Abstract

We present numerical studies of nonlinear propagation for picosecond pulses focused in water. Depending on the pulse duration and focusing conditions, for some input powers self-focusing may precede laser-induced breakdown and vice versa. We derive a criterion that predicts the relative roles of laser-induced breakdown and self-focusing.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Penzkofer, A. Laubereau, W. Kaiser, Phys. Rev. Lett. 31, 863 (1973).
    [CrossRef]
  2. W. L. Smith, P. Lui, N. Bloembergen, Phys. Rev. A 15, 2396 (1977).
    [CrossRef]
  3. B. A. Rockwell, W. P. Roach, M. E. Rogers, M. W. Mayo, C. A. Toth, C. P. Cain, G. D. Noojin, Opt. Lett. 18, 1792 (1993).
    [CrossRef] [PubMed]
  4. R. Birngruber, C. A. Puliafito, A. Gawande, W. Lin, R. W. Schoenlein, J. G. Fujimoto, IEEE J. Quantum Electron. QE-23, 1836 (1987).
    [CrossRef]
  5. P. A. Barnes, K. E. Rieckhoff, Appl. Phys. Lett. 13, 282 (1968).
    [CrossRef]
  6. E. Yablonovitch, N. Bloembergen, Phys. Rev. Lett. 29, 907 (1972).
    [CrossRef]
  7. C. A. Sacchi, J. Opt. Soc. Am. B 8, 337 (1991).
    [CrossRef]
  8. C. A. Puliafito, R. F. Steinert, IEEE J. Quantum Electron. QE-20, 1442 (1984).
    [CrossRef]
  9. F. Docchio, C. A. Saachi, J. Marshall, Lasers Opthalmol. 1, 83 (1986); Europhys. Lett. 6, 407 (1988).
  10. B. Zysset, J. G. Fujimoto, T. F. Deutsch, Appl. Phys. B 48, 139 (1989).
    [CrossRef]
  11. S. A. Boppart, C. A. Toth, W. P. Roach, B. A. Rockwell, Proc. Soc. Photo-Opt. Instrum. Eng. 1882, 347 (1993).
  12. E. W. Van Stryland, M. J. Soileau, A. L. Smirl, W. E. Williams, Phys. Rev. B 23, 2144 (1981).
    [CrossRef]
  13. F. A. Ilkov, L. Sh. Ilkov, S. L. Shin, Opt. Lett. 18, 681 (1993).
    [CrossRef] [PubMed]
  14. M. D. Feit, J. A. Fleck, Appl. Phys. Lett. 24, 169 (1974).
    [CrossRef]
  15. J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
    [CrossRef]
  16. P. K. Kennedy, “A first-order model for computation of laser-induced breakdown thresholds in ocular and aqueous media: Part I—Theory,” submitted toIEEE J. Quantum Electron.; P. K. Kennedy, S. A. Boppart, D. X. Hammer, B. A. Rockwell, G. D. Noojin, W. P. Roach, “A first-order model for computation of laser-induced breakdown thresholds in ocular and aqueous media: Part II—Code description and comparison to experiment,” submitted toIEEE J. Quantum Electron.
  17. F. Docchio, Europhys. Lett. 6, 407 (1988).
    [CrossRef]
  18. See, for example,P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), pp. 480–496.
  19. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), pp. 528–540.
  20. P. K. Kennedy, Armstrong Laboratory, Brooks Air Force Base, Texas (personal communication, 1995).
  21. E. Yablonovitch, Phys. Rev. Lett. 60, 795 (1988).
    [CrossRef] [PubMed]

1993 (3)

1991 (1)

1989 (1)

B. Zysset, J. G. Fujimoto, T. F. Deutsch, Appl. Phys. B 48, 139 (1989).
[CrossRef]

1988 (2)

F. Docchio, Europhys. Lett. 6, 407 (1988).
[CrossRef]

E. Yablonovitch, Phys. Rev. Lett. 60, 795 (1988).
[CrossRef] [PubMed]

1987 (1)

R. Birngruber, C. A. Puliafito, A. Gawande, W. Lin, R. W. Schoenlein, J. G. Fujimoto, IEEE J. Quantum Electron. QE-23, 1836 (1987).
[CrossRef]

1986 (1)

F. Docchio, C. A. Saachi, J. Marshall, Lasers Opthalmol. 1, 83 (1986); Europhys. Lett. 6, 407 (1988).

1984 (1)

C. A. Puliafito, R. F. Steinert, IEEE J. Quantum Electron. QE-20, 1442 (1984).
[CrossRef]

1981 (1)

E. W. Van Stryland, M. J. Soileau, A. L. Smirl, W. E. Williams, Phys. Rev. B 23, 2144 (1981).
[CrossRef]

1977 (1)

