Abstract

The dynamics of ultrashort pulses generated by a monolithic passively mode-locked vertical cavity surface-emitting laser containing a multiple quantum well gain region and a single quantum well saturable absorber are studied. We introduce a self-consistent computational model based on the finite-difference time-domain method, which describes the complete dynamics of surface-emitting lasers. The model consists of a set of coupled equations that accounts for the interrelations among the electromagnetic field, material polarization, carrier density, and lattice and plasma temperatures. The material response is incorporated via the effective semiconductor Bloch equations. The thermal effects are included through two coupled equations that relate the lattice and plasma temperatures to the carrier-phonon scattering effects. A comparison of the results obtained with and without the inclusion of thermal effects clearly demonstrates the effects of plasma heating. Finally, we also investigate the interplay between various relaxation rates, namely, the carrier-phonon scattering rate and the rate of heat loss to the ambient heat sink, and their relative influence on the system dynamics.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, “Minimum temperature sensitivity of 1.55 μm vertical-cavity lasers at −30 nm gain offset,” Appl. Phys. Lett. 72, 1814-1816 (1998).
    [CrossRef]
  2. G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, “Comprehensive numerical modeling of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 607-616 (1996).
    [CrossRef]
  3. H. L. Rao, M. J. Steel, R. Scarmozzino, and R. M. Osgood, “VCSEL design using the bidirectional beam-propagation method,” IEEE J. Quantum Electron. 37, 1435-1440 (2001).
    [CrossRef]
  4. S. Riyopoulos, D. Dialetis, J. Inman, and A. Phillips, “Active-cavity vertical-cavity surface-emitting laser eigenmodes with simple analytic representation,” J. Opt. Soc. Am. B 18, 1268-1284 (2001).
    [CrossRef]
  5. M. Bahl, H. Rao, N.-C. Panoiu, and R. M. Osgood, Jr., “Simulation of mode-locked surface-emitting lasers through a finite-difference time-domain algorithm,” Opt. Lett. 29, 1689-1691 (2004).
    [CrossRef] [PubMed]
  6. M. Bahl, N.-C. Panoiu, and R. M. Osgood, Jr., “Modeling ultrashort field dynamics in surface emitting lasers by using finite-difference time-domain method,” IEEE J. Quantum Electron. 41, 1244-1252 (2005).
    [CrossRef]
  7. J. Mulet and S. Balle, “Mode-locking dynamics in electrically driven vertical-external-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1148-1156 (2005).
    [CrossRef]
  8. W. H. P. Pernice, F. P. Payne, and D. F. G. Gallagher, “A finite-difference time-domain method for the simulation of gain materials with carrier diffusion in photonic crystals,” J. Lightwave Technol. 25, 2306-2314 (2007).
    [CrossRef]
  9. Q. Zhang, K. Jasim, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Operation of a passively mode-locked extended-cavity surface-emitting diode laser in multi-GHz regime,” Electron. Lett. 3, 885-887 (2004).
  10. K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Passively modelocked vertical extended cavity surface emitting diode laser,” Electron. Lett. 39, 373-375 (2003).
    [CrossRef]
  11. I.N.Duling, ed., Compact Sources of Ultrashort Pulses (Cambridge U. Press, 1995).
    [CrossRef]
  12. A. J. Lowery, “New dynamic semiconductor laser model based on the transmission line modeling method,” IEE Proc.-J: Optoelectron. 134, 281-289 (1987).
    [CrossRef]
  13. W. B. Jiang, D. Derickson, R. Mirin, and J. E. Bowers, “Analysis of laser pulse chirping in mode-locked vertical cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 1309-1318 (1993).
    [CrossRef]
  14. W. Yang and A. Gopinath, “Study of passive mode locking of semiconductor lasers using time-domain modeling,” IEEE J. Quantum Electron. 63, 2717-2719 (1993).
  15. L. M. Zhang, S. F. Yu, M. Nowell, D. D. Marcenac, and J. E. Carroll, “Dynamic analysis of radiation and side mode suppression in second-order DFB lasers using time-domain large signal traveling wave model,” IEEE J. Quantum Electron. 30, 1389-1395 (1994).
    [CrossRef]
  16. D. Jones, L. Zhang, and D. Marcenac, “Dynamics of monolithic passively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 31, 1051-1058 (1995).
    [CrossRef]
  17. B. Kim, Y. Chung, and S. Kim, “Dynamic analysis of mode-locked sampled-grating distributed Bragg reflector laser diodes,” IEEE J. Quantum Electron. 35, 1623-1629 (1999).
    [CrossRef]
  18. J. Park and Y. Kawakami, “Time-domain models for the performance simulation of semiconductor optical amplifiers,” Opt. Express 14, 2956-2968 (2006).
    [CrossRef] [PubMed]
  19. T. L. Koch, L. C. Chiu, C. Harder, and A. Yariv, “Picosecond carrier dynamics and laser action in optically pumped buried hetrostructure lasers,” Appl. Phys. Lett. 41, 6-8 (1982).
    [CrossRef]
  20. M. P. Kesler and E. P. Ippen, “Subpicosecond gain dynamics in GaAlAs laser diodes,” Appl. Phys. Lett. 51, 1765-1767 (1987).
    [CrossRef]
  21. C. Ning, R. A. Indik, and J. V. Moloney, “Effective Bloch equations for semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. 33, 1543-1550 (1997).
    [CrossRef]
  22. T. V. Sarkisyan, A. N. Oraevsky, A. T. Rosenberger, R. L. Rolleigh, and D. K. Bandy, “Nonlinear gain and carrier temperature dynamics in semiconductor laser media,” J. Opt. Soc. Am. B 15, 1107-1119 (1998).
    [CrossRef]
  23. J. W. Scott, S. W. Corrzine, D. B. Young, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295-1308 (1993).
    [CrossRef]
  24. J. Piprek, H. Wenzel, and G. Sztefka, “Modeling thermal effects on the light vs. current characteristic of gain-guided vertical-cavity surface-emitting lasers,” J. Lightwave Technol. 6, 139-142 (1994).
  25. B. Lu, P. Zhou, J. Cheng, and K. J. Malloy, “High temperature pulsed and CW operation and thermally stable threshold characteristics of vertical-cavity surface-emitting semiconductor lasers grown by metal-organic chemical vapor deposition,” Appl. Phys. Lett. 65, 1337-1339 (1994).
    [CrossRef]
  26. C. Ning, R. A. Indik, and J. V. Moloney, “Self-consistent approach to thermal effects in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 12, 1993-2004 (1995).
    [CrossRef]
  27. T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279-3292 (1998).
    [CrossRef]
  28. W. Nakwaski and M. Osinski, “Thermal properties of vertical-cavity surface-emitting semiconductor lasers,” Prog. Opt. 38, 165-262 (1998).
    [CrossRef]
  29. K. Bohringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. I. Theoretical formulation,” Prog. Quantum Electron. 32, 159-246 (2008).
    [CrossRef]
  30. K. Bohringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. II. Spatio-temporal dynamics,” Prog. Quantum Electron. 32, 247-307 (2008).
    [CrossRef]
  31. W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals (Springer, 1999), p. 204.
  32. K. Hasebe, Y. Onishi, and F. Koyama, “All-optical regenerator with re-polarization function based on dual optical injection VCSEL,” IEICE Electron. Express 2, 338-343 (2005).
    [CrossRef]
  33. M. Bahl, “Electromagnetic simulations of active and nonlinear photonic devices,” Ph.D. dissertation (Columbia University, 2005).
  34. M. Bahl, N.-C. Panoiu, and R. M. Osgood, Jr., in Proceedings of the IEEE Conference on Lightwave Technologies in Instrumentation and Measurement (IEEE, 2004), pp. 17-22.
    [CrossRef]
  35. W. H. Press, S. A. Teukoisky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, 1997).

