Abstract

Similar to edge-emitting lasers, vertical cavity surface emitting lasers (VCSELs) subjected to optical feedback are known for exhibiting erratic fluctuations of their optical power at slow and fast time scales; these are called low-frequency fluctuations (LFF). Here, we demonstrate both experimentally and numerically that the chaotic itinerancy in phase space associated with LFF has a deep connection with the creation of non-local correlations at multiple time scales between the two linear polarization modes. Our result provides a novel framework to interpret the unknown origin of spectral signatures in the optical power of chaotic lasers with optical feedback, which were observed in the past two decades.

© 2017 Optical Society of America

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References

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    [Crossref]
  3. K. D. Choquette, R. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quant. 1(2), 661–666 (1995).
    [Crossref]
  4. M. Willemsen, M. Van Exter, and J. Woerdman, “Anatomy of a polarization switch of a vertical-cavity laser,” Phys. Rev. Lett. 84(19), 4337 (2000).
    [Crossref] [PubMed]
  5. M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
    [Crossref]
  6. J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quant. 3(2), 353–358 (1997).
    [Crossref]
  7. M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28(17), 1543–1545 (2003).
    [Crossref] [PubMed]
  8. M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).
  9. S. Jiang, Z. Pan, M. Dagenais, R. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993).
    [Crossref]
  10. H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72(19), 2355–2357 (1998).
    [Crossref]
  11. M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, “Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays,” Nat. Photonics 9, 450–455 (2015).
    [Crossref]
  12. T. Sano, “Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50(3), 2719 (1994).
    [Crossref] [PubMed]
  13. M. Sciamanna, C. Masoller, N. B. Abraham, F. Rogister, P. Mégret, and M. Blondel, “Different regimes of low-frequency fluctuations in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 20(1), 37–44 (2003).
    [Crossref]
  14. M. Sondermann, H. Bohnet, and T. Ackemann, “Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback,” Phys. Rev. A 67(2), 021802 (2003).
    [Crossref]
  15. A. Naumenko, N. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
    [Crossref]
  16. M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback: experiment and model,” J. Opt. Soc. Am. B 16(11), 2114–2123 (1999).
    [Crossref]
  17. A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
    [Crossref]
  18. M. Sondermann and T. Ackemann, “Correlation properties and drift phenomena in the dynamics of vertical-cavity surface-emitting lasers with optical feedback,” Opt. Express 13(7), 2707–2715 (2005).
    [Crossref] [PubMed]
  19. P. Besnard, B. Meziane, K. Ait-Ameur, and G. Stephan, “Microwave spectra in external-cavity semiconductor lasers: Theoretical modeling of multipass resonances,” IEEE J. Quantum Elect. 30, 1713–1722 (1994).
    [Crossref]
  20. M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55(6), 6414 (1997).
    [Crossref]
  21. L. Langley, J. Mørk, and K. Shore, “Dynamical and noise properties of laser diodes subject to strong optical feedback,” Opt. Lett. 19(24), 2137–2139 (1994).
    [Crossref] [PubMed]
  22. J. Sacher, W. Elsässer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224 (1989).
    [Crossref] [PubMed]
  23. B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, “Reconstruction of time-delay systems from chaotic time series,” Phys. Rev. E 64, 056216 (2001).
    [Crossref]
  24. M. San Miguel, Q. Feng, and J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728 (1995).
    [Crossref] [PubMed]
  25. C. Masoller, “Coexistence of attractors in a laser diode with optical feedback from a large external cavity,” Phys. Rev. A 50(3), 2569 (1994).
    [Crossref] [PubMed]
  26. C. Masoller and N. Abraham, “Stability and dynamical properties of the coexisting attractors of an external-cavity semiconductor laser,” Phys. Rev. A 57(2), 1313 (1998).
    [Crossref]
  27. M. Van Exter, R. Hendriks, J. Woerdman, and C. Van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Optics communications 110(1), 137–140 (1994).
    [Crossref]
  28. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Elect. 16(3), 347–355 (1980).
    [Crossref]
  29. 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 Journal of Quantum Electronics 45(7), 879–1891 (2009).
    [Crossref]

2015 (1)

M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, “Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays,” Nat. Photonics 9, 450–455 (2015).
[Crossref]

2013 (1)

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
[Crossref]

2009 (1)

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 Journal of Quantum Electronics 45(7), 879–1891 (2009).
[Crossref]

2007 (1)

M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).

