Abstract

We have experimentally studied modal dynamics of a vertical-cavity surface-emitting laser (VCSEL) above the threshold of higher-order transverse modes when the VCSEL is subject to isotropic optical feedback. The dynamics of the higher-order mode reveals resemblance to the so-called low-frequency fluctuation (LFF) and the transition from LFF to coherence collapse near the threshold of single-transverse-mode VCSEL. Influence of control parameters on the dynamics is investigated, and possible mechanism of the dynamics is discussed.

© 2010 Optical Society of America

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  1. Y. C. Chung and Y. H. Lee, “Spectral characteristics of vertical-cavity surface-emitting lasers with external optical feedback,” IEEE Photon. Technol. Lett. 3, 597–599 (1991).
    [CrossRef]
  2. S. Jiang, M. Dagenais, and R. A. Morgan, “Spectral characteristics of vertical-cavity surface-emitting lasers with strong external optical feedback,” IEEE Photon. Technol. Lett. 7, 739–741 (1995).
    [CrossRef]
  3. P. S. Spencer, C. R. Mirasso, and K. A. Shore, “Effect of strong optical feedback on vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 10, 191–193 (1998).
    [CrossRef]
  4. 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, 2114–2123 (1999).
    [CrossRef]
  5. 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, 2355–2357 (1998).
    [CrossRef]
  6. K. Panajotov, M. Arizaleta, M. Camarena, H. Thienpont, H. J. Unold, J. M. Ostermann, and R. Michalzik, “Polarization switching induced by phase change in extremely short external cavity vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 84, 2763–2765 (2004).
    [CrossRef]
  7. P. Besnard, F. Robert, M. L. Chares, and G. M. Stephan, “Theoretical modeling of vertical-cavity surface-emitting lasers with polarized optical feedback,” Phys. Rev. A 56, 3191–3205 (1997).
    [CrossRef]
  8. C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
    [CrossRef]
  9. A. V. Naumenko, N. A. 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, 033805 (2003).
    [CrossRef]
  10. G. Giacomelli, F. Marin, and M. Romanelli, “Multi-time-scale dynamics of a laser with polarized optical feedback,” Phys. Rev. A 67, 053809 (2003).
    [CrossRef]
  11. N. Fujiwara, Y. Takiguchi, and J. Ohtsubo, “Observation of low-frequency fluctuations in vertical-cavity surface-emitting lasers,” Opt. Lett. 28, 896–898 (2003).
    [CrossRef] [PubMed]
  12. Y. Hong and K. A. Shore, “Influence of optical feedback time-delay on power-drops in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1054–1057 (2005).
    [CrossRef]
  13. A. Torcini, S. Barland, G. Giacomelli, and F. Marin, “Low-frequency fluctuations in vertical cavity lasers: experiments versus Lang-Kobayashi dynamics,” Phys. Rev. A 74, 063801 (2006).
    [CrossRef]
  14. P. Besnard, B. Meziane, and G. M. Stephan, “Feedback phenomena in a semiconductor laser induced by distant reflectors,” IEEE J. Quantum Electron. 29, 1271–1284 (1993).
    [CrossRef]
  15. T. Heil, I. Fischer, and W. Elsäßer, “Coexistence of low-frequency fluctuations and stable emission on a single high-gain mode in semiconductor lasers with external optical feedback,” Phys. Rev. A 58, R2672–R2675 (1998).
    [CrossRef]
  16. 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. Quantum Electron. 3, 353–358 (1997).
    [CrossRef]
  17. M. S. Torre, C. Masoller, and P. Mandel, “Transverse-mode dynamics in vertical-cavity surface-emitting lasers with optical feedback,” Phys. Rev. A 66, 053817 (2002).
    [CrossRef]
  18. H. Lin, Z. J. Lapin, B. Malla, and A. Valle, “Polarization dynamics in a multi-transverse-mode vertical-cavity surface-emitting laser subject to optical feedback,” Phys. Rev. A 77, 033813 (2008).
    [CrossRef]
  19. A. Valle, H. Lin, Z. J. Lapin, and B. Malla, “Analysis of the polarization dynamics in a multitransverse-mode vertical-cavity surface-emitting laser with isotropic optical feedback,” Phys. Rev. A 78, 033828 (2008).
    [CrossRef]
  20. Y. K. Chembo, S. K. Mandre, I. Fischer, W. Elsässer, and P. Colet, “Controlling the emission properties of multimode vertical-cavity surface-emitting lasers via polarization- and frequency-selective feedback,” Phys. Rev. A 79, 013817 (2009).
    [CrossRef]
  21. B. Tell, K. Brown-Goebeler, R. E. Leibenguth, F. M. Baez, and Y. H. Lee, “Temperature dependence of GaAs-AlGaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 60, 683–685 (1992).
    [CrossRef]
  22. K. D. Choquette, D. A. Richie, and R. E. Leibenguth, “Temperature dependence of gain-guided vertical-cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062–2064 (1994).
    [CrossRef]
  23. M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,” Phys. Rev. A 68, 033822 (2003).
    [CrossRef]
  24. A. Valle, “Selection and modulation of higher-order transverse modes in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 34, 1924–1932 (1998).
    [CrossRef]
  25. T. Ackemann, M. Sondermann, A. Naumenko, and N. A. Loiko, “Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting laser subject to optical feedback,” Appl. Phys. B 77, 739–746 (2003).
    [CrossRef]
  26. T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
    [CrossRef]
  27. H. Lin, J. HoShue, Z. J. Lapin, and A. Valle, “Polarization instabilities in a multi-transverse-mode vertical-cavity surface-emitting laser with polarized optical feedback,” Opt. Commun. 283, 1424–1433 (2010).
    [CrossRef]
  28. G. H. M. van Tartwijk, A. M. Levine, and D. Lenstra, “Sysyphus effect in semiconductor lasers with optical feedback,” IEEE J. Sel. Top. Quantum Electron. 1, 466–472 (1995).
    [CrossRef]
  29. T. Sano, “Antimode dynamics and chaotic itinerancyin the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50, 2719–2726 (1994).
    [CrossRef] [PubMed]

