Abstract

We propose an effective procedure, based on rather simple mathematical calculations, for optimal cavity design for a variety of laser geometries. In addition to the well-known guidelines from the literature, we suggest ways for the further optimization of a four-mirror cavity. The possibilities of using three- and two-mirror resonators for building compact Kerr-lens lasers are considered.

© 1997 Optical Society of America

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References

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  1. D. E. Spence, P. N. Kean, and W. Sibbett, “60-fsec pulse generation from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 16, 42 (1991).
    [CrossRef] [PubMed]
  2. A. Stingl, M. Lenzner, Ch. Spielmann, F. Krausz, and R. Szipocs, “Generation of bandwidth-limited 8-fs optical pulses from a mirror-dispersion-controlled Ti:sapphire laser,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 252.
  3. G. P. A. Malcolm and A. I. Ferguson, “Self-mode locking of a diode-pumped Nd:YLF laser,” Opt. Lett. 16, 1967 (1991).
    [CrossRef] [PubMed]
  4. M. Ramaswamy, A. S. Gouveia-Neto, D. K. Negus, J. A. Izatt, and J. G. Fujimoto, “2.3-ps pulses from a Kerr-lens mode-locked lamp-pumped Nd:YLF laser with a microdot mirror,” Opt. Lett. 18, 1825 (1993).
    [CrossRef] [PubMed]
  5. K. X. Liu, C. J. Flood, D. R. Walker, and H. M. van Driel, “Kerr lens mode locking a diode-pumped Nd:YAG laser,” Opt. Lett. 19, 1361 (1992).
    [CrossRef]
  6. A. Sennaroglu, C. R. Pollock, and H. Nathel, “Continuous-wave self-mode-locked operation of a femtosecond Cr4+:YAG laser,” Opt. Lett. 19, 390 (1994).
    [PubMed]
  7. Y. Pang, V. Yanovsky, F. Wise, and B. I. Minkov, “Self-mode-locked Cr:forsterite laser,” Opt. Lett. 18, 1168 (1993).
    [CrossRef] [PubMed]
  8. J. M. Evans, D. E. Spence, W. Sibbett, B. H. T. Chai, and A. Meller, “50-fs pulse generation from a self-mode-locked Cr:LiSrAlF6 laser,” Opt. Lett. 17, 1447 (1992).
    [CrossRef]
  9. P. M. W. French, R. Mellish, J. R. Teylor, P. J. Delfyett, and L. T. Florez, “Mode-locked all-solid-state diode-pumped Cr:LiSAF laser,” Opt. Lett. 18, 1934 (1993).
    [CrossRef] [PubMed]
  10. J. R. Lincoln, M. J. P. Dymott, and A. J. Ferguson, “Femtosecond pulses from an all-solid-state Kerr-lens mode-locked Cr:LiSAF laser,” Opt. Lett. 19, 1210 (1994).
    [CrossRef] [PubMed]
  11. P. Li Kam Wa, B. H. T. Chai, and A. Miller, “Self-mode-locked Cr3+:LiCaAlF6 laser,” Opt. Lett. 17, 1438 (1992).
    [CrossRef]
  12. C. Radzewicz, C. W. Pearson, and J. S. Krasinski, “Use of ZnS as an additional highly nonlinear element in a Ti:sapphire self-modelocked laser,” Opt. Commun. 102, 464 (1993).
    [CrossRef]
  13. M. Piche, “Beam reshaping and self-mode-locking in nonlinear laser resonators,” Opt. Commun. 86, 156 (1991).
    [CrossRef]
  14. T. Brabec, Ch. Spielmann, P. F. Curley, and F. Kraus, “Kerr-lens mode locking,” Opt. Lett. 17, 1292 (1991).
    [CrossRef]
  15. H. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytical theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086 (1992).
    [CrossRef]
  16. T. Brabec, P. F. Curley, Ch. Spielmann, E. Winter, and A. J. Schmidt, “Hard-aperture Kerr-lens mode locking,” J. Opt. Soc. Am. B 10, 1029 (1993).
    [CrossRef]
  17. V. Magni, G. Cerullo, and S. De Silvestri, “ABCD matrix analysis of propagation of Gaussian beams through Kerr media,” Opt. Commun. 96, 348 (1993).
    [CrossRef]
  18. V. Magni, G. Cerullo, and S. De Silvestri, “Close form Gaussian beam analysis of resonators containing a Kerr medium for femtosecond lasers,” Opt. Commun. 101, 365 (1993).
    [CrossRef]
  19. G. Cerullo, S. De Silvestri, V. Magni, and L. Pallaro, “Resonators for Kerr-lens mode-locked femtosecond Ti:sapphire lasers,” Opt. Lett. 19, 807 (1994).
    [CrossRef] [PubMed]
  20. G. Cerullo, S. De Silvestri, and V. Magni, “Self-starting Kerr-lens mode locking of a Ti:sapphire laser,” Opt. Lett. 19, 1040 (1994).
    [CrossRef] [PubMed]
  21. G. Cerullo, S. De Silvestri, and V. Magni, “Astigmatism in Gaussian-beam self-focusing and in resonators for Kerr-lens mode locking,” J. Opt. Soc. Am. B 12, 476 (1995).
    [CrossRef]
  22. J. Herrmann, “Theory of Kerr-lens mode locking: role of self-focusing and radially varying gain,” J. Opt. Soc. Am. B 11, 498 (1994).
    [CrossRef]
  23. V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror-cavity solid-state lasers by Kerr self-focusing,” J. Opt. Soc. Am. B 12, 462 (1995).
    [CrossRef]
  24. M. Ramaswamy and J. G. Fujimoto, “Compact dispersion-compensating geometry for Kerr-lens mode-locked femtosecond lasers,” Opt. Lett. 19, 1756 (1994).
    [CrossRef]
  25. S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992), Chap. 2, p. 85.

