Abstract

A focused ultrashort pulse can reach high enough intensity that non-linear ionization dominates its interaction with transparent media while still having relatively low fluence. In this case, the energy extracted from the beam can counter self-focusing by energy depletion and plasma formation, providing controlled energy deposition that can modify the material in a highly local manner. We demonstrate that non-linear absorption limits the intensity that can be reached and that the energy is deposited prior to the focus. We model the energy distribution, and predict and measure the energy transmitted through the focus. We establish the threshold intensity for non-linear ionization in dielectrics at ~1013 W cm-2. We use the refractive index modification that the non-linear ionization causes in glass to image the spatial distribution of the energy deposition.

© 2005 Optical Society of America

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References

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  1. K. M. Davis, K. Miura, N. Suguimoto, and K. Hirao, �??Writing waveguides in glass with a femtosecond laser,�?? Opt. Lett. 21, 1729�??1731 (1996).
    [CrossRef] [PubMed]
  2. A. M. Streltsov and N. F. Borrelli, �??Study of femtosecond-laser-written waveguides in glasses,�?? J. Opt. Soc. Am. B 19, 2496�??2504 (2002).
    [CrossRef]
  3. V. R. Bhardwaj, P. B. Corkum, D. M. Rayner, C. Hnatovsky, E. Simova, and R. S. Taylor, �??Stress in femtosecond-laser-written waveguides in fused silica,�?? Opt. Lett. 29, 1312�??1314 (2004).
    [CrossRef] [PubMed]
  4. R. S. Taylor, C. Hnatovsky, E. Simova, D. M. Rayner, V. R. Bhardwaj, and P. B. Corkum, �??Femtosecond laser fabrication of nanostructures in silica glass,�?? Opt. Lett. 28, 1043�??1045 (2003).
    [CrossRef] [PubMed]
  5. A. Marcinkevi�?ius, S. Juodkazis, M. Watanabe, M. Miwa, S. Matsuo, and H. Misawa, �??Femtosecond laser-assisted three-dimensional microfabrication in silica,�?? Opt. Lett. 26, 277�??279 (2001).
    [CrossRef]
  6. N. Shen, C. B. Schaffer, D. Datta, and E. Mazur, �??Photodisruption in biological tissues and single cells using femtosecond laser pulses,�?? in Conference on Lasers and Electro-Optics, pp. 403�??404 (Baltimore, MD, 2001).
  7. M. F. Yanik, H. Cinar, H. N. Cinar, A. D. Chisholm, Y. Jin, and A. Ben-Yakar, �??Neurosurgery: Functional regeneration after laser axotomy,�?? Nature 432, 822 (2004).
    [CrossRef] [PubMed]
  8. V. Keldysh, �??Ionization in the field of a strong electromagnetic wave,�?? Sov. Phys. JETP 20, 1307�??1314 (1965).
  9. D. von der Linde and H. Schüler, �??Breakdown threshold and plasma formation in femtosecond laser-solid interaction,�?? J. Opt. Soc. Am. B 13, 216�??222 (1996).
    [CrossRef]
  10. J. Krüger andW. Kautek, �??Femtosecond-pulse visible laser processing of transparent materials,�?? Appl. Surf. Sci. 96-98, 430�??438 (1996).
    [CrossRef]
  11. S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, �??Tunneling ionization of noble gases in a high-intensity laser field,�?? Phys. Rev. Lett. 63, 2212�??2215 (1989).
    [CrossRef] [PubMed]
  12. P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, �??Supercontinuum generation in gases,�?? Phys. Rev. Lett. 57, 2268�??2271 (1986).
    [CrossRef] [PubMed]
  13. O. M. Efimov, L. B. Glebov, S. Grantham, and M. Richardson, �??Photoionization of silicate glasses exposed to IR femtosecond pulses,�?? J. Non-crystal. Solids 253, 58�??67 (1999).
    [CrossRef]
  14. A. Vogel, J. Noack, K. Nahen, D. Theisen, S. Busch, U. Parlitz, D. Hammer, G. Noojin, B. Rockwell, and R. Birngruber, �??Energy balance of optical breakdown in water at nanosecond to femtosecond time scales,�?? Appl. Phys. B 68, 271�??280 (1999).
    [CrossRef]
  15. L. N. Gaier, M. Lein, M. I. Stockman, P. L. Knight, P. B. Corkum, M. Y. Ivanov, and G. L. Yudin, �??Ultrafast multiphoton forest fires and fractals in clusters and dielectrics,�?? J. Phys. B: At. Mol. Phys. 37, L57�??L67 (2004).
    [CrossRef]
  16. G. L. Yudin, L. N. Gaier, M. Lein, P. L. Knight, P. B. Corkum, and M. Y. Ivanov, �??Hole-Assisted Energy Deposition in Clusters and Dielectrics in Multiphoton Regime,�?? Laser Physics 14, 51-56 (2004).
  17. W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, S. L. Chin, �??Intensity clamping of a femtosecond laser pulse in condensed matter,�?? Opt. Commun. 202, 189�??197 (2002).
    [CrossRef]
  18. M. Lenzner, J. Krger, S. Sartania, Z. Cheng, C. Spielmann, G. Mourou,W. Kautek, and F. Krausz, �??Femtosecond Optical Breakdown in Dielectrics,�?? Phys. Rev. Lett. 80, 4076�??4079 (1998).
    [CrossRef]

