Abstract

We report on the theoretical analysis of a detector type influence on the normal deflection signal in photothermal experiments. Two cases are examined. In the first, the quadrant photodiode was considered as the detector; in the second the signal from the position detector, which measures the central moment displacement of the probe beam, was analyzed. Both analyses were carried out within the framework of the complex ray theory. The normal photodeflection signal was found to depend on the type of detector used in the photothermal deflection experiments for some parameters of its setup.

© 2008 Optical Society of America

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  1. B. C. Li and R. Gupta, “Simultaneous measurement of absorption coefficient, thermal diffusivity, and flow velocity in a gas jet with pulsed photothermal deflection spectroscopy,” J. Appl. Phys. 89, 859-868 (2001).
    [CrossRef]
  2. K. Tanaka, T. Gotoh, N. Yoshida, and S. Nonomura, “Photothermal deflection spectroscopy of chalcogenide glasses,” J. Appl. Phys. 91, 125-128 (2002).
    [CrossRef]
  3. C. Hu, J. Zhao, and J. Shen, “Continuous wave photothermal deflection spectrometry based on Fresnel diffraction theory: experimental applications,” Rev. Sci. Instrum. 74, 459-461(2003).
    [CrossRef]
  4. J. Bodzenta, B. Burak, A. Jagoda, and B. Stanczyk, “Thermal conductivity of AlN and AlN-GaN thin films deposited on Si and GaAs substrates,” Diamond Relat. Mater. 14, 1169-1174(2005).
    [CrossRef]
  5. J. Bodzenta and M. Pyka, “Photothermal measurement with mirage effect for investigation of LiNbO3 single crystals,” J. Phys. IV 137, 259-263 (2006).
    [CrossRef]
  6. L. C. Aamodt and J. C. Murphy, “Photothermal measurement using a localized excitation source,” J. Appl. Phys. 52, 4903-4914 (1981).
    [CrossRef]
  7. L. C. Aamodt and J. C. Murphy, “Thermal effects in photothermal spectroscopy and photothermal imaging,” J. Appl. Phys. 54, 581-591 (1983).
    [CrossRef]
  8. E. Legal Lasalle, F. Lepoutre, and J. P. Roger, “Probe beam size effects in photothermal deflection experiments,” J. Appl. Phys. 64, 1-5 (1988).
    [CrossRef]
  9. A. L. Glazov and K. L. Muratikov, “Photodeflection signal formation in thermal wave spectroscopy and microscopy of solids within the framework of wave optics. 'Mirage' effect geometry,” Opt. Commun. 84, 283-289 (1991).
    [CrossRef]
  10. A. L. Glazov and K. L. Muratikov, “Calculation of the photodeflection signal in the framework of wave optics,” Tech. Phys. 38, 344-352 (1993).
  11. J. F. Power, S. W. Fu, and M. A. Schweitzer, “Depth profiling of optical absorption in thin films via the mirage effect and a new inverse scattering theory. Part i: principles and methodology,” Appl. Spectrosc. 54, 12A-41A (2000).
    [CrossRef]
  12. J. Zhao, J. Shen, and C. Hu, “Continuous-wave photothermal deflection spectroscopy with fundamental and harmonic responses,” Opt. Lett. 27, 1755-1757 (2002).
    [CrossRef]
  13. J. H. Rohling, J. Shen, J. Zhou, and C. E. Gu, “Probe beam size effect on the measurement of the distance between the probe beam and the sample in photothermal deflection,” Opt. Lett. 31, 44-46 (2006).
    [CrossRef] [PubMed]
  14. H. Rohling, J. Shen, J. Zhou, and C. E. Gu, “Application of the diffraction theory for photothermal deflection to the measurement of the temperature coefficient of the refractive index of a binary gas mixture,” J. Appl. Phys. 99, 103107 (2006).
    [CrossRef]
  15. D. Korte Kobylińska, R. J. Bukowski, B. Burak, J. Bodzenta, and S. Kochowski, “The complex ray theory of photodeflection signal formation-comparison with the ray theory and the experimental results,” J. Appl. Phys. 100, 063501 (2006).
    [CrossRef]
  16. D. Korte Kobylińska, R. J. Bukowski, B. Burak, J. Bodzenta, and S. Kochowski, “Photodeflection signal formation in photothermal measurements: comparison of the complex ray theory, the ray theory, the wave theory, and experimental results,” Appl. Opt. 46, 5216-5227 (2007).
    [CrossRef]
  17. R. J. Bukowski, “Complex geometrical optics application for description of Gaussian beam propagation in optically homogenous media,” in Proceedings of Second National Conference “Physical Grounds on Nondestructive Investigation (Silesian University of Technology, 1997), pp. 45-55 (in Polish).

