Abstract

A rigorous theoretical model has been developed that describes the effects of optical saturation on the deflection signals in cw photothermal experiments. In this model the spatial profile of the excitation beam has been taken into account. Numerical calculations have been performed to determine the saturation behavior of the cw photothermal deflection signals at both the fundamental and the second-harmonic frequencies for sine-wave modulation of the excitation beam. Saturation behavior for square-wave modulation has also been investigated.

© 2001 Optical Society of America

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References

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  1. S. E. Bialkowski, Photothermal Spectroscopy Methods in Chemical Analysis (Wiley, New York, 1996).
  2. N. J. Dovichi, “Thermo-optical spectrophotometries in analytical chemistry,” CRC Crit. Rev. Anal. Chem. 17, 357–423 (1987).
    [CrossRef]
  3. A. Chartier, S. E. Bialkowski, “Accurate measurements of organic dye solutions by use of pulsed laser photothermal deflection spectroscopy,” Anal. Chem. 67, 2672–2684 (1995).
    [CrossRef] [PubMed]
  4. S. E. Bialkowski, “Accounting for absorption saturation effects in pulsed infrared laser-excited photothermal spectroscopy,” Appl. Opt. 32, 3177–3189 (1993).
    [CrossRef] [PubMed]
  5. A. Mandelis, J. Vanniasinkam, “Theory of nonradiative decay dynamics in intensely pumped solid-state laser media via laser photothermal diagnostics,” J. Appl. Phys. 80, 6107–6119 (1996).
    [CrossRef]
  6. B. C. Li, R. Gupta, “Effect of optical saturation on pulsed photothermal deflection signals in flowing media,” J. Appl. Phys. 88, 5515–5526 (2000).
    [CrossRef]
  7. J. Georges, N. Arnaud, L. Parise, “Limitations arising from optical saturation in fluorescence and thermal lens spectrometers using pulsed laser excitation: application to the determination of the fluorescence quantum yield of Rhodamine 6G,” Appl. Spectrosc. 50, 1505–1511 (1996).
    [CrossRef]
  8. S. B. Peralta, A. Mandelis, “Optical saturation in the photothermal spectroscopy of fluorescent materials,” Appl. Phys. A 50, 353–356 (1990).
    [CrossRef]
  9. G. Ramis-Ramos, J. J. B. Baeza, E. F. S. Alfonso, “A model for optical saturation thermal lens spectrometry,” Anal. Chim. Acta 296, 107–113 (1994).
    [CrossRef]
  10. Y. M. Biosca, G. Ramis-Ramos, “Optical saturation thermal lens spectrometry in nonpolar solvents,” Anal. Chim. Acta. 345, 257–263 (1997).
    [CrossRef]
  11. S. E. Bialkowski, A. Chartier, “Using slow measurement systems to measure fast excited-state kinetics with nonlinear rate-competitive optical bleaching,” in Photoacoustic and Photothermal Phenomena: Tenth International Conference, F. Scudieri, M. Bertolotti, eds., AIP Conf. Proc.463, 14–17 (1999).
  12. N. M. Ozisik, Heat Conduction (Wiley, New York, 1980).
  13. A. Rose, R. Vyas, R. Gupta, “Pulsed photothermal deflection spectroscopy in a flowing medium: a quantitative investigation,” Appl. Opt. 25, 4626–4643 (1986).
    [CrossRef] [PubMed]
  14. P. C. Claspy, “Infrared optoacoustic spectroscopy and detection,” in Optoacoustic Spectroscopy and Detection, Y. H. Pao, ed. (Academic, London, 1977).
  15. A. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy (Wiley, New York, 1980).

2000 (1)

B. C. Li, R. Gupta, “Effect of optical saturation on pulsed photothermal deflection signals in flowing media,” J. Appl. Phys. 88, 5515–5526 (2000).
[CrossRef]

1997 (1)

Y. M. Biosca, G. Ramis-Ramos, “Optical saturation thermal lens spectrometry in nonpolar solvents,” Anal. Chim. Acta. 345, 257–263 (1997).
[CrossRef]

1996 (2)

1995 (1)

A. Chartier, S. E. Bialkowski, “Accurate measurements of organic dye solutions by use of pulsed laser photothermal deflection spectroscopy,” Anal. Chem. 67, 2672–2684 (1995).
[CrossRef] [PubMed]

1994 (1)

G. Ramis-Ramos, J. J. B. Baeza, E. F. S. Alfonso, “A model for optical saturation thermal lens spectrometry,” Anal. Chim. Acta 296, 107–113 (1994).
[CrossRef]

1993 (1)

1990 (1)

S. B. Peralta, A. Mandelis, “Optical saturation in the photothermal spectroscopy of fluorescent materials,” Appl. Phys. A 50, 353–356 (1990).
[CrossRef]

1987 (1)

N. J. Dovichi, “Thermo-optical spectrophotometries in analytical chemistry,” CRC Crit. Rev. Anal. Chem. 17, 357–423 (1987).
[CrossRef]

1986 (1)

Alfonso, E. F. S.

