Abstract

An approach based on the finite-difference time-domain method is developed for simulating the dynamics of passive mode locking in vertical-cavity surface-emitting lasers (VCSELs). The material response is modeled by the effective semiconductor Bloch equations through a resonant polarization term in the Maxwell’s equations. Nonlinear gain saturation is incorporated through a gain compression factor in the equation governing the dynamics of the resonant polarization. An extended-cavity VCSEL with a quantum-well saturable absorber is simulated, and stable mode-locking pulses are obtained. Fine features of the spatial profile of the mode-locked pulses are also studied within this approach.

© 2004 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, Appl. Phys. Lett. 72, 1814 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. A. Nagra and R. York, IEEE Trans. Antennas Propag. 46, 334 (1998).
    [CrossRef]
  8. H. Rao, “Optical electromagnetics simulation of strongly reflective structures of integrated photonics,” Ph.D. dissertation (Columbia University, New York, 2002).
  9. J. A. Gruetzmacher and N. F. Scherer, Opt. Lett. 28, 573 (2003).
    [CrossRef] [PubMed]
  10. C. Ning, R. Indik, and J. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
    [CrossRef]
  11. W. W. Chow and S. W. Koch, in Semiconductor Laser Fundamentals (Springer, New York, 1999).
    [CrossRef]
  12. K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, Electron. Lett. 39, 373 (2003).
    [CrossRef]
  13. F. X. Kärtner, J. Aus der Au, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 4, 159 (1998).
    [CrossRef]
  14. S. W. Corzine, R. S. Geels, J. W. Scott, R. Yan, and L. A. Coldren, IEEE J. Quantum Electron. 25, 151 (1989).
    [CrossRef]

2003 (2)

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, Electron. Lett. 39, 373 (2003).
[CrossRef]

J. A. Gruetzmacher and N. F. Scherer, Opt. Lett. 28, 573 (2003).
[CrossRef] [PubMed]

2001 (1)

1998 (4)

F. X. Kärtner, J. Aus der Au, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 4, 159 (1998).
[CrossRef]

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, Appl. Phys. Lett. 72, 1814 (1998).
[CrossRef]

J. P. Seurin, G. Liu, D. C. Barnes, D. I. Babic, S. W. Corzine, and M. Tan, Microwave Opt. Technol. Lett. 18, 385 (1998).
[CrossRef]

A. Nagra and R. York, IEEE Trans. Antennas Propag. 46, 334 (1998).
[CrossRef]

1997 (1)

C. Ning, R. Indik, and J. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
[CrossRef]

1995 (1)

1993 (2)

W. B. Jiang, D. Derickson, R. Mirin, and J. E. Bowers, IEEE J. Quantum Electron. 29, 1309 (1993).
[CrossRef]

W. Yang and A. Gopinath, Appl. Phys. Lett. 63, 2717 (1993).
[CrossRef]

1989 (1)

S. W. Corzine, R. S. Geels, J. W. Scott, R. Yan, and L. A. Coldren, IEEE J. Quantum Electron. 25, 151 (1989).
[CrossRef]

Akulova, Y. A.

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, Appl. Phys. Lett. 72, 1814 (1998).
[CrossRef]

Aus der Au, J.

F. X. Kärtner, J. Aus der Au, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 4, 159 (1998).
[CrossRef]

Babic, D. I.

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, Appl. Phys. Lett. 72, 1814 (1998).
[CrossRef]

J. P. Seurin, G. Liu, D. C. Barnes, D. I. Babic, S. W. Corzine, and M. Tan, Microwave Opt. Technol. Lett. 18, 385 (1998).
[CrossRef]

Barnes, D. C.

J. P. Seurin, G. Liu, D. C. Barnes, D. I. Babic, S. W. Corzine, and M. Tan, Microwave Opt. Technol. Lett. 18, 385 (1998).
[CrossRef]

Bowers, J. E.

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, Appl. Phys. Lett. 72, 1814 (1998).
[CrossRef]

W. B. Jiang, D. Derickson, R. Mirin, and J. E. Bowers, IEEE J. Quantum Electron. 29, 1309 (1993).
[CrossRef]

Carey, G.