2007 (1)

2006 (4)

J. H. Rohling, J. Shen, J. Zhou, and C. E. Gu, “Probe beam size effect on the measurement of the distance between the probe beam and the sample in photothermal deflection,” Opt. Lett. 31, 44-46 (2006).
[CrossRef] [PubMed]

H. Rohling, J. Shen, J. Zhou, and C. E. Gu, “Application of the diffraction theory for photothermal deflection to the measurement of the temperature coefficient of the refractive index of a binary gas mixture,” J. Appl. Phys. 99, 103107 (2006).
[CrossRef]

D. Korte Kobylińska, R. J. Bukowski, B. Burak, J. Bodzenta, and S. Kochowski, “The complex ray theory of photodeflection signal formation-comparison with the ray theory and the experimental results,” J. Appl. Phys. 100, 063501 (2006).
[CrossRef]

J. Bodzenta and M. Pyka, “Photothermal measurement with mirage effect for investigation of LiNbO3 single crystals,” J. Phys. IV 137, 259-263 (2006).
[CrossRef]

2005 (1)

J. Bodzenta, B. Burak, A. Jagoda, and B. Stanczyk, “Thermal conductivity of AlN and AlN-GaN thin films deposited on Si and GaAs substrates,” Diamond Relat. Mater. 14, 1169-1174(2005).
[CrossRef]

2003 (1)

C. Hu, J. Zhao, and J. Shen, “Continuous wave photothermal deflection spectrometry based on Fresnel diffraction theory: experimental applications,” Rev. Sci. Instrum. 74, 459-461(2003).
[CrossRef]

2002 (2)

K. Tanaka, T. Gotoh, N. Yoshida, and S. Nonomura, “Photothermal deflection spectroscopy of chalcogenide glasses,” J. Appl. Phys. 91, 125-128 (2002).
[CrossRef]

J. Zhao, J. Shen, and C. Hu, “Continuous-wave photothermal deflection spectroscopy with fundamental and harmonic responses,” Opt. Lett. 27, 1755-1757 (2002).
[CrossRef]

2001 (1)

B. C. Li and R. Gupta, “Simultaneous measurement of absorption coefficient, thermal diffusivity, and flow velocity in a gas jet with pulsed photothermal deflection spectroscopy,” J. Appl. Phys. 89, 859-868 (2001).
[CrossRef]

2000 (1)

1993 (1)

A. L. Glazov and K. L. Muratikov, “Calculation of the photodeflection signal in the framework of wave optics,” Tech. Phys. 38, 344-352 (1993).

1991 (1)

A. L. Glazov and K. L. Muratikov, “Photodeflection signal formation in thermal wave spectroscopy and microscopy of solids within the framework of wave optics. 'Mirage' effect geometry,” Opt. Commun. 84, 283-289 (1991).
[CrossRef]

1988 (1)

E. Legal Lasalle, F. Lepoutre, and J. P. Roger, “Probe beam size effects in photothermal deflection experiments,” J. Appl. Phys. 64, 1-5 (1988).
[CrossRef]

1983 (1)

L. C. Aamodt and J. C. Murphy, “Thermal effects in photothermal spectroscopy and photothermal imaging,” J. Appl. Phys. 54, 581-591 (1983).
[CrossRef]

1981 (1)

L. C. Aamodt and J. C. Murphy, “Photothermal measurement using a localized excitation source,” J. Appl. Phys. 52, 4903-4914 (1981).
[CrossRef]

Aamodt, L. C.

L. C. Aamodt and J. C. Murphy, “Thermal effects in photothermal spectroscopy and photothermal imaging,” J. Appl. Phys. 54, 581-591 (1983).
[CrossRef]

L. C. Aamodt and J. C. Murphy, “Photothermal measurement using a localized excitation source,” J. Appl. Phys. 52, 4903-4914 (1981).
[CrossRef]

Bodzenta, J.

