Abstract

We report an investigation of white-light continuum generation and self-focusing by 140-fs Ti:sapphire laser pulses in extended transparent media. It is found that continuum generation is triggered by self-focusing and that both phenomena depend on the medium’s bandgap. There is a bandgap threshold for continuum generation. Above that threshold the continuum’s width increases with increasing bandgap. Furthermore, the beam’s self-focal diameter is discontinuous across the threshold. To explain the observations a mechanism is proposed that involves multiphoton excitation of electrons into the conduction band at the self-focus; the generated free electrons cause spectral superbroadening and limit the self-focal diameter. The continuum beam’s surprisingly low divergence is then investigated and explained in terms of a Kerr lensing effect.

© 1999 Optical Society of America

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1998 (3)

1997 (4)

1996 (3)

A. Brodeur, F. A. Ilkov, and S. L. Chin, Opt. Commun. 129, 193 (1996).
[CrossRef]

M. Wittman and A. Penzkofer, Opt. Commun. 126, 308 (1996).
[CrossRef]

J. Ranka, R. W. Schirmer, and A. Gaeta, Phys. Rev. Lett. 77, 3783 (1996).
[CrossRef] [PubMed]

1995 (1)

E. N. Glezer, Y. Siegal, L. Huang, and E. Mazur, Phys. Rev. B 51, 6959 (1995).
[CrossRef]

1994 (1)

1993 (4)

1992 (2)

1988 (1)

1986 (1)

1984 (1)

1983 (1)

1977 (1)

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

1975 (2)

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

Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975).
[CrossRef]

1973 (2)

N. Bloembergen, Opt. Commun. 8, 285 (1973).
[CrossRef]

F. H. M. Faisal, J. Phys. B 6, L89 (1973).
[CrossRef]

1972 (1)

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

1970 (2)

V. I. Talanov, JETP Lett. 11, 199 (1970).

R. R. Alfano and S. L. Shapiro, Phys. Rev. Lett. 24, 584 (1970).
[CrossRef]

1969 (1)

M. Maier, W. Kaiser, and J. A. Giordmaine, Phys. Rev. 177, 580 (1969).
[CrossRef]

1968 (1)

R. G. Brewer and C. H. Lee, Phys. Rev. Lett. 21, 267 (1968).
[CrossRef]

1967 (1)

F. Shimizu, Phys. Rev. Lett. 19, 1097 (1967).
[CrossRef]

1966 (2)

Yu. P. Raizer, Sov. Phys. Usp. 8, 650 (1966).
[CrossRef]

E. Garmire, R. Y. Chiao, and C. H. Townes, Phys. Rev. Lett. 16, 347 (1966).
[CrossRef]

1965 (1)

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

Alfano, R. R.

Beidoun, A.

A. Penzkofer, A. Beidoun, and H.-J. Lehmeier, Opt. Quantum Electron. 25, 317 (1993).
[CrossRef]

Bloembergen, N.

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

N. Bloembergen, Opt. Commun. 8, 285 (1973).
[CrossRef]

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

Brewer, R. G.

R. G. Brewer and C. H. Lee, Phys. Rev. Lett. 21, 267 (1968).
[CrossRef]

Brodeur, A.

Chernev, P.

Chiao, R. Y.

E. Garmire, R. Y. Chiao, and C. H. Townes, Phys. Rev. Lett. 16, 347 (1966).
[CrossRef]

Chien, C.-Y.

Chin, S. L.

Clement, T. S.

Cook, K.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, and C. R. Thompson, IEEE J. Quantum Electron. 33, 127 (1997).
[CrossRef]

Cui, Y.

Diddams, S. A.

Eaton, H. K.

Faisal, F. H. M.

F. H. M. Faisal, J. Phys. B 6, L89 (1973).
[CrossRef]

Feit, M. D.

Feng, Q.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, and C. R. Thompson, IEEE J. Quantum Electron. 33, 127 (1997).
[CrossRef]

Fleck, J. A.