W. L. Smith, P. Lui, N. Bloembergen, Phys. Rev. A 15, 2396 (1977).
[CrossRef]

1975 (1)

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

1974 (1)

M. D. Feit, J. A. Fleck, Appl. Phys. Lett. 24, 169 (1974).
[CrossRef]

1973 (1)

A. Penzkofer, A. Laubereau, W. Kaiser, Phys. Rev. Lett. 31, 863 (1973).
[CrossRef]

1972 (1)

E. Yablonovitch, N. Bloembergen, Phys. Rev. Lett. 29, 907 (1972).
[CrossRef]

1968 (1)

P. A. Barnes, K. E. Rieckhoff, Appl. Phys. Lett. 13, 282 (1968).
[CrossRef]

Barnes, P. A.

P. A. Barnes, K. E. Rieckhoff, Appl. Phys. Lett. 13, 282 (1968).
[CrossRef]

Birngruber, R.

R. Birngruber, C. A. Puliafito, A. Gawande, W. Lin, R. W. Schoenlein, J. G. Fujimoto, IEEE J. Quantum Electron. QE-23, 1836 (1987).
[CrossRef]

Bloembergen, N.

W. L. Smith, P. Lui, N. Bloembergen, Phys. Rev. A 15, 2396 (1977).
[CrossRef]

E. Yablonovitch, N. Bloembergen, Phys. Rev. Lett. 29, 907 (1972).
[CrossRef]

Boppart, S. A.

S. A. Boppart, C. A. Toth, W. P. Roach, B. A. Rockwell, Proc. Soc. Photo-Opt. Instrum. Eng. 1882, 347 (1993).

Cain, C. P.

Deutsch, T. F.

B. Zysset, J. G. Fujimoto, T. F. Deutsch, Appl. Phys. B 48, 139 (1989).
[CrossRef]

Docchio, F.

F. Docchio, Europhys. Lett. 6, 407 (1988).
[CrossRef]

F. Docchio, C. A. Saachi, J. Marshall, Lasers Opthalmol. 1, 83 (1986); Europhys. Lett. 6, 407 (1988).

Eberly, J. H.

See, for example,P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), pp. 480–496.

Feit, M. D.

M. D. Feit, J. A. Fleck, Appl. Phys. Lett. 24, 169 (1974).
[CrossRef]

Fleck, J. A.

M. D. Feit, J. A. Fleck, Appl. Phys. Lett. 24, 169 (1974).
[CrossRef]

Fujimoto, J. G.

B. Zysset, J. G. Fujimoto, T. F. Deutsch, Appl. Phys. B 48, 139 (1989).
[CrossRef]

R. Birngruber, C. A. Puliafito, A. Gawande, W. Lin, R. W. Schoenlein, J. G. Fujimoto, IEEE J. Quantum Electron. QE-23, 1836 (1987).
[CrossRef]

Gawande, A.

R. Birngruber, C. A. Puliafito, A. Gawande, W. Lin, R. W. Schoenlein, J. G. Fujimoto, IEEE J. Quantum Electron. QE-23, 1836 (1987).
[CrossRef]

Ilkov, F. A.

Ilkov, L. Sh.

Kaiser, W.

A. Penzkofer, A. Laubereau, W. Kaiser, Phys. Rev. Lett. 31, 863 (1973).
[CrossRef]

Kennedy, P. K.

P. K. Kennedy, Armstrong Laboratory, Brooks Air Force Base, Texas (personal communication, 1995).

P. K. Kennedy, “A first-order model for computation of laser-induced breakdown thresholds in ocular and aqueous media: Part I—Theory,” submitted toIEEE J. Quantum Electron.; P. K. Kennedy, S. A. Boppart, D. X. Hammer, B. A. Rockwell, G. D. Noojin, W. P. Roach, “A first-order model for computation of laser-induced breakdown thresholds in ocular and aqueous media: Part II—Code description and comparison to experiment,” submitted toIEEE J. Quantum Electron.

Laubereau, A.

A. Penzkofer, A. Laubereau, W. Kaiser, Phys. Rev. Lett. 31, 863 (1973).
[CrossRef]

Lin, W.

R. Birngruber, C. A. Puliafito, A. Gawande, W. Lin, R. W. Schoenlein, J. G. Fujimoto, IEEE J. Quantum Electron. QE-23, 1836 (1987).
[CrossRef]

Lui, P.

W. L. Smith, P. Lui, N. Bloembergen, Phys. Rev. A 15, 2396 (1977).
[CrossRef]

Marburger, J. H.

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Marshall, J.