1995

1994

1993

T. Brabec, P. F. Curley, Ch. Spielmann, E. Winter, and A. J. Schmidt, “Hard-aperture Kerr-lens mode locking,” J. Opt. Soc. Am. B 10, 1029 (1993).
[CrossRef]

V. Magni, G. Cerullo, and S. De Silvestri, “ABCD matrix analysis of propagation of Gaussian beams through Kerr media,” Opt. Commun. 96, 348 (1993).
[CrossRef]

V. Magni, G. Cerullo, and S. De Silvestri, “Close form Gaussian beam analysis of resonators containing a Kerr medium for femtosecond lasers,” Opt. Commun. 101, 365 (1993).
[CrossRef]

C. Radzewicz, C. W. Pearson, and J. S. Krasinski, “Use of ZnS as an additional highly nonlinear element in a Ti:sapphire self-modelocked laser,” Opt. Commun. 102, 464 (1993).
[CrossRef]

P. M. W. French, R. Mellish, J. R. Teylor, P. J. Delfyett, and L. T. Florez, “Mode-locked all-solid-state diode-pumped Cr:LiSAF laser,” Opt. Lett. 18, 1934 (1993).
[CrossRef] [PubMed]

Y. Pang, V. Yanovsky, F. Wise, and B. I. Minkov, “Self-mode-locked Cr:forsterite laser,” Opt. Lett. 18, 1168 (1993).
[CrossRef] [PubMed]

M. Ramaswamy, A. S. Gouveia-Neto, D. K. Negus, J. A. Izatt, and J. G. Fujimoto, “2.3-ps pulses from a Kerr-lens mode-locked lamp-pumped Nd:YLF laser with a microdot mirror,” Opt. Lett. 18, 1825 (1993).
[CrossRef] [PubMed]

1992

1991

Brabec, T.

Cerullo, G.

Chai, B. H. T.

Curley, P. F.

De Silvestri, S.

Delfyett, P. J.

Dymott, M. J. P.

Evans, J. M.

Ferguson, A. I.

Ferguson, A. J.

Flood, C. J.

Florez, L. T.

French, P. M. W.

Fujimoto, J. G.

Gouveia-Neto, A. S.

Haus, H.

H. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytical theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

Herrmann, J.

Ippen, E. P.

H. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytical theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

Izatt, J. A.

Kalashnikov, V. L.

Kalosha, V. P.

Kean, P. N.

Krasinski, J. S.

C. Radzewicz, C. W. Pearson, and J. S. Krasinski, “Use of ZnS as an additional highly nonlinear element in a Ti:sapphire self-modelocked laser,” Opt. Commun. 102, 464 (1993).
[CrossRef]

Kraus, F.