Fork, R. L.

Gaeta, A.

J. Ranka, R. W. Schirmer, and A. Gaeta, Phys. Rev. Lett. 77, 3783 (1996).
[CrossRef] [PubMed]

Gaeta, A. L.

Garmire, E.

E. Garmire, R. Y. Chiao, and C. H. Townes, Phys. Rev. Lett. 16, 347 (1966).
[CrossRef]

Giordmaine, J. A.

M. Maier, W. Kaiser, and J. A. Giordmaine, Phys. Rev. 177, 580 (1969).
[CrossRef]

Glezer, E. N.

E. N. Glezer, Y. Siegal, L. Huang, and E. Mazur, Phys. Rev. B 51, 6959 (1995).
[CrossRef]

Hammer, D. X.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, and C. R. Thompson, IEEE J. Quantum Electron. 33, 127 (1997).
[CrossRef]

He, G. S.

Hirlimann, C.

Ho, P. P.

Huang, L.

E. N. Glezer, Y. Siegal, L. Huang, and E. Mazur, Phys. Rev. B 51, 6959 (1995).
[CrossRef]

Ilkov, F. A.

Ilkova, L. Sh.

Jimbo, T.

Kaiser, W.

M. Maier, W. Kaiser, and J. A. Giordmaine, Phys. Rev. 177, 580 (1969).
[CrossRef]

Kandidov, V. P.

Keldysh, L. V.

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

Kennedy, P. K.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, and C. R. Thompson, IEEE J. Quantum Electron. 33, 127 (1997).
[CrossRef]

Kosareva, O. G.

Lee, C. H.

R. G. Brewer and C. H. Lee, Phys. Rev. Lett. 21, 267 (1968).
[CrossRef]

Lehmeier, H.-J.

A. Penzkofer, A. Beidoun, and H.-J. Lehmeier, Opt. Quantum Electron. 25, 317 (1993).
[CrossRef]

Li, Q. X.

Liu, P.

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

Luther, G. G.

Maier, M.

M. Maier, W. Kaiser, and J. A. Giordmaine, Phys. Rev. 177, 580 (1969).
[CrossRef]

Marburger, J. H.

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

Mazur, E.

E. N. Glezer, Y. Siegal, L. Huang, and E. Mazur, Phys. Rev. B 51, 6959 (1995).
[CrossRef]

Moloney, J. V.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, and C. R. Thompson, IEEE J. Quantum Electron. 33, 127 (1997).
[CrossRef]

G. G. Luther, J. V. Moloney, A. C. Newell, and E. M. Wright, Opt. Lett. 19, 862 (1994).
[CrossRef] [PubMed]

Newell, A. C.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, and C. R. Thompson, IEEE J. Quantum Electron. 33, 127 (1997).
[CrossRef]

G. G. Luther, J. V. Moloney, A. C. Newell, and E. M. Wright, Opt. Lett. 19, 862 (1994).
[CrossRef] [PubMed]

Penzkofer, A.

M. Wittman and A. Penzkofer, Opt. Commun. 126, 308 (1996).
[CrossRef]

A. Penzkofer, A. Beidoun, and H.-J. Lehmeier, Opt. Quantum Electron. 25, 317 (1993).
[CrossRef]

Petrov, V.

Prasad, P. N.

Raizer, Yu. P.

Yu. P. Raizer, Sov. Phys. Usp. 8, 650 (1966).
[CrossRef]

Ranka, J.

J. Ranka, R. W. Schirmer, and A. Gaeta, Phys. Rev. Lett. 77, 3783 (1996).
[CrossRef] [PubMed]

Ranka, J. K.

Rockwell, B. A.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, and C. R. Thompson, IEEE J. Quantum Electron. 33, 127 (1997).
[CrossRef]

Rothenberg, J.

Schirmer, R. W.

J. Ranka, R. W. Schirmer, and A. Gaeta, Phys. Rev. Lett. 77, 3783 (1996).
[CrossRef] [PubMed]

Shank, C. V.