2006 (1)

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

2005 (1)

2003 (4)

M. Sciamanna, C. Masoller, N. B. Abraham, F. Rogister, P. Mégret, and M. Blondel, “Different regimes of low-frequency fluctuations in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 20(1), 37–44 (2003).
[Crossref]

M. Sondermann, H. Bohnet, and T. Ackemann, “Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback,” Phys. Rev. A 67(2), 021802 (2003).
[Crossref]

A. Naumenko, N. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
[Crossref]

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28(17), 1543–1545 (2003).
[Crossref] [PubMed]

2001 (1)

B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, “Reconstruction of time-delay systems from chaotic time series,” Phys. Rev. E 64, 056216 (2001).
[Crossref]

2000 (1)

M. Willemsen, M. Van Exter, and J. Woerdman, “Anatomy of a polarization switch of a vertical-cavity laser,” Phys. Rev. Lett. 84(19), 4337 (2000).
[Crossref] [PubMed]

1999 (1)

1998 (3)

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998).
[Crossref]

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72(19), 2355–2357 (1998).
[Crossref]

C. Masoller and N. Abraham, “Stability and dynamical properties of the coexisting attractors of an external-cavity semiconductor laser,” Phys. Rev. A 57(2), 1313 (1998).
[Crossref]

1997 (2)

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55(6), 6414 (1997).
[Crossref]

J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quant. 3(2), 353–358 (1997).
[Crossref]

1995 (2)

K. D. Choquette, R. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quant. 1(2), 661–666 (1995).
[Crossref]

M. San Miguel, Q. Feng, and J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728 (1995).
[Crossref] [PubMed]

1994 (5)

C. Masoller, “Coexistence of attractors in a laser diode with optical feedback from a large external cavity,” Phys. Rev. A 50(3), 2569 (1994).
[Crossref] [PubMed]

L. Langley, J. Mørk, and K. Shore, “Dynamical and noise properties of laser diodes subject to strong optical feedback,” Opt. Lett. 19(24), 2137–2139 (1994).
[Crossref] [PubMed]

M. Van Exter, R. Hendriks, J. Woerdman, and C. Van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Optics communications 110(1), 137–140 (1994).
[Crossref]

P. Besnard, B. Meziane, K. Ait-Ameur, and G. Stephan, “Microwave spectra in external-cavity semiconductor lasers: Theoretical modeling of multipass resonances,” IEEE J. Quantum Elect. 30, 1713–1722 (1994).
[Crossref]

T. Sano, “Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50(3), 2719 (1994).
[Crossref] [PubMed]

1993 (1)

S. Jiang, Z. Pan, M. Dagenais, R. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993).
[Crossref]

1989 (1)

J. Sacher, W. Elsässer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224 (1989).
[Crossref] [PubMed]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Elect. 16(3), 347–355 (1980).
[Crossref]

Abraham, N.

C. Masoller and N. Abraham, “Stability and dynamical properties of the coexisting attractors of an external-cavity semiconductor laser,” Phys. Rev. A 57(2), 1313 (1998).
[Crossref]

Abraham, N. B.

Ackemann, T.

M. Sondermann and T. Ackemann, “Correlation properties and drift phenomena in the dynamics of vertical-cavity surface-emitting lasers with optical feedback,” Opt. Express 13(7), 2707–2715 (2005).
[Crossref] [PubMed]

M. Sondermann, H. Bohnet, and T. Ackemann, “Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback,” Phys. Rev. A 67(2), 021802 (2003).
[Crossref]

A. Naumenko, N. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
[Crossref]

M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback: experiment and model,” J. Opt. Soc. Am. B 16(11), 2114–2123 (1999).
[Crossref]

Agrawal, G. P.