Appl. Phys. B

A. Vogel, J. Noack, K. Nahen, D. Theisen, S. Busch, U. Parlitz, D. Hammer, G. Noojin, B. Rockwell, and R. Birngruber, �??Energy balance of optical breakdown in water at nanosecond to femtosecond time scales,�?? Appl. Phys. B 68, 271�??280 (1999).
[CrossRef]

Appl. Surf. Sci.

J. Krüger andW. Kautek, �??Femtosecond-pulse visible laser processing of transparent materials,�?? Appl. Surf. Sci. 96-98, 430�??438 (1996).
[CrossRef]

CLEO

N. Shen, C. B. Schaffer, D. Datta, and E. Mazur, �??Photodisruption in biological tissues and single cells using femtosecond laser pulses,�?? in Conference on Lasers and Electro-Optics, pp. 403�??404 (Baltimore, MD, 2001).

J. Non-crystal. Solids

O. M. Efimov, L. B. Glebov, S. Grantham, and M. Richardson, �??Photoionization of silicate glasses exposed to IR femtosecond pulses,�?? J. Non-crystal. Solids 253, 58�??67 (1999).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B: At. Mol. Phys.

L. N. Gaier, M. Lein, M. I. Stockman, P. L. Knight, P. B. Corkum, M. Y. Ivanov, and G. L. Yudin, �??Ultrafast multiphoton forest fires and fractals in clusters and dielectrics,�?? J. Phys. B: At. Mol. Phys. 37, L57�??L67 (2004).
[CrossRef]

Laser Physics

G. L. Yudin, L. N. Gaier, M. Lein, P. L. Knight, P. B. Corkum, and M. Y. Ivanov, �??Hole-Assisted Energy Deposition in Clusters and Dielectrics in Multiphoton Regime,�?? Laser Physics 14, 51-56 (2004).

Nature

M. F. Yanik, H. Cinar, H. N. Cinar, A. D. Chisholm, Y. Jin, and A. Ben-Yakar, �??Neurosurgery: Functional regeneration after laser axotomy,�?? Nature 432, 822 (2004).
[CrossRef] [PubMed]

Opt. Commun.

W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, S. L. Chin, �??Intensity clamping of a femtosecond laser pulse in condensed matter,�?? Opt. Commun. 202, 189�??197 (2002).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

M. Lenzner, J. Krger, S. Sartania, Z. Cheng, C. Spielmann, G. Mourou,W. Kautek, and F. Krausz, �??Femtosecond Optical Breakdown in Dielectrics,�?? Phys. Rev. Lett. 80, 4076�??4079 (1998).
[CrossRef]

S. Augst, D. Strickland, D. D. Meyerhofer, S. L. Chin, and J. H. Eberly, �??Tunneling ionization of noble gases in a high-intensity laser field,�?? Phys. Rev. Lett. 63, 2212�??2215 (1989).
[CrossRef] [PubMed]

P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, �??Supercontinuum generation in gases,�?? Phys. Rev. Lett. 57, 2268�??2271 (1986).
[CrossRef] [PubMed]

Sov. Phys. JETP

V. Keldysh, �??Ionization in the field of a strong electromagnetic wave,�?? Sov. Phys. JETP 20, 1307�??1314 (1965).

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Figures (6)

Fig. 1.
Fig. 1.

