Abstract

In non-degenerate two-photon microscopy (ND-TPM), the required energy for fluorescence excitation occurs via absorption of two photons of different energies derived from two synchronized pulsed laser beams. ND-TPM is a promising imaging technology offering flexibility in the choice of the photon energy for each beam. However, a formalism to quantify the efficiency of two-photon absorption (TPA) under non-degenerate excitation, relative to the resonant degenerate excitation, is missing. Here, we derive this formalism and experimentally validate our prediction for a common fluorophore, fluorescein. An accurate quantification of non-degenerate TPA is important to optimize the choice of photon energies for each fluorophore.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref] [PubMed]

2017 (2)

E. P. Perillo, J. W. Jarrett, Y. L. Liu, A. Hassan, D. C. Fernée, J. R. Goldak, A. Bonteanu, D. J. Spence, H. C. Yeh, and A. K. Dunn, “Two-color multiphoton in vivo imaging with a femtosecond diamond raman laser,” Light Sci. Appl. 6, e17095 (2017).
[Crossref]

D. R. Miller, J. W. Jarrett, A. M. Hassan, and A. K. Dunn, “Deep tissue imaging with multiphoton fluorescence microscopy,” Curr. Opin. Biomed. Eng. 4, 32–39 (2017).
[Crossref]

2016 (3)

M. H. Yang, M. Abashin, P. A. Saisan, P. Tian, C. G. Ferri, A. Devor, and Y. Fainman, “Non-degenerate 2-photon excitation in scattering medium for fluorescence microscopy,” Opt. Express 24, 30173–30187 (2016).
[Crossref]

K. Podgorski and G. Ranganathan, “Brain heating induced by near-infrared lasers during multiphoton microscopy,” J. Neurophysiol. 116, 1012–1023 (2016).
[Crossref] [PubMed]

H. S. Pattanaik, M. Reichert, J. B. Khurgin, D. J. Hagan, and E. W. Van Stryland, “Enhancement of two-photon absorption in quantum wells for extremely nondegenerate photon pairs,” IEEE J. Quantum Electron. 52, 1–14 (2016).
[Crossref]

2015 (1)

B. Xue, C. Katan, J. Bjorgaard, and T. Kobayashi, “Non-degenerate two photon absorption enhancement for laser dyes by precise lock-in detection,” AIP Adv. 5, 127138 (2015).
[Crossref]

2012 (1)

P. Mahou, M. Zimmerley, K. Loulier, K. S. Matho, G. Labroille, X. Morin, W. Supatto, J. Livet, D. Débarre, and E. Beaurepaire, “Multicolor two-photon tissue imaging by wavelength mixing,” Nat. Methods 9, 815–818 (2012).
[Crossref] [PubMed]

2011 (2)

M. Drobizhev, N. S. Makarov, S. E. Tillo, T. E. Hughes, and A. Rebane, “Two-photon absorption properties of fluorescent proteins,” Nature Methods 8, 393–399 (2011).
[Crossref] [PubMed]

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

2009 (1)

S. Quentmeier, S. Denicke, and K. H. Gericke, “Two-color two-photon fluorescence laser scanning microscopy,” J. Fluoresc. 19, 1037–1043 (2009).
[Crossref] [PubMed]

2008 (1)

C. Wang, L. Qiao, Z. Mao, Y. Cheng, and Z. Xu, “Reduced deep-tissue image degradation in three-dimensional multiphoton microscopy with concentric two-color two-photon fluorescence excitation,” J. Opt. Soc. Am. B 25, 976–982 (2008).
[Crossref]

2005 (1)

J. W. Lichtman and J. A. Conchello, “Fluorescence microscopy,” Nat. Methods 2, 910–919 (2005).
[Crossref] [PubMed]

2004 (2)

C. Ibáñez-López, I. Escobar, G. Saavedra, and M. Martínez-Corral, “Optical-sectioning improvement in two-color excitation scanning microscopy,” Microsc. Res. Tech. 64, 96–102 (2004).
[Crossref] [PubMed]

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. Schafer, A. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J.-L. Brédas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121, 3152–3160 (2004).
[Crossref] [PubMed]

2002 (1)

R. A. Negres, J. M. Hales, A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Two-photon spectroscopy and analysis with a white-light continuum probe,” Opt. Lett. 27, 270–272 (2002).
[Crossref]

2001 (1)

C. M. Blanca and C. Saloma, “Two-color excitation fluorescence microscopy through highly scattering media,” Appl. Opt. 40, 2722–2729 (2001).
[Crossref]

2000 (1)

M. O. Cambaliza and C. Saloma, “Advantages of two-color excitation fluorescence microscopy with two confocal excitation beams,” Opt. Commun. 184, 25–35 (2000).
[Crossref]

1999 (2)

S. Lindek and E. Stelzer, “Resolution improvement by nonconfocal theta microscopy,” Opt. Lett. 24, 1505–1507 (1999).
[Crossref]

K. D. Belfield, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, and R. A. Negres, “New two-photon absorbing fluorene derivatives: synthesis and nonlinear optical characterization,” Org. Lett. 1, 1575–1578 (1999).
[Crossref]

1996 (1)

C. Xu and W. W. Webb, “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm,” J. Opt. Soc. Am. B 13, 481–491 (1996).
[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]

1985 (1)

J. C. M. Diels, J. J. Fontaine, I. C. McMichael, and F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt. 24, 1270–1282 (1985).
[Crossref] [PubMed]

1970 (1)

P. Monson and W. McClain, “Polarization dependence of the two-photon absorption of tumbling molecules with application to liquid 1-chloronaphthalene and benzene,” J. Chem. Phys. 53, 29–37 (1970).
[Crossref]

1966 (1)

D. Fröhlich and H. Mahr, “Two-photon spectroscopy in anthracene,” Phys. Rev. Lett. 16, 895–897 (1966).
[Crossref]

1931 (1)

M. Göppert-Mayer, “Über Elementarakte mit zwei Quantensprüngen,” Ann. Phys. 401, 273–294 (1931).
[Crossref]

Abashin, M.

