Abstract

A linear time-domain thermoelastic (photothermoacoustic) theory of a composite solid–liquid geometry has been developed. The theory includes multiple interreflections at all interfaces, acoustic diffraction and viscosity effects, and natural mixed, rigid, and free boundary conditions at the solid surface where laser-pulse incidence occurs (air–polystyrene interface). The theory was applied to experimental pressure-wave pulses from a Nd:YAG laser in a polystyrene well target and water system used for photomechanical drug delivery studies. Good fits of the linear theory to tripolar experimental pressure waveforms were possible at laser-pulse irradiances 100MWcm2, especially at distances 5mm from the solid–fluid interface. It was further determined from the combined theoretical and experimental approach that the onset of significant hydrodynamic nonlinearity in the water appears for laser-pulse irradiances in the 165-MWcm2 range, especially at axial distances z8mm, as expected theoretically from the laser-ablation-induced nonlinearity of stress-wave propagation in the solid–water system.

© 2005 Optical Society of America

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  1. S. E. Mulholland, S. Lee, D. J. McAuliffe, and A. G. Doukas, "cell loading with laser-generated stress waves: the role of the stress gradient," Pharm. Res. 16, 514-518 (1999).
    [CrossRef] [PubMed]
  2. A. G. Doukas, D. J. McAuliffe, S. Lee, V. Venugopalan, and T. J. Flotte, "Physical factors involved in stress-wave-induced cell injury: the effect of stress gradient," Ultrasound Med. Biol. 21, 961-967 (1995).
    [CrossRef]
  3. D. C. Lamb, J. Tribble, A. G. Doukas, T. J. Flotte, R. H. Ossoff, and L. Reunisch, "Custom designed acoustic pulses," J. Biomed. Opt. 4, 217-223 (1999).
    [CrossRef] [PubMed]
  4. T. Kodama, M. R. Hamblin, and A. G. Doukas, "Cytoplasmic molecular delivery with shock waves: importance of impulse," Biophys. J. 79, 1821-1832 (2000).
    [CrossRef] [PubMed]
  5. E. F. Carome, N. A. Clark, and C. E. Moeller, "Generation of acoustic signals in liquids by ruby laser-induced thermal stress transients," Appl. Phys. Lett. 4, 95-97 (1964).
    [CrossRef]
  6. M. W. Sigrist and V. G. Mikhalevich, "New method for nonlinear acoustic studies in liquids using lasers," in Proceedings of the International Conference on LASERS '82 (STS, New Orleans, La., 1982), pp. 80-85.
  7. V. E. Gusev and A. A. Karabutov, Laser Optoacoustics (American Institute of Physics, New York, 1993).
  8. H. M. Lai and K. Young, "Theory of the pulsed optoacoustic technique," J. Acoust. Soc. Am. 72, 2000-2007 (1982).
    [CrossRef]
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  11. W. Nowacki, Dynamic Problems in Thermoelasticity (Noordhoff International, Leyden, The Netherlands, 1975).
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    [CrossRef]
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  14. A. A. Karabutov, A. I. Portyagin, O. V. Rudenko, and E. B. Cherepetskaya, "Experimental study of the propagation of short thermooptically excited acoustic pulses," Sov. Phys. Acoust. 26, 162-164 (1980).
  15. M. W. Sigrist, "Laser generation of acoustic waves in liquids and gases," J. Appl. Phys. 60, R83-R121 (1986).
    [CrossRef]
  16. M. Terzic and M. W. Sigrist, "Pulsed photoacoustic measurements of large optical absorption coefficients," J. Appl. Phys. 67, 3593-3596 (1990).
    [CrossRef]
  17. M. Terzic and M. W. Sigrist, "Diffraction characteristics of laser-induced acoustic waves in liquids," J. Appl. Phys. 56, 93-95 (1984).
    [CrossRef]
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  22. A. D. Zweig, V. Vanugopalan, and T. F. Deutsch, "Stress generated in polyimide by excimer-laser irradiation," J. Appl. Phys. 74, 4181-4189 (1993).
    [CrossRef]
  23. A. D. Zweig and T. F. Deutsch, "Shock waves generated by confined excimer laser ablation of polyimide," Appl. Phys. B: Photophys. Laser Chem. 4, 76-82 (1992).
    [CrossRef]
  24. A. G. Doukas and T. J. Flotte, "Physical characteristics and biological effects of laser-induced stress waves," Ultrasound Med. Biol. 22, 151-164 (1996).
    [CrossRef] [PubMed]
  25. T. G. Muir, C. R. Culbertson, and J. R. Clynch, "Experiments on thermoacoustic arrays with laser excitation," J. Acoust. Soc. Am. 59, 735-743 (1976).
    [CrossRef]
  26. N. S. Bakhvalov, Ya. M. Zhileykin, and E. A. Zabolotskaya, Nonlinear Theory of Acoustic Beams (Nauka, Moscow, 1982).
  27. M. F. Hamilton and C. L. Morfey, "Model equations," in Nonlinear Acoustics, M.F.Hamilton and D.T.Blackstock, eds. (Academic, New York, 1998), Chap. 3, pp. 41-63.