2008 (2)

K. Bohringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. I. Theoretical formulation,” Prog. Quantum Electron. 32, 159-246 (2008).
[CrossRef]

K. Bohringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. II. Spatio-temporal dynamics,” Prog. Quantum Electron. 32, 247-307 (2008).
[CrossRef]

2007 (1)

2006 (1)

2005 (3)

K. Hasebe, Y. Onishi, and F. Koyama, “All-optical regenerator with re-polarization function based on dual optical injection VCSEL,” IEICE Electron. Express 2, 338-343 (2005).
[CrossRef]

M. Bahl, N.-C. Panoiu, and R. M. Osgood, Jr., “Modeling ultrashort field dynamics in surface emitting lasers by using finite-difference time-domain method,” IEEE J. Quantum Electron. 41, 1244-1252 (2005).
[CrossRef]

J. Mulet and S. Balle, “Mode-locking dynamics in electrically driven vertical-external-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1148-1156 (2005).
[CrossRef]

2004 (2)

M. Bahl, H. Rao, N.-C. Panoiu, and R. M. Osgood, Jr., “Simulation of mode-locked surface-emitting lasers through a finite-difference time-domain algorithm,” Opt. Lett. 29, 1689-1691 (2004).
[CrossRef] [PubMed]

Q. Zhang, K. Jasim, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Operation of a passively mode-locked extended-cavity surface-emitting diode laser in multi-GHz regime,” Electron. Lett. 3, 885-887 (2004).

2003 (1)

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Passively modelocked vertical extended cavity surface emitting diode laser,” Electron. Lett. 39, 373-375 (2003).
[CrossRef]

2001 (2)

H. L. Rao, M. J. Steel, R. Scarmozzino, and R. M. Osgood, “VCSEL design using the bidirectional beam-propagation method,” IEEE J. Quantum Electron. 37, 1435-1440 (2001).
[CrossRef]

S. Riyopoulos, D. Dialetis, J. Inman, and A. Phillips, “Active-cavity vertical-cavity surface-emitting laser eigenmodes with simple analytic representation,” J. Opt. Soc. Am. B 18, 1268-1284 (2001).
[CrossRef]

1999 (1)

B. Kim, Y. Chung, and S. Kim, “Dynamic analysis of mode-locked sampled-grating distributed Bragg reflector laser diodes,” IEEE J. Quantum Electron. 35, 1623-1629 (1999).
[CrossRef]

1998 (4)

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, “Minimum temperature sensitivity of 1.55 μm vertical-cavity lasers at −30 nm gain offset,” Appl. Phys. Lett. 72, 1814-1816 (1998).
[CrossRef]

T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279-3292 (1998).
[CrossRef]

W. Nakwaski and M. Osinski, “Thermal properties of vertical-cavity surface-emitting semiconductor lasers,” Prog. Opt. 38, 165-262 (1998).
[CrossRef]

T. V. Sarkisyan, A. N. Oraevsky, A. T. Rosenberger, R. L. Rolleigh, and D. K. Bandy, “Nonlinear gain and carrier temperature dynamics in semiconductor laser media,” J. Opt. Soc. Am. B 15, 1107-1119 (1998).
[CrossRef]

1997 (1)

C. Ning, R. A. Indik, and J. V. Moloney, “Effective Bloch equations for semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. 33, 1543-1550 (1997).
[CrossRef]

1996 (1)

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, “Comprehensive numerical modeling of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 607-616 (1996).
[CrossRef]

1995 (2)

D. Jones, L. Zhang, and D. Marcenac, “Dynamics of monolithic passively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 31, 1051-1058 (1995).
[CrossRef]

C. Ning, R. A. Indik, and J. V. Moloney, “Self-consistent approach to thermal effects in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 12, 1993-2004 (1995).
[CrossRef]

1994 (3)

J. Piprek, H. Wenzel, and G. Sztefka, “Modeling thermal effects on the light vs. current characteristic of gain-guided vertical-cavity surface-emitting lasers,” J. Lightwave Technol. 6, 139-142 (1994).

B. Lu, P. Zhou, J. Cheng, and K. J. Malloy, “High temperature pulsed and CW operation and thermally stable threshold characteristics of vertical-cavity surface-emitting semiconductor lasers grown by metal-organic chemical vapor deposition,” Appl. Phys. Lett. 65, 1337-1339 (1994).
[CrossRef]

L. M. Zhang, S. F. Yu, M. Nowell, D. D. Marcenac, and J. E. Carroll, “Dynamic analysis of radiation and side mode suppression in second-order DFB lasers using time-domain large signal traveling wave model,” IEEE J. Quantum Electron. 30, 1389-1395 (1994).
[CrossRef]

1993 (3)

W. B. Jiang, D. Derickson, R. Mirin, and J. E. Bowers, “Analysis of laser pulse chirping in mode-locked vertical cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 1309-1318 (1993).
[CrossRef]

W. Yang and A. Gopinath, “Study of passive mode locking of semiconductor lasers using time-domain modeling,” IEEE J. Quantum Electron. 63, 2717-2719 (1993).

