Abstract

A numerical study of vertical-cavity surface-emitting lasers with optical feedback demonstrates the existence of two different types of low-frequency fluctuations (LFFs). The competition of two equally dominant polarization modes characterizes one type of LFF, while the other type is characterized by power drops in a dominant polarization mode and power bursts in the orthogonal depressed mode. We characterize and compare these two types of LFFs on the basis of their polarization properties and their dependency on the laser parameters. We show furthermore that a transition is possible from one type of LFF to the other, depending on the values of the linear anisotropies of the vertical-cavity surface-emitting laser cavity.

© 2003 Optical Society of America

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  8. S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, “High frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 3545–3547 (1993).
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  9. F. Robert, P. Besnard, M. L. Chares, and G. Stephan, “Polarization modulation dynamics of vertical-cavity surface-emitting lasers with an extended cavity,” IEEE J. Quantum Electron. 33, 2231–2239 (1997).
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  28. A. K. Jansen van Doorn, M. P. van Exter, and J. P. Woerdman, “Tailoring the birefringence in a vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 69, 3635–3637 (1996).
    [CrossRef]
  29. K. Panajotov, B. Nagler, G. Verschaffelt, A. Georgievski, H. Thienpont, J. Danckaert, and I. Veretennicoff, “Impact of in-plane anisotropic strain on the polarization behavior of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 77, 1590–1592 (2000).
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  32. F. Rogister, P. Mégret, O. Deparis, and M. Blondel, “Coexistence of in-phase and out-of-phase dynamics in a multimode external-cavity laser diode operating in the low-frequency fluctuations regime,” Phys. Rev. A 62, 061803/1(R)–061803/4(R) (2000).
    [CrossRef]
  33. A. Hohl and A. Gavrielides, “Bifurcation cascade in a semiconductor laser subject to optical feedback,” Phys. Rev. Lett. 82, 1148–1151 (1999).
    [CrossRef]
  34. P. Besnard, M. Chares, G. Stephan, and F. Robert, “Switching between polarization modes of a vertical-cavity surface-emitting laser by isotropic optical feedback,” J. Opt. Soc. Am. B 16, 1059–1063 (1999).
    [CrossRef]

2002

M. Sciamanna, F. Rogister, O. Deparis, P. Mégret, M. Blondel, and T. Erneux, “Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers,” Opt. Lett. 27, 261–263 (2002).
[CrossRef]

M. Sciamanna, F. Rogister, O. Deparis, P. Mégret, M. Blondel, and T. Erneux, “Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers: errata,” Opt. Lett. 27, 875 (2002).
[CrossRef]

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Mégret, and M. Blondel, “Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers,” Phys. Rev. A 65, 041801/1(R)-041801/4(R) (2002).
[CrossRef]

G. D. Van Wiggeren and R. Roy, “Communicating with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88, 097903/1–097903/4 (2002).

J. Danckaert, B. Nagler, J. Albert, K. Panajotov, I. Veretennicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Comm. 201, 129–137 (2002).
[CrossRef]

2000

L. Plouzennec, “Polarization gain dependence of vertical-cavity surface-emitting lasers: phenomenological modeling and experiments,” J. Appl. Phys. 87, 2649–2651 (2000).
[CrossRef]

K. Panajotov, B. Nagler, G. Verschaffelt, A. Georgievski, H. Thienpont, J. Danckaert, and I. Veretennicoff, “Impact of in-plane anisotropic strain on the polarization behavior of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 77, 1590–1592 (2000).
[CrossRef]

E. A. Vikotorov and P. Mandel, “Low frequency fluctuations in a multimode semiconductor laser with optical feedback,” Phys. Rev. Lett. 85, 3157–3160 (2000).
[CrossRef]

F. Rogister, P. Mégret, O. Deparis, and M. Blondel, “Coexistence of in-phase and out-of-phase dynamics in a multimode external-cavity laser diode operating in the low-frequency fluctuations regime,” Phys. Rev. A 62, 061803/1(R)–061803/4(R) (2000).
[CrossRef]

1999

A. Hohl and A. Gavrielides, “Bifurcation cascade in a semiconductor laser subject to optical feedback,” Phys. Rev. Lett. 82, 1148–1151 (1999).
[CrossRef]