2000

T. Kodama, M. R. Hamblin, and A. G. Doukas, "Cytoplasmic molecular delivery with shock waves: importance of impulse," Biophys. J. 79, 1821-1832 (2000).
[CrossRef] [PubMed]

1999

S. E. Mulholland, S. Lee, D. J. McAuliffe, and A. G. Doukas, "cell loading with laser-generated stress waves: the role of the stress gradient," Pharm. Res. 16, 514-518 (1999).
[CrossRef] [PubMed]

D. C. Lamb, J. Tribble, A. G. Doukas, T. J. Flotte, R. H. Ossoff, and L. Reunisch, "Custom designed acoustic pulses," J. Biomed. Opt. 4, 217-223 (1999).
[CrossRef] [PubMed]

1996

A. G. Doukas and T. J. Flotte, "Physical characteristics and biological effects of laser-induced stress waves," Ultrasound Med. Biol. 22, 151-164 (1996).
[CrossRef] [PubMed]

1995

A. G. Doukas, D. J. McAuliffe, S. Lee, V. Venugopalan, and T. J. Flotte, "Physical factors involved in stress-wave-induced cell injury: the effect of stress gradient," Ultrasound Med. Biol. 21, 961-967 (1995).
[CrossRef]

1993

M. I. Khan, T. Sun, and G. J. Diebold, "Photoacoustic waves generated by absorption of laser radiation in optically thin layers," J. Acoust. Soc. Am. 93, 1417-1425 (1993).
[CrossRef]

A. D. Zweig, V. Vanugopalan, and T. F. Deutsch, "Stress generated in polyimide by excimer-laser irradiation," J. Appl. Phys. 74, 4181-4189 (1993).
[CrossRef]

1992

A. D. Zweig and T. F. Deutsch, "Shock waves generated by confined excimer laser ablation of polyimide," Appl. Phys. B: Photophys. Laser Chem. 4, 76-82 (1992).
[CrossRef]

1990

M. Terzic and M. W. Sigrist, "Pulsed photoacoustic measurements of large optical absorption coefficients," J. Appl. Phys. 67, 3593-3596 (1990).
[CrossRef]

1986

M. W. Sigrist, "Laser generation of acoustic waves in liquids and gases," J. Appl. Phys. 60, R83-R121 (1986).
[CrossRef]

1984

M. Terzic and M. W. Sigrist, "Diffraction characteristics of laser-induced acoustic waves in liquids," J. Appl. Phys. 56, 93-95 (1984).
[CrossRef]

1982

H. M. Lai and K. Young, "Theory of the pulsed optoacoustic technique," J. Acoust. Soc. Am. 72, 2000-2007 (1982).
[CrossRef]

1981

Ya. M. Zhileikin and O. V. Rudenko, "Nonlinear and diffraction transformation of acoustic pulses," Sov. Phys. Acoust. 27, 200-202 (1981).

1980

A. A. Karabutov, A. I. Portyagin, O. V. Rudenko, and E. B. Cherepetskaya, "Experimental study of the propagation of short thermooptically excited acoustic pulses," Sov. Phys. Acoust. 26, 162-164 (1980).

1978

L. V. Burmistrova, A. A. Karabutov, A. I. Portyagin, O. V. Rudenko, and E. B. Cherepetskaya, "Method of transfer functions in problems of thermooptical sound generation," Sov. Phys. Acoust. 24, 369-374 (1978).

1976

T. G. Muir, C. R. Culbertson, and J. R. Clynch, "Experiments on thermoacoustic arrays with laser excitation," J. Acoust. Soc. Am. 59, 735-743 (1976).
[CrossRef]

1964

E. F. Carome, N. A. Clark, and C. E. Moeller, "Generation of acoustic signals in liquids by ruby laser-induced thermal stress transients," Appl. Phys. Lett. 4, 95-97 (1964).
[CrossRef]

Bakhvalov, N. S.

N. S. Bakhvalov, Ya. M. Zhileykin, and E. A. Zabolotskaya, Nonlinear Theory of Acoustic Beams (Nauka, Moscow, 1982).

Burmistrova, L. V.

L. V. Burmistrova, A. A. Karabutov, A. I. Portyagin, O. V. Rudenko, and E. B. Cherepetskaya, "Method of transfer functions in problems of thermooptical sound generation," Sov. Phys. Acoust. 24, 369-374 (1978).

Carome, E. F.

E. F. Carome, N. A. Clark, and C. E. Moeller, "Generation of acoustic signals in liquids by ruby laser-induced thermal stress transients," Appl. Phys. Lett. 4, 95-97 (1964).
[CrossRef]

Cherepetskaya, E. B.

A. A. Karabutov, A. I. Portyagin, O. V. Rudenko, and E. B. Cherepetskaya, "Experimental study of the propagation of short thermooptically excited acoustic pulses," Sov. Phys. Acoust. 26, 162-164 (1980).

L. V. Burmistrova, A. A. Karabutov, A. I. Portyagin, O. V. Rudenko, and E. B. Cherepetskaya, "Method of transfer functions in problems of thermooptical sound generation," Sov. Phys. Acoust. 24, 369-374 (1978).

Clark, N. A.

E. F. Carome, N. A. Clark, and C. E. Moeller, "Generation of acoustic signals in liquids by ruby laser-induced thermal stress transients," Appl. Phys. Lett. 4, 95-97 (1964).
[CrossRef]

Clynch, J. R.

