Abstract

We present a variation of the single-beam thermal lensing experiment to determine the two-photon absorption cross sections of classical fluorophores. The approach is based on comparison of two thermal lensing signals simultaneously induced by a one- and two-photon absorption process from a high- repetition-rate femtosecond laser system. As a consequence of this comparison, a simplified expression independent of the several experimental parameters is obtained. Additionally, because of the low incident power levels required, undesirable optical effects such as Kerr or Raman scattering are avoided. Our experimental results agree well with those recently published for luminescent methods, validating the approach.

© 2011 Optical Society of America

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  1. W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
    [CrossRef] [PubMed]
  2. M. Falconieri, “Thermo-optical effects in Z-scan measurements using high-repetition-rate lasers,” J. Opt. A 1, 662–667 (1999).
    [CrossRef]
  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 inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
    [CrossRef]
  4. S. J. Sheldon, L. V. Knight, and J. M. Thorne, “Laser-induced thermal lens effect: a new theoretical model,” Appl. Opt. 21, 1663–1669 (1982).
    [CrossRef] [PubMed]
  5. A. J. Twarowski and D. S. Kliger, “Multiphoton absorption spectra using thermal blooming: II. Two-photon spectrum of benzene,” Chem. Phys. 20, 259–264 (1977).
    [CrossRef]
  6. L. Rodriguez, L. Echevarria, and A. Fernandez, “I-scan thermal lens experiment in the pulse regime for measuring two-photon absorption coefficient,” Opt. Commun. 277, 181–185 (2007).
    [CrossRef]
  7. M. Guerra, A. Taouri, A. O. Marcano, H. Cabrera, and M. Sylla, “Measurement of nonlinear absorption coefficients of organic materials by mode-mismatched Z-scan thermal lensing technique,” Appl. Spectrosc. 61, 1128–1133 (2007).
    [CrossRef] [PubMed]
  8. A. O. Marcano, K. Williams, and N. Melikechi, “Measurement of two-photon absorption using the photo-thermal lens effect,” Opt. Commun. 281, 2598–2604 (2008).
    [CrossRef]
  9. L. Rodriguez, H. Y. Ahn, and K. D. Belfield, “Femtosecond two-photon absorption measurements based on the accumulative photo-thermal effect and the Rayleigh interferometer,” Opt. Express 17, 19617–19628 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
  11. P. F. Curley, A. I. Ferguson, J. G. White, and W. B. Amos, “Application of a femtosecond self-sustaining mode-locked Ti:sapphire laser to the field of laser scanning confocal microscopy,” Opt. Quantum Electron. 24, 851–859 (1992).
    [CrossRef]
  12. J. R. Whinnery, D. T. Miller, and F. Dabby, “Thermal convection and spherical aberration distortion of laser beams in low-loss liquids,” IEEE J. Quantum Electron. 3, 382–383 (1967).
    [CrossRef]
  13. 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, 7352–7356 (1998).
    [CrossRef]
  14. N. S. Makarov, M. Drobizhev, and A. Rebane, “Two-photon absorption standards in the 550–1600 nm excitation wavelength range,” Opt. Express 16, 4029–4047 (2008).
    [CrossRef] [PubMed]
  15. R. Sailaja, P. B. Bisht, C. P. Singh, K. S. Bindra, and S. M. Oak, “Influence of multiphoton events in measurement of two-photon absorption cross-sections and optical nonlinear parameters under femtosecond pumping,” Opt. Commun. 277, 433–439 (2007).
    [CrossRef]

2009 (1)

2008 (2)

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

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

2007 (3)

L. Rodriguez, L. Echevarria, and A. Fernandez, “I-scan thermal lens experiment in the pulse regime for measuring two-photon absorption coefficient,” Opt. Commun. 277, 181–185 (2007).
[CrossRef]

M. Guerra, A. Taouri, A. O. Marcano, H. Cabrera, and M. Sylla, “Measurement of nonlinear absorption coefficients of organic materials by mode-mismatched Z-scan thermal lensing technique,” Appl. Spectrosc. 61, 1128–1133 (2007).
[CrossRef] [PubMed]

R. Sailaja, P. B. Bisht, C. P. Singh, K. S. Bindra, and S. M. Oak, “Influence of multiphoton events in measurement of two-photon absorption cross-sections and optical nonlinear parameters under femtosecond pumping,” Opt. Commun. 277, 433–439 (2007).
[CrossRef]

1999 (1)

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

1998 (1)

1996 (1)

1992 (1)

P. F. Curley, A. I. Ferguson, J. G. White, and W. B. Amos, “Application of a femtosecond self-sustaining mode-locked Ti:sapphire laser to the field of laser scanning confocal microscopy,” Opt. Quantum Electron. 24, 851–859 (1992).
[CrossRef]

1990 (1)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

1982 (1)

1977 (1)

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

1967 (1)

J. R. Whinnery, D. T. Miller, and F. Dabby, “Thermal convection and spherical aberration distortion of laser beams in low-loss liquids,” IEEE J. Quantum Electron. 3, 382–383 (1967).
[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 inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[CrossRef]

Ahn, H. Y.