J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quant. 3(2), 353–358 (1997).
[Crossref]

Ait-Ameur, K.

P. Besnard, B. Meziane, K. Ait-Ameur, and G. Stephan, “Microwave spectra in external-cavity semiconductor lasers: Theoretical modeling of multipass resonances,” IEEE J. Quantum Elect. 30, 1713–1722 (1994).
[Crossref]

Arteaga, M. A.

M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).

Balle, S.

M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, “Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays,” Nat. Photonics 9, 450–455 (2015).
[Crossref]

M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback: experiment and model,” J. Opt. Soc. Am. B 16(11), 2114–2123 (1999).
[Crossref]

Barland, S.

M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, “Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays,” Nat. Photonics 9, 450–455 (2015).
[Crossref]

M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback: experiment and model,” J. Opt. Soc. Am. B 16(11), 2114–2123 (1999).
[Crossref]

Besnard, P.

P. Besnard, B. Meziane, K. Ait-Ameur, and G. Stephan, “Microwave spectra in external-cavity semiconductor lasers: Theoretical modeling of multipass resonances,” IEEE J. Quantum Elect. 30, 1713–1722 (1994).
[Crossref]

Bezruchko, B. P.

B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, “Reconstruction of time-delay systems from chaotic time series,” Phys. Rev. E 64, 056216 (2001).
[Crossref]

Blondel, M.

Bohnet, H.

M. Sondermann, H. Bohnet, and T. Ackemann, “Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback,” Phys. Rev. A 67(2), 021802 (2003).
[Crossref]

Choquette, K. D.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72(19), 2355–2357 (1998).
[Crossref]

K. D. Choquette, R. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quant. 1(2), 661–666 (1995).
[Crossref]

Citrin, D. S.

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 Journal of Quantum Electronics 45(7), 879–1891 (2009).
[Crossref]

Dagenais, M.

S. Jiang, Z. Pan, M. Dagenais, R. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993).
[Crossref]

Danckaert, J.

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998).
[Crossref]

Elsäßer, W.

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

Elsässer, W.

J. Sacher, W. Elsässer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224 (1989).
[Crossref] [PubMed]

Feng, Q.

M. San Miguel, Q. Feng, and J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728 (1995).
[Crossref] [PubMed]

Fischer, I.

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

Gavrielides, A.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72(19), 2355–2357 (1998).
[Crossref]

Giacomelli, G.

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55(6), 6414 (1997).
[Crossref]

Giudici, M.

M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, “Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays,” Nat. Photonics 9, 450–455 (2015).
[Crossref]

M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, “Polarization dynamics in vertical-cavity surface-emitting lasers with optical feedback: experiment and model,” J. Opt. Soc. Am. B 16(11), 2114–2123 (1999).
[Crossref]

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55(6), 6414 (1997).
[Crossref]

Göbel, E. O.

J. Sacher, W. Elsässer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224 (1989).
[Crossref] [PubMed]

Green, C.

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55(6), 6414 (1997).
[Crossref]

Hendriks, R.

M. Van Exter, R. Hendriks, J. Woerdman, and C. Van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Optics communications 110(1), 137–140 (1994).
[Crossref]

Hohl, A.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72(19), 2355–2357 (1998).
[Crossref]

Hou, H.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72(19), 2355–2357 (1998).
[Crossref]

Javaloyes, J.

M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, “Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays,” Nat. Photonics 9, 450–455 (2015).
[Crossref]

Jiang, S.

S. Jiang, Z. Pan, M. Dagenais, R. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993).
[Crossref]

Karavaev, A. S.

B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, “Reconstruction of time-delay systems from chaotic time series,” Phys. Rev. E 64, 056216 (2001).
[Crossref]

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Elect. 16(3), 347–355 (1980).
[Crossref]

Kojima, K.