M. H. Yang, M. Abashin, P. A. Saisan, P. Tian, C. G. Ferri, A. Devor, and Y. Fainman, “Non-degenerate 2-photon excitation in scattering medium for fluorescence microscopy,” Opt. Express 24, 30173–30187 (2016).
[Crossref]

Beaurepaire, E.

P. Mahou, M. Zimmerley, K. Loulier, K. S. Matho, G. Labroille, X. Morin, W. Supatto, J. Livet, D. Débarre, and E. Beaurepaire, “Multicolor two-photon tissue imaging by wavelength mixing,” Nat. Methods 9, 815–818 (2012).
[Crossref] [PubMed]

Belfield, K. D.

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. Schafer, A. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J.-L. Brédas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121, 3152–3160 (2004).
[Crossref] [PubMed]

K. D. Belfield, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, and R. A. Negres, “New two-photon absorbing fluorene derivatives: synthesis and nonlinear optical characterization,” Org. Lett. 1, 1575–1578 (1999).
[Crossref]

Bjorgaard, J.

B. Xue, C. Katan, J. Bjorgaard, and T. Kobayashi, “Non-degenerate two photon absorption enhancement for laser dyes by precise lock-in detection,” AIP Adv. 5, 127138 (2015).
[Crossref]

Blanca, C. M.

C. M. Blanca and C. Saloma, “Two-color excitation fluorescence microscopy through highly scattering media,” Appl. Opt. 40, 2722–2729 (2001).
[Crossref]

Bonteanu, A.

E. P. Perillo, J. W. Jarrett, Y. L. Liu, A. Hassan, D. C. Fernée, J. R. Goldak, A. Bonteanu, D. J. Spence, H. C. Yeh, and A. K. Dunn, “Two-color multiphoton in vivo imaging with a femtosecond diamond raman laser,” Light Sci. Appl. 6, e17095 (2017).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear optics (Elsevier, 2003).

Brédas, J.-L.

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. Schafer, A. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J.-L. Brédas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121, 3152–3160 (2004).
[Crossref] [PubMed]

Cambaliza, M. O.

M. O. Cambaliza and C. Saloma, “Advantages of two-color excitation fluorescence microscopy with two confocal excitation beams,” Opt. Commun. 184, 25–35 (2000).
[Crossref]

Cheng, Y.

C. Wang, L. Qiao, Z. Mao, Y. Cheng, and Z. Xu, “Reduced deep-tissue image degradation in three-dimensional multiphoton microscopy with concentric two-color two-photon fluorescence excitation,” J. Opt. Soc. Am. B 25, 976–982 (2008).
[Crossref]

Cirloganu, C. M.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Conchello, J. A.

J. W. Lichtman and J. A. Conchello, “Fluorescence microscopy,” Nat. Methods 2, 910–919 (2005).
[Crossref] [PubMed]

Débarre, D.

P. Mahou, M. Zimmerley, K. Loulier, K. S. Matho, G. Labroille, X. Morin, W. Supatto, J. Livet, D. Débarre, and E. Beaurepaire, “Multicolor two-photon tissue imaging by wavelength mixing,” Nat. Methods 9, 815–818 (2012).
[Crossref] [PubMed]

Denicke, S.

S. Quentmeier, S. Denicke, and K. H. Gericke, “Two-color two-photon fluorescence laser scanning microscopy,” J. Fluoresc. 19, 1037–1043 (2009).
[Crossref] [PubMed]

Denk, W.

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

Devor, A.

M. H. Yang, M. Abashin, P. A. Saisan, P. Tian, C. G. Ferri, A. Devor, and Y. Fainman, “Non-degenerate 2-photon excitation in scattering medium for fluorescence microscopy,” Opt. Express 24, 30173–30187 (2016).
[Crossref]

Diels, J. C. M.

J. C. M. Diels, J. J. Fontaine, I. C. McMichael, and F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt. 24, 1270–1282 (1985).
[Crossref] [PubMed]

Drobizhev, M.

M. Drobizhev, N. S. Makarov, S. E. Tillo, T. E. Hughes, and A. Rebane, “Two-photon absorption properties of fluorescent proteins,” Nature Methods 8, 393–399 (2011).
[Crossref] [PubMed]

Dunn, A. K.

D. R. Miller, J. W. Jarrett, A. M. Hassan, and A. K. Dunn, “Deep tissue imaging with multiphoton fluorescence microscopy,” Curr. Opin. Biomed. Eng. 4, 32–39 (2017).
[Crossref]

E. P. Perillo, J. W. Jarrett, Y. L. Liu, A. Hassan, D. C. Fernée, J. R. Goldak, A. Bonteanu, D. J. Spence, H. C. Yeh, and A. K. Dunn, “Two-color multiphoton in vivo imaging with a femtosecond diamond raman laser,” Light Sci. Appl. 6, e17095 (2017).
[Crossref]

Escobar, I.

C. Ibáñez-López, I. Escobar, G. Saavedra, and M. Martínez-Corral, “Optical-sectioning improvement in two-color excitation scanning microscopy,” Microsc. Res. Tech. 64, 96–102 (2004).
[Crossref] [PubMed]

Fainman, Y.

M. H. Yang, M. Abashin, P. A. Saisan, P. Tian, C. G. Ferri, A. Devor, and Y. Fainman, “Non-degenerate 2-photon excitation in scattering medium for fluorescence microscopy,” Opt. Express 24, 30173–30187 (2016).
[Crossref]

Fernée, D. C.

E. P. Perillo, J. W. Jarrett, Y. L. Liu, A. Hassan, D. C. Fernée, J. R. Goldak, A. Bonteanu, D. J. Spence, H. C. Yeh, and A. K. Dunn, “Two-color multiphoton in vivo imaging with a femtosecond diamond raman laser,” Light Sci. Appl. 6, e17095 (2017).
[Crossref]

Ferri, C. G.