P. Besnard, M. Chares, G. Stephan, and F. Robert, “Switching between polarization modes of a vertical-cavity surface-emitting laser by isotropic optical feedback,” J. Opt. Soc. Am. B 16, 1059–1063 (1999).
[CrossRef]

C. Masoller and N. B. Abraham, “Polarization dynamics of vertical-cavity surface-emitting lasers with optical feedback through a quarter-wave plate,” Appl. Phys. Lett. 74, 1078–1080 (1999).
[CrossRef]

J. Dellunde, A. Valle, L. Pesquera, and K. A. Shore, “Transverse-mode selection and noise properties of external-cavity vertical-cavity surface-emitting lasers including multiple-reflection effects,” J. Opt. Soc. Am. B 16, 2131–2139 (1999).
[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]

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

1998

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]

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

1997

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

F. Robert, P. Besnard, M. L. Chares, and G. Stephan, “Polarization modulation dynamics of vertical-cavity surface-emitting lasers with an extended cavity,” IEEE J. Quantum Electron. 33, 2231–2239 (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]

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]

1996

A. K. Jansen van Doorn, M. P. van Exter, and J. P. Woerdman, “Tailoring the birefringence in a vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 69, 3635–3637 (1996).
[CrossRef]

1995

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

K. Iga, “Surface-emitting laser-Its birth and generation of new optoelectronics field,” IEEE J. Sel. Top. Quantum Electron. 1, 667–673 (1995).

1993

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

1991

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 24, 1402–1409 (1991).
[CrossRef]

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

1980

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

1979

H. Soda, K. Iga, C. Kitahara, and Y. Suematsu, “GaInAsP/InP surface emitting injection lasers,” Jpn. J. Appl. Phys. 18, 2329–2330 (1979).
[CrossRef]

Abraham, N. B.

C. Masoller and N. B. Abraham, “Polarization dynamics of vertical-cavity surface-emitting lasers with optical feedback through a quarter-wave plate,” Appl. Phys. Lett. 74, 1078–1080 (1999).
[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]

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

Ackemann, T.

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]

Albert, J.

J. Danckaert, B. Nagler, J. Albert, K. Panajotov, I. Veretennicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Comm. 201, 129–137 (2002).
[CrossRef]

Balle, S.

Barland, S.

Besnard, P.

P. Besnard, M. Chares, G. Stephan, and F. Robert, “Switching between polarization modes of a vertical-cavity surface-emitting laser by isotropic optical feedback,” J. Opt. Soc. Am. B 16, 1059–1063 (1999).
[CrossRef]

F. Robert, P. Besnard, M. L. Chares, and G. Stephan, “Polarization modulation dynamics of vertical-cavity surface-emitting lasers with an extended cavity,” IEEE J. Quantum Electron. 33, 2231–2239 (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]

Blondel, M.

M. Sciamanna, F. Rogister, O. Deparis, P. Mégret, M. Blondel, and T. Erneux, “Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers,” Opt. Lett. 27, 261–263 (2002).
[CrossRef]

M. Sciamanna, F. Rogister, O. Deparis, P. Mégret, M. Blondel, and T. Erneux, “Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers: errata,” Opt. Lett. 27, 875 (2002).
[CrossRef]

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Mégret, and M. Blondel, “Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers,” Phys. Rev. A 65, 041801/1(R)-041801/4(R) (2002).
[CrossRef]

F. Rogister, P. Mégret, O. Deparis, and M. Blondel, “Coexistence of in-phase and out-of-phase dynamics in a multimode external-cavity laser diode operating in the low-frequency fluctuations regime,” Phys. Rev. A 62, 061803/1(R)–061803/4(R) (2000).
[CrossRef]

Chang-Hasnain, C. J.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 24, 1402–1409 (1991).
[CrossRef]

Chares, M.

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]

F. Robert, P. Besnard, M. L. Chares, and G. Stephan, “Polarization modulation dynamics of vertical-cavity surface-emitting lasers with an extended cavity,” IEEE J. Quantum Electron. 33, 2231–2239 (1997).
[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]

Chung, Y. C.

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

Dagenais, M.

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

Danckaert, J.

