Abstract

A rapid, straightforward method for measuring the two-photon absorption cross sections in liquid samples based on both the accumulative photo-thermal effect and the Rayleigh interferometery is described and demonstrated. This technique combines the sensitivity of the thermal lens approach and the accuracy of interferometry techniques. Focusing a high repetition rate laser beam in the sample, generating a localized change in its refractive index, induces the photo-thermal phase shift. By recording and processing two interference patterns, this technique allows the rapid estimation of the two-photon absorption cross section of the sample. Significantly, the experimental results demonstrate that this new method can be used with both fluorescent and non-fluorescent samples.

© 2009 OSA

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References

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  1. P. Sengupta, J. Balaji, S. Banerjee, R. Philip, G. R. Kumar, and S. Maiti, “Sensitive measurement of absolute two-photon absorption cross sections,” J. Chem. Phys. 112(21), 9201–9205 (2000).
    [CrossRef]
  2. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
    [CrossRef]
  3. A. Dragornir, J. G. McInerney, D. N. Nikogosyan, and A. A. Ruth, “Two-photon absorption coefficients of several liquids at 264 nm,” IEEE J. Quantum Electron. 38(1), 31–36 (2002).
    [CrossRef]
  4. C. Xu and W. Webb, “Measurements of two-photon excitation cross section of molecular fluorophores with data from 690 to 1050nm,” J. Opt. Soc. Am. B 13(3), 481–491 (1996).
    [CrossRef]
  5. P. Kaatz and D. P. Shelton, “Two-photon fluorescence cross-section measurements calibrated with hyper-Rayleigh scattering,” J. Opt. Soc. Am. B 16(6), 998–1006 (1999).
    [CrossRef]
  6. N. S. Makarov, M. Drobizhev, and A. Rebane, “Two-photon absorption standards in the 550-1600 nm excitation wavelength range,” Opt. Express 16(6), 4029–4047 (2008).
    [CrossRef] [PubMed]
  7. A. Marcano O., “K. Williams, N. Melikechi, “Measurement of two-photon absorption using the photo-thermal lens effect,” Opt. Commun. 281, 2598–2604 (2008).
  8. N. J. Dovichi and J. M. Harris, “Laser Induced Thermal Lens Effect for Calorimetric Trace Analysis,” Anal. Chem. 51(6), 728–731 (1979).
    [CrossRef]
  9. A. J. Twarowski and D. S. Kliger, “Multiphoton absorption spectra using thermal bloomingII. Two-photon spectrum of benzene,” Chem. Phys. 20(2), 259–264 (1977).
    [CrossRef]
  10. M. Falconieri, “Thermo-optical effects in Z-scan measurements using high-repetition-rate lasers,” J. Opt. A, Pure Appl. Opt. 1(6), 662–667 (1999).
    [CrossRef]
  11. J. Stone, “Measurements of the Absorption of Light in Low-Loss Liquids,” J. Opt. Soc. Am. 62(3), 327–333 (1972).
    [CrossRef]
  12. L. Rodriguez, C. Simos, M. Sylla, A. Marcanoo, and X. Nguyenphu, “New holographic technique for third-order optical properties measurement,” Opt. Commun. 247(4-6), 453–460 (2005).
    [CrossRef]
  13. M. Born, and E. Wolf, Principles of Optics, (Cambridge University Press, 1999).
  14. M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69(2), 133–136 (1999).
    [CrossRef]
  15. S. J. Sheldon, L. V. Knight, and J. M. Thorne, “Laser-induced thermal lens effect: a new theoretical model,” Appl. Opt. 21(9), 1663–1669 (1982).
    [CrossRef] [PubMed]
  16. R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3-4), 433–438 (2004).
    [CrossRef]
  17. S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003).
    [CrossRef]
  18. C. Gorecki, “Interferogram analysis using a Fourier transform method for automatic 3D surface measurement,” Pure Appl. Opt. 1(2), 103–110 (1992).
    [CrossRef]
  19. M. A. Albota, C. Xu, and W. W. Webb, “Two-photon fluorescence excitation cross sections of biomolecular probes from 690 to 960 nm,” Appl. Opt. 37(31), 7352–7356 (1998).
    [CrossRef]

2008 (2)

A. Marcano O., “K. Williams, N. Melikechi, “Measurement of two-photon absorption using the photo-thermal lens effect,” Opt. Commun. 281, 2598–2604 (2008).