J. W. Scott, S. W. Corrzine, D. B. Young, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295-1308 (1993).
[CrossRef]

1987 (2)

M. P. Kesler and E. P. Ippen, “Subpicosecond gain dynamics in GaAlAs laser diodes,” Appl. Phys. Lett. 51, 1765-1767 (1987).
[CrossRef]

A. J. Lowery, “New dynamic semiconductor laser model based on the transmission line modeling method,” IEE Proc.-J: Optoelectron. 134, 281-289 (1987).
[CrossRef]

1982 (1)

T. L. Koch, L. C. Chiu, C. Harder, and A. Yariv, “Picosecond carrier dynamics and laser action in optically pumped buried hetrostructure lasers,” Appl. Phys. Lett. 41, 6-8 (1982).
[CrossRef]

Akulova, Y. A.

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, “Minimum temperature sensitivity of 1.55 μm vertical-cavity lasers at −30 nm gain offset,” Appl. Phys. Lett. 72, 1814-1816 (1998).
[CrossRef]

Babic, D. I.

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, “Minimum temperature sensitivity of 1.55 μm vertical-cavity lasers at −30 nm gain offset,” Appl. Phys. Lett. 72, 1814-1816 (1998).
[CrossRef]

Bahl, M.

M. Bahl, N.-C. Panoiu, and R. M. Osgood, Jr., “Modeling ultrashort field dynamics in surface emitting lasers by using finite-difference time-domain method,” IEEE J. Quantum Electron. 41, 1244-1252 (2005).
[CrossRef]

M. Bahl, H. Rao, N.-C. Panoiu, and R. M. Osgood, Jr., “Simulation of mode-locked surface-emitting lasers through a finite-difference time-domain algorithm,” Opt. Lett. 29, 1689-1691 (2004).
[CrossRef] [PubMed]

M. Bahl, “Electromagnetic simulations of active and nonlinear photonic devices,” Ph.D. dissertation (Columbia University, 2005).

M. Bahl, N.-C. Panoiu, and R. M. Osgood, Jr., in Proceedings of the IEEE Conference on Lightwave Technologies in Instrumentation and Measurement (IEEE, 2004), pp. 17-22.
[CrossRef]

Balle, S.

J. Mulet and S. Balle, “Mode-locking dynamics in electrically driven vertical-external-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1148-1156 (2005).
[CrossRef]

Bandy, D. K.

Bohringer, K.

K. Bohringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. I. Theoretical formulation,” Prog. Quantum Electron. 32, 159-246 (2008).
[CrossRef]

K. Bohringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. II. Spatio-temporal dynamics,” Prog. Quantum Electron. 32, 247-307 (2008).
[CrossRef]

Bowers, J. E.

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, “Minimum temperature sensitivity of 1.55 μm vertical-cavity lasers at −30 nm gain offset,” Appl. Phys. Lett. 72, 1814-1816 (1998).
[CrossRef]

W. B. Jiang, D. Derickson, R. Mirin, and J. E. Bowers, “Analysis of laser pulse chirping in mode-locked vertical cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 1309-1318 (1993).
[CrossRef]

Carey, G.

Q. Zhang, K. Jasim, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Operation of a passively mode-locked extended-cavity surface-emitting diode laser in multi-GHz regime,” Electron. Lett. 3, 885-887 (2004).

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Passively modelocked vertical extended cavity surface emitting diode laser,” Electron. Lett. 39, 373-375 (2003).
[CrossRef]

Carroll, J. E.

L. M. Zhang, S. F. Yu, M. Nowell, D. D. Marcenac, and J. E. Carroll, “Dynamic analysis of radiation and side mode suppression in second-order DFB lasers using time-domain large signal traveling wave model,” IEEE J. Quantum Electron. 30, 1389-1395 (1994).
[CrossRef]

Cheng, J.

B. Lu, P. Zhou, J. Cheng, and K. J. Malloy, “High temperature pulsed and CW operation and thermally stable threshold characteristics of vertical-cavity surface-emitting semiconductor lasers grown by metal-organic chemical vapor deposition,” Appl. Phys. Lett. 65, 1337-1339 (1994).
[CrossRef]

Chiu, L. C.

T. L. Koch, L. C. Chiu, C. Harder, and A. Yariv, “Picosecond carrier dynamics and laser action in optically pumped buried hetrostructure lasers,” Appl. Phys. Lett. 41, 6-8 (1982).
[CrossRef]

Choquette, K. D.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, “Comprehensive numerical modeling of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 607-616 (1996).
[CrossRef]

Chow, W. W.

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals (Springer, 1999), p. 204.

Chung, Y.

B. Kim, Y. Chung, and S. Kim, “Dynamic analysis of mode-locked sampled-grating distributed Bragg reflector laser diodes,” IEEE J. Quantum Electron. 35, 1623-1629 (1999).
[CrossRef]

Coldren, L. A.

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, “Minimum temperature sensitivity of 1.55 μm vertical-cavity lasers at −30 nm gain offset,” Appl. Phys. Lett. 72, 1814-1816 (1998).
[CrossRef]

J. W. Scott, S. W. Corrzine, D. B. Young, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295-1308 (1993).
[CrossRef]

Corrzine, S. W.

J. W. Scott, S. W. Corrzine, D. B. Young, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295-1308 (1993).
[CrossRef]

Corzine, S. W.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, “Comprehensive numerical modeling of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 607-616 (1996).
[CrossRef]

Derickson, D.

W. B. Jiang, D. Derickson, R. Mirin, and J. E. Bowers, “Analysis of laser pulse chirping in mode-locked vertical cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 1309-1318 (1993).
[CrossRef]

Dialetis, D.

Flannery, B. P.

W. H. Press, S. A. Teukoisky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, 1997).

Gallagher, D. F. G.

