Abstract

We present the results of modeling of nanosecond pulse propagation in optically absorbing liquid media. Acoustic and electromagnetic wave equations must be solved simultaneously to model refractive index changes due to thermal expansion and/or electrostriction, which are highly transient phenomena on a nanosecond time scale. Although we consider situations with cylindrical symmetry and where the paraxial approximation is valid, this is still a computation-intensive problem, as beam propagation through optically thick media must be modeled. We compare the full solution of the acoustic wave equation with the approximation of instantaneous expansion (steady-state solution) and hence determine the regimes of validity of this approximation. We also find that the refractive index change obtained from the photo-acoustic equation overshoots its steady-state value once the ratio between the pulsewidth and the acoustic transit time exceeds a factor of unity.

© 1999 Optical Society of America

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References

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  1. J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
    [Crossref]
  2. S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, “Thermal self-action of laser beams,” IEEE J. Quantum Electron. QE- 4, 568–575 (1968).
    [Crossref]
  3. C. K. N. Patel and A. C. Tam, “Pulsed optoacoustic spectroscopy of condensed matter,” Rev. Mod. Phys. 53, 517–550 (1981).
    [Crossref]
  4. J. N. Hayes, “Thermal blooming of laser beams in fluids,” Appl. Opt. 11, 455–461 (1972).
    [Crossref] [PubMed]
  5. A. J. Twarowski and D. S. Kliger, “Multiphoton absorption spectra using thermal blooming. I. Theory,” Chem. Phys. 20, 251–258 (1977).
  6. S. J. Sheldon, L. V. Knight, and J. M. Thorne, “Laser-induced thermal lens effect: a new theoretical model,” Appl. Opt. 21, 1663–1669 (1982).
    [Crossref] [PubMed]
  7. P. R. Longaker and M. M. Litvak, “Perturbation of the refractive index of absorbing media by a pulsed laser beam,” J. Appl. Phys. 40, 4033–4041 (1969)
    [Crossref]
  8. Gu Liu, “Theory of the photoacoustic effect in condensed matter,” Appl. Opt. 21, 955–960 (1982)
    [Crossref] [PubMed]
  9. C. A. Carter and J. M. Harris, “Comparison of models describing the thermal lens effect,” Appl. Opt. 23, 476–481 (1984).
    [Crossref] [PubMed]
  10. A. M. Olaizola, G. Da Costa, and J. A. Castillo, “Geometrical interpretation of a laser-induced thermal lens,” Opt. Eng. 32, 1125–1130 (1993).
    [Crossref]
  11. F. Jurgensen and W. Schroer, “Studies on the diffraction image of a thermal lens,” Appl. Opt. 34, 41–50 (1995).
    [Crossref] [PubMed]
  12. S. Wu and N. J. Dovichi, “Fresnel diffraction theory for steady-state thermal lens measurements in thin films,” J. Appl. Phys. 67, 1170–1182 (1990).
    [Crossref]
  13. S. R. J. Brueck, H. Kildal, and L. J. Belanger, “Photo-acoustic and photo-refractive detection of small absorptions in liquids,” Opt. Comm. 34, 199–204 (1980).
    [Crossref]
  14. J. -M. Heritier, “Electrostrictive limit and focusing effects in pulsed photoacoustic detection,” Opt. Comm. 44, 267–272 (1983).
    [Crossref]
  15. P. Brochard, V. Grolier-Mazza, and R. Cabanel, “Thermal nonlinear refraction in dye solutions: a study of the transient regime,” J. Opt. Soc. Am. B 14, 405–414 (1997)
    [Crossref]
  16. D. J. Hagan, T. Xia, A. A. Said, T. H. Wei, and E. W. Van Stryland, “High Dynamic Range Passive Optical Limiters,” Int. J. Nonlinear Opt. Phys. 2, 483–501 (1993).
    [Crossref]
  17. P. Miles, “Bottleneck optical limiters: the optimal use of excited-state absorbers,” Appl. Opt. 33, 6965–6979 (1994).
    [Crossref] [PubMed]
  18. T. Xia, D. J. Hagan, A. Dogariu, A. A. Said, and E. W. Van Stryland, “Optimization of optical limiting devices based on excited-state absorption,” Appl. Opt. 36, 4110–4122 (1997).
    [Crossref] [PubMed]
  19. T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
    [Crossref]
  20. Jian-Gio Tian et al, “Position dispersion and optical limiting resulting from thermally induced nonlinearities in Chinese tea,” Appl. Opt. 32, (1993).
    [Crossref] [PubMed]
  21. Y. M. Cheung and S. K. Gayen, “Optical nonlinearities of tea studied by Z-scan and four-wave mixing techniques,” J. Opt. Soc. Am. B 11, 636–643 (1994).
    [Crossref]
  22. J. Castillo and V. P. Kozich et al, “Thermal lensing resulting from one- and two-photon absorption studied with a two-color time-resolved Z-scan,” Opt. Lett. 19, 171–173 (1994).
    [Crossref] [PubMed]
  23. D. Landau and E. M. Lifshitz, Course of theoretical physics. Volume 6. Fluid mechanics, (Pergamon Press).
  24. T. Xia, “Modeling and experimental studies of nonlinear optical self-action,” Ph.D. thesis, Univ. of Central Florida (1994).
  25. R. W. Boyd, Nonlinear optics, (Academic Press, Inc.1992).
  26. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical recipes. The art of scientific computing, (Cambridge University Press, 1986).
  27. D. Kovsh, S Yang, D. J. Hagan, and E. W. Van Stryland “Software for computer modeling of laser pulse propagation through the optical system with nonlinear optical elements,” Proc. SPIE 3472, 163–177 (1998).
    [Crossref]
  28. D. Kovsh, S. Yang, D. Hagan, and E. Van Stryland, “Nonlinear optical beam propagation for optical limiting,” submitted to Applied Optics.
  29. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
    [Crossref] [PubMed]