Li Kam Wa, P.

Lincoln, J. R.

Liu, K. X.

Magni, V.

Malcolm, G. P. A.

Meller, A.

Mellish, R.

Mikhailov, V. P.

Miller, A.

Minkov, B. I.

Nathel, H.

Negus, D. K.

Pallaro, L.

Pang, Y.

Pearson, C. W.

C. Radzewicz, C. W. Pearson, and J. S. Krasinski, “Use of ZnS as an additional highly nonlinear element in a Ti:sapphire self-modelocked laser,” Opt. Commun. 102, 464 (1993).
[CrossRef]

Piche, M.

M. Piche, “Beam reshaping and self-mode-locking in nonlinear laser resonators,” Opt. Commun. 86, 156 (1991).
[CrossRef]

Pollock, C. R.

Poloyko, I. G.

Radzewicz, C.

C. Radzewicz, C. W. Pearson, and J. S. Krasinski, “Use of ZnS as an additional highly nonlinear element in a Ti:sapphire self-modelocked laser,” Opt. Commun. 102, 464 (1993).
[CrossRef]

Ramaswamy, M.

Schmidt, A. J.

Sennaroglu, A.

Sibbett, W.

Spence, D. E.

Spielmann, Ch.

Teylor, J. R.

van Driel, H. M.

Walker, D. R.

Winter, E.

Wise, F.

Yanovsky, V.

IEEE J. Quantum Electron.

H. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytical theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

C. Radzewicz, C. W. Pearson, and J. S. Krasinski, “Use of ZnS as an additional highly nonlinear element in a Ti:sapphire self-modelocked laser,” Opt. Commun. 102, 464 (1993).
[CrossRef]

M. Piche, “Beam reshaping and self-mode-locking in nonlinear laser resonators,” Opt. Commun. 86, 156 (1991).
[CrossRef]

V. Magni, G. Cerullo, and S. De Silvestri, “ABCD matrix analysis of propagation of Gaussian beams through Kerr media,” Opt. Commun. 96, 348 (1993).
[CrossRef]

V. Magni, G. Cerullo, and S. De Silvestri, “Close form Gaussian beam analysis of resonators containing a Kerr medium for femtosecond lasers,” Opt. Commun. 101, 365 (1993).
[CrossRef]

Opt. Lett.

D. E. Spence, P. N. Kean, and W. Sibbett, “60-fsec pulse generation from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 16, 42 (1991).
[CrossRef] [PubMed]

G. P. A. Malcolm and A. I. Ferguson, “Self-mode locking of a diode-pumped Nd:YLF laser,” Opt. Lett. 16, 1967 (1991).
[CrossRef] [PubMed]

T. Brabec, Ch. Spielmann, P. F. Curley, and F. Kraus, “Kerr-lens mode locking,” Opt. Lett. 17, 1292 (1991).
[CrossRef]

P. Li Kam Wa, B. H. T. Chai, and A. Miller, “Self-mode-locked Cr3+:LiCaAlF6 laser,” Opt. Lett. 17, 1438 (1992).
[CrossRef]

J. M. Evans, D. E. Spence, W. Sibbett, B. H. T. Chai, and A. Meller, “50-fs pulse generation from a self-mode-locked Cr:LiSrAlF6 laser,” Opt. Lett. 17, 1447 (1992).
[CrossRef]

Y. Pang, V. Yanovsky, F. Wise, and B. I. Minkov, “Self-mode-locked Cr:forsterite laser,” Opt. Lett. 18, 1168 (1993).
[CrossRef] [PubMed]

M. Ramaswamy, A. S. Gouveia-Neto, D. K. Negus, J. A. Izatt, and J. G. Fujimoto, “2.3-ps pulses from a Kerr-lens mode-locked lamp-pumped Nd:YLF laser with a microdot mirror,” Opt. Lett. 18, 1825 (1993).
[CrossRef] [PubMed]

P. M. W. French, R. Mellish, J. R. Teylor, P. J. Delfyett, and L. T. Florez, “Mode-locked all-solid-state diode-pumped Cr:LiSAF laser,” Opt. Lett. 18, 1934 (1993).
[CrossRef] [PubMed]