Gopinath, A.

W. Yang and A. Gopinath, “Study of passive mode locking of semiconductor lasers using time-domain modeling,” IEEE J. Quantum Electron. 63, 2717-2719 (1993).

Ha, W.

Q. Zhang, K. Jasim, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Operation of a passively mode-locked extended-cavity surface-emitting diode laser in multi-GHz regime,” Electron. Lett. 3, 885-887 (2004).

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Passively modelocked vertical extended cavity surface emitting diode laser,” Electron. Lett. 39, 373-375 (2003).
[CrossRef]

Hadley, G. R.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, “Comprehensive numerical modeling of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 607-616 (1996).
[CrossRef]

Harder, C.

T. L. Koch, L. C. Chiu, C. Harder, and A. Yariv, “Picosecond carrier dynamics and laser action in optically pumped buried hetrostructure lasers,” Appl. Phys. Lett. 41, 6-8 (1982).
[CrossRef]

Harkness, G. K.

T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279-3292 (1998).
[CrossRef]

Hasebe, K.

K. Hasebe, Y. Onishi, and F. Koyama, “All-optical regenerator with re-polarization function based on dual optical injection VCSEL,” IEICE Electron. Express 2, 338-343 (2005).
[CrossRef]

Hess, O.

K. Bohringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. II. Spatio-temporal dynamics,” Prog. Quantum Electron. 32, 247-307 (2008).
[CrossRef]

K. Bohringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. I. Theoretical formulation,” Prog. Quantum Electron. 32, 159-246 (2008).
[CrossRef]

Indik, R. A.

T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279-3292 (1998).
[CrossRef]

C. Ning, R. A. Indik, and J. V. Moloney, “Effective Bloch equations for semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. 33, 1543-1550 (1997).
[CrossRef]

C. Ning, R. A. Indik, and J. V. Moloney, “Self-consistent approach to thermal effects in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 12, 1993-2004 (1995).
[CrossRef]

Inman, J.

Ippen, E.

Q. Zhang, K. Jasim, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Operation of a passively mode-locked extended-cavity surface-emitting diode laser in multi-GHz regime,” Electron. Lett. 3, 885-887 (2004).

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Passively modelocked vertical extended cavity surface emitting diode laser,” Electron. Lett. 39, 373-375 (2003).
[CrossRef]

Ippen, E. P.

M. P. Kesler and E. P. Ippen, “Subpicosecond gain dynamics in GaAlAs laser diodes,” Appl. Phys. Lett. 51, 1765-1767 (1987).
[CrossRef]

Jasim, K.

Q. Zhang, K. Jasim, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Operation of a passively mode-locked extended-cavity surface-emitting diode laser in multi-GHz regime,” Electron. Lett. 3, 885-887 (2004).

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Passively modelocked vertical extended cavity surface emitting diode laser,” Electron. Lett. 39, 373-375 (2003).
[CrossRef]

Jiang, W. B.

W. B. Jiang, D. Derickson, R. Mirin, and J. E. Bowers, “Analysis of laser pulse chirping in mode-locked vertical cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 1309-1318 (1993).
[CrossRef]

Jones, D.

D. Jones, L. Zhang, and D. Marcenac, “Dynamics of monolithic passively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 31, 1051-1058 (1995).
[CrossRef]

Kawakami, Y.

Kesler, M. P.

M. P. Kesler and E. P. Ippen, “Subpicosecond gain dynamics in GaAlAs laser diodes,” Appl. Phys. Lett. 51, 1765-1767 (1987).
[CrossRef]

Kim, B.

B. Kim, Y. Chung, and S. Kim, “Dynamic analysis of mode-locked sampled-grating distributed Bragg reflector laser diodes,” IEEE J. Quantum Electron. 35, 1623-1629 (1999).
[CrossRef]

Kim, S.

B. Kim, Y. Chung, and S. Kim, “Dynamic analysis of mode-locked sampled-grating distributed Bragg reflector laser diodes,” IEEE J. Quantum Electron. 35, 1623-1629 (1999).
[CrossRef]

Koch, S. W.

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals (Springer, 1999), p. 204.

Koch, T. L.

T. L. Koch, L. C. Chiu, C. Harder, and A. Yariv, “Picosecond carrier dynamics and laser action in optically pumped buried hetrostructure lasers,” Appl. Phys. Lett. 41, 6-8 (1982).
[CrossRef]

Koyama, F.

K. Hasebe, Y. Onishi, and F. Koyama, “All-optical regenerator with re-polarization function based on dual optical injection VCSEL,” IEICE Electron. Express 2, 338-343 (2005).
[CrossRef]

Lear, K. L.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, “Comprehensive numerical modeling of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 607-616 (1996).
[CrossRef]

Lowery, A. J.

A. J. Lowery, “New dynamic semiconductor laser model based on the transmission line modeling method,” IEE Proc.-J: Optoelectron. 134, 281-289 (1987).
[CrossRef]

Lu, B.

B. Lu, P. Zhou, J. Cheng, and K. J. Malloy, “High temperature pulsed and CW operation and thermally stable threshold characteristics of vertical-cavity surface-emitting semiconductor lasers grown by metal-organic chemical vapor deposition,” Appl. Phys. Lett. 65, 1337-1339 (1994).
[CrossRef]

Malloy, K. J.

B. Lu, P. Zhou, J. Cheng, and K. J. Malloy, “High temperature pulsed and CW operation and thermally stable threshold characteristics of vertical-cavity surface-emitting semiconductor lasers grown by metal-organic chemical vapor deposition,” Appl. Phys. Lett. 65, 1337-1339 (1994).
[CrossRef]

Marcenac, D.

D. Jones, L. Zhang, and D. Marcenac, “Dynamics of monolithic passively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 31, 1051-1058 (1995).
[CrossRef]

Marcenac, D. D.

L. M. Zhang, S. F. Yu, M. Nowell, D. D. Marcenac, and J. E. Carroll, “Dynamic analysis of radiation and side mode suppression in second-order DFB lasers using time-domain large signal traveling wave model,” IEEE J. Quantum Electron. 30, 1389-1395 (1994).
[CrossRef]

Mirin, R.