1998 (1)

D. Kovsh, S Yang, D. J. Hagan, and E. W. Van Stryland “Software for computer modeling of laser pulse propagation through the optical system with nonlinear optical elements,” Proc. SPIE 3472, 163–177 (1998).
[Crossref]

1997 (2)

1995 (1)

1994 (3)

1993 (3)

Jian-Gio Tian et al, “Position dispersion and optical limiting resulting from thermally induced nonlinearities in Chinese tea,” Appl. Opt. 32, (1993).
[Crossref] [PubMed]

D. J. Hagan, T. Xia, A. A. Said, T. H. Wei, and E. W. Van Stryland, “High Dynamic Range Passive Optical Limiters,” Int. J. Nonlinear Opt. Phys. 2, 483–501 (1993).
[Crossref]

A. M. Olaizola, G. Da Costa, and J. A. Castillo, “Geometrical interpretation of a laser-induced thermal lens,” Opt. Eng. 32, 1125–1130 (1993).
[Crossref]

1992 (1)

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[Crossref]

1990 (1)

S. Wu and N. J. Dovichi, “Fresnel diffraction theory for steady-state thermal lens measurements in thin films,” J. Appl. Phys. 67, 1170–1182 (1990).
[Crossref]

1989 (1)

1984 (1)

1983 (1)

J. -M. Heritier, “Electrostrictive limit and focusing effects in pulsed photoacoustic detection,” Opt. Comm. 44, 267–272 (1983).
[Crossref]

1982 (2)

1981 (1)

C. K. N. Patel and A. C. Tam, “Pulsed optoacoustic spectroscopy of condensed matter,” Rev. Mod. Phys. 53, 517–550 (1981).
[Crossref]

1980 (1)

S. R. J. Brueck, H. Kildal, and L. J. Belanger, “Photo-acoustic and photo-refractive detection of small absorptions in liquids,” Opt. Comm. 34, 199–204 (1980).
[Crossref]

1977 (1)

A. J. Twarowski and D. S. Kliger, “Multiphoton absorption spectra using thermal blooming. I. Theory,” Chem. Phys. 20, 251–258 (1977).

