Abstract

We investigate numerically the effects of optical feedback on the intensity noise of vertical-cavity surface-emitting lasers (VCSEL’s) under single-mode and two-mode operations. Our model includes transverse effects such as carrier diffusion and spatial hole-burning. Results indicate that the relative-intensity noise is relatively unaffected at low feedback levels except for a narrowing and enhancement of the relaxation-oscillation peak. At higher feedback levels, the VCSEL ceases to operate continuously, and its output becomes chaotic, following a period-doubling or a quasi-periodic route depending on the feedback level and the length of the external cavity. In the chaotic regime, the relative-intensity noise is enhanced by more than 20 dB. The critical feedback level at which the VCSEL output becomes chaotic depends on whether the laser operates in one or two transverse modes and how strongly these transverse modes are coupled through spatial hole-burning.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. J. Chang-Hasnain, in Semiconductor Lasers: Past, Present and Future, G. P. Agrawal, ed. (American Institute of Physics, Woodbury, New York, 1995), Chap. 5.
  2. C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of VCSELs,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
    [CrossRef]
  3. Y. C. Chong and Y. H. Lee, “Spectral characteristics of VCSEL with external optical feedback,” IEEE Photon. Technol. Lett. 3, 597–599 (1991).
    [CrossRef]
  4. U. Fiedler, “Design of VCSEL’s for feedback insensitive data transmission and external cavity active mode-locking,” IEEE J. Sel. Top. Quantum Electron. 1, 442–449 (1995).
    [CrossRef]
  5. M. A. Hadley, G. C. Wilson, K. Y. Lau, and J. S. Smith, “High single-transverse-mode output from external-cavity surface-emitting laser diodes,” Appl. Phys. Lett. 63, 1607–1609 (1993).
    [CrossRef]
  6. G. C. Wilson, M. A. Hadley, J. S. Smith, and K. Y. Lau, “High single-mode output power from compact external microcavity surface-emitting laser diode,” Appl. Phys. Lett. 63, 3265–3267 (1993).
    [CrossRef]
  7. K. P. Ho, J. D. Walker, and J. M. Kahn, “External optical feedback effects on intensity noise of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 5, 892–895 (1993).
  8. H. M. Chen, K. Tai, K. F. Huang, Y. H. Kao, and J. D. Wynn, “Instability in SEL due to external optical feedback,” J. Appl. Phys. 73, 16–20 (1993).
    [CrossRef]
  9. J. P. Zhang, “Numerical simulation for VCSEL with external optical feedback,” Microw. Opt. Technol. Lett. 7, 359–361 (1994).
    [CrossRef]
  10. A. Valle, J. Sarma, and K. A. Shore, “Spatial hole-burning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
    [CrossRef]
  11. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).
  12. G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, New York, 1993).
  13. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 327–355 (1980).
    [CrossRef]
  14. A. T. Ryan, G. P. Agrawal, G. R. Gray, and E. C. Cage, “Optical-feedback-induced chaos and its control in multimode semiconductor lasers,” IEEE J. Quantum Electron. 30, 668–679 (1994).
    [CrossRef]
  15. C. H. Chong and J. Sarma, “Lasing mode selection in vertical-cavity surface-emitting laser diodes,” IEEE Photon. Technol. Lett. 5, 761–764 (1993).
    [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. J. Mørk, J. Mark, and B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65, 1999–2002 (1990).
    [CrossRef]
  18. J. Y. Law and G. P. Agrawal, “Mode-partition noise in vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 9, 437–439 (1997).
    [CrossRef]
  19. J. Y. Law, G. H. M. van Tartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on injection dynamics in vertical-cavity surface-emitting lasers,” Quantum Semiclass. Opt. 9, 737–747 (1997).
    [CrossRef]

1997 (3)

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]

J. Y. Law and G. P. Agrawal, “Mode-partition noise in vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 9, 437–439 (1997).
[CrossRef]

J. Y. Law, G. H. M. van Tartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on injection dynamics in vertical-cavity surface-emitting lasers,” Quantum Semiclass. Opt. 9, 737–747 (1997).
[CrossRef]