2010 (1)

H. Lin, J. HoShue, Z. J. Lapin, and A. Valle, “Polarization instabilities in a multi-transverse-mode vertical-cavity surface-emitting laser with polarized optical feedback,” Opt. Commun. 283, 1424–1433 (2010).
[CrossRef]

2009 (1)

Y. K. Chembo, S. K. Mandre, I. Fischer, W. Elsässer, and P. Colet, “Controlling the emission properties of multimode vertical-cavity surface-emitting lasers via polarization- and frequency-selective feedback,” Phys. Rev. A 79, 013817 (2009).
[CrossRef]

2008 (2)

H. Lin, Z. J. Lapin, B. Malla, and A. Valle, “Polarization dynamics in a multi-transverse-mode vertical-cavity surface-emitting laser subject to optical feedback,” Phys. Rev. A 77, 033813 (2008).
[CrossRef]

A. Valle, H. Lin, Z. J. Lapin, and B. Malla, “Analysis of the polarization dynamics in a multitransverse-mode vertical-cavity surface-emitting laser with isotropic optical feedback,” Phys. Rev. A 78, 033828 (2008).
[CrossRef]

2006 (1)

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, “Low-frequency fluctuations in vertical cavity lasers: experiments versus Lang-Kobayashi dynamics,” Phys. Rev. A 74, 063801 (2006).
[CrossRef]

2005 (1)

Y. Hong and K. A. Shore, “Influence of optical feedback time-delay on power-drops in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1054–1057 (2005).
[CrossRef]

2004 (1)

K. Panajotov, M. Arizaleta, M. Camarena, H. Thienpont, H. J. Unold, J. M. Ostermann, and R. Michalzik, “Polarization switching induced by phase change in extremely short external cavity vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 84, 2763–2765 (2004).
[CrossRef]

2003 (6)

T. Ackemann, M. Sondermann, A. Naumenko, and N. A. Loiko, “Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting laser subject to optical feedback,” Appl. Phys. B 77, 739–746 (2003).
[CrossRef]

T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[CrossRef]

A. V. Naumenko, N. A. 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, 033805 (2003).
[CrossRef]

G. Giacomelli, F. Marin, and M. Romanelli, “Multi-time-scale dynamics of a laser with polarized optical feedback,” Phys. Rev. A 67, 053809 (2003).
[CrossRef]

N. Fujiwara, Y. Takiguchi, and J. Ohtsubo, “Observation of low-frequency fluctuations in vertical-cavity surface-emitting lasers,” Opt. Lett. 28, 896–898 (2003).
[CrossRef] [PubMed]

M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,” Phys. Rev. A 68, 033822 (2003).
[CrossRef]

2002 (1)

M. S. Torre, C. Masoller, and P. Mandel, “Transverse-mode dynamics in vertical-cavity surface-emitting lasers with optical feedback,” Phys. Rev. A 66, 053817 (2002).
[CrossRef]

1999 (2)

C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
[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, 2114–2123 (1999).
[CrossRef]

1998 (4)

P. S. Spencer, C. R. Mirasso, and K. A. Shore, “Effect of strong optical feedback on vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 10, 191–193 (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, 2355–2357 (1998).
[CrossRef]

T. Heil, I. Fischer, and W. Elsäßer, “Coexistence of low-frequency fluctuations and stable emission on a single high-gain mode in semiconductor lasers with external optical feedback,” Phys. Rev. A 58, R2672–R2675 (1998).
[CrossRef]

A. Valle, “Selection and modulation of higher-order transverse modes in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 34, 1924–1932 (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. Quantum Electron. 3, 353–358 (1997).
[CrossRef]

P. Besnard, F. Robert, M. L. Chares, and G. M. Stephan, “Theoretical modeling of vertical-cavity surface-emitting lasers with polarized optical feedback,” Phys. Rev. A 56, 3191–3205 (1997).
[CrossRef]

