Abstract

The influence of weak optical feedback on the dynamics of a single longitudinal mode vertical-cavity surface-emitting laser (VCSEL) is studied experimentally under conditions when the feedback power is sufficiently low so as to avoid the onset of chaos. The VCSEL dynamics divides into two regimes depending on the ratio of the relaxation oscillation frequency to the external cavity mode spacing. In the long cavity regime, the modulation frequency response of the VCSEL exhibits resonances corresponding to the frequencies of the external cavity modes, while for the short cavity regime the modulation response of the VCSEL at the cavity resonances remains very low while the relaxation oscillation frequency is shifted and the modulation response at the shifted frequency exhibits a sharpened and enhanced resonance.

© 2010 Optical Society of America

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  1. C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Nonlinear spectroscopy with a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
    [CrossRef]
  2. H. P. Zappe, M. Hess, M. Moser, R. Hovel, K. Gulden, H.-P. Gauggel, and F. Monti di Sopra, “Narrow-linewidth vertical-cavity surface-emitting lasers for oxygen detection,” Appl. Opt. 39, 2475–2479 (2000).
    [CrossRef]
  3. U. Fiedler, G. Reiner, P. Schnitzer, and K. J. Ebeling, “Top surface-emitting vertical-cavity laser diodes for 10-Gb∕s data transmission,” IEEE Photonics Technol. Lett. 8, 746–748 (1996).
    [CrossRef]
  4. D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, Y. Long, and K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photonics Technol. Lett. 7, 1225–1227 (1995).
    [CrossRef]
  5. D. Strekalov, A. B. Matsko, N. Yu, A. A. Savchenkov, and L. Maleki, “Application of vertical cavity surface emitting lasers in self-oscillating atomic clocks,” J. Mod. Opt. 53, 2469–2484 (2006).
    [CrossRef]
  6. J. Kitching, S. Knappe, M. Vukicevic, L. Hollberg, R. Wynands, and W. Weidmann, “A microwave frequency reference based on VCSEL-driven dark line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
    [CrossRef]
  7. N. Gavra, V. Ruseva, and M. Rosenbluh, “Enhancement in microwave modulation efficiency of vertical cavity surface-emitting laser by optical feedback,” Appl. Phys. Lett. 92, 221113 (2008).
    [CrossRef]
  8. J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81, 421–442 (2005).
    [CrossRef]
  9. L. Hollberg and M. Ohtsu, “Modulatable narrow-linewidth semiconductor lasers,” Appl. Phys. Lett. 53, 944–946 (1988).
    [CrossRef]
  10. J. S. Cohen, R. R. Drenten, and B. H. Verbeeck, “The effect of optical feedback on the relaxation oscillation in semiconductor lasers,” IEEE J. Quantum Electron. 24, 1989–1995 (1988).
    [CrossRef]
  11. B. Tromborg, J. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20, 1023–1032 (1984).
    [CrossRef]
  12. R. Tkach and A. Chraplyvy, “Regimes of feedback effects in 1.5-μm distributed feedback lasers,” J. Lightwave Technol. 4, 1655–1661 (1986).
    [CrossRef]
  13. A. T. Ryan, G. P. Agrawal, G. R. Gray, and E. C. Gage, “Optical-feedback-induced chaos and its control in multimode semiconductor lasers,” IEEE J. Quantum Electron. 30, 668–679 (1994).
    [CrossRef]
  14. G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163–1169 (1984).
    [CrossRef]
  15. G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (van Nostrand Reinhold, 1993).
  16. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
    [CrossRef]
  17. R. O. Miles, A. Dandridge, A. B. Tveten, H. F. Taylor, and T. G. Giallorenzi, “Feedback-induced line broadening in cw channel-substrate planar laser diodes,” Appl. Phys. Lett. 37, 990–992 (1980).
    [CrossRef]
  18. L. N. Langley and K. A. Shore, “Effect of optical feedback on the noise properties of vertical cavity surface emitting lasers,” Optoelectronics, IEE Proceedings 144, 34–38 (1997).
    [CrossRef]
  19. 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]
  20. C. H. L. Quay, I. Z. Maxwell, and J. A. Hudgings, “Coherence collapse and redshifting in vertical-cavity surface-emitting lasers exposed to strong optical feedback,” J. Appl. Phys. 90, 5856–5858 (2001).
    [CrossRef]
  21. J. Y. Law and G. P. Agrawal, “Feedback-induced chaos and intensity-noise enhancement in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 15, 562–569 (1998).
    [CrossRef]
  22. J. Mork, J. Mark, and B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65, 1999 (1990).
    [CrossRef] [PubMed]
  23. S. Fukuchi, S.-Y. Ye, and J. Ohtsubo, “Relaxation oscillation enhancement and coherence collapse in semiconductor lasers with optical feedback,” Opt. Rev. 6, 365–371 (1999).
    [CrossRef]
  24. J. Ye, H. Li, and J. G. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47, 2249 (1993).
    [CrossRef] [PubMed]