J. Danckaert, B. Nagler, J. Albert, K. Panajotov, I. Veretennicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Comm. 201, 129–137 (2002).
[CrossRef]

K. Panajotov, B. Nagler, G. Verschaffelt, A. Georgievski, H. Thienpont, J. Danckaert, and I. Veretennicoff, “Impact of in-plane anisotropic strain on the polarization behavior of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 77, 1590–1592 (2000).
[CrossRef]

Dellunde, J.

Deparis, O.

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Mégret, and M. Blondel, “Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers,” Phys. Rev. A 65, 041801/1(R)-041801/4(R) (2002).
[CrossRef]

M. Sciamanna, F. Rogister, O. Deparis, P. Mégret, M. Blondel, and T. Erneux, “Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers: errata,” Opt. Lett. 27, 875 (2002).
[CrossRef]

M. Sciamanna, F. Rogister, O. Deparis, P. Mégret, M. Blondel, and T. Erneux, “Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers,” Opt. Lett. 27, 261–263 (2002).
[CrossRef]

F. Rogister, P. Mégret, O. Deparis, and M. Blondel, “Coexistence of in-phase and out-of-phase dynamics in a multimode external-cavity laser diode operating in the low-frequency fluctuations regime,” Phys. Rev. A 62, 061803/1(R)–061803/4(R) (2000).
[CrossRef]

Erneux, T.

M. Sciamanna, F. Rogister, O. Deparis, P. Mégret, M. Blondel, and T. Erneux, “Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers,” Opt. Lett. 27, 261–263 (2002).
[CrossRef]

M. Sciamanna, F. Rogister, O. Deparis, P. Mégret, M. Blondel, and T. Erneux, “Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers: errata,” Opt. Lett. 27, 875 (2002).
[CrossRef]

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Mégret, and M. Blondel, “Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers,” Phys. Rev. A 65, 041801/1(R)-041801/4(R) (2002).
[CrossRef]

J. Danckaert, B. Nagler, J. Albert, K. Panajotov, I. Veretennicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Comm. 201, 129–137 (2002).
[CrossRef]

Feng, Q.

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

Florez, L. T.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 24, 1402–1409 (1991).
[CrossRef]

Gavrielides, A.

A. Hohl and A. Gavrielides, “Bifurcation cascade in a semiconductor laser subject to optical feedback,” Phys. Rev. Lett. 82, 1148–1151 (1999).
[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]

Georgievski, A.

K. Panajotov, B. Nagler, G. Verschaffelt, A. Georgievski, H. Thienpont, J. Danckaert, and I. Veretennicoff, “Impact of in-plane anisotropic strain on the polarization behavior of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 77, 1590–1592 (2000).
[CrossRef]

Giudici, M.

Harbison, J. P.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 24, 1402–1409 (1991).
[CrossRef]

Hasnain, G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 24, 1402–1409 (1991).
[CrossRef]

Hohl, A.

A. Hohl and A. Gavrielides, “Bifurcation cascade in a semiconductor laser subject to optical feedback,” Phys. Rev. Lett. 82, 1148–1151 (1999).
[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]

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]

Iga, K.

K. Iga, “Surface-emitting laser-Its birth and generation of new optoelectronics field,” IEEE J. Sel. Top. Quantum Electron. 1, 667–673 (1995).

H. Soda, K. Iga, C. Kitahara, and Y. Suematsu, “GaInAsP/InP surface emitting injection lasers,” Jpn. J. Appl. Phys. 18, 2329–2330 (1979).
[CrossRef]

Jansen van Doorn, A. K.

A. K. Jansen van Doorn, M. P. van Exter, and J. P. Woerdman, “Tailoring the birefringence in a vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 69, 3635–3637 (1996).
[CrossRef]

Jiang, S.

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

Kitahara, C.

H. Soda, K. Iga, C. Kitahara, and Y. Suematsu, “GaInAsP/InP surface emitting injection lasers,” Jpn. J. Appl. Phys. 18, 2329–2330 (1979).
[CrossRef]

Kobayashi, K.

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

Kojima, K.

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

Lang, R.

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

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

Mandel, P.

E. A. Vikotorov and P. Mandel, “Low frequency fluctuations in a multimode semiconductor laser with optical feedback,” Phys. Rev. Lett. 85, 3157–3160 (2000).
[CrossRef]

Martin-Regalado, J.

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

Masoller, C.