1995 (2)

S. Jiang, M. Dagenais, and R. A. Morgan, “Spectral characteristics of vertical-cavity surface-emitting lasers with strong external optical feedback,” IEEE Photon. Technol. Lett. 7, 739–741 (1995).
[CrossRef]

G. H. M. van Tartwijk, A. M. Levine, and D. Lenstra, “Sysyphus effect in semiconductor lasers with optical feedback,” IEEE J. Sel. Top. Quantum Electron. 1, 466–472 (1995).
[CrossRef]

1994 (2)

T. Sano, “Antimode dynamics and chaotic itinerancyin the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50, 2719–2726 (1994).
[CrossRef] [PubMed]

K. D. Choquette, D. A. Richie, and R. E. Leibenguth, “Temperature dependence of gain-guided vertical-cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062–2064 (1994).
[CrossRef]

1993 (1)

P. Besnard, B. Meziane, and G. M. Stephan, “Feedback phenomena in a semiconductor laser induced by distant reflectors,” IEEE J. Quantum Electron. 29, 1271–1284 (1993).
[CrossRef]

1992 (1)

B. Tell, K. Brown-Goebeler, R. E. Leibenguth, F. M. Baez, and Y. H. Lee, “Temperature dependence of GaAs-AlGaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 60, 683–685 (1992).
[CrossRef]

1991 (1)

Y. C. Chung and Y. H. Lee, “Spectral characteristics of vertical-cavity surface-emitting lasers with external optical feedback,” IEEE Photon. Technol. Lett. 3, 597–599 (1991).
[CrossRef]

Abraham, N. B.

C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
[CrossRef]

Ackemann, T.

M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,” Phys. Rev. A 68, 033822 (2003).
[CrossRef]

T. Ackemann, M. Sondermann, A. Naumenko, and N. A. Loiko, “Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting laser subject to optical feedback,” Appl. Phys. B 77, 739–746 (2003).
[CrossRef]

A. V. Naumenko, N. A. 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, 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, 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. Quantum Electron. 3, 353–358 (1997).
[CrossRef]

Arizaleta, M.

K. Panajotov, M. Arizaleta, M. Camarena, H. Thienpont, H. J. Unold, J. M. Ostermann, and R. Michalzik, “Polarization switching induced by phase change in extremely short external cavity vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 84, 2763–2765 (2004).
[CrossRef]

Baez, F. M.

B. Tell, K. Brown-Goebeler, R. E. Leibenguth, F. M. Baez, and Y. H. Lee, “Temperature dependence of GaAs-AlGaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 60, 683–685 (1992).
[CrossRef]

Balle, S.

M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,” Phys. Rev. A 68, 033822 (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, 2114–2123 (1999).
[CrossRef]

Barland, S.

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, “Low-frequency fluctuations in vertical cavity lasers: experiments versus Lang-Kobayashi dynamics,” Phys. Rev. A 74, 063801 (2006).
[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, 2114–2123 (1999).
[CrossRef]

Besnard, P.

P. Besnard, F. Robert, M. L. Chares, and G. M. Stephan, “Theoretical modeling of vertical-cavity surface-emitting lasers with polarized optical feedback,” Phys. Rev. A 56, 3191–3205 (1997).
[CrossRef]

P. Besnard, B. Meziane, and G. M. Stephan, “Feedback phenomena in a semiconductor laser induced by distant reflectors,” IEEE J. Quantum Electron. 29, 1271–1284 (1993).
[CrossRef]

Brown-Goebeler, K.

B. Tell, K. Brown-Goebeler, R. E. Leibenguth, F. M. Baez, and Y. H. Lee, “Temperature dependence of GaAs-AlGaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 60, 683–685 (1992).
[CrossRef]

Camarena, M.

K. Panajotov, M. Arizaleta, M. Camarena, H. Thienpont, H. J. Unold, J. M. Ostermann, and R. Michalzik, “Polarization switching induced by phase change in extremely short external cavity vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 84, 2763–2765 (2004).
[CrossRef]

Chares, M. L.

P. Besnard, F. Robert, M. L. Chares, and G. M. Stephan, “Theoretical modeling of vertical-cavity surface-emitting lasers with polarized optical feedback,” Phys. Rev. A 56, 3191–3205 (1997).
[CrossRef]

Chembo, Y. K.

Y. K. Chembo, S. K. Mandre, I. Fischer, W. Elsässer, and P. Colet, “Controlling the emission properties of multimode vertical-cavity surface-emitting lasers via polarization- and frequency-selective feedback,” Phys. Rev. A 79, 013817 (2009).
[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, 2355–2357 (1998).
[CrossRef]

K. D. Choquette, D. A. Richie, and R. E. Leibenguth, “Temperature dependence of gain-guided vertical-cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062–2064 (1994).
[CrossRef]

Chung, Y. C.