T. G. Muir, C. R. Culbertson, and J. R. Clynch, "Experiments on thermoacoustic arrays with laser excitation," J. Acoust. Soc. Am. 59, 735-743 (1976).
[CrossRef]

Culbertson, C. R.

T. G. Muir, C. R. Culbertson, and J. R. Clynch, "Experiments on thermoacoustic arrays with laser excitation," J. Acoust. Soc. Am. 59, 735-743 (1976).
[CrossRef]

Deutsch, T. F.

A. D. Zweig, V. Vanugopalan, and T. F. Deutsch, "Stress generated in polyimide by excimer-laser irradiation," J. Appl. Phys. 74, 4181-4189 (1993).
[CrossRef]

A. D. Zweig and T. F. Deutsch, "Shock waves generated by confined excimer laser ablation of polyimide," Appl. Phys. B: Photophys. Laser Chem. 4, 76-82 (1992).
[CrossRef]

Diebold, G. J.

M. I. Khan, T. Sun, and G. J. Diebold, "Photoacoustic waves generated by absorption of laser radiation in optically thin layers," J. Acoust. Soc. Am. 93, 1417-1425 (1993).
[CrossRef]

Doukas, A. G.

T. Kodama, M. R. Hamblin, and A. G. Doukas, "Cytoplasmic molecular delivery with shock waves: importance of impulse," Biophys. J. 79, 1821-1832 (2000).
[CrossRef] [PubMed]

D. C. Lamb, J. Tribble, A. G. Doukas, T. J. Flotte, R. H. Ossoff, and L. Reunisch, "Custom designed acoustic pulses," J. Biomed. Opt. 4, 217-223 (1999).
[CrossRef] [PubMed]

S. E. Mulholland, S. Lee, D. J. McAuliffe, and A. G. Doukas, "cell loading with laser-generated stress waves: the role of the stress gradient," Pharm. Res. 16, 514-518 (1999).
[CrossRef] [PubMed]

A. G. Doukas and T. J. Flotte, "Physical characteristics and biological effects of laser-induced stress waves," Ultrasound Med. Biol. 22, 151-164 (1996).
[CrossRef] [PubMed]

A. G. Doukas, D. J. McAuliffe, S. Lee, V. Venugopalan, and T. J. Flotte, "Physical factors involved in stress-wave-induced cell injury: the effect of stress gradient," Ultrasound Med. Biol. 21, 961-967 (1995).
[CrossRef]

Flotte, T. J.

D. C. Lamb, J. Tribble, A. G. Doukas, T. J. Flotte, R. H. Ossoff, and L. Reunisch, "Custom designed acoustic pulses," J. Biomed. Opt. 4, 217-223 (1999).
[CrossRef] [PubMed]

A. G. Doukas and T. J. Flotte, "Physical characteristics and biological effects of laser-induced stress waves," Ultrasound Med. Biol. 22, 151-164 (1996).
[CrossRef] [PubMed]

A. G. Doukas, D. J. McAuliffe, S. Lee, V. Venugopalan, and T. J. Flotte, "Physical factors involved in stress-wave-induced cell injury: the effect of stress gradient," Ultrasound Med. Biol. 21, 961-967 (1995).
[CrossRef]

Fray, A. R.

L. E. Kinsler and A. R. Fray, Fundamentals of Acoustics, 2nd ed. (Wiley, New York, 1966).

Gusev, V. E.

V. E. Gusev and A. A. Karabutov, Laser Optoacoustics (American Institute of Physics, New York, 1993).

Hamblin, M. R.

T. Kodama, M. R. Hamblin, and A. G. Doukas, "Cytoplasmic molecular delivery with shock waves: importance of impulse," Biophys. J. 79, 1821-1832 (2000).
[CrossRef] [PubMed]

Hamilton, M. F.

M. F. Hamilton and C. L. Morfey, "Model equations," in Nonlinear Acoustics, M.F.Hamilton and D.T.Blackstock, eds. (Academic, New York, 1998), Chap. 3, pp. 41-63.

Hutchins, D. A.

D. A. Hutchins, "Ultrasonic generation by pulsed lasers," in Physical Acoustics (Academic, New York, 1988), Vol. 18, Chap. 2.4.

Karabutov, A. A.

A. A. Karabutov, A. I. Portyagin, O. V. Rudenko, and E. B. Cherepetskaya, "Experimental study of the propagation of short thermooptically excited acoustic pulses," Sov. Phys. Acoust. 26, 162-164 (1980).

L. V. Burmistrova, A. A. Karabutov, A. I. Portyagin, O. V. Rudenko, and E. B. Cherepetskaya, "Method of transfer functions in problems of thermooptical sound generation," Sov. Phys. Acoust. 24, 369-374 (1978).

V. E. Gusev and A. A. Karabutov, Laser Optoacoustics (American Institute of Physics, New York, 1993).

Khan, M. I.

M. I. Khan, T. Sun, and G. J. Diebold, "Photoacoustic waves generated by absorption of laser radiation in optically thin layers," J. Acoust. Soc. Am. 93, 1417-1425 (1993).
[CrossRef]

Kinsler, L. E.

L. E. Kinsler and A. R. Fray, Fundamentals of Acoustics, 2nd ed. (Wiley, New York, 1966).

Kodama, T.