G. Ramis-Ramos, J. J. B. Baeza, E. F. S. Alfonso, “A model for optical saturation thermal lens spectrometry,” Anal. Chim. Acta 296, 107–113 (1994).
[CrossRef]

Arnaud, N.

Baeza, J. J. B.

G. Ramis-Ramos, J. J. B. Baeza, E. F. S. Alfonso, “A model for optical saturation thermal lens spectrometry,” Anal. Chim. Acta 296, 107–113 (1994).
[CrossRef]

Bialkowski, S. E.

A. Chartier, S. E. Bialkowski, “Accurate measurements of organic dye solutions by use of pulsed laser photothermal deflection spectroscopy,” Anal. Chem. 67, 2672–2684 (1995).
[CrossRef] [PubMed]

S. E. Bialkowski, “Accounting for absorption saturation effects in pulsed infrared laser-excited photothermal spectroscopy,” Appl. Opt. 32, 3177–3189 (1993).
[CrossRef] [PubMed]

S. E. Bialkowski, Photothermal Spectroscopy Methods in Chemical Analysis (Wiley, New York, 1996).

S. E. Bialkowski, A. Chartier, “Using slow measurement systems to measure fast excited-state kinetics with nonlinear rate-competitive optical bleaching,” in Photoacoustic and Photothermal Phenomena: Tenth International Conference, F. Scudieri, M. Bertolotti, eds., AIP Conf. Proc.463, 14–17 (1999).

Biosca, Y. M.

Y. M. Biosca, G. Ramis-Ramos, “Optical saturation thermal lens spectrometry in nonpolar solvents,” Anal. Chim. Acta. 345, 257–263 (1997).
[CrossRef]

Chartier, A.

A. Chartier, S. E. Bialkowski, “Accurate measurements of organic dye solutions by use of pulsed laser photothermal deflection spectroscopy,” Anal. Chem. 67, 2672–2684 (1995).
[CrossRef] [PubMed]

S. E. Bialkowski, A. Chartier, “Using slow measurement systems to measure fast excited-state kinetics with nonlinear rate-competitive optical bleaching,” in Photoacoustic and Photothermal Phenomena: Tenth International Conference, F. Scudieri, M. Bertolotti, eds., AIP Conf. Proc.463, 14–17 (1999).

Claspy, P. C.

P. C. Claspy, “Infrared optoacoustic spectroscopy and detection,” in Optoacoustic Spectroscopy and Detection, Y. H. Pao, ed. (Academic, London, 1977).

Dovichi, N. J.

N. J. Dovichi, “Thermo-optical spectrophotometries in analytical chemistry,” CRC Crit. Rev. Anal. Chem. 17, 357–423 (1987).
[CrossRef]

Georges, J.

Gupta, R.

B. C. Li, R. Gupta, “Effect of optical saturation on pulsed photothermal deflection signals in flowing media,” J. Appl. Phys. 88, 5515–5526 (2000).
[CrossRef]

A. Rose, R. Vyas, R. Gupta, “Pulsed photothermal deflection spectroscopy in a flowing medium: a quantitative investigation,” Appl. Opt. 25, 4626–4643 (1986).
[CrossRef] [PubMed]

Li, B. C.

B. C. Li, R. Gupta, “Effect of optical saturation on pulsed photothermal deflection signals in flowing media,” J. Appl. Phys. 88, 5515–5526 (2000).
[CrossRef]

Mandelis, A.

A. Mandelis, J. Vanniasinkam, “Theory of nonradiative decay dynamics in intensely pumped solid-state laser media via laser photothermal diagnostics,” J. Appl. Phys. 80, 6107–6119 (1996).
[CrossRef]

S. B. Peralta, A. Mandelis, “Optical saturation in the photothermal spectroscopy of fluorescent materials,” Appl. Phys. A 50, 353–356 (1990).
[CrossRef]

Ozisik, N. M.

N. M. Ozisik, Heat Conduction (Wiley, New York, 1980).

Parise, L.

Peralta, S. B.

S. B. Peralta, A. Mandelis, “Optical saturation in the photothermal spectroscopy of fluorescent materials,” Appl. Phys. A 50, 353–356 (1990).
[CrossRef]

Ramis-Ramos, G.

Y. M. Biosca, G. Ramis-Ramos, “Optical saturation thermal lens spectrometry in nonpolar solvents,” Anal. Chim. Acta. 345, 257–263 (1997).
[CrossRef]

G. Ramis-Ramos, J. J. B. Baeza, E. F. S. Alfonso, “A model for optical saturation thermal lens spectrometry,” Anal. Chim. Acta 296, 107–113 (1994).
[CrossRef]

Rose, A.

Rosencwaig, A.

A. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy (Wiley, New York, 1980).

Vanniasinkam, J.

A. Mandelis, J. Vanniasinkam, “Theory of nonradiative decay dynamics in intensely pumped solid-state laser media via laser photothermal diagnostics,” J. Appl. Phys. 80, 6107–6119 (1996).
[CrossRef]

Vyas, R.