N. S. Makarov, M. Drobizhev, and A. Rebane, “Two-photon absorption standards in the 550-1600 nm excitation wavelength range,” Opt. Express 16(6), 4029–4047 (2008).
[CrossRef] [PubMed]

2005 (1)

L. Rodriguez, C. Simos, M. Sylla, A. Marcanoo, and X. Nguyenphu, “New holographic technique for third-order optical properties measurement,” Opt. Commun. 247(4-6), 453–460 (2005).
[CrossRef]

2004 (1)

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3-4), 433–438 (2004).
[CrossRef]

2003 (1)

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003).
[CrossRef]

2002 (1)

A. Dragornir, J. G. McInerney, D. N. Nikogosyan, and A. A. Ruth, “Two-photon absorption coefficients of several liquids at 264 nm,” IEEE J. Quantum Electron. 38(1), 31–36 (2002).
[CrossRef]

2000 (1)

P. Sengupta, J. Balaji, S. Banerjee, R. Philip, G. R. Kumar, and S. Maiti, “Sensitive measurement of absolute two-photon absorption cross sections,” J. Chem. Phys. 112(21), 9201–9205 (2000).
[CrossRef]

1999 (3)

M. Falconieri, “Thermo-optical effects in Z-scan measurements using high-repetition-rate lasers,” J. Opt. A, Pure Appl. Opt. 1(6), 662–667 (1999).
[CrossRef]

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69(2), 133–136 (1999).
[CrossRef]

P. Kaatz and D. P. Shelton, “Two-photon fluorescence cross-section measurements calibrated with hyper-Rayleigh scattering,” J. Opt. Soc. Am. B 16(6), 998–1006 (1999).
[CrossRef]

1998 (1)

1996 (1)

1992 (1)

C. Gorecki, “Interferogram analysis using a Fourier transform method for automatic 3D surface measurement,” Pure Appl. Opt. 1(2), 103–110 (1992).
[CrossRef]

1990 (1)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[CrossRef]

1982 (1)

1979 (1)

N. J. Dovichi and J. M. Harris, “Laser Induced Thermal Lens Effect for Calorimetric Trace Analysis,” Anal. Chem. 51(6), 728–731 (1979).
[CrossRef]

1977 (1)

A. J. Twarowski and D. S. Kliger, “Multiphoton absorption spectra using thermal bloomingII. Two-photon spectrum of benzene,” Chem. Phys. 20(2), 259–264 (1977).
[CrossRef]

1972 (1)

Albota, M. A.

Baba, M.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3-4), 433–438 (2004).
[CrossRef]

Balaji, J.

P. Sengupta, J. Balaji, S. Banerjee, R. Philip, G. R. Kumar, and S. Maiti, “Sensitive measurement of absolute two-photon absorption cross sections,” J. Chem. Phys. 112(21), 9201–9205 (2000).
[CrossRef]

Banerjee, S.

P. Sengupta, J. Balaji, S. Banerjee, R. Philip, G. R. Kumar, and S. Maiti, “Sensitive measurement of absolute two-photon absorption cross sections,” J. Chem. Phys. 112(21), 9201–9205 (2000).
[CrossRef]

Chaux, R.

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003).
[CrossRef]

Couris, S.

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003).
[CrossRef]

Dovichi, N. J.