T. Kodama, M. R. Hamblin, and A. G. Doukas, "Cytoplasmic molecular delivery with shock waves: importance of impulse," Biophys. J. 79, 1821-1832 (2000).
[CrossRef] [PubMed]

Lai, H. M.

H. M. Lai and K. Young, "Theory of the pulsed optoacoustic technique," J. Acoust. Soc. Am. 72, 2000-2007 (1982).
[CrossRef]

Lamb, D. C.

D. C. Lamb, J. Tribble, A. G. Doukas, T. J. Flotte, R. H. Ossoff, and L. Reunisch, "Custom designed acoustic pulses," J. Biomed. Opt. 4, 217-223 (1999).
[CrossRef] [PubMed]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, New York, 1959), p. 283. Translation by J. B. Sykes and W. H. Reid.

Lee, S.

S. E. Mulholland, S. Lee, D. J. McAuliffe, and A. G. Doukas, "cell loading with laser-generated stress waves: the role of the stress gradient," Pharm. Res. 16, 514-518 (1999).
[CrossRef] [PubMed]

A. G. Doukas, D. J. McAuliffe, S. Lee, V. Venugopalan, and T. J. Flotte, "Physical factors involved in stress-wave-induced cell injury: the effect of stress gradient," Ultrasound Med. Biol. 21, 961-967 (1995).
[CrossRef]

Lide, D. R.

D. R. Lide, CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, Fla.), pp. 14-38.

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, New York, 1959), p. 283. Translation by J. B. Sykes and W. H. Reid.

McAuliffe, D. J.

S. E. Mulholland, S. Lee, D. J. McAuliffe, and A. G. Doukas, "cell loading with laser-generated stress waves: the role of the stress gradient," Pharm. Res. 16, 514-518 (1999).
[CrossRef] [PubMed]

A. G. Doukas, D. J. McAuliffe, S. Lee, V. Venugopalan, and T. J. Flotte, "Physical factors involved in stress-wave-induced cell injury: the effect of stress gradient," Ultrasound Med. Biol. 21, 961-967 (1995).
[CrossRef]

Mikhalevich, V. G.

M. W. Sigrist and V. G. Mikhalevich, "New method for nonlinear acoustic studies in liquids using lasers," in Proceedings of the International Conference on LASERS '82 (STS, New Orleans, La., 1982), pp. 80-85.

Moeller, C. E.

E. F. Carome, N. A. Clark, and C. E. Moeller, "Generation of acoustic signals in liquids by ruby laser-induced thermal stress transients," Appl. Phys. Lett. 4, 95-97 (1964).
[CrossRef]

Morfey, C. L.

M. F. Hamilton and C. L. Morfey, "Model equations," in Nonlinear Acoustics, M.F.Hamilton and D.T.Blackstock, eds. (Academic, New York, 1998), Chap. 3, pp. 41-63.

Muir, T. G.

T. G. Muir, C. R. Culbertson, and J. R. Clynch, "Experiments on thermoacoustic arrays with laser excitation," J. Acoust. Soc. Am. 59, 735-743 (1976).
[CrossRef]

Mulholland, S. E.

S. E. Mulholland, S. Lee, D. J. McAuliffe, and A. G. Doukas, "cell loading with laser-generated stress waves: the role of the stress gradient," Pharm. Res. 16, 514-518 (1999).
[CrossRef] [PubMed]

Nowacki, W.

W. Nowacki, Dynamic Problems in Thermoelasticity (Noordhoff International, Leyden, The Netherlands, 1975).

Ossoff, R. H.

D. C. Lamb, J. Tribble, A. G. Doukas, T. J. Flotte, R. H. Ossoff, and L. Reunisch, "Custom designed acoustic pulses," J. Biomed. Opt. 4, 217-223 (1999).
[CrossRef] [PubMed]

Portyagin, A. I.

A. A. Karabutov, A. I. Portyagin, O. V. Rudenko, and E. B. Cherepetskaya, "Experimental study of the propagation of short thermooptically excited acoustic pulses," Sov. Phys. Acoust. 26, 162-164 (1980).

L. V. Burmistrova, A. A. Karabutov, A. I. Portyagin, O. V. Rudenko, and E. B. Cherepetskaya, "Method of transfer functions in problems of thermooptical sound generation," Sov. Phys. Acoust. 24, 369-374 (1978).

Reunisch, L.

D. C. Lamb, J. Tribble, A. G. Doukas, T. J. Flotte, R. H. Ossoff, and L. Reunisch, "Custom designed acoustic pulses," J. Biomed. Opt. 4, 217-223 (1999).
[CrossRef] [PubMed]

Rudenko, O. V.

Ya. M. Zhileikin and O. V. Rudenko, "Nonlinear and diffraction transformation of acoustic pulses," Sov. Phys. Acoust. 27, 200-202 (1981).

A. A. Karabutov, A. I. Portyagin, O. V. Rudenko, and E. B. Cherepetskaya, "Experimental study of the propagation of short thermooptically excited acoustic pulses," Sov. Phys. Acoust. 26, 162-164 (1980).

L. V. Burmistrova, A. A. Karabutov, A. I. Portyagin, O. V. Rudenko, and E. B. Cherepetskaya, "Method of transfer functions in problems of thermooptical sound generation," Sov. Phys. Acoust. 24, 369-374 (1978).