2008 (1)

N. Gavra, V. Ruseva, and M. Rosenbluh, “Enhancement in microwave modulation efficiency of vertical cavity surface-emitting laser by optical feedback,” Appl. Phys. Lett. 92, 221113 (2008).
[CrossRef]

2006 (1)

D. Strekalov, A. B. Matsko, N. Yu, A. A. Savchenkov, and L. Maleki, “Application of vertical cavity surface emitting lasers in self-oscillating atomic clocks,” J. Mod. Opt. 53, 2469–2484 (2006).
[CrossRef]

2005 (1)

J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81, 421–442 (2005).
[CrossRef]

2001 (1)

C. H. L. Quay, I. Z. Maxwell, and J. A. Hudgings, “Coherence collapse and redshifting in vertical-cavity surface-emitting lasers exposed to strong optical feedback,” J. Appl. Phys. 90, 5856–5858 (2001).
[CrossRef]

2000 (3)

C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Nonlinear spectroscopy with a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
[CrossRef]

J. Kitching, S. Knappe, M. Vukicevic, L. Hollberg, R. Wynands, and W. Weidmann, “A microwave frequency reference based on VCSEL-driven dark line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
[CrossRef]

H. P. Zappe, M. Hess, M. Moser, R. Hovel, K. Gulden, H.-P. Gauggel, and F. Monti di Sopra, “Narrow-linewidth vertical-cavity surface-emitting lasers for oxygen detection,” Appl. Opt. 39, 2475–2479 (2000).
[CrossRef]

1999 (1)

S. Fukuchi, S.-Y. Ye, and J. Ohtsubo, “Relaxation oscillation enhancement and coherence collapse in semiconductor lasers with optical feedback,” Opt. Rev. 6, 365–371 (1999).
[CrossRef]

1998 (1)

1997 (1)

L. N. Langley and K. A. Shore, “Effect of optical feedback on the noise properties of vertical cavity surface emitting lasers,” Optoelectronics, IEE Proceedings 144, 34–38 (1997).
[CrossRef]

1996 (1)

U. Fiedler, G. Reiner, P. Schnitzer, and K. J. Ebeling, “Top surface-emitting vertical-cavity laser diodes for 10-Gb∕s data transmission,” IEEE Photonics Technol. Lett. 8, 746–748 (1996).
[CrossRef]

1995 (1)

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, Y. Long, and K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photonics Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

1994 (1)

A. T. Ryan, G. P. Agrawal, G. R. Gray, and E. C. Gage, “Optical-feedback-induced chaos and its control in multimode semiconductor lasers,” IEEE J. Quantum Electron. 30, 668–679 (1994).
[CrossRef]

1993 (2)

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (van Nostrand Reinhold, 1993).