Y. C. Chung and Y. H. Lee, “Spectral characteristics of vertical-cavity surface-emitting lasers with external optical feedback,” IEEE Photon. Technol. Lett. 3, 597–599 (1991).
[CrossRef]

Colet, P.

Y. K. Chembo, S. K. Mandre, I. Fischer, W. Elsässer, and P. Colet, “Controlling the emission properties of multimode vertical-cavity surface-emitting lasers via polarization- and frequency-selective feedback,” Phys. Rev. A 79, 013817 (2009).
[CrossRef]

Dagenais, M.

S. Jiang, M. Dagenais, and R. A. Morgan, “Spectral characteristics of vertical-cavity surface-emitting lasers with strong external optical feedback,” IEEE Photon. Technol. Lett. 7, 739–741 (1995).
[CrossRef]

Elsässer, W.

Y. K. Chembo, S. K. Mandre, I. Fischer, W. Elsässer, and P. Colet, “Controlling the emission properties of multimode vertical-cavity surface-emitting lasers via polarization- and frequency-selective feedback,” Phys. Rev. A 79, 013817 (2009).
[CrossRef]

T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[CrossRef]

Elsäßer, W.

T. Heil, I. Fischer, and W. Elsäßer, “Coexistence of low-frequency fluctuations and stable emission on a single high-gain mode in semiconductor lasers with external optical feedback,” Phys. Rev. A 58, R2672–R2675 (1998).
[CrossRef]

Fischer, I.

Y. K. Chembo, S. K. Mandre, I. Fischer, W. Elsässer, and P. Colet, “Controlling the emission properties of multimode vertical-cavity surface-emitting lasers via polarization- and frequency-selective feedback,” Phys. Rev. A 79, 013817 (2009).
[CrossRef]

T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[CrossRef]

T. Heil, I. Fischer, and W. Elsäßer, “Coexistence of low-frequency fluctuations and stable emission on a single high-gain mode in semiconductor lasers with external optical feedback,” Phys. Rev. A 58, R2672–R2675 (1998).
[CrossRef]

Fujiwara, N.

Gavrielides, A.

T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[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, 2355–2357 (1998).
[CrossRef]

Giacomelli, G.

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, “Low-frequency fluctuations in vertical cavity lasers: experiments versus Lang-Kobayashi dynamics,” Phys. Rev. A 74, 063801 (2006).
[CrossRef]

G. Giacomelli, F. Marin, and M. Romanelli, “Multi-time-scale dynamics of a laser with polarized optical feedback,” Phys. Rev. A 67, 053809 (2003).
[CrossRef]

Giudici, M.

Green, K.

T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[CrossRef]

Heil, T.

T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[CrossRef]

T. Heil, I. Fischer, and W. Elsäßer, “Coexistence of low-frequency fluctuations and stable emission on a single high-gain mode in semiconductor lasers with external optical feedback,” Phys. Rev. A 58, R2672–R2675 (1998).
[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, 2355–2357 (1998).
[CrossRef]

Hong, Y.

Y. Hong and K. A. Shore, “Influence of optical feedback time-delay on power-drops in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1054–1057 (2005).
[CrossRef]

HoShue, J.

H. Lin, J. HoShue, Z. J. Lapin, and A. Valle, “Polarization instabilities in a multi-transverse-mode vertical-cavity surface-emitting laser with polarized optical feedback,” Opt. Commun. 283, 1424–1433 (2010).
[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, 2355–2357 (1998).
[CrossRef]

Jiang, S.

S. Jiang, M. Dagenais, and R. A. Morgan, “Spectral characteristics of vertical-cavity surface-emitting lasers with strong external optical feedback,” IEEE Photon. Technol. Lett. 7, 739–741 (1995).
[CrossRef]

Krauskopf, B.

T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[CrossRef]

Lapin, Z. J.

H. Lin, J. HoShue, Z. J. Lapin, and A. Valle, “Polarization instabilities in a multi-transverse-mode vertical-cavity surface-emitting laser with polarized optical feedback,” Opt. Commun. 283, 1424–1433 (2010).
[CrossRef]

H. Lin, Z. J. Lapin, B. Malla, and A. Valle, “Polarization dynamics in a multi-transverse-mode vertical-cavity surface-emitting laser subject to optical feedback,” Phys. Rev. A 77, 033813 (2008).
[CrossRef]

A. Valle, H. Lin, Z. J. Lapin, and B. Malla, “Analysis of the polarization dynamics in a multitransverse-mode vertical-cavity surface-emitting laser with isotropic optical feedback,” Phys. Rev. A 78, 033828 (2008).
[CrossRef]

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. Quantum Electron. 3, 353–358 (1997).
[CrossRef]

Lee, Y. H.

B. Tell, K. Brown-Goebeler, R. E. Leibenguth, F. M. Baez, and Y. H. Lee, “Temperature dependence of GaAs-AlGaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 60, 683–685 (1992).
[CrossRef]

Y. C. Chung and Y. H. Lee, “Spectral characteristics of vertical-cavity surface-emitting lasers with external optical feedback,” IEEE Photon. Technol. Lett. 3, 597–599 (1991).
[CrossRef]

Leibenguth, R. E.