Sigrist, M. W.

M. Terzic and M. W. Sigrist, "Pulsed photoacoustic measurements of large optical absorption coefficients," J. Appl. Phys. 67, 3593-3596 (1990).
[CrossRef]

M. W. Sigrist, "Laser generation of acoustic waves in liquids and gases," J. Appl. Phys. 60, R83-R121 (1986).
[CrossRef]

M. Terzic and M. W. Sigrist, "Diffraction characteristics of laser-induced acoustic waves in liquids," J. Appl. Phys. 56, 93-95 (1984).
[CrossRef]

M. W. Sigrist and V. G. Mikhalevich, "New method for nonlinear acoustic studies in liquids using lasers," in Proceedings of the International Conference on LASERS '82 (STS, New Orleans, La., 1982), pp. 80-85.

Sun, T.

M. I. Khan, T. Sun, and G. J. Diebold, "Photoacoustic waves generated by absorption of laser radiation in optically thin layers," J. Acoust. Soc. Am. 93, 1417-1425 (1993).
[CrossRef]

Terzic, M.

M. Terzic and M. W. Sigrist, "Pulsed photoacoustic measurements of large optical absorption coefficients," J. Appl. Phys. 67, 3593-3596 (1990).
[CrossRef]

M. Terzic and M. W. Sigrist, "Diffraction characteristics of laser-induced acoustic waves in liquids," J. Appl. Phys. 56, 93-95 (1984).
[CrossRef]

Tribble, J.

D. C. Lamb, J. Tribble, A. G. Doukas, T. J. Flotte, R. H. Ossoff, and L. Reunisch, "Custom designed acoustic pulses," J. Biomed. Opt. 4, 217-223 (1999).
[CrossRef] [PubMed]

Vanugopalan, V.

A. D. Zweig, V. Vanugopalan, and T. F. Deutsch, "Stress generated in polyimide by excimer-laser irradiation," J. Appl. Phys. 74, 4181-4189 (1993).
[CrossRef]

Venugopalan, V.

A. G. Doukas, D. J. McAuliffe, S. Lee, V. Venugopalan, and T. J. Flotte, "Physical factors involved in stress-wave-induced cell injury: the effect of stress gradient," Ultrasound Med. Biol. 21, 961-967 (1995).
[CrossRef]

Young, K.

H. M. Lai and K. Young, "Theory of the pulsed optoacoustic technique," J. Acoust. Soc. Am. 72, 2000-2007 (1982).
[CrossRef]

Zabolotskaya, E. A.

N. S. Bakhvalov, Ya. M. Zhileykin, and E. A. Zabolotskaya, Nonlinear Theory of Acoustic Beams (Nauka, Moscow, 1982).

Zhileikin, Ya. M.

Ya. M. Zhileikin and O. V. Rudenko, "Nonlinear and diffraction transformation of acoustic pulses," Sov. Phys. Acoust. 27, 200-202 (1981).

Zhileykin, Ya. M.

N. S. Bakhvalov, Ya. M. Zhileykin, and E. A. Zabolotskaya, Nonlinear Theory of Acoustic Beams (Nauka, Moscow, 1982).

Zweig, A. D.

A. D. Zweig, V. Vanugopalan, and T. F. Deutsch, "Stress generated in polyimide by excimer-laser irradiation," J. Appl. Phys. 74, 4181-4189 (1993).
[CrossRef]

A. D. Zweig and T. F. Deutsch, "Shock waves generated by confined excimer laser ablation of polyimide," Appl. Phys. B: Photophys. Laser Chem. 4, 76-82 (1992).
[CrossRef]

Appl. Phys. B: Photophys. Laser Chem.

A. D. Zweig and T. F. Deutsch, "Shock waves generated by confined excimer laser ablation of polyimide," Appl. Phys. B: Photophys. Laser Chem. 4, 76-82 (1992).
[CrossRef]

Appl. Phys. Lett.

E. F. Carome, N. A. Clark, and C. E. Moeller, "Generation of acoustic signals in liquids by ruby laser-induced thermal stress transients," Appl. Phys. Lett. 4, 95-97 (1964).
[CrossRef]

Biophys. J.

T. Kodama, M. R. Hamblin, and A. G. Doukas, "Cytoplasmic molecular delivery with shock waves: importance of impulse," Biophys. J. 79, 1821-1832 (2000).
[CrossRef] [PubMed]

J. Acoust. Soc. Am.

H. M. Lai and K. Young, "Theory of the pulsed optoacoustic technique," J. Acoust. Soc. Am. 72, 2000-2007 (1982).
[CrossRef]

M. I. Khan, T. Sun, and G. J. Diebold, "Photoacoustic waves generated by absorption of laser radiation in optically thin layers," J. Acoust. Soc. Am. 93, 1417-1425 (1993).
[CrossRef]

T. G. Muir, C. R. Culbertson, and J. R. Clynch, "Experiments on thermoacoustic arrays with laser excitation," J. Acoust. Soc. Am. 59, 735-743 (1976).
[CrossRef]

J. Appl. Phys.

A. D. Zweig, V. Vanugopalan, and T. F. Deutsch, "Stress generated in polyimide by excimer-laser irradiation," J. Appl. Phys. 74, 4181-4189 (1993).
[CrossRef]