C. Masoller and N. B. Abraham, “Polarization dynamics of vertical-cavity surface-emitting lasers with optical feedback through a quarter-wave plate,” Appl. Phys. Lett. 74, 1078–1080 (1999).
[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]

Mégret, P.

M. Sciamanna, F. Rogister, O. Deparis, P. Mégret, M. Blondel, and T. Erneux, “Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers,” Opt. Lett. 27, 261–263 (2002).
[CrossRef]

M. Sciamanna, F. Rogister, O. Deparis, P. Mégret, M. Blondel, and T. Erneux, “Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers: errata,” Opt. Lett. 27, 875 (2002).
[CrossRef]

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Mégret, and M. Blondel, “Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers,” Phys. Rev. A 65, 041801/1(R)-041801/4(R) (2002).
[CrossRef]

F. Rogister, P. Mégret, O. Deparis, and M. Blondel, “Coexistence of in-phase and out-of-phase dynamics in a multimode external-cavity laser diode operating in the low-frequency fluctuations regime,” Phys. Rev. A 62, 061803/1(R)–061803/4(R) (2000).
[CrossRef]

Miguel, M. San

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

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

Mirasso, C. R.

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

Moloney, J. V.

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

Morgan, R. A.

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

Nagler, B.

J. Danckaert, B. Nagler, J. Albert, K. Panajotov, I. Veretennicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Comm. 201, 129–137 (2002).
[CrossRef]

K. Panajotov, B. Nagler, G. Verschaffelt, A. Georgievski, H. Thienpont, J. Danckaert, and I. Veretennicoff, “Impact of in-plane anisotropic strain on the polarization behavior of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 77, 1590–1592 (2000).
[CrossRef]

Pan, Z.

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

Panajotov, K.

J. Danckaert, B. Nagler, J. Albert, K. Panajotov, I. Veretennicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Comm. 201, 129–137 (2002).
[CrossRef]

K. Panajotov, B. Nagler, G. Verschaffelt, A. Georgievski, H. Thienpont, J. Danckaert, and I. Veretennicoff, “Impact of in-plane anisotropic strain on the polarization behavior of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 77, 1590–1592 (2000).
[CrossRef]

Pesquera, L.

Plouzennec, L.

L. Plouzennec, “Polarization gain dependence of vertical-cavity surface-emitting lasers: phenomenological modeling and experiments,” J. Appl. Phys. 87, 2649–2651 (2000).
[CrossRef]

Prati, F.

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

Robert, F.

P. Besnard, M. Chares, G. Stephan, and F. Robert, “Switching between polarization modes of a vertical-cavity surface-emitting laser by isotropic optical feedback,” J. Opt. Soc. Am. B 16, 1059–1063 (1999).
[CrossRef]

F. Robert, P. Besnard, M. L. Chares, and G. Stephan, “Polarization modulation dynamics of vertical-cavity surface-emitting lasers with an extended cavity,” IEEE J. Quantum Electron. 33, 2231–2239 (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]

Rogister, F.

M. Sciamanna, F. Rogister, O. Deparis, P. Mégret, M. Blondel, and T. Erneux, “Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers: errata,” Opt. Lett. 27, 875 (2002).
[CrossRef]

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Mégret, and M. Blondel, “Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers,” Phys. Rev. A 65, 041801/1(R)-041801/4(R) (2002).
[CrossRef]

M. Sciamanna, F. Rogister, O. Deparis, P. Mégret, M. Blondel, and T. Erneux, “Bifurcation to polarization self-modulation in vertical-cavity surface-emitting lasers,” Opt. Lett. 27, 261–263 (2002).
[CrossRef]

F. Rogister, P. Mégret, O. Deparis, and M. Blondel, “Coexistence of in-phase and out-of-phase dynamics in a multimode external-cavity laser diode operating in the low-frequency fluctuations regime,” Phys. Rev. A 62, 061803/1(R)–061803/4(R) (2000).
[CrossRef]

Roy, R.

G. D. Van Wiggeren and R. Roy, “Communicating with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88, 097903/1–097903/4 (2002).

Sciamanna, M.

Shore, K. A.

J. Dellunde, A. Valle, L. Pesquera, and K. A. Shore, “Transverse-mode selection and noise properties of external-cavity vertical-cavity surface-emitting lasers including multiple-reflection effects,” J. Opt. Soc. Am. B 16, 2131–2139 (1999).
[CrossRef]

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

Soda, H.