K. D. Choquette, D. A. Richie, and R. E. Leibenguth, “Temperature dependence of gain-guided vertical-cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062–2064 (1994).
[CrossRef]

B. Tell, K. Brown-Goebeler, R. E. Leibenguth, F. M. Baez, and Y. H. Lee, “Temperature dependence of GaAs-AlGaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 60, 683–685 (1992).
[CrossRef]

Lenstra, D.

G. H. M. van Tartwijk, A. M. Levine, and D. Lenstra, “Sysyphus effect in semiconductor lasers with optical feedback,” IEEE J. Sel. Top. Quantum Electron. 1, 466–472 (1995).
[CrossRef]

Levine, A. M.

G. H. M. van Tartwijk, A. M. Levine, and D. Lenstra, “Sysyphus effect in semiconductor lasers with optical feedback,” IEEE J. Sel. Top. Quantum Electron. 1, 466–472 (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, 2355–2357 (1998).
[CrossRef]

Lin, H.

H. Lin, J. HoShue, Z. J. Lapin, and A. Valle, “Polarization instabilities in a multi-transverse-mode vertical-cavity surface-emitting laser with polarized optical feedback,” Opt. Commun. 283, 1424–1433 (2010).
[CrossRef]

H. Lin, Z. J. Lapin, B. Malla, and A. Valle, “Polarization dynamics in a multi-transverse-mode vertical-cavity surface-emitting laser subject to optical feedback,” Phys. Rev. A 77, 033813 (2008).
[CrossRef]

A. Valle, H. Lin, Z. J. Lapin, and B. Malla, “Analysis of the polarization dynamics in a multitransverse-mode vertical-cavity surface-emitting laser with isotropic optical feedback,” Phys. Rev. A 78, 033828 (2008).
[CrossRef]

Loiko, N. A.

T. Ackemann, M. Sondermann, A. Naumenko, and N. A. Loiko, “Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting laser subject to optical feedback,” Appl. Phys. B 77, 739–746 (2003).
[CrossRef]

A. V. Naumenko, N. A. 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, 033805 (2003).
[CrossRef]

Malla, B.

H. Lin, Z. J. Lapin, B. Malla, and A. Valle, “Polarization dynamics in a multi-transverse-mode vertical-cavity surface-emitting laser subject to optical feedback,” Phys. Rev. A 77, 033813 (2008).
[CrossRef]

A. Valle, H. Lin, Z. J. Lapin, and B. Malla, “Analysis of the polarization dynamics in a multitransverse-mode vertical-cavity surface-emitting laser with isotropic optical feedback,” Phys. Rev. A 78, 033828 (2008).
[CrossRef]

Mandel, P.

M. S. Torre, C. Masoller, and P. Mandel, “Transverse-mode dynamics in vertical-cavity surface-emitting lasers with optical feedback,” Phys. Rev. A 66, 053817 (2002).
[CrossRef]

Mandre, S. K.

Y. K. Chembo, S. K. Mandre, I. Fischer, W. Elsässer, and P. Colet, “Controlling the emission properties of multimode vertical-cavity surface-emitting lasers via polarization- and frequency-selective feedback,” Phys. Rev. A 79, 013817 (2009).
[CrossRef]

Marin, F.

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, “Low-frequency fluctuations in vertical cavity lasers: experiments versus Lang-Kobayashi dynamics,” Phys. Rev. A 74, 063801 (2006).
[CrossRef]

G. Giacomelli, F. Marin, and M. Romanelli, “Multi-time-scale dynamics of a laser with polarized optical feedback,” Phys. Rev. A 67, 053809 (2003).
[CrossRef]

Masoller, C.

M. S. Torre, C. Masoller, and P. Mandel, “Transverse-mode dynamics in vertical-cavity surface-emitting lasers with optical feedback,” Phys. Rev. A 66, 053817 (2002).
[CrossRef]

C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
[CrossRef]

Meziane, B.

P. Besnard, B. Meziane, and G. M. Stephan, “Feedback phenomena in a semiconductor laser induced by distant reflectors,” IEEE J. Quantum Electron. 29, 1271–1284 (1993).
[CrossRef]

Michalzik, R.

K. Panajotov, M. Arizaleta, M. Camarena, H. Thienpont, H. J. Unold, J. M. Ostermann, and R. Michalzik, “Polarization switching induced by phase change in extremely short external cavity vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 84, 2763–2765 (2004).
[CrossRef]

Mirasso, C. R.

P. S. Spencer, C. R. Mirasso, and K. A. Shore, “Effect of strong optical feedback on vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 10, 191–193 (1998).
[CrossRef]

Morgan, R. A.