Albota, M. A.

Amos, W. B.

P. F. Curley, A. I. Ferguson, J. G. White, and W. B. Amos, “Application of a femtosecond self-sustaining mode-locked Ti:sapphire laser to the field of laser scanning confocal microscopy,” Opt. Quantum Electron. 24, 851–859 (1992).
[CrossRef]

Belfield, K. D.

Bindra, K. S.

R. Sailaja, P. B. Bisht, C. P. Singh, K. S. Bindra, and S. M. Oak, “Influence of multiphoton events in measurement of two-photon absorption cross-sections and optical nonlinear parameters under femtosecond pumping,” Opt. Commun. 277, 433–439 (2007).
[CrossRef]

Bisht, P. B.

R. Sailaja, P. B. Bisht, C. P. Singh, K. S. Bindra, and S. M. Oak, “Influence of multiphoton events in measurement of two-photon absorption cross-sections and optical nonlinear parameters under femtosecond pumping,” Opt. Commun. 277, 433–439 (2007).
[CrossRef]

Cabrera, H.

Curley, P. F.

P. F. Curley, A. I. Ferguson, J. G. White, and W. B. Amos, “Application of a femtosecond self-sustaining mode-locked Ti:sapphire laser to the field of laser scanning confocal microscopy,” Opt. Quantum Electron. 24, 851–859 (1992).
[CrossRef]

Dabby, F.

J. R. Whinnery, D. T. Miller, and F. Dabby, “Thermal convection and spherical aberration distortion of laser beams in low-loss liquids,” IEEE J. Quantum Electron. 3, 382–383 (1967).
[CrossRef]

Denk, W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Drobizhev, M.

Echevarria, L.

L. Rodriguez, L. Echevarria, and A. Fernandez, “I-scan thermal lens experiment in the pulse regime for measuring two-photon absorption coefficient,” Opt. Commun. 277, 181–185 (2007).
[CrossRef]

Falconieri, M.

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

Ferguson, A. I.

P. F. Curley, A. I. Ferguson, J. G. White, and W. B. Amos, “Application of a femtosecond self-sustaining mode-locked Ti:sapphire laser to the field of laser scanning confocal microscopy,” Opt. Quantum Electron. 24, 851–859 (1992).
[CrossRef]

Fernandez, A.

L. Rodriguez, L. Echevarria, and A. Fernandez, “I-scan thermal lens experiment in the pulse regime for measuring two-photon absorption coefficient,” Opt. Commun. 277, 181–185 (2007).
[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 inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[CrossRef]

Guerra, M.

Kliger, D. S.

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

Knight, L. V.

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 inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[CrossRef]

Makarov, N. S.

Marcano, A. O.

Melikechi, N.

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

Miller, D. T.

J. R. Whinnery, D. T. Miller, and F. Dabby, “Thermal convection and spherical aberration distortion of laser beams in low-loss liquids,” IEEE J. Quantum Electron. 3, 382–383 (1967).
[CrossRef]

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 inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[CrossRef]

Oak, S. M.

R. Sailaja, P. B. Bisht, C. P. Singh, K. S. Bindra, and S. M. Oak, “Influence of multiphoton events in measurement of two-photon absorption cross-sections and optical nonlinear parameters under femtosecond pumping,” Opt. Commun. 277, 433–439 (2007).
[CrossRef]

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 inserted liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[CrossRef]

Rebane, A.

Rodriguez, L.

L. Rodriguez, H. Y. Ahn, and K. D. Belfield, “Femtosecond two-photon absorption measurements based on the accumulative photo-thermal effect and the Rayleigh interferometer,” Opt. Express 17, 19617–19628 (2009).
[CrossRef] [PubMed]

L. Rodriguez, L. Echevarria, and A. Fernandez, “I-scan thermal lens experiment in the pulse regime for measuring two-photon absorption coefficient,” Opt. Commun. 277, 181–185 (2007).
[CrossRef]

Sailaja, R.

R. Sailaja, P. B. Bisht, C. P. Singh, K. S. Bindra, and S. M. Oak, “Influence of multiphoton events in measurement of two-photon absorption cross-sections and optical nonlinear parameters under femtosecond pumping,” Opt. Commun. 277, 433–439 (2007).
[CrossRef]

Sheldon, S. J.

Singh, C. P.

R. Sailaja, P. B. Bisht, C. P. Singh, K. S. Bindra, and S. M. Oak, “Influence of multiphoton events in measurement of two-photon absorption cross-sections and optical nonlinear parameters under femtosecond pumping,” Opt. Commun. 277, 433–439 (2007).
[CrossRef]

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Sylla, M.