H. Soda, K. Iga, C. Kitahara, and Y. Suematsu, “GaInAsP/InP surface emitting injection lasers,” Jpn. J. Appl. Phys. 18, 2329–2330 (1979).
[CrossRef]

Spencer, P.

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

Stephan, G.

P. Besnard, M. Chares, G. Stephan, and F. Robert, “Switching between polarization modes of a vertical-cavity surface-emitting laser by isotropic optical feedback,” J. Opt. Soc. Am. B 16, 1059–1063 (1999).
[CrossRef]

F. Robert, P. Besnard, M. L. Chares, and G. Stephan, “Polarization modulation dynamics of vertical-cavity surface-emitting lasers with an extended cavity,” IEEE J. Quantum Electron. 33, 2231–2239 (1997).
[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]

Stoffel, N. G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 24, 1402–1409 (1991).
[CrossRef]

Suematsu, Y.

H. Soda, K. Iga, C. Kitahara, and Y. Suematsu, “GaInAsP/InP surface emitting injection lasers,” Jpn. J. Appl. Phys. 18, 2329–2330 (1979).
[CrossRef]

Thienpont, H.

K. Panajotov, B. Nagler, G. Verschaffelt, A. Georgievski, H. Thienpont, J. Danckaert, and I. Veretennicoff, “Impact of in-plane anisotropic strain on the polarization behavior of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 77, 1590–1592 (2000).
[CrossRef]

Tredicce, J. R.

Valle, A.

van Exter, M. P.

A. K. Jansen van Doorn, M. P. van Exter, and J. P. Woerdman, “Tailoring the birefringence in a vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 69, 3635–3637 (1996).
[CrossRef]

Van Wiggeren, G. D.

G. D. Van Wiggeren and R. Roy, “Communicating with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88, 097903/1–097903/4 (2002).

Veretennicoff, I.

J. Danckaert, B. Nagler, J. Albert, K. Panajotov, I. Veretennicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Comm. 201, 129–137 (2002).
[CrossRef]

K. Panajotov, B. Nagler, G. Verschaffelt, A. Georgievski, H. Thienpont, J. Danckaert, and I. Veretennicoff, “Impact of in-plane anisotropic strain on the polarization behavior of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 77, 1590–1592 (2000).
[CrossRef]

Verschaffelt, G.

K. Panajotov, B. Nagler, G. Verschaffelt, A. Georgievski, H. Thienpont, J. Danckaert, and I. Veretennicoff, “Impact of in-plane anisotropic strain on the polarization behavior of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 77, 1590–1592 (2000).
[CrossRef]

Vikotorov, E. A.

E. A. Vikotorov and P. Mandel, “Low frequency fluctuations in a multimode semiconductor laser with optical feedback,” Phys. Rev. Lett. 85, 3157–3160 (2000).
[CrossRef]

Von Lehmen, A. C.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 24, 1402–1409 (1991).
[CrossRef]

Woerdman, J. P.

A. K. Jansen van Doorn, M. P. van Exter, and J. P. Woerdman, “Tailoring the birefringence in a vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 69, 3635–3637 (1996).
[CrossRef]

Appl. Phys. Lett.

S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, “High frequency polarization self-modulation in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 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, 2355–2357 (1998).
[CrossRef]

C. Masoller and N. B. Abraham, “Polarization dynamics of vertical-cavity surface-emitting lasers with optical feedback through a quarter-wave plate,” Appl. Phys. Lett. 74, 1078–1080 (1999).
[CrossRef]

A. K. Jansen van Doorn, M. P. van Exter, and J. P. Woerdman, “Tailoring the birefringence in a vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 69, 3635–3637 (1996).
[CrossRef]

K. Panajotov, B. Nagler, G. Verschaffelt, A. Georgievski, H. Thienpont, J. Danckaert, and I. Veretennicoff, “Impact of in-plane anisotropic strain on the polarization behavior of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 77, 1590–1592 (2000).
[CrossRef]

IEEE J. Quantum Electron.