N. J. Dovichi and J. M. Harris, “Laser Induced Thermal Lens Effect for Calorimetric Trace Analysis,” Anal. Chem. 51(6), 728–731 (1979).
[CrossRef]

Dragornir, A.

A. Dragornir, J. G. McInerney, D. N. Nikogosyan, and A. A. Ruth, “Two-photon absorption coefficients of several liquids at 264 nm,” IEEE J. Quantum Electron. 38(1), 31–36 (2002).
[CrossRef]

Drobizhev, M.

Falconieri, M.

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69(2), 133–136 (1999).
[CrossRef]

M. Falconieri, “Thermo-optical effects in Z-scan measurements using high-repetition-rate lasers,” J. Opt. A, Pure Appl. Opt. 1(6), 662–667 (1999).
[CrossRef]

Faucher, O.

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003).
[CrossRef]

Ganeev, R. A.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3-4), 433–438 (2004).
[CrossRef]

Gorecki, C.

C. Gorecki, “Interferogram analysis using a Fourier transform method for automatic 3D surface measurement,” Pure Appl. Opt. 1(2), 103–110 (1992).
[CrossRef]

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[CrossRef]

Harris, J. M.

N. J. Dovichi and J. M. Harris, “Laser Induced Thermal Lens Effect for Calorimetric Trace Analysis,” Anal. Chem. 51(6), 728–731 (1979).
[CrossRef]

Ishizawa, N.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3-4), 433–438 (2004).
[CrossRef]

Kaatz, P.

Kliger, D. S.

A. J. Twarowski and D. S. Kliger, “Multiphoton absorption spectra using thermal bloomingII. Two-photon spectrum of benzene,” Chem. Phys. 20(2), 259–264 (1977).
[CrossRef]

Knight, L. V.

Koudoumas, E.

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003).
[CrossRef]

Kumar, G. R.

P. Sengupta, J. Balaji, S. Banerjee, R. Philip, G. R. Kumar, and S. Maiti, “Sensitive measurement of absolute two-photon absorption cross sections,” J. Chem. Phys. 112(21), 9201–9205 (2000).
[CrossRef]

Kuroda, H.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3-4), 433–438 (2004).
[CrossRef]

Lavorel, B.

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003).
[CrossRef]

Maiti, S.

P. Sengupta, J. Balaji, S. Banerjee, R. Philip, G. R. Kumar, and S. Maiti, “Sensitive measurement of absolute two-photon absorption cross sections,” J. Chem. Phys. 112(21), 9201–9205 (2000).
[CrossRef]

Makarov, N. S.

Marcano O., A.

A. Marcano O., “K. Williams, N. Melikechi, “Measurement of two-photon absorption using the photo-thermal lens effect,” Opt. Commun. 281, 2598–2604 (2008).

Marcanoo, A.

L. Rodriguez, C. Simos, M. Sylla, A. Marcanoo, and X. Nguyenphu, “New holographic technique for third-order optical properties measurement,” Opt. Commun. 247(4-6), 453–460 (2005).
[CrossRef]

McInerney, J. G.

A. Dragornir, J. G. McInerney, D. N. Nikogosyan, and A. A. Ruth, “Two-photon absorption coefficients of several liquids at 264 nm,” IEEE J. Quantum Electron. 38(1), 31–36 (2002).
[CrossRef]

Michaut, X.

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003).
[CrossRef]

Nguyenphu, X.

L. Rodriguez, C. Simos, M. Sylla, A. Marcanoo, and X. Nguyenphu, “New holographic technique for third-order optical properties measurement,” Opt. Commun. 247(4-6), 453–460 (2005).
[CrossRef]

Nikogosyan, D. N.

A. Dragornir, J. G. McInerney, D. N. Nikogosyan, and A. A. Ruth, “Two-photon absorption coefficients of several liquids at 264 nm,” IEEE J. Quantum Electron. 38(1), 31–36 (2002).
[CrossRef]

Philip, R.