M. W. Sigrist, "Laser generation of acoustic waves in liquids and gases," J. Appl. Phys. 60, R83-R121 (1986).
[CrossRef]

M. Terzic and M. W. Sigrist, "Pulsed photoacoustic measurements of large optical absorption coefficients," J. Appl. Phys. 67, 3593-3596 (1990).
[CrossRef]

M. Terzic and M. W. Sigrist, "Diffraction characteristics of laser-induced acoustic waves in liquids," J. Appl. Phys. 56, 93-95 (1984).
[CrossRef]

J. Biomed. Opt.

D. C. Lamb, J. Tribble, A. G. Doukas, T. J. Flotte, R. H. Ossoff, and L. Reunisch, "Custom designed acoustic pulses," J. Biomed. Opt. 4, 217-223 (1999).
[CrossRef] [PubMed]

Pharm. Res.

S. E. Mulholland, S. Lee, D. J. McAuliffe, and A. G. Doukas, "cell loading with laser-generated stress waves: the role of the stress gradient," Pharm. Res. 16, 514-518 (1999).
[CrossRef] [PubMed]

Sov. Phys. Acoust.

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Figures (15)

Fig. 1
Fig. 1

One-dimensional cross-sectional geometry of the model showing the direction of the incident laser pulse.

Fig. 2
Fig. 2

Experimental setup of our laser PTA drug delivery system.

Fig. 3
Fig. 3

Experimental PTA data and theoretical fit for laser-pulse energy of 60 mJ and an axial hydrophone distance z = 2 mm . The fit parameters are B = 0.162 , c s μ s = 2.2 × 10 8 s 1 , L = 1.27 × 10 3 m , r as = 1.86 × 10 4 , τ R = 9.52 × 10 8 s .

Fig. 4
Fig. 4

Experimental PTA data and theoretical fit for a laser-pulse energy of 60 mJ and an axial hydrophone distance z = 5 mm . The fit parameters are B = 0.404 , c s μ s = 2.2 × 10 8 s 1 , L = 1.30 × 10 3 m , r as = 1.86 × 10 4 , τ R = 8.76 × 10 8 s .

Fig. 5
Fig. 5

Experimental PTA data and theoretical fit for a laser-pulse energy of 60 mJ and an axial hydrophone distance z = 8 mm . The fit parameters are B = 0.646 , c s μ s = 2.2 × 10 8 s 1 , L = 1.31 × 10 3 m , r as = 1.86 × 10 4 , τ R = 8.90 × 10 8 s .

Fig. 6
Fig. 6

Experimental PTA data and theoretical fit for a laser-pulse energy of 100 mJ and an axial hydrophone distance z = 2 mm . The fit parameters are B = 0.011 , c s μ s = 2.2 × 10 8 s 1 , L = 1.25 × 10 3 m , r as = 1.86 × 10 4 , τ R = 8.76 × 10 8 s .

Fig. 7
Fig. 7

Experimental PTA data and theoretical fit for a laser-pulse energy of 100 mJ and an axial hydrophone distance z = 5 mm . The fit parameters are B = 0.043 , c s μ s = 2.2 × 10 8 s 1 , L = 1.28 × 10 3 m , r as = 1.86 × 10 4 , τ R = 8.90 × 10 8 s .

Fig. 8
Fig. 8

Experimental PTA data and theoretical fit for a laser-pulse energy of 100 mJ and an axial hydrophone distance z = 8 mm . The fit parameters are B = 0.069 , c s μ s = 2.2 × 10 8 s 1 , L = 1.28 × 10 3 m , r as = 1.86 × 10 4 , τ R = 9.02 × 10 8 s .

Fig. 9
Fig. 9

Experimental PTA data and theoretical fit for a laser-pulse energy of 165 mJ and an axial hydrophone distance z = 2 mm . The fit parameters are B = 0.022 , c s μ s = 1.98 × 10 8 s 1 , L = 1.35 × 10 3 m , r as = 1.73 × 10 4 , τ R = 1.05 × 10 7 s .

Fig. 10
Fig. 10

Experimental PTA data and theoretical fit for a laser-pulse energy of 165 mJ and an axial hydrophone distance z = 5 mm . The fit parameters are B = 0.036 , c s μ s = 3.17 × 10 8 s 1 , L = 1.35 × 10 3 m , r as = 1.73 × 10 4 , τ R = 9.02 × 10 8 s .

Fig. 11
Fig. 11

Experimental PTA data and theoretical fit for a laser-pulse energy of 165 mJ and an axial hydrophone distance z = 8 mm . The fit parameters are B = 0.006 , c s μ s = 1.98 × 10 8 s 1 , L = 1.41 × 10 3 m , r as = 1.73 × 10 4 , τ R = 1.07 × 10 8 s .

Fig. 12
Fig. 12

Experimental PTA data and theoretical fit for a laser-pulse energy of 265 mJ and an axial hydrophone distance z = 2 mm . The fit parameters are B = 0.094 , c s μ s = 1.54 × 10 8 s 1 , L = 1.35 × 10 3 m , r as = 67 × 10 4 , τ R = 8.93 × 10 8 s .

Fig. 13
Fig. 13

Experimental PTA data and theoretical fit for a laser-pulse energy of 265 mJ and an axial hydrophone distance z = 5 mm . The fit parameters are B = 0.047 , c s μ s = 1.54 × 10 8 s 1 , L = 1.37 × 10 3 m , r as = 67 × 10 4 , τ R = 1.07 × 10 8 s .