F. Docchio, C. A. Saachi, J. Marshall, Lasers Opthalmol. 1, 83 (1986); Europhys. Lett. 6, 407 (1988).

Mayo, M. W.

Milonni, P. W.

See, for example,P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), pp. 480–496.

Noojin, G. D.

Penzkofer, A.

A. Penzkofer, A. Laubereau, W. Kaiser, Phys. Rev. Lett. 31, 863 (1973).
[CrossRef]

Puliafito, C. A.

R. Birngruber, C. A. Puliafito, A. Gawande, W. Lin, R. W. Schoenlein, J. G. Fujimoto, IEEE J. Quantum Electron. QE-23, 1836 (1987).
[CrossRef]

C. A. Puliafito, R. F. Steinert, IEEE J. Quantum Electron. QE-20, 1442 (1984).
[CrossRef]

Rieckhoff, K. E.

P. A. Barnes, K. E. Rieckhoff, Appl. Phys. Lett. 13, 282 (1968).
[CrossRef]

Roach, W. P.

B. A. Rockwell, W. P. Roach, M. E. Rogers, M. W. Mayo, C. A. Toth, C. P. Cain, G. D. Noojin, Opt. Lett. 18, 1792 (1993).
[CrossRef] [PubMed]

S. A. Boppart, C. A. Toth, W. P. Roach, B. A. Rockwell, Proc. Soc. Photo-Opt. Instrum. Eng. 1882, 347 (1993).

Rockwell, B. A.

S. A. Boppart, C. A. Toth, W. P. Roach, B. A. Rockwell, Proc. Soc. Photo-Opt. Instrum. Eng. 1882, 347 (1993).

B. A. Rockwell, W. P. Roach, M. E. Rogers, M. W. Mayo, C. A. Toth, C. P. Cain, G. D. Noojin, Opt. Lett. 18, 1792 (1993).
[CrossRef] [PubMed]

Rogers, M. E.

Saachi, C. A.

F. Docchio, C. A. Saachi, J. Marshall, Lasers Opthalmol. 1, 83 (1986); Europhys. Lett. 6, 407 (1988).

Sacchi, C. A.

Schoenlein, R. W.

R. Birngruber, C. A. Puliafito, A. Gawande, W. Lin, R. W. Schoenlein, J. G. Fujimoto, IEEE J. Quantum Electron. QE-23, 1836 (1987).
[CrossRef]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), pp. 528–540.

Shin, S. L.

Smirl, A. L.

E. W. Van Stryland, M. J. Soileau, A. L. Smirl, W. E. Williams, Phys. Rev. B 23, 2144 (1981).
[CrossRef]

Smith, W. L.

W. L. Smith, P. Lui, N. Bloembergen, Phys. Rev. A 15, 2396 (1977).
[CrossRef]

Soileau, M. J.

E. W. Van Stryland, M. J. Soileau, A. L. Smirl, W. E. Williams, Phys. Rev. B 23, 2144 (1981).
[CrossRef]

Steinert, R. F.

C. A. Puliafito, R. F. Steinert, IEEE J. Quantum Electron. QE-20, 1442 (1984).
[CrossRef]

Toth, C. A.

S. A. Boppart, C. A. Toth, W. P. Roach, B. A. Rockwell, Proc. Soc. Photo-Opt. Instrum. Eng. 1882, 347 (1993).

B. A. Rockwell, W. P. Roach, M. E. Rogers, M. W. Mayo, C. A. Toth, C. P. Cain, G. D. Noojin, Opt. Lett. 18, 1792 (1993).
[CrossRef] [PubMed]

Van Stryland, E. W.

E. W. Van Stryland, M. J. Soileau, A. L. Smirl, W. E. Williams, Phys. Rev. B 23, 2144 (1981).
[CrossRef]

Williams, W. E.

E. W. Van Stryland, M. J. Soileau, A. L. Smirl, W. E. Williams, Phys. Rev. B 23, 2144 (1981).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 60, 795 (1988).
[CrossRef] [PubMed]

E. Yablonovitch, N. Bloembergen, Phys. Rev. Lett. 29, 907 (1972).
[CrossRef]

Zysset, B.