S. Jiang, Z. Pan, M. Dagenais, R. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993).
[Crossref]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Elect. 16(3), 347–355 (1980).
[Crossref]

Langley, L.

Law, J. Y.

J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quant. 3(2), 353–358 (1997).
[Crossref]

Lear, K. L.

K. D. Choquette, R. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quant. 1(2), 661–666 (1995).
[Crossref]

Leibenguth, R. E.

K. D. Choquette, R. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quant. 1(2), 661–666 (1995).
[Crossref]

Li, H.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72(19), 2355–2357 (1998).
[Crossref]

Locquet, A.

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 Journal of Quantum Electronics 45(7), 879–1891 (2009).
[Crossref]

Loiko, N.

A. Naumenko, N. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
[Crossref]

López-Amo, M.

M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).

Marconi, M.

M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, “Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays,” Nat. Photonics 9, 450–455 (2015).
[Crossref]

Masoller, C.

M. Sciamanna, C. Masoller, N. B. Abraham, F. Rogister, P. Mégret, and M. Blondel, “Different regimes of low-frequency fluctuations in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 20(1), 37–44 (2003).
[Crossref]

C. Masoller and N. Abraham, “Stability and dynamical properties of the coexisting attractors of an external-cavity semiconductor laser,” Phys. Rev. A 57(2), 1313 (1998).
[Crossref]

C. Masoller, “Coexistence of attractors in a laser diode with optical feedback from a large external cavity,” Phys. Rev. A 50(3), 2569 (1994).
[Crossref] [PubMed]

Mégret, P.

Meziane, B.

P. Besnard, B. Meziane, K. Ait-Ameur, and G. Stephan, “Microwave spectra in external-cavity semiconductor lasers: Theoretical modeling of multipass resonances,” IEEE J. Quantum Elect. 30, 1713–1722 (1994).
[Crossref]

Michalzik, R.

R. Michalzik, VCSELs: Fundamentals, Technology and Applications of Vertical-Cavity Surface-Emitting Lasers, vol. 166 (Springer, 2012).

Moloney, J.

M. San Miguel, Q. Feng, and J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728 (1995).
[Crossref] [PubMed]

Morgan, R.

S. Jiang, Z. Pan, M. Dagenais, R. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993).
[Crossref]

Mørk, J.

Naumenko, A.

A. Naumenko, N. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
[Crossref]

Nespolo, U.

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55(6), 6414 (1997).
[Crossref]

Ortin, S.

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 Journal of Quantum Electronics 45(7), 879–1891 (2009).
[Crossref]

Pan, Z.

S. Jiang, Z. Pan, M. Dagenais, R. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993).
[Crossref]

Panajotov, K.

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
[Crossref]

M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28(17), 1543–1545 (2003).
[Crossref] [PubMed]

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998).
[Crossref]

Peeters, M.

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998).
[Crossref]

Peil, M.

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

Ponomarenko, V. I.

B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, “Reconstruction of time-delay systems from chaotic time series,” Phys. Rev. E 64, 056216 (2001).
[Crossref]

Prokhorov, M. D.

B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, “Reconstruction of time-delay systems from chaotic time series,” Phys. Rev. E 64, 056216 (2001).
[Crossref]

Rogister, F.

Rontani, D.

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 Journal of Quantum Electronics 45(7), 879–1891 (2009).
[Crossref]

Ryvkin, B.

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998).
[Crossref]

Sacher, J.

J. Sacher, W. Elsässer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224 (1989).
[Crossref] [PubMed]

San Miguel, M.

M. San Miguel, Q. Feng, and J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728 (1995).
[Crossref] [PubMed]

Sano, T.

T. Sano, “Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50(3), 2719 (1994).
[Crossref] [PubMed]

Schneider, R.

K. D. Choquette, R. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quant. 1(2), 661–666 (1995).
[Crossref]

Sciamanna, M.