Fig. 14
Fig. 14

Experimental PTA data and theoretical fit for a laser-pulse energy of 265 mJ and an axial hydrophone distance z = 8 mm . The fit parameters are B = 0.076 , c s μ s = 1.54 × 10 8 s 1 , L = 1.41 × 10 3 m , r as = 67 × 10 4 , τ R = 1.0 × 10 8 s .

Fig. 15
Fig. 15

PTA peak pressure of the primary condensation pulse in water versus incident laser fluence for three locations of the hydrophone. z = 8 mm (triangles), z = 5 mm (circles), z = 2 mm (squares).

Equations (69)

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ρ f ( r , t ) = ρ f 0 + ρ 1 ( r , t ) ,
V ( r , t ) = Ψ f ( r , t ) ,
2 Ψ f ( r , t ) t 2 c f 0 2 2 Ψ f ( r , t ) = ( T f 0 c f 0 2 β C P ) S 1 ( r , t ) t .
γ 1 = T f 0 c f 0 2 β 2 C P 1 ,
2 Ψ f ( r , t ) t 2 c f 0 2 2 Ψ f ( r , t ) = c f 0 2 β ρ f 0 C P Q ( r , t ) ,
P f ( r , t ) = ρ f 0 t Ψ f ( r , t ) ,
U s ( r , t ) = Φ s ( r , t ) .
2 Φ s ( r , t ) 1 c s 2 2 t 2 Φ s ( r , t ) = ( K s β s ρ s c s 2 ) Θ s ( r , t ) ,
P s ( r , t ) = ρ s 2 t 2 Φ s ( r , t ) .
ϕ s ( z , ω ) = 1 2 π Φ s ( z , t ) exp ( i ω t ) d t
d 2 d z 2 ϕ s ( z , ω ) + k s 2 ϕ s ( z , ω ) = ( K s β s ρ s c s 2 ) ϑ s ( z , ω ) , L z 0 ,
d 2 d z 2 ϑ s ( z , ω ) ( i ω α s ) ϑ s ( z , ω ) = 1 λ s H ( z , ω ) ,
H ( z , ω ) = μ s I 0 exp [ μ s ( L + z ) + i ω t ] .
ϑ s ( z , ω ) = ( i I 0 μ s ω ρ s C s P ) exp [ μ s ( L + z ) ] ,
ϕ s ( z , ω ) = A s 1 exp ( i k s z ) + A s 2 exp ( i k s z ) + D s exp [ μ s ( L + z ) ] ,
D s = i K s β s I 0 μ s ρ s 2 c s 2 C s P ω ( μ s 2 + k s 2 ) .
d 2 d z 2 ψ f ( z , ω ) + k 0 f 2 ψ f ( z , ω ) = 0 , 0 z .
ψ f ( z , ω ) = C 1 exp ( i k 0 f z ) .
ψ a ( z , ω ) = C 2 exp [ i k a ( z + L ) ] .
σ z z ( z , t ) = ρ s c s 2 u z z ( z , t ) K s β s Θ s ( z , t ) .
u z z ( z , t ) = 2 z 2 Φ s ( z , t ) ,
ρ s c s 2 d 2 d z 2 ϕ ( 0 , ω ) K s β s ϑ s ( 0 , ω ) = p f ( 0 , ω ) = i ρ f 0 ω ψ f ( 0 , ω ) ,
ρ s c s 2 d 2 d z 2 ϕ s ( L , ω ) K s β s ϑ s ( L , ω ) = p a ( L , ω ) = i ρ a ω ψ a ( L , ω ) ,
V s ( z , t ) = t U s ( z , t ) = 2 z t Φ s ( z , t ) v s ( z , ω ) = i ω d d z ϕ s ( z , ω ) .
i ω d d z ϕ s ( 0 , ω ) = d d z ψ f ( 0 , ω ) ,
i ω d d z ϕ s ( L , ω ) = d d z ψ a ( L , ω ) .
A s 2 = I 0 K s β s μ s [ μ s c a ( ρ a ρ s ) + i ω ] exp ( i k s L ) ρ s 2 c s 2 C s P ω 2 ( μ s 2 + k s 2 ) ( 1 + r as ) [ 1 R f s R as exp ( 2 i k s L ) ] ,
A s 1 = R f s A s 2 ,
r i j = ρ i c i ρ j c j
R i j = 1 r i j 1 + r i j
p f ( z , ω ) = ρ s ω 2 T f s A s 2 ( ω ) exp ( i k 0 f z ) ,
T i j = 2 1 + r i j
p f ( z , ω ) = I 0 K s T f s c s ( 1 + r as ) [ r as Γ R s ( ω ) + Γ F s ( ω ) ] exp ( i k 0 f z ) n = 0 ( R f s R as ) n exp [ i ( 2 n + 1 ) k s L ] .
Γ R s ( ω ) β s ρ s C s P ( μ s 2 μ s 2 + k s 2 ) ,
Γ F s ( ω ) i β s ρ s C s P ( μ s k s μ s 2 + k s 2 ) ,
τ μ s = 1 μ s [ c s ( ρ a ρ s ) ] T ω ,