A. Sennaroglu, C. R. Pollock, and H. Nathel, “Continuous-wave self-mode-locked operation of a femtosecond Cr4+:YAG laser,” Opt. Lett. 19, 390 (1994).
[PubMed]

G. Cerullo, S. De Silvestri, V. Magni, and L. Pallaro, “Resonators for Kerr-lens mode-locked femtosecond Ti:sapphire lasers,” Opt. Lett. 19, 807 (1994).
[CrossRef] [PubMed]

G. Cerullo, S. De Silvestri, and V. Magni, “Self-starting Kerr-lens mode locking of a Ti:sapphire laser,” Opt. Lett. 19, 1040 (1994).
[CrossRef] [PubMed]

J. R. Lincoln, M. J. P. Dymott, and A. J. Ferguson, “Femtosecond pulses from an all-solid-state Kerr-lens mode-locked Cr:LiSAF laser,” Opt. Lett. 19, 1210 (1994).
[CrossRef] [PubMed]

K. X. Liu, C. J. Flood, D. R. Walker, and H. M. van Driel, “Kerr lens mode locking a diode-pumped Nd:YAG laser,” Opt. Lett. 19, 1361 (1992).
[CrossRef]

M. Ramaswamy and J. G. Fujimoto, “Compact dispersion-compensating geometry for Kerr-lens mode-locked femtosecond lasers,” Opt. Lett. 19, 1756 (1994).
[CrossRef]

Other

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, New York, 1992), Chap. 2, p. 85.

A. Stingl, M. Lenzner, Ch. Spielmann, F. Krausz, and R. Szipocs, “Generation of bandwidth-limited 8-fs optical pulses from a mirror-dispersion-controlled Ti:sapphire laser,” in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 252.

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Figures (7)

Fig. 1
Fig. 1

Resonator configurations: a, four-mirror; b, three-mirror; c, two-mirror. M1–M4, mirrors; A, aperture; z, nonlinear crystal with length z.

Fig. 2
Fig. 2

Small-signal transmission derivative for a four-mirror resonator (in units of 5×10-7 cm2/kW): a, L1=L2=80 cm; b, L1=L2=50 cm; c, L1=L2=25 cm. f2=2 (curves 1), 4 (curves 2), 6 (curves 3), 5 cm (dotted curves). d=1 cm is the distance from the end mirror; z=1 cm; D=1 mm.

Fig. 3
Fig. 3

Small-signal transmission for a four-mirror resonator. L1=L3=80 cm (curve 1), L1=L3=50 cm (curve 2), and L1=L3=25 cm (curve 3); f2=4 cm, d=1 cm, z=1 cm, D=1 mm.

Fig. 4
Fig. 4

Small-signal transmission derivative for a four-mirror resonator (in units of 5×10-7 cm2/kW). L3=80 cm (curve 1); L3=50 cm (curve 2); L3=10 cm (curve 3); and L3=0.5 cm (curve 4). L1=80 cm, f2=4 cm, d=1 cm, z=1 cm, D=1 mm.

Fig. 5
Fig. 5

Small-signal transmission derivative for a three-mirror resonator (in units of 5×10-7 cm2/kW). f3= (curve 1), f3=15 cm (curve 2), and f3=7 cm (curve 3); D=0.8 (curves 1–3), D=1 (dashed curve), and D=0.5 mm (dotted curve). f1=, L2=10 cm, d=1 cm, z=1 cm.

Fig. 6
Fig. 6

Stability zones for a two-mirror resonator: a, f1=10 cm; b, f1=20 cm.

Fig. 7
Fig. 7

Small-signal transmission derivative for a two-mirror resonator (in units of 5×10-7 cm2/kW). f1=5 cm (curve 1), f1=50 cm (curve 2), f1= (curve 3). d=1 cm, z=1 cm, D=1 mm.

Equations (7)

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

E(r)=E0ρ-1/2 exp(-kr2/2ρ-ikr2/2R)
q=Aq+BCq+D,
a1i=Wi-Yi,
ai1=L3Wi+Yi(1-L3/f2),
z+i12k0Δ+iβ1|E|2E(r, z)=0,
ρ=[(C1z0+C2)2+C3]/C1,
R=ρ/(C1z0+C2),

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