M. H. Yang, M. Abashin, P. A. Saisan, P. Tian, C. G. Ferri, A. Devor, and Y. Fainman, “Non-degenerate 2-photon excitation in scattering medium for fluorescence microscopy,” Opt. Express 24, 30173–30187 (2016).
[Crossref]

Fishman, D. A.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Fontaine, J. J.

J. C. M. Diels, J. J. Fontaine, I. C. McMichael, and F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt. 24, 1270–1282 (1985).
[Crossref] [PubMed]

Fröhlich, D.

D. Fröhlich and H. Mahr, “Two-photon spectroscopy in anthracene,” Phys. Rev. Lett. 16, 895–897 (1966).
[Crossref]

Gericke, K. H.

S. Quentmeier, S. Denicke, and K. H. Gericke, “Two-color two-photon fluorescence laser scanning microscopy,” J. Fluoresc. 19, 1037–1043 (2009).
[Crossref] [PubMed]

Goldak, J. R.

E. P. Perillo, J. W. Jarrett, Y. L. Liu, A. Hassan, D. C. Fernée, J. R. Goldak, A. Bonteanu, D. J. Spence, H. C. Yeh, and A. K. Dunn, “Two-color multiphoton in vivo imaging with a femtosecond diamond raman laser,” Light Sci. Appl. 6, e17095 (2017).
[Crossref]

Göppert-Mayer, M.

M. Göppert-Mayer, “Über Elementarakte mit zwei Quantensprüngen,” Ann. Phys. 401, 273–294 (1931).
[Crossref]

Hagan, D. J.

H. S. Pattanaik, M. Reichert, J. B. Khurgin, D. J. Hagan, and E. W. Van Stryland, “Enhancement of two-photon absorption in quantum wells for extremely nondegenerate photon pairs,” IEEE J. Quantum Electron. 52, 1–14 (2016).
[Crossref]

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. Schafer, A. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J.-L. Brédas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121, 3152–3160 (2004).
[Crossref] [PubMed]

R. A. Negres, J. M. Hales, A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Two-photon spectroscopy and analysis with a white-light continuum probe,” Opt. Lett. 27, 270–272 (2002).
[Crossref]

K. D. Belfield, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, and R. A. Negres, “New two-photon absorbing fluorene derivatives: synthesis and nonlinear optical characterization,” Org. Lett. 1, 1575–1578 (1999).
[Crossref]

Hales, J. M.

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. Schafer, A. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J.-L. Brédas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121, 3152–3160 (2004).
[Crossref] [PubMed]

R. A. Negres, J. M. Hales, A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Two-photon spectroscopy and analysis with a white-light continuum probe,” Opt. Lett. 27, 270–272 (2002).
[Crossref]

Hassan, A.

E. P. Perillo, J. W. Jarrett, Y. L. Liu, A. Hassan, D. C. Fernée, J. R. Goldak, A. Bonteanu, D. J. Spence, H. C. Yeh, and A. K. Dunn, “Two-color multiphoton in vivo imaging with a femtosecond diamond raman laser,” Light Sci. Appl. 6, e17095 (2017).
[Crossref]

Hassan, A. M.

D. R. Miller, J. W. Jarrett, A. M. Hassan, and A. K. Dunn, “Deep tissue imaging with multiphoton fluorescence microscopy,” Curr. Opin. Biomed. Eng. 4, 32–39 (2017).
[Crossref]

Hughes, T. E.

M. Drobizhev, N. S. Makarov, S. E. Tillo, T. E. Hughes, and A. Rebane, “Two-photon absorption properties of fluorescent proteins,” Nature Methods 8, 393–399 (2011).
[Crossref] [PubMed]

Ibáñez-López, C.

C. Ibáñez-López, I. Escobar, G. Saavedra, and M. Martínez-Corral, “Optical-sectioning improvement in two-color excitation scanning microscopy,” Microsc. Res. Tech. 64, 96–102 (2004).
[Crossref] [PubMed]

Jarrett, J. W.

E. P. Perillo, J. W. Jarrett, Y. L. Liu, A. Hassan, D. C. Fernée, J. R. Goldak, A. Bonteanu, D. J. Spence, H. C. Yeh, and A. K. Dunn, “Two-color multiphoton in vivo imaging with a femtosecond diamond raman laser,” Light Sci. Appl. 6, e17095 (2017).
[Crossref]

D. R. Miller, J. W. Jarrett, A. M. Hassan, and A. K. Dunn, “Deep tissue imaging with multiphoton fluorescence microscopy,” Curr. Opin. Biomed. Eng. 4, 32–39 (2017).
[Crossref]

Katan, C.

B. Xue, C. Katan, J. Bjorgaard, and T. Kobayashi, “Non-degenerate two photon absorption enhancement for laser dyes by precise lock-in detection,” AIP Adv. 5, 127138 (2015).
[Crossref]

Khurgin, J. B.

H. S. Pattanaik, M. Reichert, J. B. Khurgin, D. J. Hagan, and E. W. Van Stryland, “Enhancement of two-photon absorption in quantum wells for extremely nondegenerate photon pairs,” IEEE J. Quantum Electron. 52, 1–14 (2016).
[Crossref]

Kobat, D.

D. Kobat, G. Zhu, and C. Xu, “Background reduction with two-color two-beam multiphoton excitation,” in Biomedical Optics (Optical Society of America, 2008), p. BMF6.
[Crossref]

Kobayashi, T.

B. Xue, C. Katan, J. Bjorgaard, and T. Kobayashi, “Non-degenerate two photon absorption enhancement for laser dyes by precise lock-in detection,” AIP Adv. 5, 127138 (2015).
[Crossref]

Kobyakov, A.

R. A. Negres, J. M. Hales, A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Two-photon spectroscopy and analysis with a white-light continuum probe,” Opt. Lett. 27, 270–272 (2002).
[Crossref]

Kwon, O.

