Abstract

We investigate theoretically the polarization dynamics of vertical-cavity surface-emitting lasers (VCSELs) subjected to negative optoelectronic feedback. As we vary the feedback delay and strength, the VCSEL exhibits interesting nonlinear dynamics in the two-linear polarized directions. The output instability and negative current modulation induced by delayed feedback can also cause polarization switching (PS) to happen. In addition, we investigate the case when the free-running VCSEL emits in the modulated-elliptical state and find that the laser experiences in succession the elliptical polarization, the x-mode polarization, and the mixed-mode polarization states with an increasing feedback strength.

© 2007 Optical Society of America

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  1. S. Tang and J. M. Liu, "Experimental verification of anticipated and retarded synchronization in chaotic semiconductor lasers," Phys. Rev. Lett. 90, 194101 (2003).
    [CrossRef] [PubMed]
  2. F. Y. Lin and J. M. Liu, "Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback," IEEE J. Quantum Electron. 39, 562-568 (2003).
    [CrossRef]
  3. M. C. Chiang, H. F. Chen, and J. M. Liu, "Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback," IEEE J. Quantum Electron. 41, 1333-1340 (2005).
    [CrossRef]
  4. S. Tang, R. Vicente, M. C. Chiang, C. R. Mirasso, and J. M. Liu, "Nonlinear dynamics of semiconductor lasers with mutual optoelectronic coupling," IEEE J. Sel. Top. Quantum Electron. 10, 936-943 (2004).
    [CrossRef]
  5. G. Q. Xia, S. C. Chan, and J. M. Liu, "Multistability in a semiconductor laser with optoelectronic feedback," Opt. Express 15, 572-576 (2007).
    [CrossRef] [PubMed]
  6. Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, "Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 2999-3001 (1993).
    [CrossRef]
  7. Y. Hong, P. S. Spencer, and K. A. Shore, "Suppression of polarization switching in vertical-cavity surface-emitting lasers by use of optical feedback," Opt. Lett. 29, 2151-2153 (2004).
    [CrossRef] [PubMed]
  8. J. Paul, C. Masoller, Y. Hong, P. S. Spencer, and K. A. Shore, "Experimental study of polarisation switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation," Opt. Lett. 31, 748-750 (2006).
    [CrossRef] [PubMed]
  9. M. Sciamanna and K. Panajotov, "Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers," Phys. Rev. A 73, 023811 (2006).
    [CrossRef]
  10. M. Sciamanna, C. Masoller, F. Rogister, P. Mégret, N. B. Abraham, and M. Blondel, "Fast pulsing dynamics of a vertical-cavity surface-emitting laser operating in the low-frequency fluctuation regime," Phys. Rev. A 68, 015805 (2003).
    [CrossRef]
  11. 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, 2707-2715 (2005).
    [CrossRef] [PubMed]
  12. A. Tabaka, M. Pcil, 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, 013810 (2006).
    [CrossRef]
  13. W. L. Zhang, W. Pan, B. Luo, X. F. Li, X. H. Zou, and M. Y. Wang, "Polarization switching of mutually coupled vertical-cavity surface-emitting lasers," J. Opt. Soc. Am. B 24, 1276-1282 (2007).
    [CrossRef]
  14. J. Houliha, D. Goulding, T. Busch, C. Masoller, and G. Huyet, "Experimental investigation of a bistable system in the presence of noise and delay," Phys. Rev. Lett. 92, 050601 (2004).
  15. H. H. Lu, S. G. Tzeng, Y. W. Chuang, Y. C. Chi, and C. W. Liao, "Bidirectional radio-over-DWDM transport systems based injection-locked vcsels and optoelectronic feedback techniques," IEEE Photon. Technol. Lett. 19, 315-317 (2007).
    [CrossRef]
  16. M. S. Miguel, Q. Feng, and J. V. Moloney, "Light-polarization dynamics in surface-emitting semiconductor lasers," Phys. Rev. A 52, 1728-1739 (1995).
    [CrossRef]
  17. J. M. Regalado, F. Prati, M. S. Miguel, and N. B. Abraham, "Polarization properties of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 33, 765-783 (1997).
    [CrossRef]
  18. T. Ackemann and M. Sondermann, "Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 78, 3574-3576 (2001).
    [CrossRef]

2007 (3)

2006 (3)

A. Tabaka, M. Pcil, 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, 013810 (2006).
[CrossRef]

J. Paul, C. Masoller, Y. Hong, P. S. Spencer, and K. A. Shore, "Experimental study of polarisation switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation," Opt. Lett. 31, 748-750 (2006).
[CrossRef] [PubMed]

M. Sciamanna and K. Panajotov, "Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers," Phys. Rev. A 73, 023811 (2006).
[CrossRef]

2005 (2)

M. C. Chiang, H. F. Chen, and J. M. Liu, "Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback," IEEE J. Quantum Electron. 41, 1333-1340 (2005).
[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, 2707-2715 (2005).
[CrossRef] [PubMed]

2004 (3)

Y. Hong, P. S. Spencer, and K. A. Shore, "Suppression of polarization switching in vertical-cavity surface-emitting lasers by use of optical feedback," Opt. Lett. 29, 2151-2153 (2004).
[CrossRef] [PubMed]

J. Houliha, D. Goulding, T. Busch, C. Masoller, and G. Huyet, "Experimental investigation of a bistable system in the presence of noise and delay," Phys. Rev. Lett. 92, 050601 (2004).