D. Korte Kobylińska, R. J. Bukowski, B. Burak, J. Bodzenta, and S. Kochowski, “Photodeflection signal formation in photothermal measurements: comparison of the complex ray theory, the ray theory, the wave theory, and experimental results,” Appl. Opt. 46, 5216-5227 (2007).
[CrossRef]

J. Bodzenta and M. Pyka, “Photothermal measurement with mirage effect for investigation of LiNbO3 single crystals,” J. Phys. IV 137, 259-263 (2006).
[CrossRef]

D. Korte Kobylińska, R. J. Bukowski, B. Burak, J. Bodzenta, and S. Kochowski, “The complex ray theory of photodeflection signal formation-comparison with the ray theory and the experimental results,” J. Appl. Phys. 100, 063501 (2006).
[CrossRef]

J. Bodzenta, B. Burak, A. Jagoda, and B. Stanczyk, “Thermal conductivity of AlN and AlN-GaN thin films deposited on Si and GaAs substrates,” Diamond Relat. Mater. 14, 1169-1174(2005).
[CrossRef]

Bukowski, R. J.

D. Korte Kobylińska, R. J. Bukowski, B. Burak, J. Bodzenta, and S. Kochowski, “Photodeflection signal formation in photothermal measurements: comparison of the complex ray theory, the ray theory, the wave theory, and experimental results,” Appl. Opt. 46, 5216-5227 (2007).
[CrossRef]

D. Korte Kobylińska, R. J. Bukowski, B. Burak, J. Bodzenta, and S. Kochowski, “The complex ray theory of photodeflection signal formation-comparison with the ray theory and the experimental results,” J. Appl. Phys. 100, 063501 (2006).
[CrossRef]

R. J. Bukowski, “Complex geometrical optics application for description of Gaussian beam propagation in optically homogenous media,” in Proceedings of Second National Conference “Physical Grounds on Nondestructive Investigation (Silesian University of Technology, 1997), pp. 45-55 (in Polish).

Burak, B.

D. Korte Kobylińska, R. J. Bukowski, B. Burak, J. Bodzenta, and S. Kochowski, “Photodeflection signal formation in photothermal measurements: comparison of the complex ray theory, the ray theory, the wave theory, and experimental results,” Appl. Opt. 46, 5216-5227 (2007).
[CrossRef]

D. Korte Kobylińska, R. J. Bukowski, B. Burak, J. Bodzenta, and S. Kochowski, “The complex ray theory of photodeflection signal formation-comparison with the ray theory and the experimental results,” J. Appl. Phys. 100, 063501 (2006).
[CrossRef]

J. Bodzenta, B. Burak, A. Jagoda, and B. Stanczyk, “Thermal conductivity of AlN and AlN-GaN thin films deposited on Si and GaAs substrates,” Diamond Relat. Mater. 14, 1169-1174(2005).
[CrossRef]

Fu, S. W.

Glazov, A. L.

A. L. Glazov and K. L. Muratikov, “Calculation of the photodeflection signal in the framework of wave optics,” Tech. Phys. 38, 344-352 (1993).

A. L. Glazov and K. L. Muratikov, “Photodeflection signal formation in thermal wave spectroscopy and microscopy of solids within the framework of wave optics. 'Mirage' effect geometry,” Opt. Commun. 84, 283-289 (1991).
[CrossRef]

Gotoh, T.

K. Tanaka, T. Gotoh, N. Yoshida, and S. Nonomura, “Photothermal deflection spectroscopy of chalcogenide glasses,” J. Appl. Phys. 91, 125-128 (2002).
[CrossRef]

Gu, C. E.

J. H. Rohling, J. Shen, J. Zhou, and C. E. Gu, “Probe beam size effect on the measurement of the distance between the probe beam and the sample in photothermal deflection,” Opt. Lett. 31, 44-46 (2006).
[CrossRef] [PubMed]

H. Rohling, J. Shen, J. Zhou, and C. E. Gu, “Application of the diffraction theory for photothermal deflection to the measurement of the temperature coefficient of the refractive index of a binary gas mixture,” J. Appl. Phys. 99, 103107 (2006).
[CrossRef]

Gupta, R.

B. C. Li and R. Gupta, “Simultaneous measurement of absorption coefficient, thermal diffusivity, and flow velocity in a gas jet with pulsed photothermal deflection spectroscopy,” J. Appl. Phys. 89, 859-868 (2001).
[CrossRef]

Hu, C.

C. Hu, J. Zhao, and J. Shen, “Continuous wave photothermal deflection spectrometry based on Fresnel diffraction theory: experimental applications,” Rev. Sci. Instrum. 74, 459-461(2003).
[CrossRef]

J. Zhao, J. Shen, and C. Hu, “Continuous-wave photothermal deflection spectroscopy with fundamental and harmonic responses,” Opt. Lett. 27, 1755-1757 (2002).
[CrossRef]

Jagoda, A.

