Abstract

We describe a calibrated two-beam mode-mismatched thermal lens experiment aimed at determination of the absorption coefficient and the photothermal parameters of a nearly transparent material. The use of a collimated probe beam in the presence of a focused excitation beam optimizes the thermal lens experiment. The signal becomes independent from the Rayleigh parameters and waist positions of the beams. We apply this method to determine the absolute value of the thermal diffusivity and absorption coefficient of distilled water at 533nm.

© 2006 Optical Society of America

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  1. N. J. Dovichi, "Thermo-optical spectrophotometries in analytical chemistry," Crit. Rev. Anal. Chem. 17, 357-423 (1987).
    [CrossRef]
  2. R. D. Snook and R. D. Lowe, "Thermal lens spectrometry, a review," Analyst (London) 120, 2052-2068 (1994).
  3. N. J. Dovichi and J. M. Harris, "Laser induced thermal lens effect for calorimetric trace analysis," Anal. Chem. 51, 728-731 (1979).
    [CrossRef]
  4. S. E. Bialkowski, Photothermal Spectroscopy Methods for Chemical Analysis (Wiley, 1996).
  5. 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 liquids samples," Bull. Am. Phys. Soc. 9, 501 (1964).
  6. J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, "Long transient effects in lasers with lasers with inserted liquid samples," J. Appl. Phys. 36, 3-8 (1965).
    [CrossRef]
  7. R. C. C. Leite, R. S. Moore, and J. R. Whinnery, "Low absorption measurement by mean of the thermal lens effect using a He-Ne laser," Appl. Phys. Lett. 5, 141-143 (1964).
    [CrossRef]
  8. D. Solimini, "Loss measurement of organic materials at 6328 Å," J. Appl. Phys. 37, 3314-3315 (1966).
    [CrossRef]
  9. H. Ma, A. S. Gomes, and C. B. de Araujo, "Measurement of nondegenerate optical nonlinearity using a two-color single beam method," Appl. Phys. Lett. 59, 2666-2668 (1991).
    [CrossRef]
  10. M. Sheik-Bahae, J. Wang, R. De Salvo, D. J. Hagan, and E. Van Stryland, "Measurement of nondegenerate nonlinearities using a two-color Z-scan," Opt. Lett. 17, 258-260 (1992).
    [CrossRef] [PubMed]
  11. J. Castillo, V. P. Kozich, and A. Marcano O., "Thermal lensing due to one- and two-photon absorption studied with two-color time resolved Z-scan," Opt. Lett. 19, 171-173 (1994).
    [CrossRef] [PubMed]
  12. J. Shen, R. D. Lowe, and R. D. Snook, "A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry," Chem. Phys. 165, 385-396 (1992).
    [CrossRef]
  13. J. Shen, A. J. Soroka, and R. D. Snook, "A model for cw laser induced mode-mismatched thermal lens spectrometry based on probe beam profile image detection," J. Appl. Phys. 78, 700-708 (1995).
    [CrossRef]
  14. A. Marcano O., C. Loper, and N. Melikechi, "Pump-probe mode-mismatched thermal lens Z-scan," J. Opt. Soc. Am. B 19, 119-124 (2002).
    [CrossRef]
  15. A. Marcano O., L. Rodríguez, and N. Melikechi, "Thermal lensing in extended samples," Appl. Spectrosc. 56, 1504-1507 (2002).
    [CrossRef]
  16. R. M. Pope and E. S. Fry, "Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements," Appl. Opt. 36, 8710-8722 (1997).
    [CrossRef]

2002 (2)

1997 (1)

1995 (1)

J. Shen, A. J. Soroka, and R. D. Snook, "A model for cw laser induced mode-mismatched thermal lens spectrometry based on probe beam profile image detection," J. Appl. Phys. 78, 700-708 (1995).
[CrossRef]

1994 (2)

1992 (2)

J. Shen, R. D. Lowe, and R. D. Snook, "A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry," Chem. Phys. 165, 385-396 (1992).
[CrossRef]

M. Sheik-Bahae, J. Wang, R. De Salvo, D. J. Hagan, and E. Van Stryland, "Measurement of nondegenerate nonlinearities using a two-color Z-scan," Opt. Lett. 17, 258-260 (1992).
[CrossRef] [PubMed]

1991 (1)

H. Ma, A. S. Gomes, and C. B. de Araujo, "Measurement of nondegenerate optical nonlinearity using a two-color single beam method," Appl. Phys. Lett. 59, 2666-2668 (1991).
[CrossRef]

1987 (1)

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

1979 (1)

N. J. Dovichi and J. M. Harris, "Laser induced thermal lens effect for calorimetric trace analysis," Anal. Chem. 51, 728-731 (1979).
[CrossRef]

1966 (1)

D. Solimini, "Loss measurement of organic materials at 6328 Å," J. Appl. Phys. 37, 3314-3315 (1966).
[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 lasers with inserted liquid samples," J. Appl. Phys. 36, 3-8 (1965).
[CrossRef]

1964 (2)

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, "Low absorption measurement by mean of the thermal lens effect using a He-Ne laser," Appl. Phys. Lett. 5, 141-143 (1964).
[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 liquids samples," Bull. Am. Phys. Soc. 9, 501 (1964).

