Abstract

We present a general form of master equation for nonlinear-optical cavities that can be described by an ABCD matrix. It includes as special cases some previous models of spatiotemporal effects in lasers.

© 1996 Optical Society of America

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References

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  1. L. A. LugiatoChaos Solitons Fractals 4, 1251 (1994).
    [CrossRef]
  2. J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, P. W. E. SmithOpt. Lett. 15, 471 (1990).
    [CrossRef] [PubMed]
  3. T. Brabec, C. Spielmann, P. F. Curley, F. KrauszOpt. Lett. 17, 1292 (1992).
    [CrossRef] [PubMed]
  4. H. A. Haus, J. G. Fujimoto, E. P. IppenJ. Opt. Soc. Am. B 8, 2068 (1991).
    [CrossRef]
  5. L. A. Lugiato, G. L. Oppo, J. R. Tredicce, L. M. Narducci, M. A. PernigoJ. Opt. Soc. Am. B 7, 1019 (1990).
    [CrossRef]
  6. H. A. Haus, J. G. Fujimoto, E. P. IppenIEEE J. Quantum Electron. 28, 2086 (1992).
    [CrossRef]
  7. C. Paré, L. Gagnon, P. A. BélangerOpt. Commun. 74, 228 (1989).
    [CrossRef]
  8. P. A. Bélanger, L. Gagnon, C. ParéOpt. Lett. 14, 943 (1989).
    [CrossRef] [PubMed]
  9. A. SiegmanLasers (University Science, Mill Valley, Calif., 1986).
  10. P. BauesOpto-Electronics 1, 37 (1969).
    [CrossRef]
  11. J. S. A. CollinsJ. Opt. Soc. Am. 60, 1168 (1970).
    [CrossRef]
  12. A. M. Dunlop“Models for Kerr lens mode-locking,” Ph.D. dissertation (University of Strathclyde, Glasgow, Scotland, 1995).
  13. D. R. Heatley, A. M. Dunlop, W. J. FirthOpt. Lett. 18, 170 (1993).
    [CrossRef] [PubMed]
  14. V. Magni, G. Cerullo, S. DeSilvestriOpt. Commun. 101, 365 (1993).
    [CrossRef]
  15. A. Agnesi, G. C. RealiOpt. Commun. 110, 109 (1994).
    [CrossRef]
  16. P. Coullet, L. Gil, F. RoccaOpt. Commun. 73, 403 (1989).
    [CrossRef]
  17. M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van StrylandOpt. Eng. 30, 1228 (1991).
    [CrossRef]

1994 (2)

L. A. LugiatoChaos Solitons Fractals 4, 1251 (1994).
[CrossRef]

A. Agnesi, G. C. RealiOpt. Commun. 110, 109 (1994).
[CrossRef]

1993 (2)

D. R. Heatley, A. M. Dunlop, W. J. FirthOpt. Lett. 18, 170 (1993).
[CrossRef] [PubMed]

V. Magni, G. Cerullo, S. DeSilvestriOpt. Commun. 101, 365 (1993).
[CrossRef]

1992 (2)

T. Brabec, C. Spielmann, P. F. Curley, F. KrauszOpt. Lett. 17, 1292 (1992).
[CrossRef] [PubMed]

H. A. Haus, J. G. Fujimoto, E. P. IppenIEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

1991 (2)

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

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van StrylandOpt. Eng. 30, 1228 (1991).
[CrossRef]

1990 (2)

1989 (3)

C. Paré, L. Gagnon, P. A. BélangerOpt. Commun. 74, 228 (1989).
[CrossRef]

P. A. Bélanger, L. Gagnon, C. ParéOpt. Lett. 14, 943 (1989).
[CrossRef] [PubMed]

P. Coullet, L. Gil, F. RoccaOpt. Commun. 73, 403 (1989).
[CrossRef]

1970 (1)

1969 (1)

P. BauesOpto-Electronics 1, 37 (1969).
[CrossRef]

Agnesi, A.

A. Agnesi, G. C. RealiOpt. Commun. 110, 109 (1994).
[CrossRef]

Aitchison, J. S.

Baues, P.

P. BauesOpto-Electronics 1, 37 (1969).
[CrossRef]

Bélanger, P. A.

C. Paré, L. Gagnon, P. A. BélangerOpt. Commun. 74, 228 (1989).
[CrossRef]

P. A. Bélanger, L. Gagnon, C. ParéOpt. Lett. 14, 943 (1989).
[CrossRef] [PubMed]

Brabec, T.

Cerullo, G.

V. Magni, G. Cerullo, S. DeSilvestriOpt. Commun. 101, 365 (1993).
[CrossRef]

Collins, J. S. A.

Coullet, P.

P. Coullet, L. Gil, F. RoccaOpt. Commun. 73, 403 (1989).
[CrossRef]

Curley, P. F.

DeSilvestri, S.

V. Magni, G. Cerullo, S. DeSilvestriOpt. Commun. 101, 365 (1993).
[CrossRef]

Dunlop, A. M.

D. R. Heatley, A. M. Dunlop, W. J. FirthOpt. Lett. 18, 170 (1993).
[CrossRef] [PubMed]

A. M. Dunlop“Models for Kerr lens mode-locking,” Ph.D. dissertation (University of Strathclyde, Glasgow, Scotland, 1995).