1995 (2)

U. Fiedler, “Design of VCSEL’s for feedback insensitive data transmission and external cavity active mode-locking,” IEEE J. Sel. Top. Quantum Electron. 1, 442–449 (1995).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, “Spatial hole-burning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[CrossRef]

1994 (2)

J. P. Zhang, “Numerical simulation for VCSEL with external optical feedback,” Microw. Opt. Technol. Lett. 7, 359–361 (1994).
[CrossRef]

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

1993 (5)

C. H. Chong and J. Sarma, “Lasing mode selection in vertical-cavity surface-emitting laser diodes,” IEEE Photon. Technol. Lett. 5, 761–764 (1993).
[CrossRef]

M. A. Hadley, G. C. Wilson, K. Y. Lau, and J. S. Smith, “High single-transverse-mode output from external-cavity surface-emitting laser diodes,” Appl. Phys. Lett. 63, 1607–1609 (1993).
[CrossRef]

G. C. Wilson, M. A. Hadley, J. S. Smith, and K. Y. Lau, “High single-mode output power from compact external microcavity surface-emitting laser diode,” Appl. Phys. Lett. 63, 3265–3267 (1993).
[CrossRef]

K. P. Ho, J. D. Walker, and J. M. Kahn, “External optical feedback effects on intensity noise of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 5, 892–895 (1993).

H. M. Chen, K. Tai, K. F. Huang, Y. H. Kao, and J. D. Wynn, “Instability in SEL due to external optical feedback,” J. Appl. Phys. 73, 16–20 (1993).
[CrossRef]

1991 (2)

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of VCSELs,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Y. C. Chong and Y. H. Lee, “Spectral characteristics of VCSEL with external optical feedback,” IEEE Photon. Technol. Lett. 3, 597–599 (1991).
[CrossRef]

1990 (1)

J. Mørk, J. Mark, and B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65, 1999–2002 (1990).
[CrossRef]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 327–355 (1980).
[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]

J. Y. Law and G. P. Agrawal, “Mode-partition noise in vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 9, 437–439 (1997).
[CrossRef]

J. Y. Law, G. H. M. van Tartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on injection dynamics in vertical-cavity surface-emitting lasers,” Quantum Semiclass. Opt. 9, 737–747 (1997).
[CrossRef]

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

Cage, E. C.

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

Chang-Hasnain, C. J.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of VCSELs,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Chen, H. M.

H. M. Chen, K. Tai, K. F. Huang, Y. H. Kao, and J. D. Wynn, “Instability in SEL due to external optical feedback,” J. Appl. Phys. 73, 16–20 (1993).
[CrossRef]

Chong, C. H.

C. H. Chong and J. Sarma, “Lasing mode selection in vertical-cavity surface-emitting laser diodes,” IEEE Photon. Technol. Lett. 5, 761–764 (1993).
[CrossRef]

Chong, Y. C.

Y. C. Chong and Y. H. Lee, “Spectral characteristics of VCSEL with external optical feedback,” IEEE Photon. Technol. Lett. 3, 597–599 (1991).
[CrossRef]

Fiedler, U.

U. Fiedler, “Design of VCSEL’s for feedback insensitive data transmission and external cavity active mode-locking,” IEEE J. Sel. Top. Quantum Electron. 1, 442–449 (1995).
[CrossRef]

Gray, G. R.

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

Hadley, M. A.

M. A. Hadley, G. C. Wilson, K. Y. Lau, and J. S. Smith, “High single-transverse-mode output from external-cavity surface-emitting laser diodes,” Appl. Phys. Lett. 63, 1607–1609 (1993).
[CrossRef]

G. C. Wilson, M. A. Hadley, J. S. Smith, and K. Y. Lau, “High single-mode output power from compact external microcavity surface-emitting laser diode,” Appl. Phys. Lett. 63, 3265–3267 (1993).
[CrossRef]

Harbison, J. P.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of VCSELs,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Hasnain, G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of VCSELs,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Ho, K. P.

K. P. Ho, J. D. Walker, and J. M. Kahn, “External optical feedback effects on intensity noise of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 5, 892–895 (1993).