W. B. Jiang, D. Derickson, R. Mirin, and J. E. Bowers, “Analysis of laser pulse chirping in mode-locked vertical cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 1309-1318 (1993).
[CrossRef]

Moloney, J. V.

T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279-3292 (1998).
[CrossRef]

C. Ning, R. A. Indik, and J. V. Moloney, “Effective Bloch equations for semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. 33, 1543-1550 (1997).
[CrossRef]

C. Ning, R. A. Indik, and J. V. Moloney, “Self-consistent approach to thermal effects in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 12, 1993-2004 (1995).
[CrossRef]

Mooradian, A.

Q. Zhang, K. Jasim, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Operation of a passively mode-locked extended-cavity surface-emitting diode laser in multi-GHz regime,” Electron. Lett. 3, 885-887 (2004).

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Passively modelocked vertical extended cavity surface emitting diode laser,” Electron. Lett. 39, 373-375 (2003).
[CrossRef]

Mulet, J.

J. Mulet and S. Balle, “Mode-locking dynamics in electrically driven vertical-external-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1148-1156 (2005).
[CrossRef]

Nakwaski, W.

W. Nakwaski and M. Osinski, “Thermal properties of vertical-cavity surface-emitting semiconductor lasers,” Prog. Opt. 38, 165-262 (1998).
[CrossRef]

Ning, C.

C. Ning, R. A. Indik, and J. V. Moloney, “Effective Bloch equations for semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. 33, 1543-1550 (1997).
[CrossRef]

C. Ning, R. A. Indik, and J. V. Moloney, “Self-consistent approach to thermal effects in vertical-cavity surface-emitting lasers,” J. Opt. Soc. Am. B 12, 1993-2004 (1995).
[CrossRef]

Ning, C. Z.

T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279-3292 (1998).
[CrossRef]

Nowell, M.

L. M. Zhang, S. F. Yu, M. Nowell, D. D. Marcenac, and J. E. Carroll, “Dynamic analysis of radiation and side mode suppression in second-order DFB lasers using time-domain large signal traveling wave model,” IEEE J. Quantum Electron. 30, 1389-1395 (1994).
[CrossRef]

Nurmikko, A. V.

Q. Zhang, K. Jasim, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Operation of a passively mode-locked extended-cavity surface-emitting diode laser in multi-GHz regime,” Electron. Lett. 3, 885-887 (2004).

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Passively modelocked vertical extended cavity surface emitting diode laser,” Electron. Lett. 39, 373-375 (2003).
[CrossRef]

Onishi, Y.

K. Hasebe, Y. Onishi, and F. Koyama, “All-optical regenerator with re-polarization function based on dual optical injection VCSEL,” IEICE Electron. Express 2, 338-343 (2005).
[CrossRef]

Oraevsky, A. N.

Osgood, R. M.

M. Bahl, N.-C. Panoiu, and R. M. Osgood, Jr., “Modeling ultrashort field dynamics in surface emitting lasers by using finite-difference time-domain method,” IEEE J. Quantum Electron. 41, 1244-1252 (2005).
[CrossRef]

M. Bahl, H. Rao, N.-C. Panoiu, and R. M. Osgood, Jr., “Simulation of mode-locked surface-emitting lasers through a finite-difference time-domain algorithm,” Opt. Lett. 29, 1689-1691 (2004).
[CrossRef] [PubMed]

H. L. Rao, M. J. Steel, R. Scarmozzino, and R. M. Osgood, “VCSEL design using the bidirectional beam-propagation method,” IEEE J. Quantum Electron. 37, 1435-1440 (2001).
[CrossRef]

M. Bahl, N.-C. Panoiu, and R. M. Osgood, Jr., in Proceedings of the IEEE Conference on Lightwave Technologies in Instrumentation and Measurement (IEEE, 2004), pp. 17-22.
[CrossRef]

Osinski, M.

W. Nakwaski and M. Osinski, “Thermal properties of vertical-cavity surface-emitting semiconductor lasers,” Prog. Opt. 38, 165-262 (1998).
[CrossRef]

Panoiu, N. -C.

M. Bahl, N.-C. Panoiu, and R. M. Osgood, Jr., “Modeling ultrashort field dynamics in surface emitting lasers by using finite-difference time-domain method,” IEEE J. Quantum Electron. 41, 1244-1252 (2005).
[CrossRef]

M. Bahl, H. Rao, N.-C. Panoiu, and R. M. Osgood, Jr., “Simulation of mode-locked surface-emitting lasers through a finite-difference time-domain algorithm,” Opt. Lett. 29, 1689-1691 (2004).
[CrossRef] [PubMed]

M. Bahl, N.-C. Panoiu, and R. M. Osgood, Jr., in Proceedings of the IEEE Conference on Lightwave Technologies in Instrumentation and Measurement (IEEE, 2004), pp. 17-22.
[CrossRef]

Park, J.

Payne, F. P.

Pernice, W. H. P.

Phillips, A.

Piprek, J.

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, “Minimum temperature sensitivity of 1.55 μm vertical-cavity lasers at −30 nm gain offset,” Appl. Phys. Lett. 72, 1814-1816 (1998).
[CrossRef]

J. Piprek, H. Wenzel, and G. Sztefka, “Modeling thermal effects on the light vs. current characteristic of gain-guided vertical-cavity surface-emitting lasers,” J. Lightwave Technol. 6, 139-142 (1994).

Press, W. H.

W. H. Press, S. A. Teukoisky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, 1997).

Rao, H.

Rao, H. L.

H. L. Rao, M. J. Steel, R. Scarmozzino, and R. M. Osgood, “VCSEL design using the bidirectional beam-propagation method,” IEEE J. Quantum Electron. 37, 1435-1440 (2001).
[CrossRef]

Riyopoulos, S.

Rolleigh, R. L.

Rosenberger, A. T.

Rossler, T.

T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279-3292 (1998).
[CrossRef]

Sarkisyan, T. V.

Scarmozzino, R.

H. L. Rao, M. J. Steel, R. Scarmozzino, and R. M. Osgood, “VCSEL design using the bidirectional beam-propagation method,” IEEE J. Quantum Electron. 37, 1435-1440 (2001).
[CrossRef]

Scott, J. W.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, “Comprehensive numerical modeling of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 607-616 (1996).
[CrossRef]

J. W. Scott, S. W. Corrzine, D. B. Young, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295-1308 (1993).
[CrossRef]

Steel, M. J.