S. Jiang, M. Dagenais, and R. A. Morgan, “Spectral characteristics of vertical-cavity surface-emitting lasers with strong external optical feedback,” IEEE Photon. Technol. Lett. 7, 739–741 (1995).
[CrossRef]

Mulet, J.

M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,” Phys. Rev. A 68, 033822 (2003).
[CrossRef]

Naumenko, A.

T. Ackemann, M. Sondermann, A. Naumenko, and N. A. Loiko, “Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting laser subject to optical feedback,” Appl. Phys. B 77, 739–746 (2003).
[CrossRef]

Naumenko, A. V.

A. V. Naumenko, N. A. 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, 033805 (2003).
[CrossRef]

Ohtsubo, J.

Ostermann, J. M.

K. Panajotov, M. Arizaleta, M. Camarena, H. Thienpont, H. J. Unold, J. M. Ostermann, and R. Michalzik, “Polarization switching induced by phase change in extremely short external cavity vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 84, 2763–2765 (2004).
[CrossRef]

Panajotov, K.

K. Panajotov, M. Arizaleta, M. Camarena, H. Thienpont, H. J. Unold, J. M. Ostermann, and R. Michalzik, “Polarization switching induced by phase change in extremely short external cavity vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 84, 2763–2765 (2004).
[CrossRef]

Richie, D. A.

K. D. Choquette, D. A. Richie, and R. E. Leibenguth, “Temperature dependence of gain-guided vertical-cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062–2064 (1994).
[CrossRef]

Robert, F.

P. Besnard, F. Robert, M. L. Chares, and G. M. Stephan, “Theoretical modeling of vertical-cavity surface-emitting lasers with polarized optical feedback,” Phys. Rev. A 56, 3191–3205 (1997).
[CrossRef]

Romanelli, M.

G. Giacomelli, F. Marin, and M. Romanelli, “Multi-time-scale dynamics of a laser with polarized optical feedback,” Phys. Rev. A 67, 053809 (2003).
[CrossRef]

Sano, T.

T. Sano, “Antimode dynamics and chaotic itinerancyin the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50, 2719–2726 (1994).
[CrossRef] [PubMed]

Shore, K. A.

Y. Hong and K. A. Shore, “Influence of optical feedback time-delay on power-drops in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1054–1057 (2005).
[CrossRef]

P. S. Spencer, C. R. Mirasso, and K. A. Shore, “Effect of strong optical feedback on vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 10, 191–193 (1998).
[CrossRef]

Sondermann, M.

A. V. Naumenko, N. A. 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, 033805 (2003).
[CrossRef]

T. Ackemann, M. Sondermann, A. Naumenko, and N. A. Loiko, “Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting laser subject to optical feedback,” Appl. Phys. B 77, 739–746 (2003).
[CrossRef]

M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,” Phys. Rev. A 68, 033822 (2003).
[CrossRef]

Spencer, P. S.

P. S. Spencer, C. R. Mirasso, and K. A. Shore, “Effect of strong optical feedback on vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 10, 191–193 (1998).
[CrossRef]

Stephan, G. M.

P. Besnard, F. Robert, M. L. Chares, and G. M. Stephan, “Theoretical modeling of vertical-cavity surface-emitting lasers with polarized optical feedback,” Phys. Rev. A 56, 3191–3205 (1997).
[CrossRef]

P. Besnard, B. Meziane, and G. M. Stephan, “Feedback phenomena in a semiconductor laser induced by distant reflectors,” IEEE J. Quantum Electron. 29, 1271–1284 (1993).
[CrossRef]

Takiguchi, Y.

Tell, B.

B. Tell, K. Brown-Goebeler, R. E. Leibenguth, F. M. Baez, and Y. H. Lee, “Temperature dependence of GaAs-AlGaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 60, 683–685 (1992).
[CrossRef]

Thienpont, H.

K. Panajotov, M. Arizaleta, M. Camarena, H. Thienpont, H. J. Unold, J. M. Ostermann, and R. Michalzik, “Polarization switching induced by phase change in extremely short external cavity vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 84, 2763–2765 (2004).
[CrossRef]

Torcini, A.

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, “Low-frequency fluctuations in vertical cavity lasers: experiments versus Lang-Kobayashi dynamics,” Phys. Rev. A 74, 063801 (2006).
[CrossRef]

Torre, M. S.

M. S. Torre, C. Masoller, and P. Mandel, “Transverse-mode dynamics in vertical-cavity surface-emitting lasers with optical feedback,” Phys. Rev. A 66, 053817 (2002).
[CrossRef]

Tredicce, J. R.

Unold, H. J.

K. Panajotov, M. Arizaleta, M. Camarena, H. Thienpont, H. J. Unold, J. M. Ostermann, and R. Michalzik, “Polarization switching induced by phase change in extremely short external cavity vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 84, 2763–2765 (2004).
[CrossRef]

Valle, A.