Shapiro, S. L.

R. R. Alfano and S. L. Shapiro, Phys. Rev. Lett. 24, 584 (1970).
[CrossRef]

Shen, Y. R.

Shimizu, F.

F. Shimizu, Phys. Rev. Lett. 19, 1097 (1967).
[CrossRef]

Siegal, Y.

E. N. Glezer, Y. Siegal, L. Huang, and E. Mazur, Phys. Rev. B 51, 6959 (1995).
[CrossRef]

Smith, W. L.

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

Talanov, V. I.

V. I. Talanov, JETP Lett. 11, 199 (1970).

Thompson, C. R.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, and C. R. Thompson, IEEE J. Quantum Electron. 33, 127 (1997).
[CrossRef]

Tomlinson, W. J.

Townes, C. H.

E. Garmire, R. Y. Chiao, and C. H. Townes, Phys. Rev. Lett. 16, 347 (1966).
[CrossRef]

Wilson, K. R.

Wittman, M.

M. Wittman and A. Penzkofer, Opt. Commun. 126, 308 (1996).
[CrossRef]

Wright, E. M.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, and C. R. Thompson, IEEE J. Quantum Electron. 33, 127 (1997).
[CrossRef]

G. G. Luther, J. V. Moloney, A. C. Newell, and E. M. Wright, Opt. Lett. 19, 862 (1994).
[CrossRef] [PubMed]

Xing, Q.

Xu, G. C.

Yablonovitch, E.

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

Yakovlev, V. V.

Yang, G. Y.

Yen, R.

Yoo, K. M.

Zozulya, A. A.

Appl. Opt. (3)

IEEE J. Quantum Electron. (1)

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, and C. R. Thompson, IEEE J. Quantum Electron. 33, 127 (1997).
[CrossRef]

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

J. Phys. B (1)

F. H. M. Faisal, J. Phys. B 6, L89 (1973).
[CrossRef]

JETP Lett. (1)

V. I. Talanov, JETP Lett. 11, 199 (1970).

Opt. Commun. (3)

A. Brodeur, F. A. Ilkov, and S. L. Chin, Opt. Commun. 129, 193 (1996).
[CrossRef]

M. Wittman and A. Penzkofer, Opt. Commun. 126, 308 (1996).
[CrossRef]

N. Bloembergen, Opt. Commun. 8, 285 (1973).
[CrossRef]

Opt. Lett. (10)

Opt. Quantum Electron. (1)

A. Penzkofer, A. Beidoun, and H.-J. Lehmeier, Opt. Quantum Electron. 25, 317 (1993).
[CrossRef]

Phys. Rev. (1)

M. Maier, W. Kaiser, and J. A. Giordmaine, Phys. Rev. 177, 580 (1969).
[CrossRef]

Phys. Rev. A (1)

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

Phys. Rev. B (1)

E. N. Glezer, Y. Siegal, L. Huang, and E. Mazur, Phys. Rev. B 51, 6959 (1995).
[CrossRef]

Phys. Rev. Lett. (7)

A. Brodeur and S. L. Chin, Phys. Rev. Lett. 80, 4406 (1998).
[CrossRef]

R. G. Brewer and C. H. Lee, Phys. Rev. Lett. 21, 267 (1968).
[CrossRef]

E. Garmire, R. Y. Chiao, and C. H. Townes, Phys. Rev. Lett. 16, 347 (1966).
[CrossRef]

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

R. R. Alfano and S. L. Shapiro, Phys. Rev. Lett. 24, 584 (1970).
[CrossRef]

J. Ranka, R. W. Schirmer, and A. Gaeta, Phys. Rev. Lett. 77, 3783 (1996).
[CrossRef] [PubMed]

F. Shimizu, Phys. Rev. Lett. 19, 1097 (1967).
[CrossRef]

Prog. Quantum Electron. (2)