Huang, K. F.

H. M. Chen, K. Tai, K. F. Huang, Y. H. Kao, and J. D. Wynn, “Instability in SEL due to external optical feedback,” J. Appl. Phys. 73, 16–20 (1993).
[CrossRef]

Kahn, J. M.

K. P. Ho, J. D. Walker, and J. M. Kahn, “External optical feedback effects on intensity noise of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 5, 892–895 (1993).

Kao, Y. H.

H. M. Chen, K. Tai, K. F. Huang, Y. H. Kao, and J. D. Wynn, “Instability in SEL due to external optical feedback,” J. Appl. Phys. 73, 16–20 (1993).
[CrossRef]

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 327–355 (1980).
[CrossRef]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 327–355 (1980).
[CrossRef]

Lau, K. Y.

G. C. Wilson, M. A. Hadley, J. S. Smith, and K. Y. Lau, “High single-mode output power from compact external microcavity surface-emitting laser diode,” Appl. Phys. Lett. 63, 3265–3267 (1993).
[CrossRef]

M. A. Hadley, G. C. Wilson, K. Y. Lau, and J. S. Smith, “High single-transverse-mode output from external-cavity surface-emitting laser diodes,” Appl. Phys. Lett. 63, 1607–1609 (1993).
[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]

J. Y. Law, G. H. M. van Tartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on injection dynamics in vertical-cavity surface-emitting lasers,” Quantum Semiclass. Opt. 9, 737–747 (1997).
[CrossRef]

J. Y. Law and G. P. Agrawal, “Mode-partition noise in vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 9, 437–439 (1997).
[CrossRef]

Lee, Y. H.

Y. C. Chong and Y. H. Lee, “Spectral characteristics of VCSEL with external optical feedback,” IEEE Photon. Technol. Lett. 3, 597–599 (1991).
[CrossRef]

Mark, J.

J. Mørk, J. Mark, and B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65, 1999–2002 (1990).
[CrossRef]

Mørk, J.

J. Mørk, J. Mark, and B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65, 1999–2002 (1990).
[CrossRef]

Ryan, A. T.

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

Sarma, J.

A. Valle, J. Sarma, and K. A. Shore, “Spatial hole-burning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[CrossRef]

C. H. Chong and J. Sarma, “Lasing mode selection in vertical-cavity surface-emitting laser diodes,” IEEE Photon. Technol. Lett. 5, 761–764 (1993).
[CrossRef]

Shore, K. A.

A. Valle, J. Sarma, and K. A. Shore, “Spatial hole-burning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[CrossRef]

Smith, J. S.

M. A. Hadley, G. C. Wilson, K. Y. Lau, and J. S. Smith, “High single-transverse-mode output from external-cavity surface-emitting laser diodes,” Appl. Phys. Lett. 63, 1607–1609 (1993).
[CrossRef]

G. C. Wilson, M. A. Hadley, J. S. Smith, and K. Y. Lau, “High single-mode output power from compact external microcavity surface-emitting laser diode,” Appl. Phys. Lett. 63, 3265–3267 (1993).
[CrossRef]

Stoffel, N. G.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of VCSELs,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Tai, K.

H. M. Chen, K. Tai, K. F. Huang, Y. H. Kao, and J. D. Wynn, “Instability in SEL due to external optical feedback,” J. Appl. Phys. 73, 16–20 (1993).
[CrossRef]

Tromborg, B.

J. Mørk, J. Mark, and B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65, 1999–2002 (1990).
[CrossRef]

Valle, A.

A. Valle, J. Sarma, and K. A. Shore, “Spatial hole-burning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[CrossRef]

van Tartwijk, G. H. M.

J. Y. Law, G. H. M. van Tartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on injection dynamics in vertical-cavity surface-emitting lasers,” Quantum Semiclass. Opt. 9, 737–747 (1997).
[CrossRef]

Von Lehmen, A. C.

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of VCSELs,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

Walker, J. D.

K. P. Ho, J. D. Walker, and J. M. Kahn, “External optical feedback effects on intensity noise of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 5, 892–895 (1993).