Self-limitation of non-linear absorption of a focused laser beam in transparent dielectric material. The intensity dependence of a highly non-linear absorption is approximated by a step function. Far from the focus absorption is negligible because the intensity is below the threshold for non-linear absorption, Ih . As the beam approaches the focus and Ih is exceeded the intensity is clamped at Ih energy is removed from the beam.

Fig. 2.
Fig. 2.

a) Transmission of a high intensity femtosecond laser pulse through a 0.8 mm thick Pyrex sample as a function of focal position for a range of pulse energies. b) Adsorption when the focus was centered in the sample as a function of intensity. The points are the experimental measurements and the solid line is the result of the model described in the text with the threshold intensity, Ih set at 9.8×1012 W cm-2. The dashed curve is obtained by numerical analysis using the ionization probabilities predicted by Keldysh theory for Pyrex glass (Bandgap ≈4.5 eV). In all cases the sample was moved orthogonally to the laser beam to expose a fresh volume of the sample on every shot.

Fig. 3.
Fig. 3.

Spectrum of a femtosecond laser pulse (1.5 µJ, 40 fs) following transmission through a focus (NA 0.25) in fused silica (blue curve). The 37 MW pulse contains 15 times the critical power for self-focusing. The red curve shows the spectrum of the pulse prior to entering the sample.

Fig. 4.
Fig. 4.

Modelled energy distributions following highly non-linear absorption of a focused, short-pulse laser beam in dielectric material at pulse energies of (a) 100 nJ, (b) 250 nJ and (c) 1000 nJ. The contours are at 50 J cm-3 intervals. The distributions are over z, the distance from the nominal focal plane, and r, the radial distance from the beam axis. With a pulse duration of 50 fs (full width at 1/e) and a beam radius, ω0, of 1.6 µm the corresponding peak intensities are (a) 2.8×1013 W cm-2, (b) 7×1013 W cm-2 and (c) 28×1013 W cm-2. The threshold intensity was 0.98×1013 W cm-2 corresponding to an energy threshold of 35 nJ. These are the threshold and beam parameters used to model the experimental transmission results in Fig. 2. The shaded areas mark regions where the energy density is >250 J cm-3. At 800 nm this is equivalent to an absorption of 1021 photons per cm3 and creation of a carriers density of ~1/10 the critical density.

Fig. 5.
Fig. 5.

Modelled peak energy densities, Nmax , as a function of peak focused laser pulse intensity (top scale) or pulse energy (bottom scale) for several threshold intensities, Ih . The right scale gives the density in terms of photons absorbed. The laser pulse has the same characteristics as in Fig. 4.

Fig. 6.
Fig. 6.

Optical micrograph showing modification inside BK7 glass by a 1.3 µJ, 50 fs FWHM femtosecond laser pulse. To increase contrast in the micrograph a stack of 50 single shots made at a spacing of 4 µm is viewed from the side. The beam diameter was 3.2 µm so there is little overlap between the shots, especially at the focus. The contours depict the plasma density as predicted by the non-linear adsorption model described in the text. The contours are at densities from 0.8×1020 to 7.5×1020 cm-3 in steps of 1.7×1020 cm-3 and are offset from the laser axis for clarity.

Equations (9)

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d E A d t = π ω 0 2 ( I 0 e t 2 τ 2 I h ) π r h 2 I h .
d E A d t = π ω 0 2 e t 2 τ 2 { 1 I h I 0 e t 2 τ 2 ( 1 + ln I 0 e t 2 τ 2 I h ) } .
E A = E 0 { erf ( ln I 0 I h ) 2 π I h I 0 ( 1 + 2 3 ln I 0 I h ) ln I 0 I h } .
I ( z , r , t ) = I 0 1 + z 2 z 0 2 exp r 2 ω 0 2 ( 1 + z 2 z 0 2 ) exp t 2 τ 2
I z = 2 z z 0 2 + z 2 I .
I a z = 2 z z 0 2 + z 2 I h [ r < r h ; t h < t < t h ]
= 0 [ r r h ; t t h ] .
N ( z , r ) = 4 I h τ z z 0 2 + z 2 ln ( I 0 I h ( 1 + z 2 z 0 2 ) ) r 2 ω 0 2 ( 1 + z 2 z 0 2 ) .
ln ( I 0 I h ( 1 + z max 2 z 0 2 ) ) = z max 2 ( z 0 2 z max 2 )

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