Abstract

We present the results of Z-scan studies carried out on fused silica at 1064nm and 532nm with two different nanosecond pulse durations. Such measurements in silica and in the nanosecond regime are possible thanks to a high sensitivity setting up of the Z-scan method and in-situ characterizations of the spatio-temporal parameters of the beam. Besides, with the use of a newly adapted numerical simulation only the calibration errors of the measurement devices are significant. In these conditions, we found a higher value of the nonlinear refractive index than in the femtosecond regime and we show that these values depend on pulse duration, which indicates the contribution of nanosecond mechanisms like electrostriction.

© 2004 Optical Society of America

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References

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  1. P. N. Butcher and D. Cotter, The elements of nonlinear optics (Cambridge University Press, 1990).
    [Crossref]
  2. R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
    [Crossref]
  3. A. Feldman, D. Horowitz, and R. M. Waxler, “Mechanisms for self-focusing in optical glasses,” IEEE J. Quantum Electron. QE-9, 1054–1061 (November 1973).
    [Crossref]
  4. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 4, 760–769 (April 1990).
    [Crossref]
  5. N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601–608, 1978.
    [Crossref]
  6. L. Gallais, J.Y. Natoli, and C. Amra, “Statistical study of single and multiple pulse laser-induced damage in glasses,” Opt. Express 10, 1465–1474 (2002), http://www.opticsexpress.org
    [Crossref] [PubMed]
  7. T. Olivier, F. Billard, and H. Akhouayri, “Z-scan theoretical and experimental studies for accurate measurements of nonlinear refractive index and absorption of optical glasses near damage threshold,” presented at the 35th Laser Damage Symposium, Boulder, United-States, Sept 2003.
  8. B. K. Rhee, J. S. Byun, and E. W. Van Stryland, “Z-scan using circularly symmetric beams,” J. Opt. Soc. Am. B 13, 2720–2723 (December 1996).
    [Crossref]
  9. M. D. Feit and J. A. Fleck, “Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beams,” J. Opt. Soc. Am. B 5, 3, 633–640 (March 1988).
    [Crossref]
  10. A. J. S. Hamilton, “Uncorrelated modes of the nonlinear power spectrum,” Mon. Not. R. Astron. Soc. 312, 257, (2000).
    [Crossref]
  11. D. Milam and M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry: Application to optical materials for high-power neodynium lasers,” J. Appl. Phys. 47, 6, 2497–2501 (June 1976).
    [Crossref]
  12. W. T. White III, W. L Smith, and D. Milam, “Direct measurement of the nonlinear refractive-index coefficient gamma at 355 nm in fused silica and BK-10 glass,” Opt. Lett. 9, 11, 10–12 (January 1984).
    [Crossref]

2002 (1)

2000 (1)

A. J. S. Hamilton, “Uncorrelated modes of the nonlinear power spectrum,” Mon. Not. R. Astron. Soc. 312, 257, (2000).
[Crossref]

1996 (1)

1990 (1)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 4, 760–769 (April 1990).
[Crossref]

1988 (1)

1984 (1)

1978 (1)

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601–608, 1978.
[Crossref]

1976 (1)

D. Milam and M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry: Application to optical materials for high-power neodynium lasers,” J. Appl. Phys. 47, 6, 2497–2501 (June 1976).
[Crossref]

1973 (1)

A. Feldman, D. Horowitz, and R. M. Waxler, “Mechanisms for self-focusing in optical glasses,” IEEE J. Quantum Electron. QE-9, 1054–1061 (November 1973).
[Crossref]

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[Crossref]

Akhouayri, H.

T. Olivier, F. Billard, and H. Akhouayri, “Z-scan theoretical and experimental studies for accurate measurements of nonlinear refractive index and absorption of optical glasses near damage threshold,” presented at the 35th Laser Damage Symposium, Boulder, United-States, Sept 2003.

Amra, C.

Billard, F.

T. Olivier, F. Billard, and H. Akhouayri, “Z-scan theoretical and experimental studies for accurate measurements of nonlinear refractive index and absorption of optical glasses near damage threshold,” presented at the 35th Laser Damage Symposium, Boulder, United-States, Sept 2003.

Boling, N. L.

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601–608, 1978.
[Crossref]

Butcher, P. N.

P. N. Butcher and D. Cotter, The elements of nonlinear optics (Cambridge University Press, 1990).
[Crossref]

Byun, J. S.

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[Crossref]

Cotter, D.

P. N. Butcher and D. Cotter, The elements of nonlinear optics (Cambridge University Press, 1990).
[Crossref]

Feit, M. D.

Feldman, A.

A. Feldman, D. Horowitz, and R. M. Waxler, “Mechanisms for self-focusing in optical glasses,” IEEE J. Quantum Electron. QE-9, 1054–1061 (November 1973).
[Crossref]

Fleck, J. A.

Gallais, L.

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[Crossref]

Glass, A. J.

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601–608, 1978.
[Crossref]

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 4, 760–769 (April 1990).
[Crossref]

Hamilton, A. J. S.