Wilson, G. C.

G. C. Wilson, M. A. Hadley, J. S. Smith, and K. Y. Lau, “High single-mode output power from compact external microcavity surface-emitting laser diode,” Appl. Phys. Lett. 63, 3265–3267 (1993).
[CrossRef]

M. A. Hadley, G. C. Wilson, K. Y. Lau, and J. S. Smith, “High single-transverse-mode output from external-cavity surface-emitting laser diodes,” Appl. Phys. Lett. 63, 1607–1609 (1993).
[CrossRef]

Wynn, J. D.

H. M. Chen, K. Tai, K. F. Huang, Y. H. Kao, and J. D. Wynn, “Instability in SEL due to external optical feedback,” J. Appl. Phys. 73, 16–20 (1993).
[CrossRef]

Zhang, J. P.

J. P. Zhang, “Numerical simulation for VCSEL with external optical feedback,” Microw. Opt. Technol. Lett. 7, 359–361 (1994).
[CrossRef]

Appl. Phys. Lett. (2)

M. A. Hadley, G. C. Wilson, K. Y. Lau, and J. S. Smith, “High single-transverse-mode output from external-cavity surface-emitting laser diodes,” Appl. Phys. Lett. 63, 1607–1609 (1993).
[CrossRef]

G. C. Wilson, M. A. Hadley, J. S. Smith, and K. Y. Lau, “High single-mode output power from compact external microcavity surface-emitting laser diode,” Appl. Phys. Lett. 63, 3265–3267 (1993).
[CrossRef]

IEEE J. Quantum Electron. (5)

K. P. Ho, J. D. Walker, and J. M. Kahn, “External optical feedback effects on intensity noise of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 5, 892–895 (1993).

C. J. Chang-Hasnain, J. P. Harbison, G. Hasnain, A. C. Von Lehmen, and N. G. Stoffel, “Dynamic, polarization and transverse mode characteristics of VCSELs,” IEEE J. Quantum Electron. 27, 1402–1408 (1991).
[CrossRef]

A. Valle, J. Sarma, and K. A. Shore, “Spatial hole-burning effects on the dynamics of vertical-cavity surface-emitting laser diodes,” IEEE J. Quantum Electron. 31, 1423–1431 (1995).
[CrossRef]

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 327–355 (1980).
[CrossRef]

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

U. Fiedler, “Design of VCSEL’s for feedback insensitive data transmission and external cavity active mode-locking,” IEEE J. Sel. Top. Quantum Electron. 1, 442–449 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

Y. C. Chong and Y. H. Lee, “Spectral characteristics of VCSEL with external optical feedback,” IEEE Photon. Technol. Lett. 3, 597–599 (1991).
[CrossRef]

C. H. Chong and J. Sarma, “Lasing mode selection in vertical-cavity surface-emitting laser diodes,” IEEE Photon. Technol. Lett. 5, 761–764 (1993).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

J. Y. Law and G. P. Agrawal, “Mode-partition noise in vertical-cavity surface-emitting laser,” IEEE Photonics Technol. Lett. 9, 437–439 (1997).
[CrossRef]

J. Appl. Phys. (1)

H. M. Chen, K. Tai, K. F. Huang, Y. H. Kao, and J. D. Wynn, “Instability in SEL due to external optical feedback,” J. Appl. Phys. 73, 16–20 (1993).
[CrossRef]

Microw. Opt. Technol. Lett. (1)

J. P. Zhang, “Numerical simulation for VCSEL with external optical feedback,” Microw. Opt. Technol. Lett. 7, 359–361 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

J. Mørk, J. Mark, and B. Tromborg, “Route to chaos and competition between relaxation oscillations for a semiconductor laser with optical feedback,” Phys. Rev. Lett. 65, 1999–2002 (1990).
[CrossRef]

Quantum Semiclass. Opt. (1)

J. Y. Law, G. H. M. van Tartwijk, and G. P. Agrawal, “Effects of transverse-mode competition on injection dynamics in vertical-cavity surface-emitting lasers,” Quantum Semiclass. Opt. 9, 737–747 (1997).
[CrossRef]

Other (3)

N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).