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. Schafer, A. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J.-L. Brédas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121, 3152–3160 (2004).
[Crossref] [PubMed]

Labroille, G.

P. Mahou, M. Zimmerley, K. Loulier, K. S. Matho, G. Labroille, X. Morin, W. Supatto, J. Livet, D. Débarre, and E. Beaurepaire, “Multicolor two-photon tissue imaging by wavelength mixing,” Nat. Methods 9, 815–818 (2012).
[Crossref] [PubMed]

Lichtman, J. W.

J. W. Lichtman and J. A. Conchello, “Fluorescence microscopy,” Nat. Methods 2, 910–919 (2005).
[Crossref] [PubMed]

Lindek, S.

S. Lindek and E. Stelzer, “Resolution improvement by nonconfocal theta microscopy,” Opt. Lett. 24, 1505–1507 (1999).
[Crossref]

Liu, Y. L.

E. P. Perillo, J. W. Jarrett, Y. L. Liu, A. Hassan, D. C. Fernée, J. R. Goldak, A. Bonteanu, D. J. Spence, H. C. Yeh, and A. K. Dunn, “Two-color multiphoton in vivo imaging with a femtosecond diamond raman laser,” Light Sci. Appl. 6, e17095 (2017).
[Crossref]

Livet, J.

P. Mahou, M. Zimmerley, K. Loulier, K. S. Matho, G. Labroille, X. Morin, W. Supatto, J. Livet, D. Débarre, and E. Beaurepaire, “Multicolor two-photon tissue imaging by wavelength mixing,” Nat. Methods 9, 815–818 (2012).
[Crossref] [PubMed]

Loulier, K.

P. Mahou, M. Zimmerley, K. Loulier, K. S. Matho, G. Labroille, X. Morin, W. Supatto, J. Livet, D. Débarre, and E. Beaurepaire, “Multicolor two-photon tissue imaging by wavelength mixing,” Nat. Methods 9, 815–818 (2012).
[Crossref] [PubMed]

Mahou, P.

P. Mahou, M. Zimmerley, K. Loulier, K. S. Matho, G. Labroille, X. Morin, W. Supatto, J. Livet, D. Débarre, and E. Beaurepaire, “Multicolor two-photon tissue imaging by wavelength mixing,” Nat. Methods 9, 815–818 (2012).
[Crossref] [PubMed]

Mahr, H.

D. Fröhlich and H. Mahr, “Two-photon spectroscopy in anthracene,” Phys. Rev. Lett. 16, 895–897 (1966).
[Crossref]

Makarov, N. S.

M. Drobizhev, N. S. Makarov, S. E. Tillo, T. E. Hughes, and A. Rebane, “Two-photon absorption properties of fluorescent proteins,” Nature Methods 8, 393–399 (2011).
[Crossref] [PubMed]

Mao, Z.

C. Wang, L. Qiao, Z. Mao, Y. Cheng, and Z. Xu, “Reduced deep-tissue image degradation in three-dimensional multiphoton microscopy with concentric two-color two-photon fluorescence excitation,” J. Opt. Soc. Am. B 25, 976–982 (2008).
[Crossref]

Martínez-Corral, M.

C. Ibáñez-López, I. Escobar, G. Saavedra, and M. Martínez-Corral, “Optical-sectioning improvement in two-color excitation scanning microscopy,” Microsc. Res. Tech. 64, 96–102 (2004).
[Crossref] [PubMed]

Matho, K. S.

P. Mahou, M. Zimmerley, K. Loulier, K. S. Matho, G. Labroille, X. Morin, W. Supatto, J. Livet, D. Débarre, and E. Beaurepaire, “Multicolor two-photon tissue imaging by wavelength mixing,” Nat. Methods 9, 815–818 (2012).
[Crossref] [PubMed]

McClain, W.

P. Monson and W. McClain, “Polarization dependence of the two-photon absorption of tumbling molecules with application to liquid 1-chloronaphthalene and benzene,” J. Chem. Phys. 53, 29–37 (1970).
[Crossref]

McMichael, I. C.

J. C. M. Diels, J. J. Fontaine, I. C. McMichael, and F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt. 24, 1270–1282 (1985).
[Crossref] [PubMed]

Miller, D. R.

D. R. Miller, J. W. Jarrett, A. M. Hassan, and A. K. Dunn, “Deep tissue imaging with multiphoton fluorescence microscopy,” Curr. Opin. Biomed. Eng. 4, 32–39 (2017).
[Crossref]

Monroe, M.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Monson, P.

P. Monson and W. McClain, “Polarization dependence of the two-photon absorption of tumbling molecules with application to liquid 1-chloronaphthalene and benzene,” J. Chem. Phys. 53, 29–37 (1970).
[Crossref]

Morales, A.

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. Schafer, A. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J.-L. Brédas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121, 3152–3160 (2004).
[Crossref] [PubMed]

Morin, X.

P. Mahou, M. Zimmerley, K. Loulier, K. S. Matho, G. Labroille, X. Morin, W. Supatto, J. Livet, D. Débarre, and E. Beaurepaire, “Multicolor two-photon tissue imaging by wavelength mixing,” Nat. Methods 9, 815–818 (2012).
[Crossref] [PubMed]

Negres, R. A.

R. A. Negres, J. M. Hales, A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Two-photon spectroscopy and analysis with a white-light continuum probe,” Opt. Lett. 27, 270–272 (2002).
[Crossref]

K. D. Belfield, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, and R. A. Negres, “New two-photon absorbing fluorene derivatives: synthesis and nonlinear optical characterization,” Org. Lett. 1, 1575–1578 (1999).
[Crossref]

Pacher, P.

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. Schafer, A. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J.-L. Brédas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121, 3152–3160 (2004).
[Crossref] [PubMed]

Padilha, L. A.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Pattanaik, H. S.