Bialkowski, S. E.

S. E. Bialkowski, Photothermal Spectroscopy Methods for Chemical Analysis (Wiley, 1996).

Castillo, J.

de Araujo, C. B.

H. Ma, A. S. Gomes, and C. B. de Araujo, "Measurement of nondegenerate optical nonlinearity using a two-color single beam method," Appl. Phys. Lett. 59, 2666-2668 (1991).
[CrossRef]

De Salvo, R.

Dovichi, N. J.

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

N. J. Dovichi and J. M. Harris, "Laser induced thermal lens effect for calorimetric trace analysis," Anal. Chem. 51, 728-731 (1979).
[CrossRef]

Fry, E. S.

Gomes, A. S.

H. Ma, A. S. Gomes, and C. B. de Araujo, "Measurement of nondegenerate optical nonlinearity using a two-color single beam method," Appl. Phys. Lett. 59, 2666-2668 (1991).
[CrossRef]

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 lasers with inserted liquid samples," J. Appl. Phys. 36, 3-8 (1965).
[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 liquids samples," Bull. Am. Phys. Soc. 9, 501 (1964).

Hagan, D. J.

Harris, J. M.

N. J. Dovichi and J. M. Harris, "Laser induced thermal lens effect for calorimetric trace analysis," Anal. Chem. 51, 728-731 (1979).
[CrossRef]

Kozich, V. P.

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 lasers with inserted liquid samples," J. Appl. Phys. 36, 3-8 (1965).
[CrossRef]

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, "Low absorption measurement by mean of the thermal lens effect using a He-Ne laser," Appl. Phys. Lett. 5, 141-143 (1964).
[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 liquids samples," Bull. Am. Phys. Soc. 9, 501 (1964).

Loper, C.

Lowe, R. D.

R. D. Snook and R. D. Lowe, "Thermal lens spectrometry, a review," Analyst (London) 120, 2052-2068 (1994).

J. Shen, R. D. Lowe, and R. D. Snook, "A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry," Chem. Phys. 165, 385-396 (1992).
[CrossRef]

Ma, H.

H. Ma, A. S. Gomes, and C. B. de Araujo, "Measurement of nondegenerate optical nonlinearity using a two-color single beam method," Appl. Phys. Lett. 59, 2666-2668 (1991).
[CrossRef]

Marcano O., A.

Melikechi, N.

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 lasers with inserted liquid samples," J. Appl. Phys. 36, 3-8 (1965).
[CrossRef]

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, "Low absorption measurement by mean of the thermal lens effect using a He-Ne laser," Appl. Phys. Lett. 5, 141-143 (1964).
[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 liquids samples," Bull. Am. Phys. Soc. 9, 501 (1964).

Pope, R. M.

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 lasers with inserted liquid samples," J. Appl. Phys. 36, 3-8 (1965).
[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 liquids samples," Bull. Am. Phys. Soc. 9, 501 (1964).

Rodríguez, L.

Sheik-Bahae, M.

Shen, J.

J. Shen, A. J. Soroka, and R. D. Snook, "A model for cw laser induced mode-mismatched thermal lens spectrometry based on probe beam profile image detection," J. Appl. Phys. 78, 700-708 (1995).
[CrossRef]

J. Shen, R. D. Lowe, and R. D. Snook, "A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry," Chem. Phys. 165, 385-396 (1992).
[CrossRef]

Snook, R. D.

J. Shen, A. J. Soroka, and R. D. Snook, "A model for cw laser induced mode-mismatched thermal lens spectrometry based on probe beam profile image detection," J. Appl. Phys. 78, 700-708 (1995).
[CrossRef]

R. D. Snook and R. D. Lowe, "Thermal lens spectrometry, a review," Analyst (London) 120, 2052-2068 (1994).

J. Shen, R. D. Lowe, and R. D. Snook, "A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry," Chem. Phys. 165, 385-396 (1992).
[CrossRef]

Solimini, D.

D. Solimini, "Loss measurement of organic materials at 6328 Å," J. Appl. Phys. 37, 3314-3315 (1966).
[CrossRef]

Soroka, A. J.

J. Shen, A. J. Soroka, and R. D. Snook, "A model for cw laser induced mode-mismatched thermal lens spectrometry based on probe beam profile image detection," J. Appl. Phys. 78, 700-708 (1995).
[CrossRef]

Van Stryland, E.

Wang, J.

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 lasers with inserted liquid samples," J. Appl. Phys. 36, 3-8 (1965).
[CrossRef]

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, "Low absorption measurement by mean of the thermal lens effect using a He-Ne laser," Appl. Phys. Lett. 5, 141-143 (1964).
[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 liquids samples," Bull. Am. Phys. Soc. 9, 501 (1964).

