Abstract

We present absolute two-photon absorption (2PA) spectra of 15 commercial organic dyes covering an extended range of excitation wavelengths, 550–1600 nm. The 2PA is measured with an estimated accuracy ±10% using a femtosecond fluorescence excitation method. The data are corrected for the variations of the pulse duration and the beam profile with the excitation wavelength, and are applicable as reference standards for 2PA measurements.

© 2008 Optical Society of America

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    [CrossRef]
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    [PubMed]
  7. A. Karotki, M. Kruk, M. Drobizhev, A. Rebane, E. Nickel, and C. W. Spangler, "Efficient singlet oxygen generation upon two-photon excitation of new porphyrin with enhanced nonlinear absorption," IEEE J. Sel. Top. Quantum Electron. 7, 971-975 (2001).
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    [CrossRef] [PubMed]
  26. P. Kaatz and D. P. Shelton, "Two-photon fluorescence cross-section measurements calibrated with hyper-Rayleigh scattering," J. Opt. Soc. Am. B 16, 998-1006 (1999).
    [CrossRef]
  27. J. M. Song, T. Inoue, H. Kawazumi, and T. Ogawa, "Determination of two photon absorption cross section of fluorescein using a mode locked titanium sapphire laser," Anal. Sci. 15, 601-603 (1999).
    [CrossRef]
  28. P. Sengupta, J. Balaji, S. Banerjee, R. Phillip, G. R. Kumar, and S. Maiti, "Sensitive measurement of absolute two-photon absorption cross sections," J. Chem. Phys. 112, 9201-9205 (2000).
    [CrossRef]
  29. D. A. Oulianov, I. V. Tomov, A. S. Dvornikov, and P. M. Rentzepis, "Observations on the measurement of two-photon absorption cross-section," Opt. Commun. 191, 235-243 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  34. A. Rebane, N. Christensson, M. Drobizhev, Y. Stepanenko, and C. W. Spangler, "Quantum interference in organic solid," Opt. Express 13, 6033-6038 (2005).
    [CrossRef] [PubMed]
  35. M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Röckel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J.-L. Brédas, "Structure-property relationships for two-photon absorbing chromophores: Bis-donor diphenylpolyene and bis(styryl)benzene derivatives," J. Am. Chem. Soc. 122, 9500-9510 (2000).
    [CrossRef]
  36. J. N. Demas and G. A. Crosby, "The measurement of photoluminescence quantum yields. A review," J. Phys. Chem. 75, 991-1024 (1971).
    [CrossRef]
  37. T. Karstens and K. Kobs, "Rhodamine B and Rhodamine 101 as reference substances for fluorescence quantum yield measurements," J. Phys. Chem. 84, 1871-1872 (1980).
    [CrossRef]
  38. O. S. Finikova, T. Troxler, A. Senes, W. F. DeGrado, R. M. Hochstrasser, and S. A. Vinogradov, "Energy and electron transfer in enhanced two-photon-absorbing systems with triplet cores," J. Phys. Chem. A 111, 6977-6990 (2007).
    [CrossRef] [PubMed]
  39. G. A. Reynolds and K. H. Drexhage, "New coumarin dyes with rigidized structure for flashlamp-pumped lasers," Chem. Phys. Lett. 13, 222-225 (1975).
  40. A. Fischer, C. Cremer, and E. H. K. Stelzer, "Fluorescence of coumarins and xanthenes after two-photon absorption with a pulsed titanium-sapphire laser," Appl. Opt. 34, 1989-2003 (1995).
    [CrossRef] [PubMed]
  41. M. Drobizhev, A. Karotki, Y. Dzenis, A. Rebane, Z. Y. Suo, and C. W. Spangler, "Strong cooperative enhancement of two-photon absorption in dendrimers," J. Phys. Chem. B 107, 7540-7543 (2003).
    [CrossRef]
  42. Z. Huang, X. Wang, B. Li, C. Lv, J. Xu, W. Jiang, X. Tao, S. Qian, Y. Chui, and P. Yang, "Two-photon absorption of new multibranched chromophores based on bis(diphenylamino)stilbene," Opt. Mater. 29, 1084-1090 (2007).
    [CrossRef]
  43. W. W. Stewart, "Synthesis of 3,6-disulfonated 4-aminonaphthalimides," J. Am. Chem. Soc. 103, 7615-7620 (1981).
    [CrossRef]
  44. A. Karotki, M. Khurana, J. R. Lepock, and B. C. Wilson, "Simultaneous two-photon excitation of photofrin in relation to photodynamic therapy," Photochem. Photobiol. 82, 443-452 (2006).
    [CrossRef] [PubMed]
  45. M. Kruk, A. Karotki, M. Drobizhev, V. Kuzmitsky, V. Gael, and A. Rebane, "Two-photon absorption of tetraphenylporphin free base," J. Lumin. 105, 45-55 (2003).
    [CrossRef]
  46. M. Morone, L. Beverina, A. Abbotto, F. Silvestri, E. Collini, C. Ferrante, R. Bozio, and G. A. Pagani, "Enhancement of two-photon absorption cross-section and singlet-oxygen generation in porphyrins upon ?-functionalization with donor-acceptor substituents," Org. Lett. 8, 2719-2722 (2006).
    [CrossRef] [PubMed]
  47. T. Ishi-i, Y. Taguri, S. Kato, M. Shigeiva, H. Gorohmaru, S. Maeda, and S. Mataka, "Singlet oxygen generation by two-photon excitation of porphyrin derivatives having two-photon-absorbing benzothiadiazole chromophores," J. Mater. Chem. 17, 3341-3346 (2007).
    [CrossRef]
  48. M. Drobizhev, N. S. Makarov, Y. Stepanenko, and A. Rebane, "Near-infrared two-photon absorption in phthalocyanines: enhancement of lowest gerade-gerade transition by symmetrical electron-accepting substitution," J. Chem. Phys. 124, 224701 (2006).
    [CrossRef] [PubMed]
  49. 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]
  50. G. O. Clay, C. B. Schaffer, and D. Kleinfeld, "Large two-photon absorptivity of hemoglobin in the infrared range of 780-880 nm," J. Chem. Phys. 126, 025102 (2007).
    [CrossRef] [PubMed]