J. Ye, H. Li, and J. G. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47, 2249 (1993).
[CrossRef] [PubMed]

1991 (1)

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]

1990 (1)

J. Mork, J. Mark, and B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65, 1999 (1990).
[CrossRef] [PubMed]

1988 (2)

L. Hollberg and M. Ohtsu, “Modulatable narrow-linewidth semiconductor lasers,” Appl. Phys. Lett. 53, 944–946 (1988).
[CrossRef]

J. S. Cohen, R. R. Drenten, and B. H. Verbeeck, “The effect of optical feedback on the relaxation oscillation in semiconductor lasers,” IEEE J. Quantum Electron. 24, 1989–1995 (1988).
[CrossRef]

1986 (1)

R. Tkach and A. Chraplyvy, “Regimes of feedback effects in 1.5-μm distributed feedback lasers,” J. Lightwave Technol. 4, 1655–1661 (1986).
[CrossRef]

1984 (2)

B. Tromborg, J. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20, 1023–1032 (1984).
[CrossRef]

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163–1169 (1984).
[CrossRef]

1980 (2)

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

R. O. Miles, A. Dandridge, A. B. Tveten, H. F. Taylor, and T. G. Giallorenzi, “Feedback-induced line broadening in cw channel-substrate planar laser diodes,” Appl. Phys. Lett. 37, 990–992 (1980).
[CrossRef]

Acket, G.

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163–1169 (1984).
[CrossRef]

Affolderbach, C.

C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Nonlinear spectroscopy with a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
[CrossRef]

Agrawal, G. P.

J. Y. Law and G. P. Agrawal, “Feedback-induced chaos and intensity-noise enhancement in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 15, 562–569 (1998).
[CrossRef]

A. T. Ryan, G. P. Agrawal, G. R. Gray, and E. C. Gage, “Optical-feedback-induced chaos and its control in multimode semiconductor lasers,” IEEE J. Quantum Electron. 30, 668–679 (1994).
[CrossRef]

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (van Nostrand Reinhold, 1993).

Babic, D. I.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, Y. Long, and K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photonics Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Bowers, J. E.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, Y. Long, and K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photonics Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Carey, K.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, Y. Long, and K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photonics Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Chraplyvy, A.

R. Tkach and A. Chraplyvy, “Regimes of feedback effects in 1.5-μm distributed feedback lasers,” J. Lightwave Technol. 4, 1655–1661 (1986).
[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]

Cohen, J. S.

J. S. Cohen, R. R. Drenten, and B. H. Verbeeck, “The effect of optical feedback on the relaxation oscillation in semiconductor lasers,” IEEE J. Quantum Electron. 24, 1989–1995 (1988).
[CrossRef]

Dandridge, A.

R. O. Miles, A. Dandridge, A. B. Tveten, H. F. Taylor, and T. G. Giallorenzi, “Feedback-induced line broadening in cw channel-substrate planar laser diodes,” Appl. Phys. Lett. 37, 990–992 (1980).
[CrossRef]

Den Boef, A.

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163–1169 (1984).
[CrossRef]

Drenten, R. R.

J. S. Cohen, R. R. Drenten, and B. H. Verbeeck, “The effect of optical feedback on the relaxation oscillation in semiconductor lasers,” IEEE J. Quantum Electron. 24, 1989–1995 (1988).
[CrossRef]

Dutta, N. K.

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (van Nostrand Reinhold, 1993).

Ebeling, K. J.

U. Fiedler, G. Reiner, P. Schnitzer, and K. J. Ebeling, “Top surface-emitting vertical-cavity laser diodes for 10-Gb∕s data transmission,” IEEE Photonics Technol. Lett. 8, 746–748 (1996).
[CrossRef]

Fiedler, U.

U. Fiedler, G. Reiner, P. Schnitzer, and K. J. Ebeling, “Top surface-emitting vertical-cavity laser diodes for 10-Gb∕s data transmission,” IEEE Photonics Technol. Lett. 8, 746–748 (1996).
[CrossRef]

Fukuchi, S.