J. Bodzenta, B. Burak, A. Jagoda, and B. Stanczyk, “Thermal conductivity of AlN and AlN-GaN thin films deposited on Si and GaAs substrates,” Diamond Relat. Mater. 14, 1169-1174(2005).
[CrossRef]

Kobylinska, D. Korte

D. Korte Kobylińska, R. J. Bukowski, B. Burak, J. Bodzenta, and S. Kochowski, “Photodeflection signal formation in photothermal measurements: comparison of the complex ray theory, the ray theory, the wave theory, and experimental results,” Appl. Opt. 46, 5216-5227 (2007).
[CrossRef]

D. Korte Kobylińska, R. J. Bukowski, B. Burak, J. Bodzenta, and S. Kochowski, “The complex ray theory of photodeflection signal formation-comparison with the ray theory and the experimental results,” J. Appl. Phys. 100, 063501 (2006).
[CrossRef]

Kochowski, S.

D. Korte Kobylińska, R. J. Bukowski, B. Burak, J. Bodzenta, and S. Kochowski, “Photodeflection signal formation in photothermal measurements: comparison of the complex ray theory, the ray theory, the wave theory, and experimental results,” Appl. Opt. 46, 5216-5227 (2007).
[CrossRef]

D. Korte Kobylińska, R. J. Bukowski, B. Burak, J. Bodzenta, and S. Kochowski, “The complex ray theory of photodeflection signal formation-comparison with the ray theory and the experimental results,” J. Appl. Phys. 100, 063501 (2006).
[CrossRef]

Lasalle, E. Legal

E. Legal Lasalle, F. Lepoutre, and J. P. Roger, “Probe beam size effects in photothermal deflection experiments,” J. Appl. Phys. 64, 1-5 (1988).
[CrossRef]

Lepoutre, F.

E. Legal Lasalle, F. Lepoutre, and J. P. Roger, “Probe beam size effects in photothermal deflection experiments,” J. Appl. Phys. 64, 1-5 (1988).
[CrossRef]

Li, B. C.

B. C. Li and R. Gupta, “Simultaneous measurement of absorption coefficient, thermal diffusivity, and flow velocity in a gas jet with pulsed photothermal deflection spectroscopy,” J. Appl. Phys. 89, 859-868 (2001).
[CrossRef]

Muratikov, K. L.

A. L. Glazov and K. L. Muratikov, “Calculation of the photodeflection signal in the framework of wave optics,” Tech. Phys. 38, 344-352 (1993).

A. L. Glazov and K. L. Muratikov, “Photodeflection signal formation in thermal wave spectroscopy and microscopy of solids within the framework of wave optics. 'Mirage' effect geometry,” Opt. Commun. 84, 283-289 (1991).
[CrossRef]

Murphy, J. C.

L. C. Aamodt and J. C. Murphy, “Thermal effects in photothermal spectroscopy and photothermal imaging,” J. Appl. Phys. 54, 581-591 (1983).
[CrossRef]

L. C. Aamodt and J. C. Murphy, “Photothermal measurement using a localized excitation source,” J. Appl. Phys. 52, 4903-4914 (1981).
[CrossRef]

Nonomura, S.

K. Tanaka, T. Gotoh, N. Yoshida, and S. Nonomura, “Photothermal deflection spectroscopy of chalcogenide glasses,” J. Appl. Phys. 91, 125-128 (2002).
[CrossRef]

Power, J. F.

Pyka, M.

J. Bodzenta and M. Pyka, “Photothermal measurement with mirage effect for investigation of LiNbO3 single crystals,” J. Phys. IV 137, 259-263 (2006).
[CrossRef]

Roger, J. P.

E. Legal Lasalle, F. Lepoutre, and J. P. Roger, “Probe beam size effects in photothermal deflection experiments,” J. Appl. Phys. 64, 1-5 (1988).
[CrossRef]

Rohling, H.

H. Rohling, J. Shen, J. Zhou, and C. E. Gu, “Application of the diffraction theory for photothermal deflection to the measurement of the temperature coefficient of the refractive index of a binary gas mixture,” J. Appl. Phys. 99, 103107 (2006).
[CrossRef]

Rohling, J. H.

Schweitzer, M. A.

Shen, J.