Anal. Chem. (1)

A. Chartier, S. E. Bialkowski, “Accurate measurements of organic dye solutions by use of pulsed laser photothermal deflection spectroscopy,” Anal. Chem. 67, 2672–2684 (1995).
[CrossRef] [PubMed]

Anal. Chim. Acta (1)

G. Ramis-Ramos, J. J. B. Baeza, E. F. S. Alfonso, “A model for optical saturation thermal lens spectrometry,” Anal. Chim. Acta 296, 107–113 (1994).
[CrossRef]

Anal. Chim. Acta. (1)

Y. M. Biosca, G. Ramis-Ramos, “Optical saturation thermal lens spectrometry in nonpolar solvents,” Anal. Chim. Acta. 345, 257–263 (1997).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. A (1)

S. B. Peralta, A. Mandelis, “Optical saturation in the photothermal spectroscopy of fluorescent materials,” Appl. Phys. A 50, 353–356 (1990).
[CrossRef]

Appl. Spectrosc. (1)

CRC Crit. Rev. Anal. Chem. (1)

N. J. Dovichi, “Thermo-optical spectrophotometries in analytical chemistry,” CRC Crit. Rev. Anal. Chem. 17, 357–423 (1987).
[CrossRef]

J. Appl. Phys. (2)

A. Mandelis, J. Vanniasinkam, “Theory of nonradiative decay dynamics in intensely pumped solid-state laser media via laser photothermal diagnostics,” J. Appl. Phys. 80, 6107–6119 (1996).
[CrossRef]

B. C. Li, R. Gupta, “Effect of optical saturation on pulsed photothermal deflection signals in flowing media,” J. Appl. Phys. 88, 5515–5526 (2000).
[CrossRef]

Other (5)

S. E. Bialkowski, Photothermal Spectroscopy Methods in Chemical Analysis (Wiley, New York, 1996).

P. C. Claspy, “Infrared optoacoustic spectroscopy and detection,” in Optoacoustic Spectroscopy and Detection, Y. H. Pao, ed. (Academic, London, 1977).

A. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy (Wiley, New York, 1980).

S. E. Bialkowski, A. Chartier, “Using slow measurement systems to measure fast excited-state kinetics with nonlinear rate-competitive optical bleaching,” in Photoacoustic and Photothermal Phenomena: Tenth International Conference, F. Scudieri, M. Bertolotti, eds., AIP Conf. Proc.463, 14–17 (1999).

N. M. Ozisik, Heat Conduction (Wiley, New York, 1980).

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Figures (7)

Fig. 1
Fig. 1

Spatial profile of the source term at (a) the fundamental frequency and (b) the second-harmonic frequency, obtained with different excitation intensities, I 0/I S = 1, 5, 10, and 100, as labeled.

Fig. 2
Fig. 2

Amplitudes of (a) the fundamental and (b) the second-harmonic components of the source term, as a function of the excitation intensity, at different positions of the beam r/ a = 0, 0.5, and 1.0, as labeled.

Fig. 3
Fig. 3

(a) Fundamental and (b) second-harmonic components of the temperature rise as a function of radial position, obtained with different excitation intensities, I 0/I S = 1, 5, 10, and 100, as labeled.

Fig. 4
Fig. 4

(a) Fundamental and (b) second-harmonic components of the collinear deflection as a function of the radial position, obtained with different excitation intensities, I 0/I S = 1, 5, 10, and 100, as labeled.

Fig. 5
Fig. 5

Dependence of the maximum deflection amplitude and of the position of the maximum deflection on the excitation intensity for the fundamental and the second-harmonic components: solid curves, deflection amplitude; dotted curves, position.

Fig. 6
Fig. 6

Comparison of the saturation behaviors of the fundamental components of the deflection signals obtained with square wave and sine wave modulations: solid curves, results for the square wave modulation; dashed curves, results for the sine wave modulation.

Fig. 7
Fig. 7

Saturation behaviors of the fundamental and the second-harmonic components of the photothermal deflection signals for absorbing media with inhomogeneously broadened line shapes.

Equations (15)

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α=α0/1+I/IS
α=α0/1+I/IS1/2
2Tr, t-1DTr, tt=-Qr, tKth,
Ir, t=12Ir1+cosωt,
Ir=I0exp-2r2a2=2P0πa2exp-2r2a2,
Qr, t=αIr, t=12α0Ir1+cosωt1+Ir2IS1+cosωth,
Qr, t=12 a0r+m=1M amrcosmωt,
amr=2ωπ0π/ω Qr, tcosmωtdt  m=0, 1, 2, .
Tmr, t=12Tmrexpimωt+c.c.  m=1, 2, 
Tmr=0 δJ0δrAmδKthδ2+imωDdδ  m=1, 2, ,
Amδ=0 rJ0δramrdr  m=1, 2, .
ϕr, t=1n0dndT l Tr, tr,
ϕmr=1n0dndT l 0 δ2J1δrAmδKthδ2+imωDdδ  m=1, 2, ,
a1r=2πα0Ir1+Ir/ISh,
a2r=0.

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