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

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

F. Robert, P. Besnard, M. L. Chares, and G. Stephan, “Polarization modulation dynamics of vertical-cavity surface-emitting lasers with an extended cavity,” IEEE J. Quantum Electron. 33, 2231–2239 (1997).
[CrossRef]

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, L. T. Florez, and N. G. Stoffel, “Dynamic, polarization, and transverse mode characteristics of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 24, 1402–1409 (1991).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

K. Iga, “Surface-emitting laser-Its birth and generation of new optoelectronics field,” IEEE J. Sel. Top. Quantum Electron. 1, 667–673 (1995).

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]

IEEE Photonics Technol. Lett.

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

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

J. Appl. Phys.

L. Plouzennec, “Polarization gain dependence of vertical-cavity surface-emitting lasers: phenomenological modeling and experiments,” J. Appl. Phys. 87, 2649–2651 (2000).
[CrossRef]

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

H. Soda, K. Iga, C. Kitahara, and Y. Suematsu, “GaInAsP/InP surface emitting injection lasers,” Jpn. J. Appl. Phys. 18, 2329–2330 (1979).
[CrossRef]

Opt. Comm.

J. Danckaert, B. Nagler, J. Albert, K. Panajotov, I. Veretennicoff, and T. Erneux, “Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers,” Opt. Comm. 201, 129–137 (2002).
[CrossRef]

Opt. Lett.

Phys. Rev. A

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Mégret, and M. Blondel, “Bifurcation bridges between external-cavity modes lead to polarization self-modulation in vertical-cavity surface-emitting lasers,” Phys. Rev. A 65, 041801/1(R)-041801/4(R) (2002).
[CrossRef]

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

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]

F. Rogister, P. Mégret, O. Deparis, and M. Blondel, “Coexistence of in-phase and out-of-phase dynamics in a multimode external-cavity laser diode operating in the low-frequency fluctuations regime,” Phys. Rev. A 62, 061803/1(R)–061803/4(R) (2000).
[CrossRef]

Phys. Rev. Lett.

A. Hohl and A. Gavrielides, “Bifurcation cascade in a semiconductor laser subject to optical feedback,” Phys. Rev. Lett. 82, 1148–1151 (1999).
[CrossRef]

E. A. Vikotorov and P. Mandel, “Low frequency fluctuations in a multimode semiconductor laser with optical feedback,” Phys. Rev. Lett. 85, 3157–3160 (2000).
[CrossRef]

G. D. Van Wiggeren and R. Roy, “Communicating with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88, 097903/1–097903/4 (2002).

Other

I. Fischer, T. Heil, and W. Elsässer, “Emission dynamics of semiconductor lasers subject to delayed optical feedback: an experimentalist’s perspective,” in Fundamental Issues of Nonlinear Dynamics, B. Krauskopf and D. Lenstra, eds. (AIP Conference Proceedings, Melville, New York, 2000), Vol. 548, pp. 218–237.

M. Sciamanna, K. Panajotov, P. Mégret, H. Thienpont, M. Blondel, and I. Veretennicoff, “Optical feedback induced polarization mode-hopping in vertical-cavity surface-emitting lasers,” presented at the OSA Annual Meeting, Orlando, Florida (October 3, 2002).

H. Kawaguchi, Bistabilities and Nonlinearities in Laser Diodes (Artech House, Norwood, Mass., 1994).

M. S. Torre, C. Masoller, and P. Mandel, “Transverse mode dynamics in vertical-cavity surface-emitting lasers with optical feedback,” Phys. Rev. A (to be published).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, (North-Holland, Amsterdam, 1977).

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Figures (8)

Fig. 1
Fig. 1

Type I LFF. (a) The total intensity Itot, (b), (c), the modal intensities Ix and Iy, and (d) the degree of polarization FP are plotted as a function of time after averaging on 1 ns. The brackets indicate averaged variables. The parameters are γa=0.1 ns-1, γp=10 ns-1, γs=50 ns-1, μ=1.8, f=60 ns-1, βsp=10-6 ns-1, τ=3 ns.

Fig. 2
Fig. 2

Same as Fig. 1 but showing type II LFF. The parameters are γa=0.5 ns-1, γp=2 ns-1, γs=50 ns-1, μ=1.1, f=40 ns-1, βsp=10-6 ns-1, τ=3 ns.