1972 (1)

1969 (1)

P. R. Longaker and M. M. Litvak, “Perturbation of the refractive index of absorbing media by a pulsed laser beam,” J. Appl. Phys. 40, 4033–4041 (1969)
[Crossref]

1968 (1)

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, “Thermal self-action of laser beams,” IEEE J. Quantum Electron. QE- 4, 568–575 (1968).
[Crossref]

1965 (1)

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[Crossref]

Akhmanov, S. A.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, “Thermal self-action of laser beams,” IEEE J. Quantum Electron. QE- 4, 568–575 (1968).
[Crossref]

Belanger, L. J.

S. R. J. Brueck, H. Kildal, and L. J. Belanger, “Photo-acoustic and photo-refractive detection of small absorptions in liquids,” Opt. Comm. 34, 199–204 (1980).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear optics, (Academic Press, Inc.1992).

Brochard, P.

Brueck, S. R. J.

S. R. J. Brueck, H. Kildal, and L. J. Belanger, “Photo-acoustic and photo-refractive detection of small absorptions in liquids,” Opt. Comm. 34, 199–204 (1980).
[Crossref]

Cabanel, R.

Carter, C. A.

Castillo, J.

Castillo, J. A.

A. M. Olaizola, G. Da Costa, and J. A. Castillo, “Geometrical interpretation of a laser-induced thermal lens,” Opt. Eng. 32, 1125–1130 (1993).
[Crossref]

Cheung, Y. M.

Costa, G. Da

A. M. Olaizola, G. Da Costa, and J. A. Castillo, “Geometrical interpretation of a laser-induced thermal lens,” Opt. Eng. 32, 1125–1130 (1993).
[Crossref]

Coulter, D. R.

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[Crossref]

Dogariu, A.

Dovichi, N. J.

S. Wu and N. J. Dovichi, “Fresnel diffraction theory for steady-state thermal lens measurements in thin films,” J. Appl. Phys. 67, 1170–1182 (1990).
[Crossref]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical recipes. The art of scientific computing, (Cambridge University Press, 1986).

Gayen, S. K.

Gordon, J. P.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[Crossref]

Grolier-Mazza, V.

Hagan, D.

D. Kovsh, S. Yang, D. Hagan, and E. Van Stryland, “Nonlinear optical beam propagation for optical limiting,” submitted to Applied Optics.

Hagan, D. J.

D. Kovsh, S Yang, D. J. Hagan, and E. W. Van Stryland “Software for computer modeling of laser pulse propagation through the optical system with nonlinear optical elements,” Proc. SPIE 3472, 163–177 (1998).
[Crossref]

T. Xia, D. J. Hagan, A. Dogariu, A. A. Said, and E. W. Van Stryland, “Optimization of optical limiting devices based on excited-state absorption,” Appl. Opt. 36, 4110–4122 (1997).
[Crossref] [PubMed]

D. J. Hagan, T. Xia, A. A. Said, T. H. Wei, and E. W. Van Stryland, “High Dynamic Range Passive Optical Limiters,” Int. J. Nonlinear Opt. Phys. 2, 483–501 (1993).
[Crossref]

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[Crossref]

Harris, J. M.

Hayes, J. N.

Heritier, J. -M.

J. -M. Heritier, “Electrostrictive limit and focusing effects in pulsed photoacoustic detection,” Opt. Comm. 44, 267–272 (1983).
[Crossref]

Jurgensen, F.

Khokhlov, R. V.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, “Thermal self-action of laser beams,” IEEE J. Quantum Electron. QE- 4, 568–575 (1968).
[Crossref]

Kildal, H.

S. R. J. Brueck, H. Kildal, and L. J. Belanger, “Photo-acoustic and photo-refractive detection of small absorptions in liquids,” Opt. Comm. 34, 199–204 (1980).
[Crossref]

Kliger, D. S.

A. J. Twarowski and D. S. Kliger, “Multiphoton absorption spectra using thermal blooming. I. Theory,” Chem. Phys. 20, 251–258 (1977).

Knight, L. V.

Kovsh, D.

D. Kovsh, S Yang, D. J. Hagan, and E. W. Van Stryland “Software for computer modeling of laser pulse propagation through the optical system with nonlinear optical elements,” Proc. SPIE 3472, 163–177 (1998).
[Crossref]

D. Kovsh, S. Yang, D. Hagan, and E. Van Stryland, “Nonlinear optical beam propagation for optical limiting,” submitted to Applied Optics.