Anal. Chem. (1)

N. J. Dovichi and J. M. Harris, "Laser induced thermal lens effect for calorimetric trace analysis," Anal. Chem. 51, 728-731 (1979).
[CrossRef]

Analyst (London) (1)

R. D. Snook and R. D. Lowe, "Thermal lens spectrometry, a review," Analyst (London) 120, 2052-2068 (1994).

Appl. Opt. (1)

Appl. Phys. Lett. (2)

H. Ma, A. S. Gomes, and C. B. de Araujo, "Measurement of nondegenerate optical nonlinearity using a two-color single beam method," Appl. Phys. Lett. 59, 2666-2668 (1991).
[CrossRef]

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, "Low absorption measurement by mean of the thermal lens effect using a He-Ne laser," Appl. Phys. Lett. 5, 141-143 (1964).
[CrossRef]

Appl. Spectrosc. (1)

Bull. Am. Phys. Soc. (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 liquids samples," Bull. Am. Phys. Soc. 9, 501 (1964).

Chem. Phys. (1)

J. Shen, R. D. Lowe, and R. D. Snook, "A model for cw laser induced mode-mismatched dual-beam thermal lens spectrometry," Chem. Phys. 165, 385-396 (1992).
[CrossRef]

Crit. Rev. Anal. Chem. (1)

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

J. Appl. Phys. (3)

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

D. Solimini, "Loss measurement of organic materials at 6328 Å," J. Appl. Phys. 37, 3314-3315 (1966).
[CrossRef]

J. Shen, A. J. Soroka, and R. D. Snook, "A model for cw laser induced mode-mismatched thermal lens spectrometry based on probe beam profile image detection," J. Appl. Phys. 78, 700-708 (1995).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

Other (1)

S. E. Bialkowski, Photothermal Spectroscopy Methods for Chemical Analysis (Wiley, 1996).

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Figures (8)

Fig. 1
Fig. 1

(a) Schematic of a normal TL experiment in which both the excitation and the probe beams are focused with similar Rayleigh parameters and beam waists displaced by a Rayleigh parameter. (b) Proposed TL experiment with a collimated probe beam in the presence of a focused excitation field.

Fig. 2
Fig. 2

TL signal as a function of sample position (Z scan) calculated from Eq. (2) for the values of the Rayleigh excitation beam parameter indicated. The rest of the parameters are λ e = 533 nm , λ p = 632 nm , z p = 10 000 cm , a e = a p = 0 cm , L = 150 cm , t = 10 s , D = 1.4 × 10 3 cm 2 s , and ϕ o = 0.028 .

Fig. 3
Fig. 3

TL signal as a function of sample position (Z scan) calculated from Eq. (2) for the values of the probe beam Rayleigh parameters indicated. The Rayleigh parameter for the excitation beam is z e = 1 cm . The rest of the parameters are as in Fig. 2.

Fig. 4
Fig. 4

Experimental setup: probe source (He–Ne laser), excitation source (diode-pumped Nd:YAG laser), probe beam collimating lenses L 1 and L 2 , mirrors M 1 and M 2 , dichroic beam splitter DB, excitation beam focusing lens L 3 , beam splitter B 1 , reference detector Ref, shutter Sh, sample S, interference filter F 1 , aperture A, signal detector Sig, current preamplifier Amp, and digital oscilloscope Osc.

Fig. 5
Fig. 5

TL photocurrent for distilled water as a function of time for an excitation power of 325 mW . The values of the probe beam aperture's transmission in the absence ( T o ) and in the presence [ T ( z , t ) ] of the excitation beam are indicated.

Fig. 6
Fig. 6

Experimental TL signal for distilled water calculated from Eq. (1) and the data of Fig. 1. The curve represents a fit of the experimental data by use of Eq. (2) and the parameters λ e = 533 nm , λ p = 632 nm , z p = 10 000 cm , z e = 0.85 cm , a e = 0 , a p = 0 cm , L = 150 cm , t = 10 s , D = 1.42 × 10 3 cm 2 s , and ϕ o = 0.028 .

Fig. 7
Fig. 7

Z-scan curves for distilled water and for the excitation beam Rayleigh parameters indicated. Solid curves are theoretical fittings of these curves by use of Eq. (2) and the parameters ϕ o = 0.024 , 0.028 , and 0.026 corresponding to z p = 0.2 , 0.85, and 3 cm , respectively, and for nearly the same excitation powers of 235, 260, and 240 mW , respectively. The rest of the parameters are as in Fig. 2.

Fig. 8
Fig. 8

Dependence on excitation power of the maximum values of the TL signal for distilled water and for z e = 3 cm . Solid line, least-squares linear fit of the experimental data.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

S ( z , t ) = [ T ( z , t ) T o ] T o ,
S ( z , t ) = Φ o K ( z , t ) ,
K ( z , t ) = arctan ( 4 m ( z ) v ( z ) t t c ( z ) { [ 1 + 2 m ( z ) + v ( z ) 2 ] 2 t t c ( z ) + [ 1 + 2 m ( z ) ] 2 + v ( z ) 2 } ) ,
Φ o = P o α l ( d n d T ) ( κ λ p )
K ( 0 , t ) = arctan [ 2 ( λ p λ e ) ( L z e ) ] .
S max = π Φ o 2 ,
α = 0.088 w 1 [ κ λ p ( l d n d T ) ] .

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