S. Fukuchi, S.-Y. Ye, and J. Ohtsubo, “Relaxation oscillation enhancement and coherence collapse in semiconductor lasers with optical feedback,” Opt. Rev. 6, 365–371 (1999).
[CrossRef]

Gage, E. C.

A. T. Ryan, G. P. Agrawal, G. R. Gray, and E. C. Gage, “Optical-feedback-induced chaos and its control in multimode semiconductor lasers,” IEEE J. Quantum Electron. 30, 668–679 (1994).
[CrossRef]

Gauggel, H.-P.

Gavra, N.

N. Gavra, V. Ruseva, and M. Rosenbluh, “Enhancement in microwave modulation efficiency of vertical cavity surface-emitting laser by optical feedback,” Appl. Phys. Lett. 92, 221113 (2008).
[CrossRef]

Giallorenzi, T. G.

R. O. Miles, A. Dandridge, A. B. Tveten, H. F. Taylor, and T. G. Giallorenzi, “Feedback-induced line broadening in cw channel-substrate planar laser diodes,” Appl. Phys. Lett. 37, 990–992 (1980).
[CrossRef]

Gray, G. R.

A. T. Ryan, G. P. Agrawal, G. R. Gray, and E. C. Gage, “Optical-feedback-induced chaos and its control in multimode semiconductor lasers,” IEEE J. Quantum Electron. 30, 668–679 (1994).
[CrossRef]

Gulden, K.

Hess, M.

Hollberg, L.

J. Kitching, S. Knappe, M. Vukicevic, L. Hollberg, R. Wynands, and W. Weidmann, “A microwave frequency reference based on VCSEL-driven dark line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
[CrossRef]

L. Hollberg and M. Ohtsu, “Modulatable narrow-linewidth semiconductor lasers,” Appl. Phys. Lett. 53, 944–946 (1988).
[CrossRef]

Hovel, R.

Hu, E. L.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, Y. Long, and K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photonics Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Hudgings, J. A.

C. H. L. Quay, I. Z. Maxwell, and J. A. Hudgings, “Coherence collapse and redshifting in vertical-cavity surface-emitting lasers exposed to strong optical feedback,” J. Appl. Phys. 90, 5856–5858 (2001).
[CrossRef]

Jung, C.

C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Nonlinear spectroscopy with a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
[CrossRef]

Kitching, J.

J. Kitching, S. Knappe, M. Vukicevic, L. Hollberg, R. Wynands, and W. Weidmann, “A microwave frequency reference based on VCSEL-driven dark line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
[CrossRef]

Knappe, S.

J. Kitching, S. Knappe, M. Vukicevic, L. Hollberg, R. Wynands, and W. Weidmann, “A microwave frequency reference based on VCSEL-driven dark line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
[CrossRef]

C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Nonlinear spectroscopy with a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
[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]

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]

Langley, L. N.

L. N. Langley and K. A. Shore, “Effect of optical feedback on the noise properties of vertical cavity surface emitting lasers,” Optoelectronics, IEE Proceedings 144, 34–38 (1997).
[CrossRef]

Law, J. Y.

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]

Lenstra, D.

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163–1169 (1984).
[CrossRef]

Li, H.

J. Ye, H. Li, and J. G. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47, 2249 (1993).
[CrossRef] [PubMed]

Long, Y.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, Y. Long, and K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photonics Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Maleki, L.

D. Strekalov, A. B. Matsko, N. Yu, A. A. Savchenkov, and L. Maleki, “Application of vertical cavity surface emitting lasers in self-oscillating atomic clocks,” J. Mod. Opt. 53, 2469–2484 (2006).
[CrossRef]

Margalit, N. M.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, Y. Long, and K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photonics Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Mark, J.

