Abstract

We present a new exact solution for ultrashort pulses generated by passively mode-locked lasers, taking into account the slow and the fast parts of the semiconductor saturable-absorber response in the nonsaturated limit.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. I. N. Duling, Opt. Lett. 16, 539 (1991).
    [CrossRef]
  2. S. Gray, A. B. Grudinin, W. H. Loh, and D. N. Payne, Opt. Lett. 20, 189 (1995).
    [CrossRef] [PubMed]
  3. M. Romagnoli, S. Wabnitz, P. Franco, M. Midrio, F. Fontana, and G. E. Town, J. Opt. Soc. Am. B 12, 72 (1995).
    [CrossRef]
  4. C.-J. Chen, P. K. A. Wai, and C. R. Menyuk, Opt. Lett. 19, 198 (1994).
    [CrossRef]
  5. H. A. Haus, J. G. Fujimoto, and E. P. Ippen, J. Opt. Soc. Am. B 8, 2068 (1991).
    [CrossRef]
  6. P. A. Belanger, J. Opt. Soc. Am. B 8, 2077 (1991).
    [CrossRef]
  7. H. A. Haus, E. P. Ippen, and K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
    [CrossRef]
  8. V. V. Afanasjev and A. B. Grudinin, Sov. Lightwave Commun. 3, 77 (1993).
  9. V. J. Matsas, D. J. Richardson, T. P. Newson, and D. N. Payne, Opt. Lett. 18, 358 (1993).
    [CrossRef] [PubMed]
  10. G. D. Peng and A. Ankiewicz, Opt. Quantum Electron. 22, 343 (1990).
    [CrossRef]
  11. M. Hofer, M. E. Fermann, F. Haberl, M. H. Ober, and A. J. Schmidt, Opt. Lett. 16, 502 (1991).
    [CrossRef] [PubMed]
  12. H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
    [CrossRef]
  13. B. C. Barnett, L. Rahman, M. N. Islam, Y. C. Chen, P. Bhattacharya, W. Riha, K. V. Reddy, A. T. Howe, K. A. Stair, H. Iwamura, S. R. Friberg, and T. Mukai, Opt. Lett. 20, 471 (1995).
    [CrossRef] [PubMed]
  14. F. X. Kärtner and U. Keller, Opt. Lett. 20, 16 (1995).
    [CrossRef]
  15. I. D. Jung, F. X. Kärtner, L. R. Brovelli, M. Kamp, and U. Keller, Opt. Lett. 20, 1892 (1995).
    [CrossRef] [PubMed]
  16. M. J. Lederer, B. Luther-Davies, H. H. Tan, and C. Jagadish, Appl. Phys. Lett. 70, 3428 (1997).
    [CrossRef]
  17. H. Haus, J. Appl. Phys. 46, 3049 (1975).
    [CrossRef]
  18. N. Akhmediev and A. Ankiewicz, Solitons, Nonlinear Pulses and Beams (Chapman & Hall, London, 1997).

1997 (1)

M. J. Lederer, B. Luther-Davies, H. H. Tan, and C. Jagadish, Appl. Phys. Lett. 70, 3428 (1997).
[CrossRef]

1995 (6)

1994 (2)

C.-J. Chen, P. K. A. Wai, and C. R. Menyuk, Opt. Lett. 19, 198 (1994).
[CrossRef]

H. A. Haus, E. P. Ippen, and K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

1993 (2)

V. V. Afanasjev and A. B. Grudinin, Sov. Lightwave Commun. 3, 77 (1993).

V. J. Matsas, D. J. Richardson, T. P. Newson, and D. N. Payne, Opt. Lett. 18, 358 (1993).
[CrossRef] [PubMed]

1991 (4)

1990 (1)

G. D. Peng and A. Ankiewicz, Opt. Quantum Electron. 22, 343 (1990).
[CrossRef]

1975 (1)

H. Haus, J. Appl. Phys. 46, 3049 (1975).
[CrossRef]

Afanasjev, V. V.

V. V. Afanasjev and A. B. Grudinin, Sov. Lightwave Commun. 3, 77 (1993).

Akhmediev, N.

N. Akhmediev and A. Ankiewicz, Solitons, Nonlinear Pulses and Beams (Chapman & Hall, London, 1997).

Ankiewicz, A.

G. D. Peng and A. Ankiewicz, Opt. Quantum Electron. 22, 343 (1990).
[CrossRef]

N. Akhmediev and A. Ankiewicz, Solitons, Nonlinear Pulses and Beams (Chapman & Hall, London, 1997).

Barnett, B. C.

Belanger, P. A.

Bhattacharya, P.

Brovelli, L. R.

Chen, C.-J.

Chen, Y. C.

Duling, I. N.

Fermann, M. E.

Fontana, F.

Franco, P.

Friberg, S. R.

Fujimoto, J. G.

Gray, S.

Grudinin, A. B.

S. Gray, A. B. Grudinin, W. H. Loh, and D. N. Payne, Opt. Lett. 20, 189 (1995).
[CrossRef] [PubMed]

V. V. Afanasjev and A. B. Grudinin, Sov. Lightwave Commun. 3, 77 (1993).

Haberl, F.

Haus, H.