Kozich, V. P.

Krindach, D. P.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, “Thermal self-action of laser beams,” IEEE J. Quantum Electron. QE- 4, 568–575 (1968).
[Crossref]

Landau, D.

D. Landau and E. M. Lifshitz, Course of theoretical physics. Volume 6. Fluid mechanics, (Pergamon Press).

Leite, R. C. C.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[Crossref]

Lifshitz, E. M.

D. Landau and E. M. Lifshitz, Course of theoretical physics. Volume 6. Fluid mechanics, (Pergamon Press).

Litvak, M. M.

P. R. Longaker and M. M. Litvak, “Perturbation of the refractive index of absorbing media by a pulsed laser beam,” J. Appl. Phys. 40, 4033–4041 (1969)
[Crossref]

Liu, Gu

Longaker, P. R.

P. R. Longaker and M. M. Litvak, “Perturbation of the refractive index of absorbing media by a pulsed laser beam,” J. Appl. Phys. 40, 4033–4041 (1969)
[Crossref]

Migulin, A. V.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, “Thermal self-action of laser beams,” IEEE J. Quantum Electron. QE- 4, 568–575 (1968).
[Crossref]

Miles, P.

Moore, R. S.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[Crossref]

Olaizola, A. M.

A. M. Olaizola, G. Da Costa, and J. A. Castillo, “Geometrical interpretation of a laser-induced thermal lens,” Opt. Eng. 32, 1125–1130 (1993).
[Crossref]

Patel, C. K. N.

C. K. N. Patel and A. C. Tam, “Pulsed optoacoustic spectroscopy of condensed matter,” Rev. Mod. Phys. 53, 517–550 (1981).
[Crossref]

Perry, J. W.

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[Crossref]

Porto, S. P. S.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[Crossref]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical recipes. The art of scientific computing, (Cambridge University Press, 1986).

Said, A. A.

Schroer, W.

Sence, M. J.

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[Crossref]

Sheik-Bahae, M.

Sheldon, S. J.

Stryland, E. Van

D. Kovsh, S. Yang, D. Hagan, and E. Van Stryland, “Nonlinear optical beam propagation for optical limiting,” submitted to Applied Optics.

Stryland, E. W. Van

D. Kovsh, S Yang, D. J. Hagan, and E. W. Van Stryland “Software for computer modeling of laser pulse propagation through the optical system with nonlinear optical elements,” Proc. SPIE 3472, 163–177 (1998).
[Crossref]

T. Xia, D. J. Hagan, A. Dogariu, A. A. Said, and E. W. Van Stryland, “Optimization of optical limiting devices based on excited-state absorption,” Appl. Opt. 36, 4110–4122 (1997).
[Crossref] [PubMed]

D. J. Hagan, T. Xia, A. A. Said, T. H. Wei, and E. W. Van Stryland, “High Dynamic Range Passive Optical Limiters,” Int. J. Nonlinear Opt. Phys. 2, 483–501 (1993).
[Crossref]

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[Crossref]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[Crossref] [PubMed]

Sukhorukov, A. P.

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, “Thermal self-action of laser beams,” IEEE J. Quantum Electron. QE- 4, 568–575 (1968).
[Crossref]

Tam, A. C.

C. K. N. Patel and A. C. Tam, “Pulsed optoacoustic spectroscopy of condensed matter,” Rev. Mod. Phys. 53, 517–550 (1981).
[Crossref]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical recipes. The art of scientific computing, (Cambridge University Press, 1986).

Thorne, J. M.

Tian, Jian-Gio

Jian-Gio Tian et al, “Position dispersion and optical limiting resulting from thermally induced nonlinearities in Chinese tea,” Appl. Opt. 32, (1993).
[Crossref] [PubMed]

Twarowski, A. J.

A. J. Twarowski and D. S. Kliger, “Multiphoton absorption spectra using thermal blooming. I. Theory,” Chem. Phys. 20, 251–258 (1977).

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical recipes. The art of scientific computing, (Cambridge University Press, 1986).

Wei, T. H.