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, Electron. Lett. 39, 373 (2003).
[CrossRef]

Chow, W. W.

W. W. Chow and S. W. Koch, in Semiconductor Laser Fundamentals (Springer, New York, 1999).
[CrossRef]

Coldren, L. A.

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, Appl. Phys. Lett. 72, 1814 (1998).
[CrossRef]

S. W. Corzine, R. S. Geels, J. W. Scott, R. Yan, and L. A. Coldren, IEEE J. Quantum Electron. 25, 151 (1989).
[CrossRef]

Corzine, S. W.

J. P. Seurin, G. Liu, D. C. Barnes, D. I. Babic, S. W. Corzine, and M. Tan, Microwave Opt. Technol. Lett. 18, 385 (1998).
[CrossRef]

S. W. Corzine, R. S. Geels, J. W. Scott, R. Yan, and L. A. Coldren, IEEE J. Quantum Electron. 25, 151 (1989).
[CrossRef]

Derickson, D.

W. B. Jiang, D. Derickson, R. Mirin, and J. E. Bowers, IEEE J. Quantum Electron. 29, 1309 (1993).
[CrossRef]

Dialetis, D.

Geels, R. S.

S. W. Corzine, R. S. Geels, J. W. Scott, R. Yan, and L. A. Coldren, IEEE J. Quantum Electron. 25, 151 (1989).
[CrossRef]

Gopinath, A.

W. Yang and A. Gopinath, Appl. Phys. Lett. 63, 2717 (1993).
[CrossRef]

Gruetzmacher, J. A.

Ha, W.

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, Electron. Lett. 39, 373 (2003).
[CrossRef]

Hadley, G. R.

Indik, R.

C. Ning, R. Indik, and J. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
[CrossRef]

Inman, J.

Ippen, E.

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, Electron. Lett. 39, 373 (2003).
[CrossRef]

Jasim, K.

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, Electron. Lett. 39, 373 (2003).
[CrossRef]

Jiang, W. B.

W. B. Jiang, D. Derickson, R. Mirin, and J. E. Bowers, IEEE J. Quantum Electron. 29, 1309 (1993).
[CrossRef]

Kärtner, F. X.

F. X. Kärtner, J. Aus der Au, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 4, 159 (1998).
[CrossRef]

Keller, U.

F. X. Kärtner, J. Aus der Au, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 4, 159 (1998).
[CrossRef]

Koch, S. W.

W. W. Chow and S. W. Koch, in Semiconductor Laser Fundamentals (Springer, New York, 1999).
[CrossRef]

Liu, G.

J. P. Seurin, G. Liu, D. C. Barnes, D. I. Babic, S. W. Corzine, and M. Tan, Microwave Opt. Technol. Lett. 18, 385 (1998).
[CrossRef]

Mirin, R.

W. B. Jiang, D. Derickson, R. Mirin, and J. E. Bowers, IEEE J. Quantum Electron. 29, 1309 (1993).
[CrossRef]

Moloney, J.

C. Ning, R. Indik, and J. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
[CrossRef]

Mooradian, A.

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, Electron. Lett. 39, 373 (2003).
[CrossRef]

Nagra, A.

A. Nagra and R. York, IEEE Trans. Antennas Propag. 46, 334 (1998).
[CrossRef]

Ning, C.

C. Ning, R. Indik, and J. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
[CrossRef]

Nurmikko, A. V.

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, Electron. Lett. 39, 373 (2003).
[CrossRef]

Phillips, A.

Piprek, J.

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, Appl. Phys. Lett. 72, 1814 (1998).
[CrossRef]

Rao, H.

H. Rao, “Optical electromagnetics simulation of strongly reflective structures of integrated photonics,” Ph.D. dissertation (Columbia University, New York, 2002).

Riyopoulos, S.

Scherer, N. F.

Scott, J. W.

S. W. Corzine, R. S. Geels, J. W. Scott, R. Yan, and L. A. Coldren, IEEE J. Quantum Electron. 25, 151 (1989).
[CrossRef]

Seurin, J. P.