H. L. Rao, M. J. Steel, R. Scarmozzino, and R. M. Osgood, “VCSEL design using the bidirectional beam-propagation method,” IEEE J. Quantum Electron. 37, 1435-1440 (2001).
[CrossRef]

Sztefka, G.

J. Piprek, H. Wenzel, and G. Sztefka, “Modeling thermal effects on the light vs. current characteristic of gain-guided vertical-cavity surface-emitting lasers,” J. Lightwave Technol. 6, 139-142 (1994).

Teukoisky, S. A.

W. H. Press, S. A. Teukoisky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, 1997).

Vetterling, W. T.

W. H. Press, S. A. Teukoisky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, 1997).

Warren, M. E.

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, “Comprehensive numerical modeling of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 607-616 (1996).
[CrossRef]

Wenzel, H.

J. Piprek, H. Wenzel, and G. Sztefka, “Modeling thermal effects on the light vs. current characteristic of gain-guided vertical-cavity surface-emitting lasers,” J. Lightwave Technol. 6, 139-142 (1994).

Yang, W.

W. Yang and A. Gopinath, “Study of passive mode locking of semiconductor lasers using time-domain modeling,” IEEE J. Quantum Electron. 63, 2717-2719 (1993).

Yariv, A.

T. L. Koch, L. C. Chiu, C. Harder, and A. Yariv, “Picosecond carrier dynamics and laser action in optically pumped buried hetrostructure lasers,” Appl. Phys. Lett. 41, 6-8 (1982).
[CrossRef]

Young, D. B.

J. W. Scott, S. W. Corrzine, D. B. Young, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295-1308 (1993).
[CrossRef]

Yu, S. F.

L. M. Zhang, S. F. Yu, M. Nowell, D. D. Marcenac, and J. E. Carroll, “Dynamic analysis of radiation and side mode suppression in second-order DFB lasers using time-domain large signal traveling wave model,” IEEE J. Quantum Electron. 30, 1389-1395 (1994).
[CrossRef]

Zhang, L.

D. Jones, L. Zhang, and D. Marcenac, “Dynamics of monolithic passively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 31, 1051-1058 (1995).
[CrossRef]

Zhang, L. M.

L. M. Zhang, S. F. Yu, M. Nowell, D. D. Marcenac, and J. E. Carroll, “Dynamic analysis of radiation and side mode suppression in second-order DFB lasers using time-domain large signal traveling wave model,” IEEE J. Quantum Electron. 30, 1389-1395 (1994).
[CrossRef]

Zhang, Q.

Q. Zhang, K. Jasim, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Operation of a passively mode-locked extended-cavity surface-emitting diode laser in multi-GHz regime,” Electron. Lett. 3, 885-887 (2004).

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Passively modelocked vertical extended cavity surface emitting diode laser,” Electron. Lett. 39, 373-375 (2003).
[CrossRef]

Zhou, P.

B. Lu, P. Zhou, J. Cheng, and K. J. Malloy, “High temperature pulsed and CW operation and thermally stable threshold characteristics of vertical-cavity surface-emitting semiconductor lasers grown by metal-organic chemical vapor deposition,” Appl. Phys. Lett. 65, 1337-1339 (1994).
[CrossRef]

Appl. Phys. Lett. (4)

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, “Minimum temperature sensitivity of 1.55 μm vertical-cavity lasers at −30 nm gain offset,” Appl. Phys. Lett. 72, 1814-1816 (1998).
[CrossRef]

T. L. Koch, L. C. Chiu, C. Harder, and A. Yariv, “Picosecond carrier dynamics and laser action in optically pumped buried hetrostructure lasers,” Appl. Phys. Lett. 41, 6-8 (1982).
[CrossRef]

M. P. Kesler and E. P. Ippen, “Subpicosecond gain dynamics in GaAlAs laser diodes,” Appl. Phys. Lett. 51, 1765-1767 (1987).
[CrossRef]

B. Lu, P. Zhou, J. Cheng, and K. J. Malloy, “High temperature pulsed and CW operation and thermally stable threshold characteristics of vertical-cavity surface-emitting semiconductor lasers grown by metal-organic chemical vapor deposition,” Appl. Phys. Lett. 65, 1337-1339 (1994).
[CrossRef]

Electron. Lett. (2)

Q. Zhang, K. Jasim, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Operation of a passively mode-locked extended-cavity surface-emitting diode laser in multi-GHz regime,” Electron. Lett. 3, 885-887 (2004).

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, “Passively modelocked vertical extended cavity surface emitting diode laser,” Electron. Lett. 39, 373-375 (2003).
[CrossRef]

IEE Proc.-J: Optoelectron. (1)

A. J. Lowery, “New dynamic semiconductor laser model based on the transmission line modeling method,” IEE Proc.-J: Optoelectron. 134, 281-289 (1987).
[CrossRef]

IEEE J. Quantum Electron. (11)

W. B. Jiang, D. Derickson, R. Mirin, and J. E. Bowers, “Analysis of laser pulse chirping in mode-locked vertical cavity surface-emitting lasers,” IEEE J. Quantum Electron. 29, 1309-1318 (1993).
[CrossRef]

W. Yang and A. Gopinath, “Study of passive mode locking of semiconductor lasers using time-domain modeling,” IEEE J. Quantum Electron. 63, 2717-2719 (1993).