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
[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 Journal of Quantum Electronics 45(7), 879–1891 (2009).
[Crossref]

M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

M. Sciamanna, C. Masoller, N. B. Abraham, F. Rogister, P. Mégret, and M. Blondel, “Different regimes of low-frequency fluctuations in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 20(1), 37–44 (2003).
[Crossref]

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28(17), 1543–1545 (2003).
[Crossref] [PubMed]

Shore, K.

Sondermann, M.

M. Sondermann and T. Ackemann, “Correlation properties and drift phenomena in the dynamics of vertical-cavity surface-emitting lasers with optical feedback,” Opt. Express 13(7), 2707–2715 (2005).
[Crossref] [PubMed]

A. Naumenko, N. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
[Crossref]

M. Sondermann, H. Bohnet, and T. Ackemann, “Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback,” Phys. Rev. A 67(2), 021802 (2003).
[Crossref]

Stephan, G.

P. Besnard, B. Meziane, K. Ait-Ameur, and G. Stephan, “Microwave spectra in external-cavity semiconductor lasers: Theoretical modeling of multipass resonances,” IEEE J. Quantum Elect. 30, 1713–1722 (1994).
[Crossref]

Tabaka, A.

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

Thienpont, H.

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
[Crossref]

M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28(17), 1543–1545 (2003).
[Crossref] [PubMed]

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998).
[Crossref]

Tredicce, J.

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55(6), 6414 (1997).
[Crossref]

Tredicce, J. R.

Valencia, M.

M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).

Van der Poel, C.

M. Van Exter, R. Hendriks, J. Woerdman, and C. Van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Optics communications 110(1), 137–140 (1994).
[Crossref]

Van Exter, M.

M. Willemsen, M. Van Exter, and J. Woerdman, “Anatomy of a polarization switch of a vertical-cavity laser,” Phys. Rev. Lett. 84(19), 4337 (2000).
[Crossref] [PubMed]

M. Van Exter, R. Hendriks, J. Woerdman, and C. Van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Optics communications 110(1), 137–140 (1994).
[Crossref]

Veretennicoff, I.

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

M. Sciamanna, K. Panajotov, H. Thienpont, I. Veretennicoff, P. Mégret, and M. Blondel, “Optical feedback induces polarization mode hopping in vertical-cavity surface-emitting lasers,” Opt. Lett. 28(17), 1543–1545 (2003).
[Crossref] [PubMed]

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998).
[Crossref]

Virte, M.

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
[Crossref]

Willemsen, M.

M. Willemsen, M. Van Exter, and J. Woerdman, “Anatomy of a polarization switch of a vertical-cavity laser,” Phys. Rev. Lett. 84(19), 4337 (2000).
[Crossref] [PubMed]

Woerdman, J.

M. Willemsen, M. Van Exter, and J. Woerdman, “Anatomy of a polarization switch of a vertical-cavity laser,” Phys. Rev. Lett. 84(19), 4337 (2000).
[Crossref] [PubMed]

M. Van Exter, R. Hendriks, J. Woerdman, and C. Van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Optics communications 110(1), 137–140 (1994).
[Crossref]

Appl. Phys. Lett. (2)

S. Jiang, Z. Pan, M. Dagenais, R. Morgan, and K. Kojima, “High-frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63(26), 3545–3547 (1993).
[Crossref]

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. D. Choquette, “Stable polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 72(19), 2355–2357 (1998).
[Crossref]

IEEE J. Quantum Elect. (2)

P. Besnard, B. Meziane, K. Ait-Ameur, and G. Stephan, “Microwave spectra in external-cavity semiconductor lasers: Theoretical modeling of multipass resonances,” IEEE J. Quantum Elect. 30, 1713–1722 (1994).
[Crossref]

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Elect. 16(3), 347–355 (1980).
[Crossref]

IEEE J. Sel. Top. Quant. (2)

K. D. Choquette, R. Schneider, K. L. Lear, and R. E. Leibenguth, “Gain-dependent polarization properties of vertical-cavity lasers,” IEEE J. Sel. Top. Quant. 1(2), 661–666 (1995).
[Crossref]