D. J. Hagan, T. Xia, A. A. Said, T. H. Wei, and E. W. Van Stryland, “High Dynamic Range Passive Optical Limiters,” Int. J. Nonlinear Opt. Phys. 2, 483–501 (1993).
[Crossref]

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[Crossref]

Whinnery, J. R.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[Crossref]

Wu, S.

S. Wu and N. J. Dovichi, “Fresnel diffraction theory for steady-state thermal lens measurements in thin films,” J. Appl. Phys. 67, 1170–1182 (1990).
[Crossref]

Xia, T.

T. Xia, D. J. Hagan, A. Dogariu, A. A. Said, and E. W. Van Stryland, “Optimization of optical limiting devices based on excited-state absorption,” Appl. Opt. 36, 4110–4122 (1997).
[Crossref] [PubMed]

D. J. Hagan, T. Xia, A. A. Said, T. H. Wei, and E. W. Van Stryland, “High Dynamic Range Passive Optical Limiters,” Int. J. Nonlinear Opt. Phys. 2, 483–501 (1993).
[Crossref]

T. Xia, “Modeling and experimental studies of nonlinear optical self-action,” Ph.D. thesis, Univ. of Central Florida (1994).

Yang, S

D. Kovsh, S Yang, D. J. Hagan, and E. W. Van Stryland “Software for computer modeling of laser pulse propagation through the optical system with nonlinear optical elements,” Proc. SPIE 3472, 163–177 (1998).
[Crossref]

Yang, S.

D. Kovsh, S. Yang, D. Hagan, and E. Van Stryland, “Nonlinear optical beam propagation for optical limiting,” submitted to Applied Optics.

Appl. Opt. (8)

Appl. Phys. B (1)

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, and D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[Crossref]

Chem. Phys. (1)

A. J. Twarowski and D. S. Kliger, “Multiphoton absorption spectra using thermal blooming. I. Theory,” Chem. Phys. 20, 251–258 (1977).

IEEE J. Quantum Electron. (1)

S. A. Akhmanov, D. P. Krindach, A. V. Migulin, A. P. Sukhorukov, and R. V. Khokhlov, “Thermal self-action of laser beams,” IEEE J. Quantum Electron. QE- 4, 568–575 (1968).
[Crossref]

Int. J. Nonlinear Opt. Phys. (1)

D. J. Hagan, T. Xia, A. A. Said, T. H. Wei, and E. W. Van Stryland, “High Dynamic Range Passive Optical Limiters,” Int. J. Nonlinear Opt. Phys. 2, 483–501 (1993).
[Crossref]

J. Appl. Phys. (3)

P. R. Longaker and M. M. Litvak, “Perturbation of the refractive index of absorbing media by a pulsed laser beam,” J. Appl. Phys. 40, 4033–4041 (1969)
[Crossref]

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[Crossref]

S. Wu and N. J. Dovichi, “Fresnel diffraction theory for steady-state thermal lens measurements in thin films,” J. Appl. Phys. 67, 1170–1182 (1990).
[Crossref]

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

Opt. Comm. (2)

S. R. J. Brueck, H. Kildal, and L. J. Belanger, “Photo-acoustic and photo-refractive detection of small absorptions in liquids,” Opt. Comm. 34, 199–204 (1980).
[Crossref]

J. -M. Heritier, “Electrostrictive limit and focusing effects in pulsed photoacoustic detection,” Opt. Comm. 44, 267–272 (1983).
[Crossref]

Opt. Eng. (1)

A. M. Olaizola, G. Da Costa, and J. A. Castillo, “Geometrical interpretation of a laser-induced thermal lens,” Opt. Eng. 32, 1125–1130 (1993).
[Crossref]

Opt. Lett. (2)

Proc. SPIE (1)

D. Kovsh, S Yang, D. J. Hagan, and E. W. Van Stryland “Software for computer modeling of laser pulse propagation through the optical system with nonlinear optical elements,” Proc. SPIE 3472, 163–177 (1998).
[Crossref]

Rev. Mod. Phys. (1)

C. K. N. Patel and A. C. Tam, “Pulsed optoacoustic spectroscopy of condensed matter,” Rev. Mod. Phys. 53, 517–550 (1981).
[Crossref]

Other (5)

D. Kovsh, S. Yang, D. Hagan, and E. Van Stryland, “Nonlinear optical beam propagation for optical limiting,” submitted to Applied Optics.