P. Sengupta, J. Balaji, S. Banerjee, R. Philip, G. R. Kumar, and S. Maiti, “Sensitive measurement of absolute two-photon absorption cross sections,” J. Chem. Phys. 112(21), 9201–9205 (2000).
[CrossRef]

Rebane, A.

Renard, M.

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003).
[CrossRef]

Rodriguez, L.

L. Rodriguez, C. Simos, M. Sylla, A. Marcanoo, and X. Nguyenphu, “New holographic technique for third-order optical properties measurement,” Opt. Commun. 247(4-6), 453–460 (2005).
[CrossRef]

Ruth, A. A.

A. Dragornir, J. G. McInerney, D. N. Nikogosyan, and A. A. Ruth, “Two-photon absorption coefficients of several liquids at 264 nm,” IEEE J. Quantum Electron. 38(1), 31–36 (2002).
[CrossRef]

Ryasnyansky, A. I.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3-4), 433–438 (2004).
[CrossRef]

Said, A. A.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[CrossRef]

Sakakibara, S.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3-4), 433–438 (2004).
[CrossRef]

Salvetti, G.

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69(2), 133–136 (1999).
[CrossRef]

Sengupta, P.

P. Sengupta, J. Balaji, S. Banerjee, R. Philip, G. R. Kumar, and S. Maiti, “Sensitive measurement of absolute two-photon absorption cross sections,” J. Chem. Phys. 112(21), 9201–9205 (2000).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[CrossRef]

Sheldon, S. J.

Shelton, D. P.

Simos, C.

L. Rodriguez, C. Simos, M. Sylla, A. Marcanoo, and X. Nguyenphu, “New holographic technique for third-order optical properties measurement,” Opt. Commun. 247(4-6), 453–460 (2005).
[CrossRef]

Stone, J.

Suzuki, M.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3-4), 433–438 (2004).
[CrossRef]

Sylla, M.

L. Rodriguez, C. Simos, M. Sylla, A. Marcanoo, and X. Nguyenphu, “New holographic technique for third-order optical properties measurement,” Opt. Commun. 247(4-6), 453–460 (2005).
[CrossRef]

Thorne, J. M.

Turu, M.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3-4), 433–438 (2004).
[CrossRef]

Twarowski, A. J.

A. J. Twarowski and D. S. Kliger, “Multiphoton absorption spectra using thermal bloomingII. Two-photon spectrum of benzene,” Chem. Phys. 20(2), 259–264 (1977).
[CrossRef]

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[CrossRef]

Webb, W.

Webb, W. W.

Wei, T.-H.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[CrossRef]

Xu, C.

Anal. Chem. (1)

N. J. Dovichi and J. M. Harris, “Laser Induced Thermal Lens Effect for Calorimetric Trace Analysis,” Anal. Chem. 51(6), 728–731 (1979).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (2)

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69(2), 133–136 (1999).
[CrossRef]

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B 78(3-4), 433–438 (2004).
[CrossRef]

Chem. Phys. (1)

A. J. Twarowski and D. S. Kliger, “Multiphoton absorption spectra using thermal bloomingII. Two-photon spectrum of benzene,” Chem. Phys. 20(2), 259–264 (1977).
[CrossRef]

Chem. Phys. Lett. (1)

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369(3-4), 318–324 (2003).
[CrossRef]

IEEE J. Quantum Electron. (2)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive Measurement of Optical Nonlinearities using a Single Beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[CrossRef]

A. Dragornir, J. G. McInerney, D. N. Nikogosyan, and A. A. Ruth, “Two-photon absorption coefficients of several liquids at 264 nm,” IEEE J. Quantum Electron. 38(1), 31–36 (2002).
[CrossRef]

J. Chem. Phys. (1)

P. Sengupta, J. Balaji, S. Banerjee, R. Philip, G. R. Kumar, and S. Maiti, “Sensitive measurement of absolute two-photon absorption cross sections,” J. Chem. Phys. 112(21), 9201–9205 (2000).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

M. Falconieri, “Thermo-optical effects in Z-scan measurements using high-repetition-rate lasers,” J. Opt. A, Pure Appl. Opt. 1(6), 662–667 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

Opt. Commun. (2)

A. Marcano O., “K. Williams, N. Melikechi, “Measurement of two-photon absorption using the photo-thermal lens effect,” Opt. Commun. 281, 2598–2604 (2008).