Fig. 3
Fig. 3

Transitions from type I to type II LFF, and vice versa, for different values of γa and γp. The other laser parameters remain fixed with the following values: μ=1.2, f=40 GHz, γs=50 ns-1, τ=3 ns, βsp=10-6 ns-1. (a), (d), and (g) show the time trace of the total intensity Itot after averaging on 1 ns. (b), (e), and (h) show the averaged x-LP mode intensity Ix. (c), (f) and (i) show the averaged y-LP mode intensity Iy. (a)–(c) correspond to type II LFF with γa=1 ns-1, γp=0.1 ns-1. (d)–(f) correspond to type I LFF with γa=0.1 ns-1, γp=0.1 ns-1. (g)–(i) correspond to type II LFF with γa=0.1 ns-1, γp=15 ns-1.

Fig. 4
Fig. 4

Fast-pulsating dynamics of total and modal intensities for type I LFF. (a) shows the unaveraged Ix (black curve) and Iy (gray curve), and corresponds to an enlargement of the LFF time trace of Fig. 1. Both modes are in partial antiphase before the power drop while exhibiting in-phase pulsating output just after the drop, hence during the recovery process. (b) and (c) show the PDFs of the total (heavy black curve) and modal (x, thin gray curve; y, dashed gray curve) intensities for a time span of 30 ns before (b) and after (c) the power drop.

Fig. 5
Fig. 5

Fast-pulsating dynamics of (a), (d) Itot, (b), (e) Ix, and (c), (f) Iy for type II LFF. The unaveraged intensities are plotted as a function of time in the time interval corresponding to one power drop of Fig. 2. (d)–(f) are enlargements of (a)–(c), respectively, to clarify the in-phase pulsating dynamics of the LP modes after the power drop.

Fig. 6
Fig. 6

Bifurcation diagram of (a) Ix and (b) Iy as a function of the feedback rate f showing one possible route to type I LFF. The parameters are γa=0.5 ns-1, γp=8 ns-1, γs=10 ns-1, μ=1.03, βsp=0, τ=1 ns.

Fig. 7
Fig. 7

Time traces of Ix (black curves) and Iy (gray curves) for (a) f=23 ns-1, (b) f=23.2 ns-1, (c) f=34 ns-1. (d)–(f) show Itot, Ix, and Iy, respectively, after averaging over 1 ns for f=60 ns-1. The figure shows type I LFF occurring after the bifurcation cascade of Fig. 6. The other parameters are as in Fig. 6.

Fig. 8
Fig. 8

Time traces of (a) the total intensity Itot and (b), (c) the modal intensities Ix and Iy, respectively, after averaging on 1 ns, showing type II LFF with the model of rate Eqs. (10)–(13). The laser and feedback parameters are the same as in Fig. 1 with xx=yy=0 and xy=yx=0.01.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

E˙x=κ(1+iα)[(N-1)Ex+inEy]-(γa+iγp)Ex+fEx(t-τ)exp(-iϕf)+[βsp(N+n)/2]1/2ξ1+[βsp(N-n)/2]1/2ξ2,
E˙y=κ(1+iα)[(N-1)Ey-inEx]+(γa+iγp)Ey+fEy(t-τ)exp(-iϕf)-i[βsp(N+n)/2]1/2ξ1+i[βsp(N-n)/2]1/2ξ2,
N˙=-γN[N-μ+N(|Ex|2+|Ey|2)+in(EyEx*-ExEy*)],
n˙=-γsn-γN[n(|Ex|2+|Ey|2)+iN(EyEx*-ExEy*)],
s0=|Ex|2+|Ey|2,
s1=2 Re{Ex*Ey},
s2=2 Im{Ex*Ey},
s3=|Ex|2-|Ey|2.
FP=s12+s22+s32s02,
E˙x=κ(1-iα)(NFx-1)Ex-(γa+iγp)Ex+fFx(t-τ)exp(-iϕf)+(βsp N/2)1/2ξ1+(βsp N/2)1/2ξ2,
E˙y=κ(1+iα)(NFy-1)Ey+(γa+iγp)Ey+fEy(t-τ)exp(-iϕf)-i(βsp N/2)1/2ξ1+i(βsp N/2)1/2ξ2,
N˙=-γN[N-μ+N(|Ex|2+|Ey|2)],
Fx,y=1-xx,yx|Ex|2-xy,yy|Ey|2.

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