J. H. Rohling, J. Shen, J. Zhou, and C. E. Gu, “Probe beam size effect on the measurement of the distance between the probe beam and the sample in photothermal deflection,” Opt. Lett. 31, 44-46 (2006).
[CrossRef] [PubMed]

H. Rohling, J. Shen, J. Zhou, and C. E. Gu, “Application of the diffraction theory for photothermal deflection to the measurement of the temperature coefficient of the refractive index of a binary gas mixture,” J. Appl. Phys. 99, 103107 (2006).
[CrossRef]

C. Hu, J. Zhao, and J. Shen, “Continuous wave photothermal deflection spectrometry based on Fresnel diffraction theory: experimental applications,” Rev. Sci. Instrum. 74, 459-461(2003).
[CrossRef]

J. Zhao, J. Shen, and C. Hu, “Continuous-wave photothermal deflection spectroscopy with fundamental and harmonic responses,” Opt. Lett. 27, 1755-1757 (2002).
[CrossRef]

Stanczyk, B.

J. Bodzenta, B. Burak, A. Jagoda, and B. Stanczyk, “Thermal conductivity of AlN and AlN-GaN thin films deposited on Si and GaAs substrates,” Diamond Relat. Mater. 14, 1169-1174(2005).
[CrossRef]

Tanaka, K.

K. Tanaka, T. Gotoh, N. Yoshida, and S. Nonomura, “Photothermal deflection spectroscopy of chalcogenide glasses,” J. Appl. Phys. 91, 125-128 (2002).
[CrossRef]

Yoshida, N.

K. Tanaka, T. Gotoh, N. Yoshida, and S. Nonomura, “Photothermal deflection spectroscopy of chalcogenide glasses,” J. Appl. Phys. 91, 125-128 (2002).
[CrossRef]

Zhao, J.

C. Hu, J. Zhao, and J. Shen, “Continuous wave photothermal deflection spectrometry based on Fresnel diffraction theory: experimental applications,” Rev. Sci. Instrum. 74, 459-461(2003).
[CrossRef]

J. Zhao, J. Shen, and C. Hu, “Continuous-wave photothermal deflection spectroscopy with fundamental and harmonic responses,” Opt. Lett. 27, 1755-1757 (2002).
[CrossRef]

Zhou, J.

H. Rohling, J. Shen, J. Zhou, and C. E. Gu, “Application of the diffraction theory for photothermal deflection to the measurement of the temperature coefficient of the refractive index of a binary gas mixture,” J. Appl. Phys. 99, 103107 (2006).
[CrossRef]

J. H. Rohling, J. Shen, J. Zhou, and C. E. Gu, “Probe beam size effect on the measurement of the distance between the probe beam and the sample in photothermal deflection,” Opt. Lett. 31, 44-46 (2006).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Spectrosc. (1)

Diamond Relat. Mater. (1)

J. Bodzenta, B. Burak, A. Jagoda, and B. Stanczyk, “Thermal conductivity of AlN and AlN-GaN thin films deposited on Si and GaAs substrates,” Diamond Relat. Mater. 14, 1169-1174(2005).
[CrossRef]

J. Appl. Phys. (7)

B. C. Li and R. Gupta, “Simultaneous measurement of absorption coefficient, thermal diffusivity, and flow velocity in a gas jet with pulsed photothermal deflection spectroscopy,” J. Appl. Phys. 89, 859-868 (2001).
[CrossRef]

K. Tanaka, T. Gotoh, N. Yoshida, and S. Nonomura, “Photothermal deflection spectroscopy of chalcogenide glasses,” J. Appl. Phys. 91, 125-128 (2002).
[CrossRef]

L. C. Aamodt and J. C. Murphy, “Photothermal measurement using a localized excitation source,” J. Appl. Phys. 52, 4903-4914 (1981).
[CrossRef]

L. C. Aamodt and J. C. Murphy, “Thermal effects in photothermal spectroscopy and photothermal imaging,” J. Appl. Phys. 54, 581-591 (1983).
[CrossRef]

E. Legal Lasalle, F. Lepoutre, and J. P. Roger, “Probe beam size effects in photothermal deflection experiments,” J. Appl. Phys. 64, 1-5 (1988).
[CrossRef]

H. Rohling, J. Shen, J. Zhou, and C. E. Gu, “Application of the diffraction theory for photothermal deflection to the measurement of the temperature coefficient of the refractive index of a binary gas mixture,” J. Appl. Phys. 99, 103107 (2006).
[CrossRef]