L. M. Zhang, S. F. Yu, M. Nowell, D. D. Marcenac, and J. E. Carroll, “Dynamic analysis of radiation and side mode suppression in second-order DFB lasers using time-domain large signal traveling wave model,” IEEE J. Quantum Electron. 30, 1389-1395 (1994).
[CrossRef]

D. Jones, L. Zhang, and D. Marcenac, “Dynamics of monolithic passively mode-locked semiconductor lasers,” IEEE J. Quantum Electron. 31, 1051-1058 (1995).
[CrossRef]

B. Kim, Y. Chung, and S. Kim, “Dynamic analysis of mode-locked sampled-grating distributed Bragg reflector laser diodes,” IEEE J. Quantum Electron. 35, 1623-1629 (1999).
[CrossRef]

C. Ning, R. A. Indik, and J. V. Moloney, “Effective Bloch equations for semiconductor lasers and amplifiers,” IEEE J. Quantum Electron. 33, 1543-1550 (1997).
[CrossRef]

M. Bahl, N.-C. Panoiu, and R. M. Osgood, Jr., “Modeling ultrashort field dynamics in surface emitting lasers by using finite-difference time-domain method,” IEEE J. Quantum Electron. 41, 1244-1252 (2005).
[CrossRef]

J. Mulet and S. Balle, “Mode-locking dynamics in electrically driven vertical-external-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1148-1156 (2005).
[CrossRef]

G. R. Hadley, K. L. Lear, M. E. Warren, K. D. Choquette, J. W. Scott, and S. W. Corzine, “Comprehensive numerical modeling of vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 32, 607-616 (1996).
[CrossRef]

H. L. Rao, M. J. Steel, R. Scarmozzino, and R. M. Osgood, “VCSEL design using the bidirectional beam-propagation method,” IEEE J. Quantum Electron. 37, 1435-1440 (2001).
[CrossRef]

J. W. Scott, S. W. Corrzine, D. B. Young, and L. A. Coldren, “Modeling temperature effects and spatial hole burning to optimize vertical-cavity surface-emitting laser performance,” IEEE J. Quantum Electron. 29, 1295-1308 (1993).
[CrossRef]

IEICE Electron. Express (1)

K. Hasebe, Y. Onishi, and F. Koyama, “All-optical regenerator with re-polarization function based on dual optical injection VCSEL,” IEICE Electron. Express 2, 338-343 (2005).
[CrossRef]

J. Lightwave Technol. (2)

J. Piprek, H. Wenzel, and G. Sztefka, “Modeling thermal effects on the light vs. current characteristic of gain-guided vertical-cavity surface-emitting lasers,” J. Lightwave Technol. 6, 139-142 (1994).

W. H. P. Pernice, F. P. Payne, and D. F. G. Gallagher, “A finite-difference time-domain method for the simulation of gain materials with carrier diffusion in photonic crystals,” J. Lightwave Technol. 25, 2306-2314 (2007).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

T. Rossler, R. A. Indik, G. K. Harkness, J. V. Moloney, and C. Z. Ning, “Modeling the interplay of thermal effects and transverse mode behavior in native-oxide-confined vertical-cavity surface-emitting lasers,” Phys. Rev. A 58, 3279-3292 (1998).
[CrossRef]

Prog. Opt. (1)

W. Nakwaski and M. Osinski, “Thermal properties of vertical-cavity surface-emitting semiconductor lasers,” Prog. Opt. 38, 165-262 (1998).
[CrossRef]

Prog. Quantum Electron. (2)

K. Bohringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. I. Theoretical formulation,” Prog. Quantum Electron. 32, 159-246 (2008).
[CrossRef]

K. Bohringer and O. Hess, “A full-time-domain approach to spatio-temporal dynamics of semiconductor lasers. II. Spatio-temporal dynamics,” Prog. Quantum Electron. 32, 247-307 (2008).
[CrossRef]

Other (5)

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals (Springer, 1999), p. 204.

M. Bahl, “Electromagnetic simulations of active and nonlinear photonic devices,” Ph.D. dissertation (Columbia University, 2005).

M. Bahl, N.-C. Panoiu, and R. M. Osgood, Jr., in Proceedings of the IEEE Conference on Lightwave Technologies in Instrumentation and Measurement (IEEE, 2004), pp. 17-22.
[CrossRef]

W. H. Press, S. A. Teukoisky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, 1997).

I.N.Duling, ed., Compact Sources of Ultrashort Pulses (Cambridge U. Press, 1995).
[CrossRef]

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 (9)

Fig. 1
Fig. 1

3D plot showing the peak gain coefficient A as a function of the carrier density and lattice and plasma temperatures. The three slices shown are at T p = 310   K , T l = 310   K , and N = 3.25 × 10 11 cm 2 . The unit for the gain coefficient scale is cm 1 . Note that the peak gain increases monotonously with N and decreases with T p and T l .

Fig. 2
Fig. 2

Variation in the peak gain coefficient A ( N , T p , T l ) with the lattice and plasma temperatures, computed for a fixed carrier density, N = 4.5 × 10 11 cm 2 .

Fig. 3
Fig. 3

Schematic of the monolithic extended-cavity VCSEL structure (see the text for the details on the geometry and material parameters).

Fig. 4
Fig. 4

Stable mode-locked pulse train that corresponds to an injection current density J = 3   mA / μ m 2 , carrier-phonon scattering rate 1 / γ T = 1   ps , and the rate of heat dissipation to ambient heat sink 1 / γ s = 2000   ps . The inset shows the details of the mode-locked pulses. Additional parameters that are constant throughout this paper are R = 1000 Ω , 1 / γ nr = 1   ns , A 0 = 3 μ m 2 , and c L = 1.862 × 10 6   J / Km 3 .

Fig. 5
Fig. 5

(a) Stable mode-locked pulse train. (b) Time dependence of the carrier density inside the gain region. (c) Time dependence of the plasma (solid curve) and lattice (dotted curve) temperatures. All plots correspond to an injection current density J = 3   mA / μ m 2 , carrier-phonon scattering rate 1 / γ T = 100   ps , and the rate of heat dissipation to ambient heat sink 1 / γ s = 2000   ps .

Fig. 6
Fig. 6

Time dependence of the carrier density inside the gain region with (solid curve) and without (dashed curve) the inclusion of thermal effects. The inset, a zoom in of the carrier density time evolution, shows small oscillations in carrier density caused by the periodic passage of the pulse through the gain region.

Fig. 7
Fig. 7

(a) Time dependence of the carrier density inside the gain region in the case in which thermal effects are included (solid curve) and the case when they are neglected (dashed curve). (b) Stable mode-locked pulse train upon incorporating the thermal effects. (c) Mode-locked pulse train when thermal effects are neglected. Note that in (b) and (c) all other laser parameters are the same.

