Abstract

A diffraction theory of continuous-wave photothermal deflection (PD) spectroscopy with fundamental and harmonic responses is presented. The displacement of the probe beam centroid is found to be a rigorous measurement of PD effect, which leads to a set of analytical solutions to the fundamental and the second-order harmonics. Harmonics are caused by the diffraction of the probe beam in the mirage region, which could not be handled by geometric-optics theory. This theory can be used to study bulk materials, thin films, and layered-structure samples. Experimental results are in good agreement with the theory.

© 2002 Optical Society of America

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  1. B. C. Li and R. Gupta, J. Appl. Phys. 89, 859 (2001).
    [CrossRef]
  2. K. Tanaka, T. Gotoh, N. Yoshida, and S. Nonomura, J. Appl. Phys. 91, 125 (2002).
    [CrossRef]
  3. L. M. Wu and A. Knoesen, J. Polym. Sci. Part B 39, 2717 (2001).
    [CrossRef]
  4. W. B. Jackson, N. M. Amer, A. C. Baccara, and D. Fournier, Appl. Opt. 20, 1333 (1981).
    [CrossRef] [PubMed]
  5. L. C. Aamodt and J. C. Murphy, J. Appl. Phys. 52, 4903 (1981).
    [CrossRef]
  6. A. L. Glazov and K. L. Muratikov, Opt. Commun. 84, 283 (1991).
    [CrossRef]
  7. Y. N. Rajakarunanayake and H. K. Wickramasinghe, Appl. Phys. Lett. 48, 218 (1986).
    [CrossRef]
  8. O. Doka, A. Miklos, and A. Lorincz, Appl. Phys. A 48, 415 (1989).
    [CrossRef]
  9. J. F. Power and M. A. Schweitzer, Opt. Eng. 36, 521 (1997).
    [CrossRef]
  10. J. F. Power, S. W. Fu, and M. A. Schweitzer, Appl. Spectrosc. 54, 110 (2000).
    [CrossRef]
  11. A. Rosencwaig and A. Gersho, J. Appl. Phys. 47, 64 (1976).
    [CrossRef]
  12. G. C. Wetsel and J. B. Spicer, Can. J. Phys. 64, 1269 (1986).
    [CrossRef]
  13. B. C. Li and R. Gupta, Appl. Opt. 40, 1563 (2001).
    [CrossRef]
  14. V. Gusev, A. Mandelis, and R. Bleiss, Appl. Phys. A 57, 229 (1993).
    [CrossRef]
  15. J. Shen, A. Mandelis, and T. Ashe, Int. J. Thermophys. 19, 579 (1998).
    [CrossRef]

2002 (1)

K. Tanaka, T. Gotoh, N. Yoshida, and S. Nonomura, J. Appl. Phys. 91, 125 (2002).
[CrossRef]

2001 (3)

L. M. Wu and A. Knoesen, J. Polym. Sci. Part B 39, 2717 (2001).
[CrossRef]

B. C. Li and R. Gupta, J. Appl. Phys. 89, 859 (2001).
[CrossRef]

B. C. Li and R. Gupta, Appl. Opt. 40, 1563 (2001).
[CrossRef]

2000 (1)

1998 (1)

J. Shen, A. Mandelis, and T. Ashe, Int. J. Thermophys. 19, 579 (1998).
[CrossRef]

1997 (1)

J. F. Power and M. A. Schweitzer, Opt. Eng. 36, 521 (1997).
[CrossRef]

1993 (1)

V. Gusev, A. Mandelis, and R. Bleiss, Appl. Phys. A 57, 229 (1993).
[CrossRef]

1991 (1)

A. L. Glazov and K. L. Muratikov, Opt. Commun. 84, 283 (1991).
[CrossRef]

1989 (1)

O. Doka, A. Miklos, and A. Lorincz, Appl. Phys. A 48, 415 (1989).
[CrossRef]

1986 (2)

Y. N. Rajakarunanayake and H. K. Wickramasinghe, Appl. Phys. Lett. 48, 218 (1986).
[CrossRef]

G. C. Wetsel and J. B. Spicer, Can. J. Phys. 64, 1269 (1986).
[CrossRef]

1981 (2)

1976 (1)

A. Rosencwaig and A. Gersho, J. Appl. Phys. 47, 64 (1976).
[CrossRef]

Aamodt, L. C.

