Non-local correlations via chaotic itinerancy in VCSEL with optical feedback

Chi-Hak Uy; Damien Rontani; Stefan Breuer; Marc Sciamanna

doi:10.1364/OE.25.006914

Non-local correlations via chaotic itinerancy in VCSEL with optical feedback

Chi-Hak Uy, Damien Rontani, Stefan Breuer, and Marc Sciamanna

Optics Express
Vol. 25,
Issue 6,
pp. 6914-6923
(2017)
•https://doi.org/10.1364/OE.25.006914

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Chi-Hak Uy, Damien Rontani, Stefan Breuer, and Marc Sciamanna, "Non-local correlations via chaotic itinerancy in VCSEL with optical feedback," Opt. Express 25, 6914-6923 (2017)

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Related Topics
Table of Contents Category
- Lasers and Laser Optics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Vertical cavity surface emitting lasers (140.7260)
- Instabilities and chaos (190.3100)
- Semiconductor lasers (250.5960)

About this Article
History
- Original Manuscript: October 17, 2016
- Revised Manuscript: December 7, 2016
- Manuscript Accepted: December 8, 2016
- Published: March 16, 2017

Accessible

Open Access

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.

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References

View by:
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|
Year
|
Author
|
Publication

R. Michalzik, VCSELs: Fundamentals, Technology and Applications of Vertical-Cavity Surface-Emitting Lasers, vol. 166 (Springer, 2012).
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]
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. 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. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7(1), 60–65 (2013).
[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]
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]
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).
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]
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]
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]
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. 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]
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. 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]
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]
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]
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]
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]
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. 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. 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]
R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Elect. 16(3), 347–355 (1980).
[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]

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)

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]

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. 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]

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]

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)

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]

1998 (3)

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. 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]

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)

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]

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]

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]

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]

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]

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]

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]

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.

Agrawal, G. P.

Ait-Ameur, K.

Arteaga, M. A.

Balle, S.

Barland, S.

Besnard, P.

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.

Choquette, K. D.

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.

Dagenais, M.

Danckaert, J.

Elsäßer, W.

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.

Gavrielides, A.

Giacomelli, G.

Giudici, M.

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.

Hendriks, R.

Hohl, A.

Hou, H.

Javaloyes, J.

Jiang, S.

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.

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.

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]

Law, J. Y.

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.

Locquet, A.

Loiko, N.

López-Amo, M.

Marconi, M.

Masoller, C.

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.

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.

Mørk, J.

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]

Naumenko, A.

Nespolo, U.

Ortin, S.

Pan, Z.

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]

Peeters, M.

Peil, M.

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.

Ryvkin, B.

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]

Shore, K.

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]

Sondermann, M.

Stephan, G.

Tabaka, A.

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]

Tredicce, J.

Tredicce, J. R.

Valencia, M.

Van der Poel, C.

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]

Veretennicoff, I.

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]

Appl. Phys. Lett. (2)

IEEE J. Quantum Elect. (2)

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]

IEEE Journal of Quantum Electronics (1)

IEEE Photonic. Tech. Lett. (1)

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]

Opt. Express (1)

Opt. Lett. (2)

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]

Optics communications (1)

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]

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]

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]

Other (1)

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

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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.

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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.

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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, γ_n = 1 ns⁻¹, γ_s = 5 ns⁻¹, β_sp = 10⁻⁴ ns⁻¹, γ_a = 0.5 rad.ns⁻¹, γ_p = 5 rad.ns⁻¹.

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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 γ_s = 50 ns⁻¹.

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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 ϕ_Y(t)−ϕ_Y(t−τ)+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.

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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.

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Fig. 7 Numerical (a) time trace of the output intensity and (b) power spectrum for τ_p = 1.66 ps, τ_s = 1 ns, α = 3, ∊ = 5 × 10⁻⁷ m³, G_N = 1.5 × 10⁴ m³ · s⁻¹, N₀ = 1.5 × 10⁸ m⁻³, J_th = 1.9 × 10¹⁷ m⁻³ · s⁻¹, p = 1, γ = 3 GHz, τ = 5 ns, ω₀τ = 0 rad.

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Equations (7)

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CSD (f) = {\tilde{I}}_{x} (f) {\tilde{I}}_{y}^{*} (f) + {\tilde{I}}_{y} (f) {\tilde{I}}_{x}^{*} (f),

\begin{array}{l} {\dot{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}), \end{array}

\dot{N} = - γ_{n} [N - μ + N ({| E_{x} |}^{2} + {| E_{y} |}^{2}) + i n (E_{y} E_{x}^{*} - E_{x} E_{y}^{*})],

\dot{n} = - γ_{s} n - γ_{n} [n ({| E_{x} |}^{2} + {| E_{y} |}^{2}) + i N (E_{y} E_{x}^{*} - E_{x} E_{y}^{*})],

\dot{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),

\dot{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}),