Fig. 8
Fig. 8

Time dependence of the plasma (solid curve) and lattice (dotted curve) temperatures for the carrier-phonon scattering rate 1 / γ T of (a) 1, (b) 10, and (c) 100 ps. All plots correspond to a rate of heat dissipation to the ambient heat sink of 1 / γ s = 2000   ps .

Fig. 9
Fig. 9

Time evolution of the plasma (solid curve) and lattice (dotted curve) temperatures determined for different characteristic rates of heat dissipation to the ambient heat sink, 1 / γ s : (a) 2000, (b) 200, and (c) 20 ps. All plots correspond to the carrier-phonon scattering rate of 1 / γ T = 100   ps .

Equations (40)

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

G ( N , ω , T p , T l ) = ω 2 ϵ 0 c n ( T l ) A 0 R { k | μ k | 2 [ f e , k ( T p , e ) + f h , k ( T p , h ) 1 ] Q k i [ ω k ( T l ) ω ] + γ } ,
ε g 0 ( T l ) = ε g 0 ( 0 ) 3.9 × 10 4 T l .
2 P t 2 + Δ ω ( N , T p , T l ) P t + ω 0 2 ( N , T p , T l ) P = 1 1 + ϵ s S [ A ( N , T p , T l ) ( N N 0 ) ] E .
P j n + 1 = L 2 M ϵ L 1 M ϵ P j n + 1 L 1 M ϵ [ 2 Q j n Δ t 2 M E j n M Δ t ϵ Δ z ( H j + ( 1 / 2 ) n + ( 1 / 2 ) H j ( 1 / 2 ) n + ( 1 / 2 ) ) ] ,
L 1 ( N , T p , T l ) = 2 Δ t 2 + Δ ω ( N , T p , T l ) Δ t + ω 0 2 ( N , T p , T l ) 2 ,
L 2 ( N , T p , T l ) = 2 Δ t 2 + Δ ω ( N , T p , T l ) Δ t ω 0 2 ( N , T p , T l ) 2 ,
M ( N , T p , T l ) = A ( N , T p , T l ) ( N j n + 1 / 2 N 0 ) 2 + ϵ s c ϵ | E j n | 2 .
d T l d t = J 2 R A 0 c L L z N w + γ nr ω 0 N c L + γ T ( T p T l ) γ s ( T l T s ) .
n ̇ α , k = n α , k τ + f ¯ α , k ( 1 n α , k ) τ 2 | E | 2 γ | μ k | 2 2 [ γ 2 + ( ω k ω ) 2 ] ( α = e , h n α , k 1 ) .
W ̇ α = W α W 0 , α τ | E | 2 G W , α ( T p , T l ) .
G W , α ( T p , T l ) = m α A 0 R { k k 2 | μ k | 2 [ f e , k ( T p ) + f h , k ( T p ) 1 ] i [ ω k ( T l ) ω ] + γ } .
N ̇ = N N 0 τ | E | 2 G N ( T p , T l ) ,
G N ( T p , T l ) = 2 A 0 R { k | μ k | 2 ( f e , k + f h , k 1 ) i ( ω k ω ) + γ } .
W ̇ α = W α T p T ̇ p + W α μ α μ ̇ α ,
N ̇ = N T p T ̇ p + N μ α μ ̇ α .
T ̇ p = ( N μ α W ̇ α W α μ α N ̇ W α T p N μ α W α μ α N T p ) J W , α W ̇ α J N , α N ̇ ,
J W , α = N μ α ( W α T p N μ α W α μ α N T p ) 1 ,
J N , α = W α μ α ( W α T p N μ α W α μ α N T p ) 1 .
T ̇ p = J W , α ( W α W 0 , α ) τ J N , α ( N N 0 ) τ | E | 2 G T , α γ T ( T p T l ) ,
G T , α = J W , α G W , α J N , α G N .
T l j n + 1 / 2 = 1 B 2 ( B 1 T l j n 1 / 2 + γ T T p j n + γ s T s + γ nr ω 0 N j n + 1 / 2 c L + J 2 R A 0 c L L z N w ) ,
T p j n + 1 = 1 C 2 { C 1 T p j n + γ T T l j n + 1 / 2 | E j n + 1 | 2 G T , α j n + 1 / 2 + 1 τ [ J W , α j n + 1 / 2 ( W α j n + 1 / 2 W 0 , α ) J N , α j n + 1 / 2 ( N j n + 1 / 2 N 0 ) ] } ,
H t = 1 μ 0 E z ,
E t = 1 ϵ ( T l ; z ) ( H z P t ) .
n ( T l ) = n ( T 0 ) + d n d T l Δ T l ,
ϵ ( T l ) = ϵ ( T 0 ) + 2 d n d T l Δ T l ϵ ( T 0 ) ϵ 0 + ( d n d T l ) 2 Δ T l 2 ϵ 0 ,
H j + ( 1 / 2 ) n + ( 1 / 2 ) = H j + ( 1 / 2 ) n ( 1 / 2 ) + Δ t μ 0 Δ z ( E j + 1 n E j n ) ,
E j n + 1 = E j n + 1 ϵ ( T l ) [ Δ t Δ z ( H j + ( 1 / 2 ) n + ( 1 / 2 ) H j ( 1 / 2 ) n + ( 1 / 2 ) ) ( P j n + 1 P j n ) ] .
N t = 2 ω 0 ( N , T p , T l ) E P t N τ + W p ,
N j n + ( 1 / 2 ) = 1 K 2 { K 1 N j n ( 1 / 2 ) + Δ t [ 2 E j n Q j n ω 0 ( N , T p , T l ) + W p ] } ,
N = 1 A 0 k f α , k ,
f α , k = 1 1 + e ( ϵ α , k μ α ) / k B T p .
N = m α π 2 0 1 1 + e ( ϵ μ α ) / k B T p d ϵ ,
N = m α k B T p π 2 ln ( 1 + e μ α / k B T p ) .
N μ α = m α π 2 ( 1 + e μ α / k B T p ) ,
N T p = N T p μ α T p N μ α .
W α = 1 A 0 k ϵ α , k f α , k .
W α = m α π 2 0 ϵ 1 + e ( ϵ μ α ) / k B T p d ϵ .
W α μ α = m α k B T p π 2 ln ( 1 + e μ α / k B T p ) ,
W α T p = 2 W α T p 1 T p W α μ α .

Metrics