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

Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975).
[CrossRef]

Sov. Phys. JETP (1)

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

Sov. Phys. Usp. (1)

Yu. P. Raizer, Sov. Phys. Usp. 8, 650 (1966).
[CrossRef]

Other (14)

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

D. Strickland and P. B. Corkum, Proc. SPIE 1413, 54 (1991); J. Opt. Soc. Am. B 11, 492 (1994).
[CrossRef]

M. M. T. Loy and Y. R. Shen, Phys. Rev. Lett. 22, 994 (1969); 25, 1333 (1970); Appl. Phys. Lett. 19, 285 (1971).
[CrossRef]

A. Brodeur and S. L. Chin, in Quantum Electronics and Laser Science Conference (QELS) Vol. 12 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), p. 71.

Q. Z. Wang, P. P. Ho, and R. R. Alfano, in Ref. 2, pp. 39–90.

P. K. Kennedy, IEEE J. Quantum Electron. 31, 2241 (1995); P. K. Kennedy, S. A. Boppart, D. X. Hammer, B. A. Rockwell, G. D. Noojin, and W. P. Roach, IEEE J. Quantum Electron. 31, 2250 (1995).
[CrossRef]

R. R. Alfano, ed., The Supercontinuum Laser Source (Springer-Verlag, New York, 1989).

A. Penzkofer, A. Laubereau, and W. Kaiser, Phys. Rev. Lett. 31, 863 (1973); A. Penzkofer, Opt. Commun. 11, 275 (1974); A. Penzkofer, A. Seilmeier, and W. Kaiser, Opt. Commun. OPCOB8 14, 363 (1975).
[CrossRef]

V. François, F. A. Ilkov, and S. L. Chin, J. Phys. B 25, 2709 (1992); Opt. Commun. 99, 241 (1993).
[CrossRef]

P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, Phys. Rev. Lett. 57, 2268 (1986); P. B. Corkum and C. Rolland, IEEE J. Quantum Electron. 25, 2634 (1989); in Ref. 2, pp. 318–336.
[CrossRef] [PubMed]

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, Philadelphia, Pa., 1976).

R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992).

The band gap is readily obtained from the absorption spectrum of the medium, which generally shows a sharp absorption edge in the UV that corresponds to the edge of the conduction band. We apply the same definition of Egap to crystals, liquids, and amorphous solids, although the band structures are not so clearly defined in liquids and amorphous solids as in crystals. The relevant physical quantity is the energy that corresponds to the absorption edge. The absorption spectra are obtained from measurements with a spectrophotometer and from the Photoelectric Spectrom etry Group (London) and the Institut fur Spektrochemie und Angewandte Spektroskopie (Dortmund), UV Atlas of Organic Compounds (Butterworth, London, 1966), Vol. 1, Sec. M; O. Madelung, ed., Landolt–Bornstein Numerical Data and Functional Relationships in Science and Technology, New Series (Springer-Verlag, Berlin, 1962), Vol. I/4, p. 872; H. H. Jaffé and M. Orchin, Theory and Application of Ultraviolet Spectroscopy (Wiley, New York, 1962); J. A. R. Samson, Techniques of Ultraviolet Spectroscopy (Wiley, New York, 1967); L. R. Koller, Ultraviolet Radiation (Wiley, New York, 1965).

D. H. Auston, in Ultrashort Light Pulses, S. L. Shapiro, ed. (Springer-Verlag, New York, 1977), pp. 123–201.

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Figures (10)

Fig. 1
Fig. 1

Experimental setup for measuring the evolution of the beam profile, the pulse spectrum, and the pulse energy during propagation.

Fig. 2
Fig. 2

(a) Beam diameter d (FWHM) at the position of the geometrical focus, as a function of input peak power. Squares, C2HCl3 (trichloroethylene); circles, water. (b) Beam profile in water with diameter dmin when P=1.1Pthsf.