J. Mork, J. Mark, and B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65, 1999 (1990).
[CrossRef] [PubMed]

Mars, D. E.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, Y. Long, and K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photonics Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Matsko, A. B.

D. Strekalov, A. B. Matsko, N. Yu, A. A. Savchenkov, and L. Maleki, “Application of vertical cavity surface emitting lasers in self-oscillating atomic clocks,” J. Mod. Opt. 53, 2469–2484 (2006).
[CrossRef]

Maxwell, I. Z.

C. H. L. Quay, I. Z. Maxwell, and J. A. Hudgings, “Coherence collapse and redshifting in vertical-cavity surface-emitting lasers exposed to strong optical feedback,” J. Appl. Phys. 90, 5856–5858 (2001).
[CrossRef]

McInerney, J. G.

J. Ye, H. Li, and J. G. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47, 2249 (1993).
[CrossRef] [PubMed]

Miles, R. O.

R. O. Miles, A. Dandridge, A. B. Tveten, H. F. Taylor, and T. G. Giallorenzi, “Feedback-induced line broadening in cw channel-substrate planar laser diodes,” Appl. Phys. Lett. 37, 990–992 (1980).
[CrossRef]

Mirin, R. P.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, Y. Long, and K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photonics Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Monti di Sopra, F.

Mork, J.

J. Mork, J. Mark, and B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65, 1999 (1990).
[CrossRef] [PubMed]

Moser, M.

Nagel, A.

C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Nonlinear spectroscopy with a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
[CrossRef]

Ohtsu, M.

L. Hollberg and M. Ohtsu, “Modulatable narrow-linewidth semiconductor lasers,” Appl. Phys. Lett. 53, 944–946 (1988).
[CrossRef]

Ohtsubo, J.

S. Fukuchi, S.-Y. Ye, and J. Ohtsubo, “Relaxation oscillation enhancement and coherence collapse in semiconductor lasers with optical feedback,” Opt. Rev. 6, 365–371 (1999).
[CrossRef]

Olesen, H.

B. Tromborg, J. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20, 1023–1032 (1984).
[CrossRef]

Osmundsen, J.

B. Tromborg, J. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20, 1023–1032 (1984).
[CrossRef]

Quay, C. H. L.

C. H. L. Quay, I. Z. Maxwell, and J. A. Hudgings, “Coherence collapse and redshifting in vertical-cavity surface-emitting lasers exposed to strong optical feedback,” J. Appl. Phys. 90, 5856–5858 (2001).
[CrossRef]

Reiner, G.

U. Fiedler, G. Reiner, P. Schnitzer, and K. J. Ebeling, “Top surface-emitting vertical-cavity laser diodes for 10-Gb∕s data transmission,” IEEE Photonics Technol. Lett. 8, 746–748 (1996).
[CrossRef]

Rosenbluh, M.

N. Gavra, V. Ruseva, and M. Rosenbluh, “Enhancement in microwave modulation efficiency of vertical cavity surface-emitting laser by optical feedback,” Appl. Phys. Lett. 92, 221113 (2008).
[CrossRef]

Ruseva, V.

N. Gavra, V. Ruseva, and M. Rosenbluh, “Enhancement in microwave modulation efficiency of vertical cavity surface-emitting laser by optical feedback,” Appl. Phys. Lett. 92, 221113 (2008).
[CrossRef]

Ryan, A. T.

A. T. Ryan, G. P. Agrawal, G. R. Gray, and E. C. Gage, “Optical-feedback-induced chaos and its control in multimode semiconductor lasers,” IEEE J. Quantum Electron. 30, 668–679 (1994).
[CrossRef]

Savchenkov, A. A.

D. Strekalov, A. B. Matsko, N. Yu, A. A. Savchenkov, and L. Maleki, “Application of vertical cavity surface emitting lasers in self-oscillating atomic clocks,” J. Mod. Opt. 53, 2469–2484 (2006).
[CrossRef]

Schnitzer, P.