H. Haus, J. Appl. Phys. 46, 3049 (1975).
[CrossRef]

Haus, H. A.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

H. A. Haus, E. P. Ippen, and K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, J. Opt. Soc. Am. B 8, 2068 (1991).
[CrossRef]

Hofer, M.

Howe, A. T.

Ippen, E. P.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

H. A. Haus, E. P. Ippen, and K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, J. Opt. Soc. Am. B 8, 2068 (1991).
[CrossRef]

Islam, M. N.

Iwamura, H.

Jagadish, C.

M. J. Lederer, B. Luther-Davies, H. H. Tan, and C. Jagadish, Appl. Phys. Lett. 70, 3428 (1997).
[CrossRef]

Jung, I. D.

Kamp, M.

Kärtner, F. X.

Keller, U.

Lederer, M. J.

M. J. Lederer, B. Luther-Davies, H. H. Tan, and C. Jagadish, Appl. Phys. Lett. 70, 3428 (1997).
[CrossRef]

Loh, W. H.

Luther-Davies, B.

M. J. Lederer, B. Luther-Davies, H. H. Tan, and C. Jagadish, Appl. Phys. Lett. 70, 3428 (1997).
[CrossRef]

Matsas, V. J.

Menyuk, C. R.

Midrio, M.

Mukai, T.

Nelson, L. E.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

Newson, T. P.

Ober, M. H.

Payne, D. N.

Peng, G. D.

G. D. Peng and A. Ankiewicz, Opt. Quantum Electron. 22, 343 (1990).
[CrossRef]

Rahman, L.

Reddy, K. V.

Richardson, D. J.

Riha, W.

Romagnoli, M.

Schmidt, A. J.

Stair, K. A.

Tamura, K.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

H. A. Haus, E. P. Ippen, and K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

Tan, H. H.

M. J. Lederer, B. Luther-Davies, H. H. Tan, and C. Jagadish, Appl. Phys. Lett. 70, 3428 (1997).
[CrossRef]

Town, G. E.

Wabnitz, S.

Wai, P. K. A.

Appl. Phys. Lett. (1)

M. J. Lederer, B. Luther-Davies, H. H. Tan, and C. Jagadish, Appl. Phys. Lett. 70, 3428 (1997).
[CrossRef]

IEEE J. Quantum Electron. (2)

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

H. A. Haus, E. P. Ippen, and K. Tamura, IEEE J. Quantum Electron. 30, 200 (1994).
[CrossRef]

J. Appl. Phys. (1)

H. Haus, J. Appl. Phys. 46, 3049 (1975).
[CrossRef]

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

Opt. Lett. (8)

Opt. Quantum Electron. (1)

G. D. Peng and A. Ankiewicz, Opt. Quantum Electron. 22, 343 (1990).
[CrossRef]

Sov. Lightwave Commun. (1)

V. V. Afanasjev and A. B. Grudinin, Sov. Lightwave Commun. 3, 77 (1993).

Other (1)

N. Akhmediev and A. Ankiewicz, Solitons, Nonlinear Pulses and Beams (Chapman & Hall, London, 1997).

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 (4)

Fig. 1
Fig. 1

Soliton profile (solid curve) and loss curve δt=δ+ϵψ2+α -tψ2dt (dashed curve) defined by the exact solution [Eq.  (7)] for ϵ=0.1, δ=-0.05, α=0.1, β=0.02, and D=+1.

Fig. 2
Fig. 2

Space of parameters δ and β in which the soliton solution [Eq.  (7)] exists. The shaded areas are defined by inequality  (9) for various values of ϵ and indicate where the solutions can exist. The parameters used in the calculation are shown.

Fig. 3
Fig. 3

Dependence of the pulse amplitude γC on the parameters of equation (6a):  α and (b) δγ=γ-.

Fig. 4
Fig. 4

Convergence from the initial condition γC exp-γt2 to the exact solution for the instantaneous parameters γ=γ-, α=0.05, ϵ=2, β=0.02, D=+1, g0=1, EL=0.335, δz=0=-0.015, δz=1000=-0.0041, and TL=100.

Equations (13)

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

iψz+D/2ψtt+ψ2ψ=igQ+ϵψ2-δsψ2×ψ+iβψtt,
gQz=-gQ-g0TL-QTRELgQ,
δst=-δs-δ0T1-ψ2EAδs,
δst=δ0ft1T1  ftdt+1,
ft=exp1T1+ψ2EAdt.
δst=δ0 exp-ψ2EAdtδ0-α-tψ2dt+,
iψz+D2ψtt+ψ2ψ=iδψ+iβψtt+iϵψ2ψ+iαψ-tψ2dt,
ψ=At-Vzexpid lnAt-VzexpiKt-iωz,
Ax=γC sechγx, d=3D+2ϵβ-9D+2ϵβ2+8ϵD-2β21/22ϵD-2β, γ=γ±=αC2±α2C4-22β-dD-2C2ϵβK2-δ1/22β-dD-2C2ϵ,
C=3dD2+4β222β-ϵD1/2, K=-αdC22β1+d2, V=KD-2βd,
ω=D2K2+γ2+βdγ2-γC2.
α2C4-22β-dD-2C2ϵβK2-δ>0.
g01+QTL/ELTR-δ0=δ,

Metrics