H. Lin, J. HoShue, Z. J. Lapin, and A. Valle, “Polarization instabilities in a multi-transverse-mode vertical-cavity surface-emitting laser with polarized optical feedback,” Opt. Commun. 283, 1424–1433 (2010).
[CrossRef]

H. Lin, Z. J. Lapin, B. Malla, and A. Valle, “Polarization dynamics in a multi-transverse-mode vertical-cavity surface-emitting laser subject to optical feedback,” Phys. Rev. A 77, 033813 (2008).
[CrossRef]

A. Valle, H. Lin, Z. J. Lapin, and B. Malla, “Analysis of the polarization dynamics in a multitransverse-mode vertical-cavity surface-emitting laser with isotropic optical feedback,” Phys. Rev. A 78, 033828 (2008).
[CrossRef]

A. Valle, “Selection and modulation of higher-order transverse modes in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 34, 1924–1932 (1998).
[CrossRef]

van Tartwijk, G. H. M.

G. H. M. van Tartwijk, A. M. Levine, and D. Lenstra, “Sysyphus effect in semiconductor lasers with optical feedback,” IEEE J. Sel. Top. Quantum Electron. 1, 466–472 (1995).
[CrossRef]

Weinkath, M.

M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,” Phys. Rev. A 68, 033822 (2003).
[CrossRef]

Appl. Phys. B (1)

T. Ackemann, M. Sondermann, A. Naumenko, and N. A. Loiko, “Polarization dynamics and low-frequency fluctuations in vertical-cavity surface-emitting laser subject to optical feedback,” Appl. Phys. B 77, 739–746 (2003).
[CrossRef]

Appl. Phys. Lett. (4)

B. Tell, K. Brown-Goebeler, R. E. Leibenguth, F. M. Baez, and Y. H. Lee, “Temperature dependence of GaAs-AlGaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett. 60, 683–685 (1992).
[CrossRef]

K. D. Choquette, D. A. Richie, and R. E. Leibenguth, “Temperature dependence of gain-guided vertical-cavity surface emitting laser polarization,” Appl. Phys. Lett. 64, 2062–2064 (1994).
[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, 2355–2357 (1998).
[CrossRef]

K. Panajotov, M. Arizaleta, M. Camarena, H. Thienpont, H. J. Unold, J. M. Ostermann, and R. Michalzik, “Polarization switching induced by phase change in extremely short external cavity vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 84, 2763–2765 (2004).
[CrossRef]

IEEE J. Quantum Electron. (3)

A. Valle, “Selection and modulation of higher-order transverse modes in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 34, 1924–1932 (1998).
[CrossRef]

Y. Hong and K. A. Shore, “Influence of optical feedback time-delay on power-drops in vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1054–1057 (2005).
[CrossRef]

P. Besnard, B. Meziane, and G. M. Stephan, “Feedback phenomena in a semiconductor laser induced by distant reflectors,” IEEE J. Quantum Electron. 29, 1271–1284 (1993).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (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. Quantum Electron. 3, 353–358 (1997).
[CrossRef]

G. H. M. van Tartwijk, A. M. Levine, and D. Lenstra, “Sysyphus effect in semiconductor lasers with optical feedback,” IEEE J. Sel. Top. Quantum Electron. 1, 466–472 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

Y. C. Chung and Y. H. Lee, “Spectral characteristics of vertical-cavity surface-emitting lasers with external optical feedback,” IEEE Photon. Technol. Lett. 3, 597–599 (1991).
[CrossRef]

S. Jiang, M. Dagenais, and R. A. Morgan, “Spectral characteristics of vertical-cavity surface-emitting lasers with strong external optical feedback,” IEEE Photon. Technol. Lett. 7, 739–741 (1995).
[CrossRef]

P. S. Spencer, C. R. Mirasso, and K. A. Shore, “Effect of strong optical feedback on vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett. 10, 191–193 (1998).
[CrossRef]

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

Opt. Commun. (1)

H. Lin, J. HoShue, Z. J. Lapin, and A. Valle, “Polarization instabilities in a multi-transverse-mode vertical-cavity surface-emitting laser with polarized optical feedback,” Opt. Commun. 283, 1424–1433 (2010).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (12)

P. Besnard, F. Robert, M. L. Chares, and G. M. Stephan, “Theoretical modeling of vertical-cavity surface-emitting lasers with polarized optical feedback,” Phys. Rev. A 56, 3191–3205 (1997).
[CrossRef]

C. Masoller and N. B. Abraham, “Low-frequency fluctuations in vertical-cavity surface-emitting semiconductor lasers with optical feedback,” Phys. Rev. A 59, 3021–3031 (1999).
[CrossRef]

A. V. Naumenko, N. A. 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, 033805 (2003).
[CrossRef]

G. Giacomelli, F. Marin, and M. Romanelli, “Multi-time-scale dynamics of a laser with polarized optical feedback,” Phys. Rev. A 67, 053809 (2003).
[CrossRef]

T. Sano, “Antimode dynamics and chaotic itinerancyin the coherence collapse of semiconductor lasers with optical feedback,” Phys. Rev. A 50, 2719–2726 (1994).
[CrossRef] [PubMed]