D. Landau and E. M. Lifshitz, Course of theoretical physics. Volume 6. Fluid mechanics, (Pergamon Press).

T. Xia, “Modeling and experimental studies of nonlinear optical self-action,” Ph.D. thesis, Univ. of Central Florida (1994).

R. W. Boyd, Nonlinear optics, (Academic Press, Inc.1992).

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical recipes. The art of scientific computing, (Cambridge University Press, 1986).

Supplementary Material (2)

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Figures (10)

Fig. 1.
Fig. 1.

Spatial distribution of the thermally induced refractive index change (τp = 4 ns, w 0 = 6 μm, TL = 80%, L = 1 mm, EIN = 5μJ). [Media 1]

Fig. 2(a).
Fig. 2(a).

Radial fluence distribution on the back surface of the sample (near field).

Fig. 2(b).
Fig. 2(b).

Radial fluence distribution on the detector (far field).

Fig. 3.
Fig. 3.

Spatial distribution of the thermally induced refractive index change (τp = 4 ns, w0 = 30 μm, TL = 80%, L = 1 mm, EIN = 125 μJ). [Media 2]

Fig. 4(a).
Fig. 4(a).

Radial fluence distribution on the back surface of the sample (near field).

Fig. 4(b).
Fig. 4(b).

Radial fluence distribution on the detector (far field).

Fig. 5.
Fig. 5.

Closed-aperture Z-scan of nigrosine solution in water (τp = 10 ns, w0 = 6 μm, TL = 90%, L = 200 μm, EIN = 2 μJ).

Fig. 6.
Fig. 6.

Closed-aperture Z-scan of nigrosine solution in water (τp = 10 ns, w0 = 30 μm, TL = 90%, L = 200 μm, EIN = 50 μJ).

Figure 7.
Figure 7.

Sensitivity (ΔTP-V ) of the closed-aperture Z-scan as a function of ratio between pulse width, τp , and acoustic transit time τac = w0 /CS . ΔTP-V is normalized to the value obtained for the steady state solution (s.s.).

Figure 8.
Figure 8.

On-axis refractive index change computed as a solution to the acoustic wave equation, Δnac(t), normalized to the steady state index distribution, Δnss(t). Values of the parameter τpac were chosen to be 0.5 (solid red), 1.5 (solid blue), 2.5 (solid green), 5.0 (dash red), 10 (dashed blue) and 15 (dashed green). The normalized Δnss(t) (with negative sign) is shown with dashed black line. The normalized intensity distribution (solid black) is plotted to show the time scale of the index changes.

Equations (12)

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ρ c p T t κ 2 T = Q ,
Δ n = ( n ρ ) T Δ ρ + ( n T ) ρ Δ T .
t [ 2 ( Δ ρ ) t 2 C S 2 2 ( Δ ρ ) ] = C S 2 β c p 2 ( α L I ) γ e 2 nc t 2 I .
2 ( Δ n ) t 2 C S 2 2 ( Δ n ) = γ e 2 β C S 2 c p t 2 ( α L I ( r , t′ ) ) dt .
Δ T ( r , t ) = 1 ρ c p t α L I ( r , t′ ) dt .
2 ( Δ n ) t 2 C S 2 2 ( Δ n ) = γ e β C S 2 2 n 2 ( Δ T ) .
Δ n ( d n d T ) Δ T ,
× × E ( r , t ) + 1 c 2 2 E ( r , t ) t 2 = μ 0 2 P ( r , t ) t 2 ,
2 jk ψ ( r , z , t ) z = 2 ψ ( r , z , t ) + ( k 0 2 χ NL ( r , z , t ) jk α L ) ψ ( r , z , t ) ,
χ NL ( r , z , t ) = χ NL ins ( r , z ) + χ NL cum ( r , z . t ) .
Re { χ NL } = 2 n 0 Δ n
Im { χ NL } = n 0 k 0 α = n 0 k 0 ( α L + α NL ) .

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