D. Korte Kobylińska, R. J. Bukowski, B. Burak, J. Bodzenta, and S. Kochowski, “The complex ray theory of photodeflection signal formation-comparison with the ray theory and the experimental results,” J. Appl. Phys. 100, 063501 (2006).
[CrossRef]

J. Phys. IV (1)

J. Bodzenta and M. Pyka, “Photothermal measurement with mirage effect for investigation of LiNbO3 single crystals,” J. Phys. IV 137, 259-263 (2006).
[CrossRef]

Opt. Commun. (1)

A. L. Glazov and K. L. Muratikov, “Photodeflection signal formation in thermal wave spectroscopy and microscopy of solids within the framework of wave optics. 'Mirage' effect geometry,” Opt. Commun. 84, 283-289 (1991).
[CrossRef]

Opt. Lett. (2)

Rev. Sci. Instrum. (1)

C. Hu, J. Zhao, and J. Shen, “Continuous wave photothermal deflection spectrometry based on Fresnel diffraction theory: experimental applications,” Rev. Sci. Instrum. 74, 459-461(2003).
[CrossRef]

Tech. Phys. (1)

A. L. Glazov and K. L. Muratikov, “Calculation of the photodeflection signal in the framework of wave optics,” Tech. Phys. 38, 344-352 (1993).

Other (1)

R. J. Bukowski, “Complex geometrical optics application for description of Gaussian beam propagation in optically homogenous media,” in Proceedings of Second National Conference “Physical Grounds on Nondestructive Investigation (Silesian University of Technology, 1997), pp. 45-55 (in Polish).

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Figures (5)

Fig. 1
Fig. 1

Schematic of the configuration.

Fig. 2
Fig. 2

Amplitude and phase of the PD signal dependence on modulation frequencies of temperature field f for different values of the probe beam radius in the waist a and for two different methods of detection: 1, 2, 3, the position detector; 1a, 2a, 3a, the quadrant photodiode; 1, 1 a a = 20 μm ; 2, 2 a a = 30 μm ; 3, 3 a a = 40 μm . The sample position was z s = 5.6 cm , the detector position z D = 66.5 cm , and the height of the probe beam over the sample h = 100 μm ; the probe beam waist position L = 5.6 cm , and the sample thickness d = 200 μm .

Fig. 3
Fig. 3

Amplitude and phase of the PD signal dependence on modulation frequencies of temperature field f for different values of the probe beam radius in the waist a and for two different methods of detection: 1, 2, 3, the position detector; 1a, 2a, 3a, the quadrant photodiode; 1, 1 a a = 20 μm ; 2, 2 a a = 30 μm ; 3, 3 a a = 40 μm . The sample position was z s = 5.6 cm , the detector position z D = 66.5 cm , and the height of the probe beam over the sample h = 100 μm ; the probe beam waist position L = 6.6 cm , and the sample thickness d = 200 μm .

Fig. 4
Fig. 4

Amplitude and phase of the PD signal dependence on the sample position z s for different values of modulation frequency of temperature field f and for two different methods of detection: 1, 2, the position detector; 1a, 2a, the quadrant photodiode; 1, 1 a f = 1 kHz ; 2, 2 a f = 3 kHz . The detector position was z D = 66.5 cm , and the height of the probe beam over the sample h = 100 μm ; the probe beam waist position L = 5.6 cm , and the sample thickness d = 200 μm .

Fig. 5
Fig. 5

Amplitude and phase of the PD signal dependence on modulation frequencies of temperature field f for two different methods of detection: 1, 2, the experimental results; 1a, 2a, the theoretical results; 1, 1a, the position detector; 2, 2a, the quadrant photodiode. The height of the probe beam over the sample was h = 150 μm ; the probe beam waist position L = 7 cm , the sample thickness d = 300 μm , and the probe beam radius in the waist a = 60 μm .