Taouri, A.

Thorne, J. M.

Twarowski, A. J.

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

Webb, W. W.

Whinnery, J. R.

J. R. Whinnery, D. T. Miller, and F. Dabby, “Thermal convection and spherical aberration distortion of laser beams in low-loss liquids,” IEEE J. Quantum Electron. 3, 382–383 (1967).
[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 liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[CrossRef]

White, J. G.

P. F. Curley, A. I. Ferguson, J. G. White, and W. B. Amos, “Application of a femtosecond self-sustaining mode-locked Ti:sapphire laser to the field of laser scanning confocal microscopy,” Opt. Quantum Electron. 24, 851–859 (1992).
[CrossRef]

Williams, K.

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

Xu, C.

Appl. Opt. (2)

Appl. Spectrosc. (1)

Chem. Phys. (1)

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

IEEE J. Quantum Electron. (1)

J. R. Whinnery, D. T. Miller, and F. Dabby, “Thermal convection and spherical aberration distortion of laser beams in low-loss liquids,” IEEE J. Quantum Electron. 3, 382–383 (1967).
[CrossRef]

J. Appl. Phys. (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 liquid samples,” J. Appl. Phys. 36, 3–8 (1965).
[CrossRef]

J. Opt. A (1)

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

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

Opt. Commun. (3)

R. Sailaja, P. B. Bisht, C. P. Singh, K. S. Bindra, and S. M. Oak, “Influence of multiphoton events in measurement of two-photon absorption cross-sections and optical nonlinear parameters under femtosecond pumping,” Opt. Commun. 277, 433–439 (2007).
[CrossRef]

L. Rodriguez, L. Echevarria, and A. Fernandez, “I-scan thermal lens experiment in the pulse regime for measuring two-photon absorption coefficient,” Opt. Commun. 277, 181–185 (2007).
[CrossRef]

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

Opt. Express (2)

Opt. Quantum Electron. (1)

P. F. Curley, A. I. Ferguson, J. G. White, and W. B. Amos, “Application of a femtosecond self-sustaining mode-locked Ti:sapphire laser to the field of laser scanning confocal microscopy,” Opt. Quantum Electron. 24, 851–859 (1992).
[CrossRef]

Science (1)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Experimental setup used to measure 2PA cross section of the classical dyes. M, mirror; Ch, chopper; F, filter; D3, D4, detectors; S, sample.

Fig. 2
Fig. 2

Absorbance spectra of the dyes used in this work. The inset shows the absorbance in the spectral region of 375 435   nm .

Fig. 3
Fig. 3

Fluorescence emission spectra of the RhB sample induced by absorption of one and two photons.

Fig. 4
Fig. 4

Typical experimental curves showing the linear dependence between S 2 / S 1 and P 2 2 / P 1 . The standard error is indicated by the error bar on each curve.

Fig. 5
Fig. 5

Experimental 2PA spectra of the Rh6G obtained after experiment calibration is done with respect to RhB. The data plotted with open triangles correspond to [14].

Tables (1)

Tables Icon

Table 1 2PA Cross Section of the Classical Dyes Measured at 800 nm of Excitation Wavelength Using TL Effect

Equations (13)

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Q ( r ) q = α q I ( r ) q f q ,
α q = q ( N A [ C ] ) ( h ν ) q 1 δ q ,
I ( r ) = 2 P exp ( 2 r 2 / w 2 ) / π w 2 ,
f q = 1 Φ λ q q λ e q ,
Δ T ( r , t ) q = ( q α q P q f q 2 π κ ( π w 2 ) q 1 ) 1 t c 0 t 1 1 + 2 q t / t c exp ( 2 q r 2 / w 2 1 + 2 q t / t c ) d t ,
Δ ϕ ( t ) q = ϕ ( r , t ) q ϕ ( 0 , t ) q = θ q t c 0 t τ [ 1 exp ( 2 q τ u ) ] d t ,
θ q = ( q α q L P q f q λ q κ ( π w 2 ) q 1 ) ( d n d T ) .
U e = U i ( u , z , t ) exp ( j Δ ϕ q ) .
U ( t ) q = B 0 ( 1 j Δ ϕ q ) exp [ ( 1 + j V ) u ] d u ,
I ( t ) q = | U ( V , t ) q | 2 I ( 0 ) q + I ( 0 ) q θ q q arctan ( 2 q V [ ( 2 q + 1 ) 2 + V 2 ] t c ( w 0 ) 2 q t + ( 1 + 2 q + V 2 ) ) .
S q = I ( ) I ( 0 ) I ( 0 ) = θ q q arctan ( 2 q V 1 + 2 q + V 2 ) .
S 2 S 1 = α 2 L A C P 2 2 P 1 ,
C = arctan { 4 V 2 / ( 5 + V 2 2 ) } 2 π w 2 2 arctan { 2 V 1 / ( 3 + V 1 2 ) } .

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