H. S. Pattanaik, M. Reichert, J. B. Khurgin, D. J. Hagan, and E. W. Van Stryland, “Enhancement of two-photon absorption in quantum wells for extremely nondegenerate photon pairs,” IEEE J. Quantum Electron. 52, 1–14 (2016).
[Crossref]

Perillo, E. P.

E. P. Perillo, J. W. Jarrett, Y. L. Liu, A. Hassan, D. C. Fernée, J. R. Goldak, A. Bonteanu, D. J. Spence, H. C. Yeh, and A. K. Dunn, “Two-color multiphoton in vivo imaging with a femtosecond diamond raman laser,” Light Sci. Appl. 6, e17095 (2017).
[Crossref]

Podgorski, K.

K. Podgorski and G. Ranganathan, “Brain heating induced by near-infrared lasers during multiphoton microscopy,” J. Neurophysiol. 116, 1012–1023 (2016).
[Crossref] [PubMed]

Qiao, L.

C. Wang, L. Qiao, Z. Mao, Y. Cheng, and Z. Xu, “Reduced deep-tissue image degradation in three-dimensional multiphoton microscopy with concentric two-color two-photon fluorescence excitation,” J. Opt. Soc. Am. B 25, 976–982 (2008).
[Crossref]

Quentmeier, S.

S. Quentmeier, S. Denicke, and K. H. Gericke, “Two-color two-photon fluorescence laser scanning microscopy,” J. Fluoresc. 19, 1037–1043 (2009).
[Crossref] [PubMed]

Ranganathan, G.

K. Podgorski and G. Ranganathan, “Brain heating induced by near-infrared lasers during multiphoton microscopy,” J. Neurophysiol. 116, 1012–1023 (2016).
[Crossref] [PubMed]

Rebane, A.

M. Drobizhev, N. S. Makarov, S. E. Tillo, T. E. Hughes, and A. Rebane, “Two-photon absorption properties of fluorescent proteins,” Nature Methods 8, 393–399 (2011).
[Crossref] [PubMed]

Reichert, M.

H. S. Pattanaik, M. Reichert, J. B. Khurgin, D. J. Hagan, and E. W. Van Stryland, “Enhancement of two-photon absorption in quantum wells for extremely nondegenerate photon pairs,” IEEE J. Quantum Electron. 52, 1–14 (2016).
[Crossref]

Saavedra, G.

C. Ibáñez-López, I. Escobar, G. Saavedra, and M. Martínez-Corral, “Optical-sectioning improvement in two-color excitation scanning microscopy,” Microsc. Res. Tech. 64, 96–102 (2004).
[Crossref] [PubMed]

Saisan, P. A.

M. H. Yang, M. Abashin, P. A. Saisan, P. Tian, C. G. Ferri, A. Devor, and Y. Fainman, “Non-degenerate 2-photon excitation in scattering medium for fluorescence microscopy,” Opt. Express 24, 30173–30187 (2016).
[Crossref]

Saloma, C.

C. M. Blanca and C. Saloma, “Two-color excitation fluorescence microscopy through highly scattering media,” Appl. Opt. 40, 2722–2729 (2001).
[Crossref]

M. O. Cambaliza and C. Saloma, “Advantages of two-color excitation fluorescence microscopy with two confocal excitation beams,” Opt. Commun. 184, 25–35 (2000).
[Crossref]

Schafer, K.

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. Schafer, A. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J.-L. Brédas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121, 3152–3160 (2004).
[Crossref] [PubMed]

Schafer, K. J.

K. D. Belfield, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, and R. A. Negres, “New two-photon absorbing fluorene derivatives: synthesis and nonlinear optical characterization,” Org. Lett. 1, 1575–1578 (1999).
[Crossref]

Simoni, F.

J. C. M. Diels, J. J. Fontaine, I. C. McMichael, and F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt. 24, 1270–1282 (1985).
[Crossref] [PubMed]

Spence, D. J.

E. P. Perillo, J. W. Jarrett, Y. L. Liu, A. Hassan, D. C. Fernée, J. R. Goldak, A. Bonteanu, D. J. Spence, H. C. Yeh, and A. K. Dunn, “Two-color multiphoton in vivo imaging with a femtosecond diamond raman laser,” Light Sci. Appl. 6, e17095 (2017).
[Crossref]

Stelzer, E.

S. Lindek and E. Stelzer, “Resolution improvement by nonconfocal theta microscopy,” Opt. Lett. 24, 1505–1507 (1999).
[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]

Supatto, W.

P. Mahou, M. Zimmerley, K. Loulier, K. S. Matho, G. Labroille, X. Morin, W. Supatto, J. Livet, D. Débarre, and E. Beaurepaire, “Multicolor two-photon tissue imaging by wavelength mixing,” Nat. Methods 9, 815–818 (2012).
[Crossref] [PubMed]

Tian, P.

M. H. Yang, M. Abashin, P. A. Saisan, P. Tian, C. G. Ferri, A. Devor, and Y. Fainman, “Non-degenerate 2-photon excitation in scattering medium for fluorescence microscopy,” Opt. Express 24, 30173–30187 (2016).
[Crossref]

Tillo, S. E.

M. Drobizhev, N. S. Makarov, S. E. Tillo, T. E. Hughes, and A. Rebane, “Two-photon absorption properties of fluorescent proteins,” Nature Methods 8, 393–399 (2011).
[Crossref] [PubMed]

Van Stryland, E. W.

H. S. Pattanaik, M. Reichert, J. B. Khurgin, D. J. Hagan, and E. W. Van Stryland, “Enhancement of two-photon absorption in quantum wells for extremely nondegenerate photon pairs,” IEEE J. Quantum Electron. 52, 1–14 (2016).
[Crossref]

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. Schafer, A. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J.-L. Brédas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121, 3152–3160 (2004).
[Crossref] [PubMed]

R. A. Negres, J. M. Hales, A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Two-photon spectroscopy and analysis with a white-light continuum probe,” Opt. Lett. 27, 270–272 (2002).
[Crossref]

K. D. Belfield, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, and R. A. Negres, “New two-photon absorbing fluorene derivatives: synthesis and nonlinear optical characterization,” Org. Lett. 1, 1575–1578 (1999).
[Crossref]

Wang, C.