Fig. 3
Fig. 3

Typical white-light continuum spectra generated in water, UV-grade fused silica, and NaCl at P=1.1Pthwl. (a) Central part. The curves are shifted vertically for clarity. (b) Anti-Stokes part. The intense wavelength components around the laser wavelength are suppressed with a BG18 color filter, which eliminates λ>630 nm. (c) Stokes part. The intense wavelength components around the laser wavelength are suppressed with a RG850 color filter, which eliminates λ<850 nm. All spectra are corrected for filter, CCD, and grating responses.

Fig. 4
Fig. 4

Anti-Stokes part of the continuum generated in LiF at P=1.1Pthwl.

Fig. 5
Fig. 5

Evolution of FWHM beam width d, anti-Stokes broadening Δω+, and the pulse energy with propagation distance in water at P=1.1Pthwl. z0 is the position of the geometrical focus, measured with a precision of ±200 µm.

Fig. 6
Fig. 6

Spectra generated in trichloroethylene and in SF-11 glass at P=1.1Pthsf. Note the absence of a long anti-Stokes wing.

Fig. 7
Fig. 7

(a) Δω+ versus bandgap in various media: a, LiF; b, CaF2; c, UV-grade fused silica; d, water; e, D2O; f, 1-propanol; g, methanol; h, NaCl; i, 1,4-dioxane; j, chloroform; k, CCl4; l, C2HCl3; m, benzene; n, CS2; o, SF-11 glass. (b) Intensity Istop required in Keldysh theory for MPE rate W=1018 cm-3 fs-1 as a function of bandgap (solid curve). The curves for W=1017 and W=1019 cm-3 fs-1 are displayed for comparison. The top axis shows the bandgap normalized to the laser photon energy.

Fig. 8
Fig. 8

Intensity and MPE rate at which self-focusing stops in water. Solid curve, the MPE rate versus intensity in water, calculated from the Keldysh theory of MPE. Dashed curve, the MPE rate versus intensity for which the Kerr index and the plasma index cancel in water, from Eq. (9) (assuming that MPE occurs in half of an optical cycle). The point where the two curves cross gives the intensity and MPE rate when self-focusing stops. We use n2=2×10-16 cm2/W, extracted from the measured critical power in water.

Fig. 9
Fig. 9

(a) Time dependence of the total change in refractive index at a self-focus in the simulation. (b) Continuum spectra generated water at P=1.1Pcrit in the experiment, in a one-dimensional simulation including the moving-focus dynamics under MPE conditions, and in simple SPM. (c) Simulated spectra associated with the following respective values of trise, tfall and Istop: 1, 100 fs, 1.3 fs, 1013 W/cm2; 2, 100 fs, 5 fs, 1013 W/cm2; 3, 50 fs, 5 fs, 1013 W/cm2; 4, 100 fs, 5 fs, 2×1013 W/cm2. The spectra are vertically shifted for clarity.

Fig. 10
Fig. 10

(a) Setup used for divergence measurements. ζ is the distance between the sample’s output surface and the geometrical focus. (b) Divergence of the continuum beam generated in UV-grade fused silica. The divergence is shown as a function of wavelength for various values of distance ζ from the output surface of the sample to the geometrical focus.

Tables (1)

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Table 1 Self-Focal Characteristics Measured in Various Media at P=1.1Ptha

Equations (11)

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Pcrit=3.77λ028πn0n2,
zf(P)=0.367ka02[(P/Pcrit-0.852)2-0.0219]1/2,
zf=zffzf+f.
Δne=-2πe2Nen0me(ω02+ν2),
ϕNL(τ)=0Ln2I(z, τ)ω0cdz,
Δω-SPM=-dϕNLdτmin
Δω+SPM=-dϕNLdτmax.
Δω±SPMω0=1/2(Q2+4±|Q|)-1,
n2I=2πe2Nen0meω02.
W[cm-3/fs]Ne[cm-3](1.3fs).
W[cm-3/fs]n0meω02n2I2πe2(1.3fs).

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