M. Sondermann, M. Weinkath, T. Ackemann, J. Mulet, and S. Balle, “Two-frequency emission and polarization dynamics at lasing threshold in vertical-cavity surface-emitting lasers,” Phys. Rev. A 68, 033822 (2003).
[CrossRef]

M. S. Torre, C. Masoller, and P. Mandel, “Transverse-mode dynamics in vertical-cavity surface-emitting lasers with optical feedback,” Phys. Rev. A 66, 053817 (2002).
[CrossRef]

H. Lin, Z. J. Lapin, B. Malla, and A. Valle, “Polarization dynamics in a multi-transverse-mode vertical-cavity surface-emitting laser subject to optical feedback,” Phys. Rev. A 77, 033813 (2008).
[CrossRef]

A. Valle, H. Lin, Z. J. Lapin, and B. Malla, “Analysis of the polarization dynamics in a multitransverse-mode vertical-cavity surface-emitting laser with isotropic optical feedback,” Phys. Rev. A 78, 033828 (2008).
[CrossRef]

Y. K. Chembo, S. K. Mandre, I. Fischer, W. Elsässer, and P. Colet, “Controlling the emission properties of multimode vertical-cavity surface-emitting lasers via polarization- and frequency-selective feedback,” Phys. Rev. A 79, 013817 (2009).
[CrossRef]

T. Heil, I. Fischer, and W. Elsäßer, “Coexistence of low-frequency fluctuations and stable emission on a single high-gain mode in semiconductor lasers with external optical feedback,” Phys. Rev. A 58, R2672–R2675 (1998).
[CrossRef]

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, “Low-frequency fluctuations in vertical cavity lasers: experiments versus Lang-Kobayashi dynamics,” Phys. Rev. A 74, 063801 (2006).
[CrossRef]

Phys. Rev. E (1)

T. Heil, I. Fischer, W. Elsässer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Experimental setup, where BS stands for nonpolarizing beam splitter, M for feedback mirror, PBS for polarizing beam splitter, PD for photodetector, and ND for neutral density filter.

Fig. 2
Fig. 2

Mode selection using an etalon. (a) Optical spectrum of the VCSEL with the strongest feedback before mode selection. (b) Optical spectra of the selected modes, in which the solid, dark blue curve is for LP 01 mode, the dotted pink curve is for LP 11 c mode, and the dashed, light blue curve is for LP 11 s mode. The insets are spatial profiles of the corresponding frequency peak. The spatial profiles of the LP 01 and LP 11 s modes were attenuated to avoid saturation at the CCD camera. The substrate temperature is 64 ° C .

Fig. 3
Fig. 3

Dynamics of individual transverse modes for 4.8 mA and the strongest feedback. (a) Polarization resolved optical spectra of the VCSEL, where the solid and dashed curves are for x and y polarization, respectively. (b) Power spectrum and (c) time trace of the x-polarization of the LP 01 mode. (d) Power spectrum and (e) time trace of the x-polarization of the LP 11 s mode.

Fig. 4
Fig. 4

Slow events in the x component of LP 01 and LP 11 s modes for 6.00 mA and the strongest feedback. (a) Polarization resolved optical spectral of the VCSEL, where the solid and dashed curves are for x and y polarization, respectively. (b) Power spectrum and (c) time trace of the LP 01 mode. (d) Power spectrum and (e) time trace of the LP 11 s mode. The weak peaks in (d) between 600 and 800 MHz are noises. The features of the time trace of the LP 11 s mode are very similar to LFF.

Fig. 5
Fig. 5

(a) Polarization resolved time traces of the total output for 6.00 mA and the strongest feedback, in which the upper, blue curve represents the x-polarized state and lower, red curve is for the y-polarized state. For convenience of visualization, the y-polarized time trace is shifted downward by 7 units. (b) The cross correlation coefficient of the orthogonally polarized states.

Fig. 6
Fig. 6

Dynamical regime featured by the low-frequency peak in the power spectrum of (a) the LP 01 mode and (b) LP 11 s mode mapped in the R - I (strength of feedback-injection current) parameter space.

Fig. 7
Fig. 7

(a) Frequency of the low-frequency peak in the power spectrum versus injection current, where the filled diamond represents the LP 01 mode and the blank square is for the LP 11 s mode. (b) Dependence of the amplitude of the low-frequency peak in the power spectrum of the LP 01 mode on the current. The peak amplitude of the LP 11 s mode varies with the current very similarly. For both (a) and (b), R = 25 % .

Fig. 8
Fig. 8

Power spectra of the x polarization of the VCSEL for I = 6.00   mA and four substrate temperatures. The spectra from bottom to top are for 24 ° C (black), 34 ° C (red), 54 ° C (blue), and 64 ° C (green), respectively. For visual convenience, the power spectra from 34 ° C to 64 ° C are shifted up by 20 dBm sequentially. The spectra are for R = 25 % .

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