A. J. S. Hamilton, “Uncorrelated modes of the nonlinear power spectrum,” Mon. Not. R. Astron. Soc. 312, 257, (2000).
[Crossref]

Horowitz, D.

A. Feldman, D. Horowitz, and R. M. Waxler, “Mechanisms for self-focusing in optical glasses,” IEEE J. Quantum Electron. QE-9, 1054–1061 (November 1973).
[Crossref]

Milam, D.

W. T. White III, W. L Smith, and D. Milam, “Direct measurement of the nonlinear refractive-index coefficient gamma at 355 nm in fused silica and BK-10 glass,” Opt. Lett. 9, 11, 10–12 (January 1984).
[Crossref]

D. Milam and M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry: Application to optical materials for high-power neodynium lasers,” J. Appl. Phys. 47, 6, 2497–2501 (June 1976).
[Crossref]

Natoli, J.Y.

Olivier, T.

T. Olivier, F. Billard, and H. Akhouayri, “Z-scan theoretical and experimental studies for accurate measurements of nonlinear refractive index and absorption of optical glasses near damage threshold,” presented at the 35th Laser Damage Symposium, Boulder, United-States, Sept 2003.

Owyoung, A.

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601–608, 1978.
[Crossref]

Rhee, B. K.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 4, 760–769 (April 1990).
[Crossref]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 4, 760–769 (April 1990).
[Crossref]

Smith, W. L

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[Crossref]

Van Stryland, E. W.

B. K. Rhee, J. S. Byun, and E. W. Van Stryland, “Z-scan using circularly symmetric beams,” J. Opt. Soc. Am. B 13, 2720–2723 (December 1996).
[Crossref]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 4, 760–769 (April 1990).
[Crossref]

Waxler, R. M.

A. Feldman, D. Horowitz, and R. M. Waxler, “Mechanisms for self-focusing in optical glasses,” IEEE J. Quantum Electron. QE-9, 1054–1061 (November 1973).
[Crossref]

Weber, M. J.

D. Milam and M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry: Application to optical materials for high-power neodynium lasers,” J. Appl. Phys. 47, 6, 2497–2501 (June 1976).
[Crossref]

Wei, T.-H.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 4, 760–769 (April 1990).
[Crossref]

White III, W. T.

IEEE J. Quantum Electron. (3)

A. Feldman, D. Horowitz, and R. M. Waxler, “Mechanisms for self-focusing in optical glasses,” IEEE J. Quantum Electron. QE-9, 1054–1061 (November 1973).
[Crossref]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 4, 760–769 (April 1990).
[Crossref]

N. L. Boling, A. J. Glass, and A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601–608, 1978.
[Crossref]

J. Appl. Phys. (1)

D. Milam and M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry: Application to optical materials for high-power neodynium lasers,” J. Appl. Phys. 47, 6, 2497–2501 (June 1976).
[Crossref]

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

Mon. Not. R. Astron. Soc. (1)

A. J. S. Hamilton, “Uncorrelated modes of the nonlinear power spectrum,” Mon. Not. R. Astron. Soc. 312, 257, (2000).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).
[Crossref]

Other (2)

P. N. Butcher and D. Cotter, The elements of nonlinear optics (Cambridge University Press, 1990).
[Crossref]

T. Olivier, F. Billard, and H. Akhouayri, “Z-scan theoretical and experimental studies for accurate measurements of nonlinear refractive index and absorption of optical glasses near damage threshold,” presented at the 35th Laser Damage Symposium, Boulder, United-States, Sept 2003.

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Figures (4)

Fig. 1.
Fig. 1.

Experimental setup. IRF: infrared filter, λ/2: half-wave plate, P: Glan-Thompson polarizer, 2ω: KTP crystal and half-wave plate, A1, A2: apertures, W1, W2, W3: wedges, RL, SL: reference and signal lenses, RP, SP: reference and signal photodiodes, RM: removable mirror for beam spatial characterization, TS: translation stage.

Fig. 2.
Fig. 2.

(Left) 2D-beam profile at the waist position at 1064nm. (Right) evolution of the on-axis intensity at 1064nm. The different curves represent simulations (solid lines), measurement (diamonds) and for comparison the case of a Gaussian beam having the same effective area Ae at the waist position (dashed lines).

Fig. 3.
Fig. 3.

Example of the normalized temporal profile p(t) (normalized output power), measured with a fast photodiode at 1064nm.

Fig. 4.
Fig. 4.

Normalized transmittance curves obtained on a 5mm-thick sample of fused silica at 1064nm (left) and at 532nm (right). The dots represent the experimental results and the solid lines represent the simulations.

Equations (4)

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n = n 0 + γ I
T ( z , t ) = 1 + Δ n ( t ) F ( z )
T ( z ) = 1 + γ E 2 π τ e A e × F ( z )
1 2 π τ e = p 2 ( t ) d t ( p ( t ) d t ) 2

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