Larrondo, M. T. Martin, A. Plastino, M. A. Fuentes, "Distinguishing noise from chaos," Phys. Rev. Lett. 99, 154102_1-154102_4 (2007).

C. Bandt, B. Pompe, "Permutation entropy: A natural complexity measure for time series," Phys. Rev. Lett. 88, 174102_1-174102_4 (2002).

Physica D (1)

J. D. Farmer, "Chaotic attractors of an infinite-dimensional dynamical system," Physica D 4, 366-393 (1982).

Other (1)

M. C. Soriano, L. Zunino, O. A. Rosso, C. R. Mirasso, "Quantifying complexity of the chaotic regime of a semiconductor laser subject to feedback via information theory measures," Proc. SPIE (2010) pp. 77202G_1-77202G_10.

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