J. Y. Law and G. P. Agrawal, “Effects of optical feedback on static and dynamic characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quant. 3(2), 353–358 (1997).
[Crossref]

IEEE Journal of Quantum Electronics (1)

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 Journal of Quantum Electronics 45(7), 879–1891 (2009).
[Crossref]

IEEE Photonic. Tech. Lett. (1)

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, “Polarization switching in VCSEL’s due to thermal lensing,” IEEE Photonic. Tech. Lett. 10(1), 6–8 (1998).
[Crossref]

J. Opt. Soc. Am. B (2)

Nat. Photonics (2)

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
[Crossref]

M. Marconi, J. Javaloyes, S. Barland, S. Balle, and M. Giudici, “Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays,” Nat. Photonics 9, 450–455 (2015).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Optics communications (1)

M. Van Exter, R. Hendriks, J. Woerdman, and C. Van der Poel, “Explanation of double-peaked intensity noise spectrum of an external-cavity semiconductor laser,” Optics communications 110(1), 137–140 (1994).
[Crossref]

Phys. Rev. A (7)

M. San Miguel, Q. Feng, and J. Moloney, “Light-polarization dynamics in surface-emitting semiconductor lasers,” Phys. Rev. A 52(2), 1728 (1995).
[Crossref] [PubMed]

C. Masoller, “Coexistence of attractors in a laser diode with optical feedback from a large external cavity,” Phys. Rev. A 50(3), 2569 (1994).
[Crossref] [PubMed]

C. Masoller and N. Abraham, “Stability and dynamical properties of the coexisting attractors of an external-cavity semiconductor laser,” Phys. Rev. A 57(2), 1313 (1998).
[Crossref]

M. Sondermann, H. Bohnet, and T. Ackemann, “Low-frequency fluctuations and polarization dynamics in vertical-cavity surface-emitting lasers with isotropic feedback,” Phys. Rev. A 67(2), 021802 (2003).
[Crossref]

A. Naumenko, N. Loiko, M. Sondermann, and T. Ackemann, “Description and analysis of low-frequency fluctuations in vertical-cavity surface-emitting lasers with isotropic optical feedback by a distant reflector,” Phys. Rev. A 68(3), 033805 (2003).
[Crossref]

A. Tabaka, M. Peil, M. Sciamanna, I. Fischer, W. Elsäßer, H. Thienpont, I. Veretennicoff, and K. Panajotov, “Dynamics of vertical-cavity surface-emitting lasers in the short external cavity regime: Pulse packages and polarization mode competition,” Phys. Rev. A 73(1), 013810 (2006).
[Crossref]

T. Sano, “Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50(3), 2719 (1994).
[Crossref] [PubMed]

Phys. Rev. E (2)

B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, “Reconstruction of time-delay systems from chaotic time series,” Phys. Rev. E 64, 056216 (2001).
[Crossref]

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55(6), 6414 (1997).
[Crossref]

Phys. Rev. Lett. (3)

J. Sacher, W. Elsässer, and E. O. Göbel, “Intermittency in the coherence collapse of a semiconductor laser with external feedback,” Phys. Rev. Lett. 63(20), 2224 (1989).
[Crossref] [PubMed]

M. Willemsen, M. Van Exter, and J. Woerdman, “Anatomy of a polarization switch of a vertical-cavity laser,” Phys. Rev. Lett. 84(19), 4337 (2000).
[Crossref] [PubMed]

M. A. Arteaga, M. Valencia, M. Sciamanna, H. Thienpont, M. López-Amo, and K. Panajotov, “Experimental evidence of coherence resonance in a time-delayed bistable system,” Phys. Rev. Lett. 99(2), 023903 (2007).

Other (1)

R. Michalzik, VCSELs: Fundamentals, Technology and Applications of Vertical-Cavity Surface-Emitting Lasers, vol. 166 (Springer, 2012).