U. Fiedler, G. Reiner, P. Schnitzer, and K. J. Ebeling, “Top surface-emitting vertical-cavity laser diodes for 10-Gb∕s data transmission,” IEEE Photonics Technol. Lett. 8, 746–748 (1996).
[CrossRef]

Shore, K. A.

L. N. Langley and K. A. Shore, “Effect of optical feedback on the noise properties of vertical cavity surface emitting lasers,” Optoelectronics, IEE Proceedings 144, 34–38 (1997).
[CrossRef]

Strekalov, D.

D. Strekalov, A. B. Matsko, N. Yu, A. A. Savchenkov, and L. Maleki, “Application of vertical cavity surface emitting lasers in self-oscillating atomic clocks,” J. Mod. Opt. 53, 2469–2484 (2006).
[CrossRef]

Streubel, K.

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, Y. Long, and K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photonics Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

Taylor, H. F.

R. O. Miles, A. Dandridge, A. B. Tveten, H. F. Taylor, and T. G. Giallorenzi, “Feedback-induced line broadening in cw channel-substrate planar laser diodes,” Appl. Phys. Lett. 37, 990–992 (1980).
[CrossRef]

Tkach, R.

R. Tkach and A. Chraplyvy, “Regimes of feedback effects in 1.5-μm distributed feedback lasers,” J. Lightwave Technol. 4, 1655–1661 (1986).
[CrossRef]

Tromborg, B.

J. Mork, J. Mark, and B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65, 1999 (1990).
[CrossRef] [PubMed]

B. Tromborg, J. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20, 1023–1032 (1984).
[CrossRef]

Tveten, A. B.

R. O. Miles, A. Dandridge, A. B. Tveten, H. F. Taylor, and T. G. Giallorenzi, “Feedback-induced line broadening in cw channel-substrate planar laser diodes,” Appl. Phys. Lett. 37, 990–992 (1980).
[CrossRef]

Vanier, J.

J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81, 421–442 (2005).
[CrossRef]

Verbeeck, B. H.

J. S. Cohen, R. R. Drenten, and B. H. Verbeeck, “The effect of optical feedback on the relaxation oscillation in semiconductor lasers,” IEEE J. Quantum Electron. 24, 1989–1995 (1988).
[CrossRef]

Verbeek, B.

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163–1169 (1984).
[CrossRef]

Vukicevic, M.

J. Kitching, S. Knappe, M. Vukicevic, L. Hollberg, R. Wynands, and W. Weidmann, “A microwave frequency reference based on VCSEL-driven dark line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
[CrossRef]

Weidmann, W.

J. Kitching, S. Knappe, M. Vukicevic, L. Hollberg, R. Wynands, and W. Weidmann, “A microwave frequency reference based on VCSEL-driven dark line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
[CrossRef]

Wiedenmann, D.

C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Nonlinear spectroscopy with a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
[CrossRef]

Wynands, R.

C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Nonlinear spectroscopy with a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
[CrossRef]

J. Kitching, S. Knappe, M. Vukicevic, L. Hollberg, R. Wynands, and W. Weidmann, “A microwave frequency reference based on VCSEL-driven dark line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
[CrossRef]

Ye, J.

J. Ye, H. Li, and J. G. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47, 2249 (1993).
[CrossRef] [PubMed]

Ye, S.-Y.

S. Fukuchi, S.-Y. Ye, and J. Ohtsubo, “Relaxation oscillation enhancement and coherence collapse in semiconductor lasers with optical feedback,” Opt. Rev. 6, 365–371 (1999).
[CrossRef]

Yu, N.

D. Strekalov, A. B. Matsko, N. Yu, A. A. Savchenkov, and L. Maleki, “Application of vertical cavity surface emitting lasers in self-oscillating atomic clocks,” J. Mod. Opt. 53, 2469–2484 (2006).
[CrossRef]

Zappe, H. P.