J. P. Seurin, G. Liu, D. C. Barnes, D. I. Babic, S. W. Corzine, and M. Tan, Microwave Opt. Technol. Lett. 18, 385 (1998).
[CrossRef]

Tan, M.

J. P. Seurin, G. Liu, D. C. Barnes, D. I. Babic, S. W. Corzine, and M. Tan, Microwave Opt. Technol. Lett. 18, 385 (1998).
[CrossRef]

Yan, R.

S. W. Corzine, R. S. Geels, J. W. Scott, R. Yan, and L. A. Coldren, IEEE J. Quantum Electron. 25, 151 (1989).
[CrossRef]

Yang, W.

W. Yang and A. Gopinath, Appl. Phys. Lett. 63, 2717 (1993).
[CrossRef]

York, R.

A. Nagra and R. York, IEEE Trans. Antennas Propag. 46, 334 (1998).
[CrossRef]

Zhang, Q.

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, Electron. Lett. 39, 373 (2003).
[CrossRef]

Appl. Phys. Lett. (2)

W. Yang and A. Gopinath, Appl. Phys. Lett. 63, 2717 (1993).
[CrossRef]

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, Appl. Phys. Lett. 72, 1814 (1998).
[CrossRef]

Electron. Lett. (1)

K. Jasim, Q. Zhang, A. V. Nurmikko, A. Mooradian, G. Carey, W. Ha, and E. Ippen, Electron. Lett. 39, 373 (2003).
[CrossRef]

IEEE J. Quantum Electron. (3)

C. Ning, R. Indik, and J. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
[CrossRef]

W. B. Jiang, D. Derickson, R. Mirin, and J. E. Bowers, IEEE J. Quantum Electron. 29, 1309 (1993).
[CrossRef]

S. W. Corzine, R. S. Geels, J. W. Scott, R. Yan, and L. A. Coldren, IEEE J. Quantum Electron. 25, 151 (1989).
[CrossRef]

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

F. X. Kärtner, J. Aus der Au, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 4, 159 (1998).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

A. Nagra and R. York, IEEE Trans. Antennas Propag. 46, 334 (1998).
[CrossRef]

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

Microwave Opt. Technol. Lett. (1)

J. P. Seurin, G. Liu, D. C. Barnes, D. I. Babic, S. W. Corzine, and M. Tan, Microwave Opt. Technol. Lett. 18, 385 (1998).
[CrossRef]

Opt. Lett. (2)

Other (2)

H. Rao, “Optical electromagnetics simulation of strongly reflective structures of integrated photonics,” Ph.D. dissertation (Columbia University, New York, 2002).

W. W. Chow and S. W. Koch, in Semiconductor Laser Fundamentals (Springer, New York, 1999).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic of our VCSEL structure. The output field is recorded at monitor position M. MQW, multiple quantum well.

Fig. 2
Fig. 2

(a) Stable pulse train for J=2 mA/µm2. The inset shows the details of the mode-locked pulses. (b) Pulse width versus intracavity pulse energy. The inset shows output intensity I versus current density J.

Fig. 3
Fig. 3

(a) Instantaneous field amplitude in the gain region. (b) Field intensity averaged over one cavity round trip. The dashed lines mark the positions of the QWs.

Equations (7)

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

tH=1/μ0zE,
tE=1/zH-tP.
tN=2/ω0EtP-N/τ+Wp,
GN,ω=ω20ncAkμk2ne,k+nh,k-1Qkiωk-ω+γ.
tt2P+ΔωNtP+ω02NP=-ANN-N0E/1+sS.
Hj+1/2n+1/2-Hj+1/2n-1/2/Δt=Ej+1n-Ejn/μ0Δz, Ejn+1-EjnΔt=Hj+1/2n+1/2-Hj-1/2n+1/2Δz-Pjn+1-PjnΔt, Njn+1/2-Njn-1/2Δt=2ωEjnQjn-Njn+1/2-Njn-1/22τ+Wp, ω02NPjn+1+Pjn2+ΔωNPjn+1-PjnΔt+Qjn+1-QjnΔt=-ANNjn+1/2-N0Ejn+1+Ejn2+scE2,
Qjn+1+Qjn/2=Pjn+1-Pjn/Δt.

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