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Figures (7)

Fig. 1
Fig. 1 (a) Experimental setup. C: collimating microscope objective, BS: beam-splitter, P: polarizer, ISO: isolator, SMF: single mode fiber, M: mirror, PD: photodiode. (b) Intensity time series of the Y-LP mode and (c) X-LP mode of VCSEL LFF Type-II regime at pumping current 1.2 J th s = 0.54 mA, time delay τ≈5 ns, temperature 15°C, and 14% threshold reduction.
Fig. 2
Fig. 2 Spectrogram of the Y-LP mode in the frequency range (a) f ∈ [200 MHz, 400 MHz] as function of the external cavity delay (b) f ∈ [0 MHz, 70 MHz] and (c) f ∈ [170 MHz, 240 MHz] as function of the pumping current. (d) CSD between X-LP and Y-LP modes. f and f+ are the two main components of the discussed double-peak structure. The fixed parameters are identical to those used in Fig. 1.
Fig. 3
Fig. 3 Numerical LFF Type-II time traces of (a) the X-LP mode, (b) the Y-LP mode, the corresponding RF spectrum for (c) X- and (d) Y-LP mode and the resulting cross-spectral density μ = 1.02, η = 9 GHz, τ = 5 ns, κ = 300 GHz, α = 3, ϕ0 = 6 rad, γn = 1 ns−1, γs = 5 ns−1, βsp = 10−4 ns−1, γa = 0.5 rad.ns−1, γp = 5 rad.ns−1.
Fig. 4
Fig. 4 (a) Numerical RF spectrum of the intensity of the Y-LP mode in external cavity frequency window, (b) trajectory in the phase space and (c) a zoom into the attractor of highest phase shift, (d) the histogram showing the number of points as function of the phase shift and (e) its corresponding zoom into the attractor of highest phase shift region. The parameters are identical to those used in Fig. 3 except for η = 3 GHz and γs = 50 ns−1.
Fig. 5
Fig. 5 (a) Typical time trace of a LFF drop-out event of the Y-LP mode. RF spectra computed by considering different window sizes in the phase space in Fig. 4(b). For ϕY(t)−ϕY(tτ)+ϕ0 range : (b) from −35 to −31 rad, (c) from −35 to −27 rad, (d) from −35 to −16 rad, (e) from −35 to −0 rad.
Fig. 6
Fig. 6 Spectrograms of Y-LP mode as a function of (a) the delay τ and (b) the current μ. Other parameters are the same as in Fig. 4.
Fig. 7
Fig. 7 Numerical (a) time trace of the output intensity and (b) power spectrum for τp = 1.66 ps, τs = 1 ns, α = 3, = 5 × 10−7 m3, GN = 1.5 × 104 m3 · s−1, N0 = 1.5 × 108 m−3, Jth = 1.9 × 1017 m−3 · s−1, p = 1, γ = 3 GHz, τ = 5 ns, ω0τ = 0 rad.

Equations (7)

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CSD ( f ) = I ˜ x ( f ) I ˜ y * ( f ) + I ˜ y ( f ) I ˜ x * ( f ) ,
E ˙ x , y = κ ( 1 + i α ) [ ( N 1 ) E x , y + i n E y , x ] ( γ a + i γ p ) E x , y + F x , y + η E x , y ( t τ ) exp ( i ϕ 0 ) ,
N ˙ = γ n [ N μ + N ( | E x | 2 + | E y | 2 ) + i n ( E y E x * E x E y * ) ] ,
n ˙ = γ s n γ n [ n ( | E x | 2 + | E y | 2 ) + i N ( E y E x * E x E y * ) ] ,
E ˙ ( t ) = 1 / 2 ( 1 + i α ) ( G N , | E | 2 1 / τ p ) E ( t ) + γ e i ω 0 τ E ( t τ ) ,
N ˙ ( t ) = p J t h N / τ s G N , | E | 2 | E ( t ) | 2 ,
G N , | E | 2 = G N ( N N 0 ) / ( 1 + | E | 2 ) ,

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