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

C. J. Chang-Hasnain, in Semiconductor Lasers: Past, Present and Future, G. P. Agrawal, ed. (American Institute of Physics, Woodbury, New York, 1995), Chap. 5.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Three types of electrical contact used and the radial intensity distributions of the transverse modes excited. (a) Narrow disc contact, (b) wide disc contact, and (c) ring contact. Dashed, solid and dotted-dashed curves represent the LP01, LP11, and LP21 transverse modes, respectively.

Fig. 2
Fig. 2

Temporal evolution of the output power under single-mode operation for several feedback levels. (a) Fext=0, (b) Fext=1.6×10-4, (c) Fext=5×10-4, (d) Fext=8.9×10-4, (e) Fext=1.6×10-3, and (f) Fext=2.8×10-3.

Fig. 3
Fig. 3

RIN spectra (thick solid curves) under single-mode operation for several feedback parameters corresponding to those used in Fig. 2. The thin solid curves show the relative-power spectra corresponding to the temporal traces shown in Fig. 2 when spontaneous emission is neglected. The feedback levels used are (a) Fext=0, (b) Fext=1.6×10-4, (c) Fext=5 ×10-4, (d) Fext=8.9×10-4, (e) Fext=1.6×10-3, and (f) Fext=2.8×10-3.

Fig. 4
Fig. 4

Temporal evolution of the output power under two-mode operation with a 4-μm disc contact (weak coupling) for several feedback levels. Solid and dashed curves represent the LP01 and LP11 modes, respectively. (a) Fext=0, (b) Fext=1.6 ×10-4, (c) Fext=5×10-4, (d) Fext=8.9×10-4, (e) Fext =1.6×10-3, and (f) Fext=2.8×10-3.

Fig. 5
Fig. 5

RIN spectra (bold curves) for the total power under two-mode operation with a 4-μm disc contact (weak coupling). The thin solid curves show the relative-power spectra corresponding to the temporal traces shown in Fig. 4 when spontaneous emission is neglected. The feedback levels used are (a) Fext=0, (b) Fext=1.6×10-4, (c) Fext=5×10-4, (d) Fext=8.9×10-4, (e) Fext=1.6×10-3, and (f) Fext=2.8×10-3.

Fig. 6
Fig. 6

Temporal evolution of the output power under two-mode operation with a ring contact (strong coupling) for several feedback levels. Solid and dashed curves represent the LP11 and LP21 modes, respectively. (a) Fext=0, (b) Fext=1.6×10-4, (c) Fext=5×10-4, (d) Fext=8.9×10-4, (e) Fext=1.6×10-3, and (f) Fext=2.8×10-3.

Fig. 7
Fig. 7

RIN spectra (thick solid curves) for the total power under two-mode operation with a ring contact (strong coupling). The thin solid curves show the relative-power spectra corresponding to the temporal traces shown in Fig. 6 when spontaneous emission is neglected. (a) Fext=0, (b) Fext=1.6×10-4, (c) Fext=5×10-4, (d) Fext=8.9×10-4, (e) Fext=1.6×10-3, and (f) Fext=2.8×10-3.

Tables (1)

Tables Icon

Table 1 Device Parameters Used in Simulations

Equations (7)

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

dEidt=12 (1-iα)[Gi(t)-γi]Ei+Fi(t)+m=1MκmEi(t-mτ)exp(imωiτ),
Nt=DT2N+J(r, ϕ)qd-Nτe-BN2-1d i=12Glocal|Ei(t)|2|ψi(r, ϕ)|2,
Gi(t)=0d02π0RaGlocal(r, ϕ, t)|ψi(r, ϕ)|2 sin2(βz)rdrdϕdz0L02π0R|ψi(r, ϕ)|2 sin2(βz)rdrdϕdz,
Fi(t)=0,
Fi(t1)Fj*(t2)=Rspδijδ(t1-t2),
κm=1τL 1-R2R2 (-1)m-1(R2Rextηc)m,
Fext=1-R2R2 R2Rext.

Metrics