S. Tang, R. Vicente, M. C. Chiang, C. R. Mirasso, and J. M. Liu, "Nonlinear dynamics of semiconductor lasers with mutual optoelectronic coupling," IEEE J. Sel. Top. Quantum Electron. 10, 936-943 (2004).
[CrossRef]

2003 (3)

S. Tang and J. M. Liu, "Experimental verification of anticipated and retarded synchronization in chaotic semiconductor lasers," Phys. Rev. Lett. 90, 194101 (2003).
[CrossRef] [PubMed]

F. Y. Lin and J. M. Liu, "Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback," IEEE J. Quantum Electron. 39, 562-568 (2003).
[CrossRef]

M. Sciamanna, C. Masoller, F. Rogister, P. Mégret, N. B. Abraham, and M. Blondel, "Fast pulsing dynamics of a vertical-cavity surface-emitting laser operating in the low-frequency fluctuation regime," Phys. Rev. A 68, 015805 (2003).
[CrossRef]

2001 (1)

T. Ackemann and M. Sondermann, "Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 78, 3574-3576 (2001).
[CrossRef]

1997 (1)

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

1995 (1)

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

1993 (1)

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

Appl. Phys. Lett. (2)

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

T. Ackemann and M. Sondermann, "Characteristics of polarization switching from the low to the high frequency mode in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 78, 3574-3576 (2001).
[CrossRef]

IEEE J. Quantum Electron. (3)

F. Y. Lin and J. M. Liu, "Nonlinear dynamics of a semiconductor laser with delayed negative optoelectronic feedback," IEEE J. Quantum Electron. 39, 562-568 (2003).
[CrossRef]

M. C. Chiang, H. F. Chen, and J. M. Liu, "Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback," IEEE J. Quantum Electron. 41, 1333-1340 (2005).
[CrossRef]

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

IEEE J. Sel. Top. Quantum Electron. (1)

S. Tang, R. Vicente, M. C. Chiang, C. R. Mirasso, and J. M. Liu, "Nonlinear dynamics of semiconductor lasers with mutual optoelectronic coupling," IEEE J. Sel. Top. Quantum Electron. 10, 936-943 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

H. H. Lu, S. G. Tzeng, Y. W. Chuang, Y. C. Chi, and C. W. Liao, "Bidirectional radio-over-DWDM transport systems based injection-locked vcsels and optoelectronic feedback techniques," IEEE Photon. Technol. Lett. 19, 315-317 (2007).
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (4)

M. Sciamanna and K. Panajotov, "Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers," Phys. Rev. A 73, 023811 (2006).
[CrossRef]

M. Sciamanna, C. Masoller, F. Rogister, P. Mégret, N. B. Abraham, and M. Blondel, "Fast pulsing dynamics of a vertical-cavity surface-emitting laser operating in the low-frequency fluctuation regime," Phys. Rev. A 68, 015805 (2003).
[CrossRef]

A. Tabaka, M. Pcil, 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, 013810 (2006).
[CrossRef]

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

Phys. Rev. Lett. (2)

S. Tang and J. M. Liu, "Experimental verification of anticipated and retarded synchronization in chaotic semiconductor lasers," Phys. Rev. Lett. 90, 194101 (2003).
[CrossRef] [PubMed]

J. Houliha, D. Goulding, T. Busch, C. Masoller, and G. Huyet, "Experimental investigation of a bistable system in the presence of noise and delay," Phys. Rev. Lett. 92, 050601 (2004).

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Figures (7)

Fig. 1
Fig. 1

(Color online) Average output intensity in the parameter space of feedback delay and index.

Fig. 2
Fig. 2

(Color online) Polarization-resolved bifurcation diagram of output intensity. In (a) [(b)], τ (η) is the stress variable.

Fig. 3
Fig. 3

Output intensity in the time and frequency domain when only the XP mode emits. From the top down, η = 0.03 , 0.04, and 0.065, respectively. In (a)–(f), τ = 3 ns .

Fig. 4
Fig. 4

(a) Polarization-resolved output intensity of the free-running laser in the time domain; (b) Average output intensity as a function of η. In (a) and (b), τ = 5 ns .

Fig. 5
Fig. 5

Polarization-resolved output intensity in the time and frequency domain with τ = 5 ns . From the top down, η = 0.005 , 0.01, 0.02, and 0.05, respectively.

Fig. 6
Fig. 6

Same plot as Figs. 5(a)–5(c), expect that η = 0.15 .

Fig. 7
Fig. 7

Correlation coefficient versus feedback index.

Equations (3)

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  d E X , Y d t = k ( 1 + j α ) ( N E X , Y E X , Y ± j n E Y , X ) ( γ a + j γ p ) E X , Y ,
d N d t = γ e N ( 1 + P ) + γ e μ [ 1 η P ( t τ ) P 0 ] j γ e n ( E Y E X * E X E Y * ) ,
d n d t = γ s n γ e n P j γ e N ( E Y E X * E X E Y * ) ,

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