Equations (65)

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

ϑ g ( x , t ) = T ( x , t ) T 0 = b g exp [ Ω 2 κ g ( x + h ) ] cos [ Ωt Ω 2 κ g ( x + h ) + φ g ] .
Δn ( T ) d n d T | T 0 ( T T 0 ) = n 0 s T ϑ g ( x , t ) .
I ( x D , y D , z D ) | A 0 ( z D ) [ 1 + a 1 ( z D ) ] | 2 | exp { i [ Ψ 0 ( z D ) + Ψ 1 ( z D ) ] } | 2 ,
a 1 ( z D ) = s T b g k g C x ( z p z 1 ) ( z D z s ) ( 1 + i z D z RC ) 1 exp ( C x x D ) [ sin ( Ωt C x x D + φ g ) i 2 z D z RC 3 x D sin ( Ωt C x x D + φ g π 4 ) ] ,
Ψ 1 = k n 0 s T ( z p z 1 ) { b g exp ( C x x D ) [ k cos ( Ωt C x x D + φ g ) + 2 k g z D x D z RC 2 ( z D z s ) ( 1 + i z D z RC 1 ) 2 sin ( Ωt C x x D + φ g π / 4 ) ] } ,
C x = k g ( 1 + i z s z RC ) ( 1 + i z D z RC ) 1 ,
S nq = K q + d y D ( 0 + 0 ) d x D I ( x D , y D , z D ) .
S np = K p + d x D I ( x D , y D = 0 , z D ) x D ,
S nq = A q cos ( Ωt + φ g + φ q ) ,
A q = K q ( A dq cos φ dq + A fq cos φ fq ) 2 + ( A dq sin φ dq + A fq sin φ fq ) 2 ,
φ q = a tan A dq sin φ dq + A fq sin φ fq A dq cos φ dq + A fq cos φ fq + φ g ,
A dq = ( A ddq cos φ ddq + A dfq cos φ dfq ) 2 + ( A ddq sin φ ddq + A dfq sin φ dfq ) 2 ,
φ dq = a tan A ddq sin φ ddq + A dfq sin φ dfp A ddq cos φ ddq + A dfq cos φ dfq ,
A fq = ( A fdq cos φ fdq + A ffq cos φ ffq ) 2 + ( A fdq sin φ fdq + A ffq sin φ ffq ) 2 ,
φ fq = a tan A fdq sin φ fdq + A ffq sin φ ffq A fdq cos φ fdq + A ffq cos φ ffq ,
A ddq = ( Re W 1 + Re W 2 ) 2 + ( Im W 1 Im W 2 ) 2 ,
φ ddq = a tan Im W 1 Im W 2 Re W 1 + Re W 2 ,
A fdq = ( Re W 3 + Re W 4 ) 2 + ( Im W 3 Im W 4 ) 2 ,
φ fdq = a tan Im W 3 Im W 4 Re W 3 + Re W 4 ,
A dfq = ( Re W 6 Re W 5 ) 2 + ( Im W 6 + Im W 5 ) 2 ,
φ dfq = a tan Re W 6 Re W 5 Im W 6 + Im W 5 ,
A ffq = ( Re W 8 Re W 7 ) 2 + ( Im W 8 + Im W 7 ) 2 ,
φ ffq = a tan Re W 8 Re W 7 Im W 7 Im W 8 ,
W 1 = α γ I m π f exp [ ( i + 1 ) 2 C x 2 4 f ] erf [ ( i + 1 ) C x 2 f ] ,
W 2 = α γ I m π f exp [ ( i 1 ) 2 C x 2 4 f ] erf [ ( i 1 ) C x 2 f ] ,
W 3 = α β I m f exp ( i π 4 ) { 1 2 π f ( i + 1 ) C x exp [ ( i + 1 ) 2 C x 2 4 f ] erf [ ( i + 1 ) C x 2 f ] + 1 } ,
W 4 = α β I m f exp ( i π 4 ) { 1 2 π f ( i 1 ) C x exp [ ( i 1 ) 2 C x 2 4 f ] erf [ ( i 1 ) C x 2 f ] + 1 } ,
W 5 = k α δ I m f exp ( i π 4 ) { 1 2 π f ( i + 1 ) C x exp [ ( i + 1 ) 2 C x 2 4 f ] erf [ ( i + 1 ) C x 2 f ] + 1 } ,
W 6 = k α δ I m f exp ( i π 4 ) { 1 2 π f ( i 1 ) C x exp [ ( i 1 ) 2 C x 2 4 f ] erf [ ( i 1 ) C x 2 f ] + 1 } ,
W 7 = k α α I m π f exp [ ( i + 1 ) 2 C x 2 4 f ] erf [ ( i + 1 ) C x 2 f ] ,