L. C. Aamodt and J. C. Murphy, J. Appl. Phys. 52, 4903 (1981).
[CrossRef]

Amer, N. M.

Ashe, T.

J. Shen, A. Mandelis, and T. Ashe, Int. J. Thermophys. 19, 579 (1998).
[CrossRef]

Baccara, A. C.

Bleiss, R.

V. Gusev, A. Mandelis, and R. Bleiss, Appl. Phys. A 57, 229 (1993).
[CrossRef]

Doka, O.

O. Doka, A. Miklos, and A. Lorincz, Appl. Phys. A 48, 415 (1989).
[CrossRef]

Fournier, D.

Fu, S. W.

Gersho, A.

A. Rosencwaig and A. Gersho, J. Appl. Phys. 47, 64 (1976).
[CrossRef]

Glazov, A. L.

A. L. Glazov and K. L. Muratikov, Opt. Commun. 84, 283 (1991).
[CrossRef]

Gotoh, T.

K. Tanaka, T. Gotoh, N. Yoshida, and S. Nonomura, J. Appl. Phys. 91, 125 (2002).
[CrossRef]

Gupta, R.

B. C. Li and R. Gupta, J. Appl. Phys. 89, 859 (2001).
[CrossRef]

B. C. Li and R. Gupta, Appl. Opt. 40, 1563 (2001).
[CrossRef]

Gusev, V.

V. Gusev, A. Mandelis, and R. Bleiss, Appl. Phys. A 57, 229 (1993).
[CrossRef]

Jackson, W. B.

Knoesen, A.

L. M. Wu and A. Knoesen, J. Polym. Sci. Part B 39, 2717 (2001).
[CrossRef]

Li, B. C.

B. C. Li and R. Gupta, Appl. Opt. 40, 1563 (2001).
[CrossRef]

B. C. Li and R. Gupta, J. Appl. Phys. 89, 859 (2001).
[CrossRef]

Lorincz, A.

O. Doka, A. Miklos, and A. Lorincz, Appl. Phys. A 48, 415 (1989).
[CrossRef]

Mandelis, A.

J. Shen, A. Mandelis, and T. Ashe, Int. J. Thermophys. 19, 579 (1998).
[CrossRef]

V. Gusev, A. Mandelis, and R. Bleiss, Appl. Phys. A 57, 229 (1993).
[CrossRef]

Miklos, A.

O. Doka, A. Miklos, and A. Lorincz, Appl. Phys. A 48, 415 (1989).
[CrossRef]

Muratikov, K. L.

A. L. Glazov and K. L. Muratikov, Opt. Commun. 84, 283 (1991).
[CrossRef]

Murphy, J. C.

L. C. Aamodt and J. C. Murphy, J. Appl. Phys. 52, 4903 (1981).
[CrossRef]

Nonomura, S.

K. Tanaka, T. Gotoh, N. Yoshida, and S. Nonomura, J. Appl. Phys. 91, 125 (2002).
[CrossRef]

Power, J. F.

Rajakarunanayake, Y. N.

Y. N. Rajakarunanayake and H. K. Wickramasinghe, Appl. Phys. Lett. 48, 218 (1986).
[CrossRef]

Rosencwaig, A.

A. Rosencwaig and A. Gersho, J. Appl. Phys. 47, 64 (1976).
[CrossRef]

Schweitzer, M. A.

Shen, J.

J. Shen, A. Mandelis, and T. Ashe, Int. J. Thermophys. 19, 579 (1998).
[CrossRef]

Spicer, J. B.

G. C. Wetsel and J. B. Spicer, Can. J. Phys. 64, 1269 (1986).
[CrossRef]

Tanaka, K.

K. Tanaka, T. Gotoh, N. Yoshida, and S. Nonomura, J. Appl. Phys. 91, 125 (2002).
[CrossRef]

Wetsel, G. C.