C. Wang, L. Qiao, Z. Mao, Y. Cheng, and Z. Xu, “Reduced deep-tissue image degradation in three-dimensional multiphoton microscopy with concentric two-color two-photon fluorescence excitation,” J. Opt. Soc. Am. B 25, 976–982 (2008).
[Crossref]

Webb, W. W.

C. Xu and W. W. Webb, “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm,” J. Opt. Soc. Am. B 13, 481–491 (1996).
[Crossref]

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

Webster, S.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Xu, C.

C. Xu and W. W. Webb, “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm,” J. Opt. Soc. Am. B 13, 481–491 (1996).
[Crossref]

D. Kobat, G. Zhu, and C. Xu, “Background reduction with two-color two-beam multiphoton excitation,” in Biomedical Optics (Optical Society of America, 2008), p. BMF6.
[Crossref]

Xu, Z.

C. Wang, L. Qiao, Z. Mao, Y. Cheng, and Z. Xu, “Reduced deep-tissue image degradation in three-dimensional multiphoton microscopy with concentric two-color two-photon fluorescence excitation,” J. Opt. Soc. Am. B 25, 976–982 (2008).
[Crossref]

Xue, B.

B. Xue, C. Katan, J. Bjorgaard, and T. Kobayashi, “Non-degenerate two photon absorption enhancement for laser dyes by precise lock-in detection,” AIP Adv. 5, 127138 (2015).
[Crossref]

Yang, M. H.

M. H. Yang, M. Abashin, P. A. Saisan, P. Tian, C. G. Ferri, A. Devor, and Y. Fainman, “Non-degenerate 2-photon excitation in scattering medium for fluorescence microscopy,” Opt. Express 24, 30173–30187 (2016).
[Crossref]

Yeh, H. C.

E. P. Perillo, J. W. Jarrett, Y. L. Liu, A. Hassan, D. C. Fernée, J. R. Goldak, A. Bonteanu, D. J. Spence, H. C. Yeh, and A. K. Dunn, “Two-color multiphoton in vivo imaging with a femtosecond diamond raman laser,” Light Sci. Appl. 6, e17095 (2017).
[Crossref]

Zhu, G.

D. Kobat, G. Zhu, and C. Xu, “Background reduction with two-color two-beam multiphoton excitation,” in Biomedical Optics (Optical Society of America, 2008), p. BMF6.
[Crossref]

Zimmerley, M.

P. Mahou, M. Zimmerley, K. Loulier, K. S. Matho, G. Labroille, X. Morin, W. Supatto, J. Livet, D. Débarre, and E. Beaurepaire, “Multicolor two-photon tissue imaging by wavelength mixing,” Nat. Methods 9, 815–818 (2012).
[Crossref] [PubMed]

Zojer, E.

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. Schafer, A. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J.-L. Brédas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121, 3152–3160 (2004).
[Crossref] [PubMed]

AIP Adv. (1)

B. Xue, C. Katan, J. Bjorgaard, and T. Kobayashi, “Non-degenerate two photon absorption enhancement for laser dyes by precise lock-in detection,” AIP Adv. 5, 127138 (2015).
[Crossref]

Ann. Phys. (1)

M. Göppert-Mayer, “Über Elementarakte mit zwei Quantensprüngen,” Ann. Phys. 401, 273–294 (1931).
[Crossref]

Appl. Opt. (2)

J. C. M. Diels, J. J. Fontaine, I. C. McMichael, and F. Simoni, “Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy,” Appl. Opt. 24, 1270–1282 (1985).
[Crossref] [PubMed]

C. M. Blanca and C. Saloma, “Two-color excitation fluorescence microscopy through highly scattering media,” Appl. Opt. 40, 2722–2729 (2001).
[Crossref]

Curr. Opin. Biomed. Eng. (1)

D. R. Miller, J. W. Jarrett, A. M. Hassan, and A. K. Dunn, “Deep tissue imaging with multiphoton fluorescence microscopy,” Curr. Opin. Biomed. Eng. 4, 32–39 (2017).
[Crossref]

IEEE J. Quantum Electron. (1)

H. S. Pattanaik, M. Reichert, J. B. Khurgin, D. J. Hagan, and E. W. Van Stryland, “Enhancement of two-photon absorption in quantum wells for extremely nondegenerate photon pairs,” IEEE J. Quantum Electron. 52, 1–14 (2016).
[Crossref]

J. Chem. Phys. (2)

P. Monson and W. McClain, “Polarization dependence of the two-photon absorption of tumbling molecules with application to liquid 1-chloronaphthalene and benzene,” J. Chem. Phys. 53, 29–37 (1970).
[Crossref]

J. M. Hales, D. J. Hagan, E. W. Van Stryland, K. Schafer, A. Morales, K. D. Belfield, P. Pacher, O. Kwon, E. Zojer, and J.-L. Brédas, “Resonant enhancement of two-photon absorption in substituted fluorene molecules,” J. Chem. Phys. 121, 3152–3160 (2004).
[Crossref] [PubMed]

J. Fluoresc. (1)

S. Quentmeier, S. Denicke, and K. H. Gericke, “Two-color two-photon fluorescence laser scanning microscopy,” J. Fluoresc. 19, 1037–1043 (2009).
[Crossref] [PubMed]

J. Neurophysiol. (1)

K. Podgorski and G. Ranganathan, “Brain heating induced by near-infrared lasers during multiphoton microscopy,” J. Neurophysiol. 116, 1012–1023 (2016).
[Crossref] [PubMed]

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

C. Xu and W. W. Webb, “Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm,” J. Opt. Soc. Am. B 13, 481–491 (1996).
[Crossref]

C. Wang, L. Qiao, Z. Mao, Y. Cheng, and Z. Xu, “Reduced deep-tissue image degradation in three-dimensional multiphoton microscopy with concentric two-color two-photon fluorescence excitation,” J. Opt. Soc. Am. B 25, 976–982 (2008).
[Crossref]