Appl. Opt. (1)

Appl. Phys. B (2)

J. Vanier, “Atomic clocks based on coherent population trapping: a review,” Appl. Phys. B 81, 421–442 (2005).
[CrossRef]

C. Affolderbach, A. Nagel, S. Knappe, C. Jung, D. Wiedenmann, and R. Wynands, “Nonlinear spectroscopy with a vertical-cavity surface-emitting laser (VCSEL),” Appl. Phys. B 70, 407–413 (2000).
[CrossRef]

Appl. Phys. Lett. (3)

R. O. Miles, A. Dandridge, A. B. Tveten, H. F. Taylor, and T. G. Giallorenzi, “Feedback-induced line broadening in cw channel-substrate planar laser diodes,” Appl. Phys. Lett. 37, 990–992 (1980).
[CrossRef]

L. Hollberg and M. Ohtsu, “Modulatable narrow-linewidth semiconductor lasers,” Appl. Phys. Lett. 53, 944–946 (1988).
[CrossRef]

N. Gavra, V. Ruseva, and M. Rosenbluh, “Enhancement in microwave modulation efficiency of vertical cavity surface-emitting laser by optical feedback,” Appl. Phys. Lett. 92, 221113 (2008).
[CrossRef]

IEEE J. Quantum Electron. (5)

J. S. Cohen, R. R. Drenten, and B. H. Verbeeck, “The effect of optical feedback on the relaxation oscillation in semiconductor lasers,” IEEE J. Quantum Electron. 24, 1989–1995 (1988).
[CrossRef]

B. Tromborg, J. Osmundsen, and H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20, 1023–1032 (1984).
[CrossRef]

A. T. Ryan, G. P. Agrawal, G. R. Gray, and E. C. Gage, “Optical-feedback-induced chaos and its control in multimode semiconductor lasers,” IEEE J. Quantum Electron. 30, 668–679 (1994).
[CrossRef]

G. Acket, D. Lenstra, A. Den Boef, and B. Verbeek, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron. 20, 1163–1169 (1984).
[CrossRef]

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

IEEE Photonics Technol. Lett. (3)

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]

U. Fiedler, G. Reiner, P. Schnitzer, and K. J. Ebeling, “Top surface-emitting vertical-cavity laser diodes for 10-Gb∕s data transmission,” IEEE Photonics Technol. Lett. 8, 746–748 (1996).
[CrossRef]

D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, Y. Long, and K. Carey, “Room-temperature continuous-wave operation of 1.54-μm vertical-cavity lasers,” IEEE Photonics Technol. Lett. 7, 1225–1227 (1995).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

J. Kitching, S. Knappe, M. Vukicevic, L. Hollberg, R. Wynands, and W. Weidmann, “A microwave frequency reference based on VCSEL-driven dark line resonances in Cs vapor,” IEEE Trans. Instrum. Meas. 49, 1313–1317 (2000).
[CrossRef]

J. Appl. Phys. (1)

C. H. L. Quay, I. Z. Maxwell, and J. A. Hudgings, “Coherence collapse and redshifting in vertical-cavity surface-emitting lasers exposed to strong optical feedback,” J. Appl. Phys. 90, 5856–5858 (2001).
[CrossRef]

J. Lightwave Technol. (1)

R. Tkach and A. Chraplyvy, “Regimes of feedback effects in 1.5-μm distributed feedback lasers,” J. Lightwave Technol. 4, 1655–1661 (1986).
[CrossRef]

J. Mod. Opt. (1)

D. Strekalov, A. B. Matsko, N. Yu, A. A. Savchenkov, and L. Maleki, “Application of vertical cavity surface emitting lasers in self-oscillating atomic clocks,” J. Mod. Opt. 53, 2469–2484 (2006).
[CrossRef]

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

Opt. Rev. (1)