G. C. Wetsel and J. B. Spicer, Can. J. Phys. 64, 1269 (1986).
[CrossRef]

Wickramasinghe, H. K.

Y. N. Rajakarunanayake and H. K. Wickramasinghe, Appl. Phys. Lett. 48, 218 (1986).
[CrossRef]

Wu, L. M.

L. M. Wu and A. Knoesen, J. Polym. Sci. Part B 39, 2717 (2001).
[CrossRef]

Yoshida, N.

K. Tanaka, T. Gotoh, N. Yoshida, and S. Nonomura, J. Appl. Phys. 91, 125 (2002).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. A (2)

V. Gusev, A. Mandelis, and R. Bleiss, Appl. Phys. A 57, 229 (1993).
[CrossRef]

O. Doka, A. Miklos, and A. Lorincz, Appl. Phys. A 48, 415 (1989).
[CrossRef]

Appl. Phys. Lett. (1)

Y. N. Rajakarunanayake and H. K. Wickramasinghe, Appl. Phys. Lett. 48, 218 (1986).
[CrossRef]

Appl. Spectrosc. (1)

Can. J. Phys. (1)

G. C. Wetsel and J. B. Spicer, Can. J. Phys. 64, 1269 (1986).
[CrossRef]

Int. J. Thermophys. (1)

J. Shen, A. Mandelis, and T. Ashe, Int. J. Thermophys. 19, 579 (1998).
[CrossRef]

J. Appl. Phys. (4)

A. Rosencwaig and A. Gersho, J. Appl. Phys. 47, 64 (1976).
[CrossRef]

B. C. Li and R. Gupta, J. Appl. Phys. 89, 859 (2001).
[CrossRef]

K. Tanaka, T. Gotoh, N. Yoshida, and S. Nonomura, J. Appl. Phys. 91, 125 (2002).
[CrossRef]

L. C. Aamodt and J. C. Murphy, J. Appl. Phys. 52, 4903 (1981).
[CrossRef]

J. Polym. Sci. Part B (1)

L. M. Wu and A. Knoesen, J. Polym. Sci. Part B 39, 2717 (2001).
[CrossRef]

Opt. Commun. (1)

A. L. Glazov and K. L. Muratikov, Opt. Commun. 84, 283 (1991).
[CrossRef]

Opt. Eng. (1)

J. F. Power and M. A. Schweitzer, Opt. Eng. 36, 521 (1997).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic drawing of the beam deflection effect, showing the geometrical and Gaussian beam parameters.

Fig. 2
Fig. 2

Fundamental and second-order harmonics with modulation frequencies. The ambient fluid was water, and the sample was rubber: (a) amplitude, (b) phase shift. Symbols, experimental results; solid curves, theoretical curves from current theory. Experimental parameters: I0=2×103 W/m2, ω0=2×10-4 m, d=2×10-3 m, λ=6.328×10-7 m, zD=0.7 m, z1=0.0 m, and dn/dt=-1.1×10-6.

Fig. 3
Fig. 3

Dependence of the fundamental signals on the distance from the probe beam center to the sample surface. The ambient fluid was air, and the sample was rubber. Symbols, experimental results; solid curves, least-squares curve-fitting results using current theory. The experimental parameters are the same as in Fig. 2, except d=5×10-3 m.

Equations (9)

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

ΔTgx,t=1-x+algθ0+exp-αgx+aθ×cosωt+φ-αgx+a,
ϕx,t=2πλdnTΔTgx,t.
uDxD,yD,zD,t=j exp-jkzDλzDu0x0,y0,z1×exp-jϕx,texp-jk2zDxD-x02+yD-y02dx0dy0,
ux=-+IDxD,yD=0,zD,txDdxD-+IDxD,yD=0,zD,tdxD.
μx0=-θ0dnTzDIg,
μx1=-2θdnTexp-agaagzD sinωt+ξ1,
μx222θ2kd2nT2 exp-2agazDagqrqi×sin2ωt+ξ2.
ξ1=φ-aga+3π4+ag2qi2+qr22kqi,
ξ2=2φ-2aga+3π4+2ag2qi2+qr2kqi.

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