W 8 = k α α I m π f exp [ ( i 1 ) 2 C x 2 4 f ] erf [ ( i 1 ) C x 2 f ] ,
I m = z R P l π a z R 2 + ( L z D ) 2 ,
f = z R 2 a 2 [ z R 2 + ( L z D ) 2 ] ,
α α = 1 2 n 0 s T b g ( z p z l ) ,
α β = i 2 2 n 0 s T b g k g ( z D z s ) ( z p z l ) z D z RC ( 1 + i z D z RC ) 1 ,
α γ = n 0 s T b g k g C x 2 i ( z D z s ) ( z p z l ) ( 1 + i z D z RC ) 1 ,
α δ 2 2 i n 0 s T b g k g z D z RC 2 ( z D z s ) ( z p z l ) z D z RC ( 1 + i z D z RC ) 2 .
S n p = A p cos ( Ωt + φ g + φ p ) ,
A p = K p ( A dp cos φ dp + A fp cos φ fp ) 2 + ( A dp sin φ dp + A fp sin φ fp ) 2 ,
φ dp = a tan A dp sin φ dp + A fp sin φ fp A dp cos φ dp + A fp cos φ fp + φ g ,
A dp = ( A ddp cos φ ddp + A dfp cos φ dfp ) 2 + ( A ddp sin φ ddp + A dfp sin φ dfp ) 2 ,
φ dp = a tan A ddp sin φ ddp + A dfp sin φ dfp A ddp cos φ ddp + A dfp cos φ dfp ,
A fp = ( A fdp cos φ fdp + A ffp cos φ ffp ) 2 + ( A fdp sin φ fdp + A ffp sin φ f fp ) 2 ,
φ fp = a tan A fdp sin φ fdp + A ffp sin φ ffp A fdp cos φ fdp + A ffp cos φ ffp ,
A ddp = 2 I p ( Re M 1 + Re M 2 ) 2 + ( Im M 2 Im M 1 ) 2 ,
φ ddp = atan Im M 2 Im M 1 Re M 1 + Re M 2 ,
A fdp = 2 I p ( Re M 3 + Re M 4 ) 2 + ( Im M 4 Im M 3 ) 2 ,
φ fdp = atan Im M 4 Im M 3 Re M 3 + Re M 4 ,
A dfp = 2 I p k ( Re M 5 Re M 6 ) 2 + ( Im M 5 + Im M 6 ) 2 ,
φ dfp = atan Re M 6 Re M 5 Im M 5 + Im M 6 ,
A ffp = 2 I p ( Re M 7 Re M 8 ) 2 + ( Im M 8 + Im M 7 ) 2 ,
φ ffp = atan Re M 8 Re M 7 Im M 7 + Im M 8 ,
M 1 = β γ 2 π f ( i + 1 ) C x f exp [ ( i + 1 ) 2 C x 2 4 f ] ,
M 2 = β γ 2 π f ( i 1 ) C x f exp [ ( i 1 ) 2 C x 2 4 f ] ,
M 3 = β β 4 exp ( i π 4 ) π f [ 2 f + ( i + 1 ) 2 C x 2 ] f 2 exp [ ( i + 1 ) 2 C x 2 4 f ] ,
M 4 = β β 4 exp ( i π 4 ) π f [ 2 f + ( i 1 ) 2 C x 2 ] f 2 exp [ ( i 1 ) 2 C x 2 4 f ] ,
M 5 = β δ 4 exp ( i π 4 ) π f [ 2 f + ( i + 1 ) 2 C x 2 ] f 2 exp [ ( i + 1 ) 2 C x 2 4 f ] ,
M 6 = β δ 4 exp ( i π 4 ) π f [ 2 f + ( i 1 ) 2 C x 2 ] f 2 exp [ ( i 1 ) 2 C x 2 4 f ] ,
M 7 = β α 2 π f ( i + 1 ) C x f exp [ ( i + 1 ) 2 C x 2 4 f ] ,
M 8 = β α 2 π f ( i ) C x f exp [ ( i 1 ) 2 C x 2 4 f ] ,
I p = z R 2 P l π a 2 [ z R 2 + ( L z D ) 2 ] ,
β α = 1 2 n 0 s T b g ( z p z l ) ,
β β = i 2 2 n 0 s T b g k g ( z D z s ) ( z p z l ) z D z RC ( 1 + i z D z RC ) 1 ,
β γ = s T n 0 b g k g C x 2 i ( z D z s ) ( z p z l ) ( 1 + i z D z RC ) 1 ,
β δ = 2 2 i n 0 s T b g k g z D z RC 2 ( z D z s ) ( z p z l ) ( 1 + i z D z RC ) 2 .

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