S. Fukuchi, S.-Y. Ye, and J. Ohtsubo, “Relaxation oscillation enhancement and coherence collapse in semiconductor lasers with optical feedback,” Opt. Rev. 6, 365–371 (1999).
[CrossRef]

Optoelectronics, IEE Proceedings (1)

L. N. Langley and K. A. Shore, “Effect of optical feedback on the noise properties of vertical cavity surface emitting lasers,” Optoelectronics, IEE Proceedings 144, 34–38 (1997).
[CrossRef]

Phys. Rev. A (1)

J. Ye, H. Li, and J. G. McInerney, “Period-doubling route to chaos in a semiconductor laser with weak optical feedback,” Phys. Rev. A 47, 2249 (1993).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

J. Mork, J. Mark, and B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65, 1999 (1990).
[CrossRef] [PubMed]

Other (1)

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (van Nostrand Reinhold, 1993).

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Figures (6)

Fig. 1
Fig. 1

Experimental setup: L, collimating lens; ND, natural density filter; PZT, piezoelectric transducer; GW, glass wedge; BS, beam splitter; Amp, amplifier; SA, rf spectrum analyzer.

Fig. 2
Fig. 2

(a) Rf spectrum analyzer spectra for different PZT voltage in the long cavity regime. For convenience, a 30 dB offset is added each time the PZT voltage raised by 1  Volt . (b) A zoom-in of a specific phase in which ν RO ν FSR 2 condition is satisfied. The effective external cavity length and mode spacing are L eff = 78.8 mm and ν FSR = 1.9 GHz respectively, F ext = 2.71 10 4 and I VCSEL = 3.8 mA . L eff includes the contribution of the different optical elements in the external cavity. The deviation of the recorded resonances from the calculated cavity modes frequency is discussed in the paper.

Fig. 3
Fig. 3

Measured resonant frequencies taken from the rf amplitude noise spectrum (squares) versus the effective external cavity length. The RO (horizontal red line) for a solitary VCSEL and the pure external cavity modes (solid curves) as a function of cavity length L are indicated to help in presenting the dynamics of the VCSEL. At each L the solid curves represent the cavity modes which tune as 1/L. For simplicity, only the relevant first three modes are shown. I VCSEL = 3.775 mA , F ext = 2.71 10 4 . The deviation of the measured resonances from the pure cavity mode curves is discussed in the paper.

Fig. 4
Fig. 4

Rf spectrum analyzer spectra for different PZT voltages in the short cavity regime. For convenience, a 30 dB offset is added each time the PZT voltage is raised. The effective external cavity length and mode spacing are L eff = 21.5 mm and ν FSR = 7 GHz , respectively, F ext = 2.71 10 4 and I VCSEL = 3.8 mA . L eff includes the contribution of the different optical elements in the external cavity.

Fig. 5
Fig. 5

Optical spectra measured by an etalon for different feedback strengths. Etalon FSR = 16.5 GHz , I VCSEL = 3.775 mA , effective external cavity length L eff = 33 mm . The feedback parameter in (a) F ext = 0 , (b) F ext = 1.65 10 4 , (c) F ext = 2.71 10 4 , (d–e) F ext = 2 10 3 with two different optical feedback phases. The asymmetry in (e) is an artifact caused by misalignment of the etalon with respect to the focusing lens.

Fig. 6
Fig. 6

Rf spectrum analyzer spectra for different feedback strengths. I VCSEL = 3.775 mA , effective external cavity length L eff = 33 mm . The feedback parameter in (a) F ext = 0 , (b) F ext = 1.65 10 4 , (c) F ext = 2.71 10 4 , (d–e) F ext = 2 10 3 with two different optical feedback phases.

Equations (2)

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ν RO = 1 2 π Γ 0 T 1 ( I I th 1 ) λ R 2 ; λ R = 1 2 T 1 I I th ,
F ext = 1 R 2 R 2 R 2 R ext

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