p f ( z , ω ) p f ( R ) ( z , ω ) + p f ( F ) ( z , ω )
p f ( R ) ( z , ω ) = I 0 K s T f s c s ( r as 1 + r as ) f s ( L , ω ) Γ R s ( ω ) exp ( i k 0 f z ) ,
p f ( F ) ( z , ω ) = I 0 K s T f s c s ( 1 1 + r as ) f s ( L , ω ) Γ F s ( ω ) exp ( i k 0 f z ) .
f s ( L , ω ) n = 0 ( R f s R as ) n exp [ i ( 2 n + 1 ) k s L ]
I ( x , y , z ; ω ) = I 0 exp [ ( r W ) 2 μ s ( z + L ) + i ω t ] .
L D ( ω ) = ω W 2 2 c f 0 .
Γ R s , F s ( ω ) Γ R s , F s ( D ) ( r , ω ) = Γ R s , F s ( ω ) 1 i ( z L D ) exp [ r 2 1 i ( z L D ) ] .
Γ R s , F s ( D ) ( 0 , ω ) = Γ R s , F s ( ω ) g f ( ω ) ,
g f ( ω , z ) = 1 1 i ( Ω f ω ) , Ω f ( z ) 2 c f 0 z W 2 .
p f ( z , ω ) = I 0 K s T f s c s ( 1 + r as ) f s ( L , ω ) [ r as Γ R s ( ω ) + Γ F s ( ω ) ] g f ( ω ) exp ( i k 0 f z ) .
ϑ s ( z , ω ) = ( i I 0 μ s ω ρ s C s P ) f P ( ω ) exp [ μ s ( L + z ) ]
P f ( z , t )
= I 0 K s T f s c s ( 1 + r as ) [ r as Γ R s ( ω ) f s ( L , ω ) f P ( ω ) g f ( ω ) exp ( i ω τ ) d ω + Γ F s ( ω ) f s ( L , ω ) f P ( ω ) g f ( ω ) exp ( i ω τ ) d ω ] ,
P f ( F ) ( z , τ ) = ( 1 r as μ s c s ) d d τ P f ( R ) ( z , τ ) .
τ n ( z ) = t z c 0 f ( 2 n + 1 ) L c s , n = 0 , 1 , 2 , ,
P f ( R ) ( z , τ 0 ) = I 0 K s T f s c s ( r as 1 + r as ) Γ R s ( ω ) g f ( ω ) exp ( i ω τ 0 ) d ω .
P 0 f ( R ) ( z , τ 0 ) = I 0 K s T f s c s ( r as 1 + r as ) Γ R s ( ω ) exp ( i ω τ 0 ) d ω .
FT 1 [ g f ( z , ω ) ] = G f ( z , t ) = 2 π { δ ( t ) Ω f ( z ) exp [ Ω f ( z ) t ] H ( t ) } ,
P f ( R ) ( z , τ 0 ) = μ s c s r as P 0 f ( F ) ( z , t ) exp [ Ω f ( z ) ( τ 0 t ) ] d t .
d 2 d z 2 ψ f ( z , ω ) + k b f 2 ψ f ( z , ω ) = 0 , 0 z < ,
k b f 2 = k 0 f 2 1 + i ν b , ν b k 0 f b ρ f c 0 f .
exp ( i k b f z ) = exp [ k 0 f ( z z A ) sin ( θ 2 ) ] exp [ i k 0 f ( z z A ) cos ( θ 2 ) ] ,
z A = ( 1 + ν b 2 ) 1 2 k 0 f .
h f ( τ ) = 1 2 c s μ s ( 1 + r as ) [ ( 1 1 + B ) exp ( c s μ s τ ) H ( τ ) ( R as 1 B ) exp ( c s μ s τ ) H ( τ ) ] + c s μ s B ( B r as ) 1 B 2 exp ( c s μ s B τ ) H ( τ ) ,
P f ( z , τ ) = I 0 C 1 f 1 ( 0 ) exp ( c s μ s τ ) H ( τ ) + I 0 [ C 1 exp ( c s μ s τ ) f 1 ( τ ) C 2 exp ( c s μ s τ ) f 2 ( τ ) + C 3 exp ( c s μ s B τ ) f 3 ( τ ) ] H ( τ ) ,
f 1 ( τ ) = τ F P ( t ) exp ( c s μ s t ) d t ,
f 2 ( τ ) = 0 τ F P ( t ) exp ( c s μ s t ) d t ,
f 3 ( τ ) = 0 τ F P ( t ) exp ( c s μ s B t ) d t .
C 1 = c s μ s ( 1 + r as ) 2 ( 1 + B ) , C 2 = c s μ s ( 1 + r as ) R as 2 ( 1 B ) ,
C 3 = c s μ s B ( B r as ) ( 1 B 2 ) .
F P ( t ) = { A 1 ( t τ R ) 2 exp [ A 2 ( t τ R ) ] + A 3 ( t τ R ) 3 exp [ A 4 ( t τ R ) ] } H ( t ) .
f m ( t ) = A m exp ( t τ m ) cos ( ω m t + ϕ m ) , t 0 .
F m ( ω ) = A m τ m 4 π [ exp ( i ϕ m ) 1 + i ω t + τ m + exp ( i ϕ m ) 1 + i ω t τ m ] .

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