Firth, W. J.

Fujimoto, J. G.

H. A. Haus, J. G. Fujimoto, E. P. IppenIEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

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

Gagnon, L.

P. A. Bélanger, L. Gagnon, C. ParéOpt. Lett. 14, 943 (1989).
[CrossRef] [PubMed]

C. Paré, L. Gagnon, P. A. BélangerOpt. Commun. 74, 228 (1989).
[CrossRef]

Gil, L.

P. Coullet, L. Gil, F. RoccaOpt. Commun. 73, 403 (1989).
[CrossRef]

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van StrylandOpt. Eng. 30, 1228 (1991).
[CrossRef]

Haus, H. A.

H. A. Haus, J. G. Fujimoto, E. P. IppenIEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

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

Heatley, D. R.

Ippen, E. P.

H. A. Haus, J. G. Fujimoto, E. P. IppenIEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

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

Jackel, J. L.

Krausz, F.

Leaird, D. E.

Lugiato, L. A.

Magni, V.

V. Magni, G. Cerullo, S. DeSilvestriOpt. Commun. 101, 365 (1993).
[CrossRef]

Narducci, L. M.

Oliver, M. K.

Oppo, G. L.

Paré, C.

P. A. Bélanger, L. Gagnon, C. ParéOpt. Lett. 14, 943 (1989).
[CrossRef] [PubMed]

C. Paré, L. Gagnon, P. A. BélangerOpt. Commun. 74, 228 (1989).
[CrossRef]

Pernigo, M. A.

Reali, G. C.

A. Agnesi, G. C. RealiOpt. Commun. 110, 109 (1994).
[CrossRef]

Rocca, F.

P. Coullet, L. Gil, F. RoccaOpt. Commun. 73, 403 (1989).
[CrossRef]

Said, A. A.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van StrylandOpt. Eng. 30, 1228 (1991).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van StrylandOpt. Eng. 30, 1228 (1991).
[CrossRef]

Siegman, A.

A. SiegmanLasers (University Science, Mill Valley, Calif., 1986).

Silberberg, Y.

Smith, P. W. E.

Soileau, M. J.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van StrylandOpt. Eng. 30, 1228 (1991).
[CrossRef]

Spielmann, C.

Tredicce, J. R.

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van StrylandOpt. Eng. 30, 1228 (1991).
[CrossRef]

Vogel, E. M.

Weiner, A. M.

Chaos Solitons Fractals (1)

L. A. LugiatoChaos Solitons Fractals 4, 1251 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. A. Haus, J. G. Fujimoto, E. P. IppenIEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

Opt. Commun. (4)

C. Paré, L. Gagnon, P. A. BélangerOpt. Commun. 74, 228 (1989).
[CrossRef]

V. Magni, G. Cerullo, S. DeSilvestriOpt. Commun. 101, 365 (1993).
[CrossRef]

A. Agnesi, G. C. RealiOpt. Commun. 110, 109 (1994).
[CrossRef]

P. Coullet, L. Gil, F. RoccaOpt. Commun. 73, 403 (1989).
[CrossRef]

Opt. Eng. (1)

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van StrylandOpt. Eng. 30, 1228 (1991).
[CrossRef]

Opt. Lett. (4)

Opto-Electronics (1)

P. BauesOpto-Electronics 1, 37 (1969).
[CrossRef]

Other (2)

A. M. Dunlop“Models for Kerr lens mode-locking,” Ph.D. dissertation (University of Strathclyde, Glasgow, Scotland, 1995).

A. SiegmanLasers (University Science, Mill Valley, Calif., 1986).

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Figures (1)

Fig. 1
Fig. 1

Dependence of round-trip cavity loss (solid curve) and phase shift (dashed curve) on the offset of the Kerr lens (KL) from the symmetric plane, calculated from Eq. (6) for the fundamental mode: total cavity length 2m, focal length of lenses 24.98 cm, Gaussian slit transmission factor exp(−x2/wa2), where wa = 350 μm, and power and nonlinearity are such that Kerr-lens focal length f obeys f = w3 × 6.6 × 10−6 m for beam width w (in micrometers).

Equations (7)

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E T = g ( 1 + 1 Ω g 2 2 t 2 ) E + i ( ϕ D 2 t 2 ) E + N ( E ) + π ^ E .
E m + 1 ( x , y ) = i λ B G d x 0 d y 0 exp { i π λ B [ D ( x 2 + y 2 ) + A ( x 0 2 + y 0 2 ) 2 ( x x 0 + y y 0 ) ] } E m ( x 0 , y 0 ) .
π ^ E = i ψ 2 T R sin ψ [ B k 2 E + i ( A D ) × ( r E + E ) + k C r 2 E ] ,
B q = ( A D ) 2 ± i sin ψ .
d A d T = i ( + n + 1 ) ψ T R A .
[ A B C D ] [ A B C D ] = [ 1 0 1 f 1 ] [ A B C D ] = [ A B C A f D B f ] .
d A d T = i ( m + n + 1 ) T R ( ψ + B 2 f sin ψ ) A .

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