Light Sci. Appl. (1)

E. P. Perillo, J. W. Jarrett, Y. L. Liu, A. Hassan, D. C. Fernée, J. R. Goldak, A. Bonteanu, D. J. Spence, H. C. Yeh, and A. K. Dunn, “Two-color multiphoton in vivo imaging with a femtosecond diamond raman laser,” Light Sci. Appl. 6, e17095 (2017).
[Crossref]

Microsc. Res. Tech. (1)

C. Ibáñez-López, I. Escobar, G. Saavedra, and M. Martínez-Corral, “Optical-sectioning improvement in two-color excitation scanning microscopy,” Microsc. Res. Tech. 64, 96–102 (2004).
[Crossref] [PubMed]

Nat. Methods (2)

P. Mahou, M. Zimmerley, K. Loulier, K. S. Matho, G. Labroille, X. Morin, W. Supatto, J. Livet, D. Débarre, and E. Beaurepaire, “Multicolor two-photon tissue imaging by wavelength mixing,” Nat. Methods 9, 815–818 (2012).
[Crossref] [PubMed]

J. W. Lichtman and J. A. Conchello, “Fluorescence microscopy,” Nat. Methods 2, 910–919 (2005).
[Crossref] [PubMed]

Nat. Photonics (1)

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Nature Methods (1)

M. Drobizhev, N. S. Makarov, S. E. Tillo, T. E. Hughes, and A. Rebane, “Two-photon absorption properties of fluorescent proteins,” Nature Methods 8, 393–399 (2011).
[Crossref] [PubMed]

Opt. Commun. (1)

M. O. Cambaliza and C. Saloma, “Advantages of two-color excitation fluorescence microscopy with two confocal excitation beams,” Opt. Commun. 184, 25–35 (2000).
[Crossref]

Opt. Express (1)

M. H. Yang, M. Abashin, P. A. Saisan, P. Tian, C. G. Ferri, A. Devor, and Y. Fainman, “Non-degenerate 2-photon excitation in scattering medium for fluorescence microscopy,” Opt. Express 24, 30173–30187 (2016).
[Crossref]

Opt. Lett. (2)

S. Lindek and E. Stelzer, “Resolution improvement by nonconfocal theta microscopy,” Opt. Lett. 24, 1505–1507 (1999).
[Crossref]

R. A. Negres, J. M. Hales, A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Two-photon spectroscopy and analysis with a white-light continuum probe,” Opt. Lett. 27, 270–272 (2002).
[Crossref]

Org. Lett. (1)

K. D. Belfield, D. J. Hagan, E. W. Van Stryland, K. J. Schafer, and R. A. Negres, “New two-photon absorbing fluorene derivatives: synthesis and nonlinear optical characterization,” Org. Lett. 1, 1575–1578 (1999).
[Crossref]

Phys. Rev. Lett. (1)

D. Fröhlich and H. Mahr, “Two-photon spectroscopy in anthracene,” Phys. Rev. Lett. 16, 895–897 (1966).
[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]

Other (2)

D. Kobat, G. Zhu, and C. Xu, “Background reduction with two-color two-beam multiphoton excitation,” in Biomedical Optics (Optical Society of America, 2008), p. BMF6.
[Crossref]

R. W. Boyd, Nonlinear optics (Elsevier, 2003).

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Figures (7)

Fig. 1
Fig. 1 Experimental setup for demonstration of non-degenerate two-photon fluorescence excitation technique. L, lens; PBS, polarizing beam splitter; λ/2, half wave plate; GS, glass slide; M, mirror; DM, dichroic mirror; BD, beam dump; FS, fluorescent sample; OL, objective lens; BPF, band pass filter; PM, power meter; PMT, photomultiplier.
Fig. 2
Fig. 2 Non-degenerate two-photon fluorescence excitation spectroscopy of fluorescein. a) A typical plot of fluorescence intensity as a function of the delay time between NIR and IR pulses. The increase in the signal at delays approaching zero is due to ND-TPE. The red line shows the fitted model (Eq. (17)). b) Color-coded ND-TPACS spectrum normalized by the D-TPACS peak at 920 nm, extracted from independent measurements of fluorescein D-TPACS, for fluorescein showing dependence of the ND-TPACS on NIR and IR wavelengths. The 2.7 eV isocline is overlaid as black dashed line. c) Normalized ND-TPACS of fluorescein, as a function of the equivalent degenerate wavelength λEq where 2/λEq = 1/λNIR + 1/λIR is shown in red circles. Since all NIR and IR wavelength combinations along one specific isocline in panel b correspond to the same equivalent wavelength, we report several ND-TPAC values for each equivalent wavelength. Independently measured D-TPACS normalized by its peak value at 920 nm is shown as blue line. Dependent D-TPACS extracted from the fluorescence intensity curve background (see panel a) and normalized by the peak value of independently measured D-TPACS at 920 nm is shown in black circles. The dashed line shows the position of the peak at 920 nm.
Fig. 3
Fig. 3 Non-degenerate two-photon fluorescence excitation dependence on a) IR excitation power (PNIR = 5 mW), and b) NIR excitation power (PIR = 15 mW). The power dependence was tested for two different wavelength combinations: λNIR = 740 nm, λIR = 1230 nm and λNIR = 850 nm, λIR = 1150 nm.
Fig. 4
Fig. 4 Beam profiles obtained by knife edge measurement for NIR, λNIR = 740 nm, and IR, λIR = 1230 nm, beams for axial positions a) z = 41 mm, b) z = 42 mm and c) z = 43 mm. The solid lines are the fits of Eq. (20) to the measured data.
Fig. 5
Fig. 5 Fluorescence emission spectra of Fluorescein generated by ND-TPE (λNIR = 740 nm, λIR = 1230 nm) and D-TPE (λNIR = 920 nm).
Fig. 6
Fig. 6 Data interpolation. a) Fluorescence intensity versus delay time between IR and NIR pulses where λNIR = 740 nm and λIR = 1100 nm. The “double peak” effect caused by irregular IR beam profile is clear in the plot. b) Color-coded ND-TPE spectrum normalized to the corresponding D-TPACs at λEq = 920 nm, for fluorescein before the interpolation process. c) Same normalized spectrum shown in panel b after removing the “double peak” data points and interpolating the data. The 2.7 eV (λEq = 920 nm) isocline is overlaid as black dashed line in (b) and (c).
Fig. 7
Fig. 7 In the λNIR = λIR limit, the generated fluorescence is an interferometric autocorrelator signal. (a) The experimental setup to study the λNIR = λIR limit. L, lens; 50 : 50, 50 : 50 beam splitter; M, mirror; DM, dichroic mirror; FS, fluorescent sample; OL, objective lens; BPF, band pass filter; PMT, photomultiplier. (b) The fluorescence generated by the setup, shown in a, is an interferometric autocorrelation trace.