B. Zysset, J. G. Fujimoto, T. F. Deutsch, Appl. Phys. B 48, 139 (1989).
[CrossRef]

Appl. Phys. B (1)

B. Zysset, J. G. Fujimoto, T. F. Deutsch, Appl. Phys. B 48, 139 (1989).
[CrossRef]

Appl. Phys. Lett. (2)

P. A. Barnes, K. E. Rieckhoff, Appl. Phys. Lett. 13, 282 (1968).
[CrossRef]

M. D. Feit, J. A. Fleck, Appl. Phys. Lett. 24, 169 (1974).
[CrossRef]

Europhys. Lett. (1)

F. Docchio, Europhys. Lett. 6, 407 (1988).
[CrossRef]

IEEE J. Quantum Electron. (2)

C. A. Puliafito, R. F. Steinert, IEEE J. Quantum Electron. QE-20, 1442 (1984).
[CrossRef]

R. Birngruber, C. A. Puliafito, A. Gawande, W. Lin, R. W. Schoenlein, J. G. Fujimoto, IEEE J. Quantum Electron. QE-23, 1836 (1987).
[CrossRef]

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

Lasers Opthalmol. (1)

F. Docchio, C. A. Saachi, J. Marshall, Lasers Opthalmol. 1, 83 (1986); Europhys. Lett. 6, 407 (1988).

Opt. Lett. (2)

Phys. Rev. A (1)

W. L. Smith, P. Lui, N. Bloembergen, Phys. Rev. A 15, 2396 (1977).
[CrossRef]

Phys. Rev. B (1)

E. W. Van Stryland, M. J. Soileau, A. L. Smirl, W. E. Williams, Phys. Rev. B 23, 2144 (1981).
[CrossRef]

Phys. Rev. Lett. (3)

A. Penzkofer, A. Laubereau, W. Kaiser, Phys. Rev. Lett. 31, 863 (1973).
[CrossRef]

E. Yablonovitch, N. Bloembergen, Phys. Rev. Lett. 29, 907 (1972).
[CrossRef]

E. Yablonovitch, Phys. Rev. Lett. 60, 795 (1988).
[CrossRef] [PubMed]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

S. A. Boppart, C. A. Toth, W. P. Roach, B. A. Rockwell, Proc. Soc. Photo-Opt. Instrum. Eng. 1882, 347 (1993).

Prog. Quantum Electron. (1)

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Other (4)

P. K. Kennedy, “A first-order model for computation of laser-induced breakdown thresholds in ocular and aqueous media: Part I—Theory,” submitted toIEEE J. Quantum Electron.; P. K. Kennedy, S. A. Boppart, D. X. Hammer, B. A. Rockwell, G. D. Noojin, W. P. Roach, “A first-order model for computation of laser-induced breakdown thresholds in ocular and aqueous media: Part II—Code description and comparison to experiment,” submitted toIEEE J. Quantum Electron.

See, for example,P. W. Milonni, J. H. Eberly, Lasers (Wiley, New York, 1988), pp. 480–496.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), pp. 528–540.

P. K. Kennedy, Armstrong Laboratory, Brooks Air Force Base, Texas (personal communication, 1995).

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 (2)

Fig. 1
Fig. 1

Theoretical curves of the critical power PLIB for LIB normalized to the critical power Pcr for SF versus the focal length f for pulse lengths tp = 10, 50, 100 ps, an input spot size w0 = 200 μm, and an initial plasma density n0 = 1014 cm−3. The filled circles are obtained from Eqs. (1) and (2): For given focal length f and pulse duration tp we chose Pin = PLIB and obtained the absorbed energy percentage η and peak electron density np numerically. These are presented as (η, np) with SF and [η, np] without SF, where np is in units of 1018 cm−3.

Fig. 2
Fig. 2

Nonlinear pulse propagation in water for tp = 10 ps, f = 4 cm, Pin = 1.5Pcr, and PLIB/Pcr = 2.3: (a) On-axis intensity |ℰ(0, z, 0)|2 (solid curve, left scale) and on-axis electron density n = (0, z, 0) (dotted curve, right scale) versus propagation distance z and (b) grayscale plot of the on-axis pulse spectrum |ɛ(0, z, Ω)|2 versus propagation distance, with Ω the pulse frequency with respect to the carrier.

Equations (8)

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

E z = i 2 k T 2 E - σ 2 ( 1 + i ω τ ) n E + i k 0 n 2 E 2 E ,
n t = ( ln 2 ) σ E g n E 2 - a n 2 .
E ( r , 0 , t ) = 2 P in π w 0 2 exp ( - r 2 w 0 2 - t 2 t p 2 - i k r 2 2 f ) ,
1 f NL = 1 f + 1 z NL ( P in ) ,
n cr ( 1 σ z 0 ) 1 + f 2 / z 0 2 f 2 / z 0 2 .
n f ( t ) = n 0 exp [ ( ln 2 ) σ 2 E g - t d t I f ( t ) ] ,
I LIB 8 π 2 ln 2 E g σ t p ln n cr n 0 .
P LIB 4 E g t p π w 0 2 σ f 2 / z 0 2 1 + f 2 / z 0 2 ln n cr n 0 .

Metrics