L. Rodriguez, C. Simos, M. Sylla, A. Marcanoo, and X. Nguyenphu, “New holographic technique for third-order optical properties measurement,” Opt. Commun. 247(4-6), 453–460 (2005).
[CrossRef]

Opt. Express (1)

Pure Appl. Opt. (1)

C. Gorecki, “Interferogram analysis using a Fourier transform method for automatic 3D surface measurement,” Pure Appl. Opt. 1(2), 103–110 (1992).
[CrossRef]

Other (1)

M. Born, and E. Wolf, Principles of Optics, (Cambridge University Press, 1999).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the thermal lens method based on a Rayleigh interferometer.

Fig. 2
Fig. 2

Top-view of the experimental setup, the laser polarization is perpendicular to the plane of the figure. A neutral density filter wheel serves as the optical attenuator.

Fig. 3
Fig. 3

Experimental interferograms: (a) linear interferogram at the initial state of the photo-thermal process, (b) nonlinear interferogram, and (c) intensity profile interferograms obtained from experimental images. The red fringes in (c) show the phase shift when the thermal lens is induced. Intensity is expressed by Gray level units (G.L.).

Fig. 4
Fig. 4

Summary of the steps used in the Fourier analysis for CS2. (a) Experimental nonlinear interferogram. (b) Filtered interference pattern. (c) Fourier space showing the Dirac’s distributions. (d) Isolated probe beam distribution carrying the photo-thermal phase shift.

Fig. 5
Fig. 5

Photo-thermal phase map extracted from interferograms shown in Figs. 3a and 3b. The red square indicates the area where the phase difference was evaluated.

Fig. 6
Fig. 6

Log-Log plots for all tested samples. The red straight lines indicate the best fit obtained by linear regression for each sample.

Fig. 7
Fig. 7

Two-photon absorption spectra for the fluorescent molecules studied. RhB and Rh6G were prepared in methanol solution, while the Fluorescein was evaluated in alkaline water.

Tables (2)

Tables Icon

Table 1 Parameters of the four samples.

Tables Icon

Table 2 Relative δ values obtained from Rh6G and Fluorescein solutions. The reference 2PA cross sections values for RhB are from reference 6.

Equations (10)

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

Q(r)=βI(r)2,
ΔT(r,t)=(βP2π2w2κ)1tc0t11+4t'/tcexp(4r2/w21+4t'/tc)dt',
ϕ(r,t)=βL​  P22πw2λκ(dndT){ln(1+4t/tc)+i=1(4r2/w2)iii![1(11+4t/tc)i]}.
Δϕ=Δϕ()Δϕ(0)1.32βL​  P22πw2λκ(dndT).
i(x,y)=a(x,y)+b(x,y)cos(2πx/Δx+ϕ(x,y)),
I(X,Y)=A(X,Y)+[FT(exp(jϕ(x,y)))*B(X,Y)]δ(XΔX,Y)       +[FT(exp(jϕ(x,y)))B(X,Y)]δ(X+ΔX,Y),
g(x,y)=b(x,y)exp(jϕ(x,y)).
Δϕ(x,y)=arctan[Im{h(x,y)}Re{h(x,y)}].
δsδr=(ΔϕsΔϕrm),
m=[Cs][Cs]Pr2Ps2[κs(dnr/dT)κr(dns/dT)](1Φrλ/2λer1Φsλ/2λes).

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