Equations (21)

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N ex ( r , t , τ ) = 1 2 σ D ( 2 ) ( λ NIR ) C ( r , t ) I NIR 2 ( r , t τ ) + 1 2 σ D ( 2 ) ( λ IR ) C ( r , t ) I IR 2 ( r , t ) + 2 σ ND ( 2 ) ( λ NIR , λ IR ) C ( r , t ) I NIR ( r , t τ ) I IR ( r , t ) ,
I IR ( r , t ) = S ( r ; λ IR ) T ( t ; λ IR )
I NIR ( r , t , τ ) = S ( r ; λ NIR ) T ( t τ ; λ NIR ) ,
T ( t ; λ ) = I 0 ( λ ) exp ( t 2 2 Γ λ 2 )
S ( r ; λ ) = [ w 0 ( λ ) w ( z ; λ ) ] 2 exp [ 2 ( r w ( z ; λ ) ) 2 ] .
w 2 ( z ; λ ) = w 0 2 ( λ ) [ 1 + ( z z 0 ( λ ) ) 2 ] , z 0 ( λ ) = π w 0 2 ( λ ) λ , w 0 ( λ ) = λ π NA ,
N ex ( t , τ ) = σ D ( 2 ) ( λ NIR ) C T 2 ( t τ ; λ NIR ) V d V [ S ( r ; λ NIR ) ] 2 + σ D ( 2 ) ( λ IR ) C T 2 ( t ; λ IR ) V d V [ S ( r ; λ IR ) ] 2 + σ ND ( 2 ) ( λ NIR , λ IR ) C T ( t ; λ IR ) T ( t τ ; λ NIR ) V d V S ( r ; λ IR ) S ( r ; λ NIR ) .
V d V S ( r ; λ 1 ) S ( r ; λ 2 ) = ( λ 1 λ 2 ) 2 2 2 π NA 4 λ 1 2 + λ 2 2 .
F ( t , τ ) = ϕ η N ex ( t , τ ) ,
F ( t , τ ) = ϕ η σ D ( 2 ) ( λ NIR ) C λ NIR 3 T 2 ( t τ ; λ NIR ) 8 π NA 4 + ϕ η σ D ( 2 ) ( λ IR ) C λ IR 3 T 2 ( t ; λ IR ) 8 π NA 4 + ϕ η σ D ( 2 ) ( λ NIR , λ IR ) C λ NIR 2 λ IR 2 T ( t τ ; λ NIR ) T ( t ; λ IR ) 2 π NA 4 λ NIR 2 + λ IR 2 .
T ( t ; λ 1 ) T ( t τ ; λ 2 ) = f 1 2 f 1 2 f d t T ( t ; λ 1 ) T ( t τ ; λ 2 ) ,
1 2 f 1 2 f d t T ( t ; λ 1 ) T ( t τ ; λ 2 ) d t T ( t ; λ 1 ) T ( t τ ; λ 2 ) .
h * g = 1 { { h } { g } } ,
d t I 0 ( λ 1 ) I 0 ( λ 2 ) exp ( ( t τ ) 2 2 Γ λ 1 2 ) exp ( t 2 2 Γ λ 2 2 ) = 2 π I 0 ( λ 1 ) I 0 ( λ 2 ) Γ λ 1 Γ λ 2 Γ x exp ( τ 2 2 Γ x 2 ) ,
P λ = I T E λ f ,
I 0 ( λ ) = 2 λ P λ π 2 π Γ λ c h f w 0 2 = 2 π NA 2 P λ Γ λ c h f λ
F ( τ ) = π C P NIR 2 λ NIR ϕ η σ D ( 2 ) ( λ NIR ) 4 f c 2 h 2 Γ NIR + π C P IR 2 λ IR ϕ η σ D ( 2 ) ( λ IR ) 4 f c 2 h 2 Γ IR + 2 π C P NIR P IR λ NIR λ IR ϕ η σ ND ( 2 ) ( λ NIR , λ IR ) f c 2 h 2 Γ x λ NIR 2 + λ IR 2 exp ( τ 2 2 Γ x 2 ) .
F ( τ = 0 ) ND ( λ NIR , λ IR ) F D ( λ D ) = 8 P NIR P IR λ NIR λ IR σ ( ND ) 2 ( λ NIR , λ IR ) Γ D Γ x P D 2 λ D σ D ( 2 ) ( λ D ) λ NIR 2 + λ IR 2 ,
σ ND ( 2 ) ( λ NIR , λ IR ) σ D ( 2 ) ( λ D ) = λ D λ NIR 2 + λ IR 2 Γ x P D 2 F ( τ = 0 ) ND ( λ NIR , λ IR ) 8 λ NIR λ IR λ D P NIR P IR F D ( λ D )
P = P 0 + 1 2 ( 1 erf ( 2 ( x x 0 ) w ) ) ,
w = w 0 1 + ( z z 1 z 0 ) 2 ,

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