2007

Z. Huang, X. Wang, B. Li, C. Lv, J. Xu, W. Jiang, X. Tao, S. Qian, Y. Chui, and P. Yang, "Two-photon absorption of new multibranched chromophores based on bis(diphenylamino)stilbene," Opt. Mater. 29, 1084-1090 (2007).
[CrossRef]

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]

G. O. Clay, C. B. Schaffer, and D. Kleinfeld, "Large two-photon absorptivity of hemoglobin in the infrared range of 780-880 nm," J. Chem. Phys. 126, 025102 (2007).
[CrossRef] [PubMed]

T. Ishi-i, Y. Taguri, S. Kato, M. Shigeiva, H. Gorohmaru, S. Maeda, and S. Mataka, "Singlet oxygen generation by two-photon excitation of porphyrin derivatives having two-photon-absorbing benzothiadiazole chromophores," J. Mater. Chem. 17, 3341-3346 (2007).
[CrossRef]

O. S. Finikova, T. Troxler, A. Senes, W. F. DeGrado, R. M. Hochstrasser, and S. A. Vinogradov, "Energy and electron transfer in enhanced two-photon-absorbing systems with triplet cores," J. Phys. Chem. A 111, 6977-6990 (2007).
[CrossRef] [PubMed]

N. S. Makarov, A. Rebane, M. Drobizhev, H. Wolleb, and H. Spahni, "Optimizing two-photon absorption for volumetric optical data storage," J. Opt. Soc. Am. B 24, 1874-1885 (2007).
[CrossRef]

2006

M. Kauert, P. C. Stoller, M. Frenz, and J. Ri?ka, "Absolute measurement of molecular two-photon absorption cross-sections using a fluorescence saturation technique," Opt. Express 14, 8434-8447 (2006).
[CrossRef]

M. Drobizhev, N. S. Makarov, Y. Stepanenko, and A. Rebane, "Near-infrared two-photon absorption in phthalocyanines: enhancement of lowest gerade-gerade transition by symmetrical electron-accepting substitution," J. Chem. Phys. 124, 224701 (2006).
[CrossRef] [PubMed]

M. Morone, L. Beverina, A. Abbotto, F. Silvestri, E. Collini, C. Ferrante, R. Bozio, and G. A. Pagani, "Enhancement of two-photon absorption cross-section and singlet-oxygen generation in porphyrins upon ?-functionalization with donor-acceptor substituents," Org. Lett. 8, 2719-2722 (2006).
[CrossRef] [PubMed]

A. Karotki, M. Khurana, J. R. Lepock, and B. C. Wilson, "Simultaneous two-photon excitation of photofrin in relation to photodynamic therapy," Photochem. Photobiol. 82, 443-452 (2006).
[CrossRef] [PubMed]

2005

M. Drobizhev, Y. Stepanenko, Y. Dzenis, A. Karotki, A. Rebane, P. N. Taylor, and H. L. Anderson, "Extremely strong near-IR two-photon absorption in conjugated porphyrin dimers: quantitative description with three-essential-states model," J. Phys. Chem. B 109, 7223-7236 (2005).
[CrossRef]

A. Rebane, N. Christensson, M. Drobizhev, Y. Stepanenko, and C. W. Spangler, "Quantum interference in organic solid," Opt. Express 13, 6033-6038 (2005).
[CrossRef] [PubMed]

2003

A. Karotki, M. Drobizhev, M. Kruk, C. Spangler, E. Nickel, N. Mamardashvili, and A. Rebane, "Enhancement of two-photon absorption in tetrapyrrolic compounds," J. Opt. Soc. Am. B 20, 321-332 (2003).
[CrossRef]

R. Kapoor, C. S. Friend, and A. Parta, "Two-photon-excited absolute emission cross-sectional measurements calibrated with a luminance meter," J. Opt. Soc. Am. B 20, 1550-1554 (2003).
[CrossRef]

M. Drobizhev, A. Karotki, Y. Dzenis, A. Rebane, Z. Y. Suo, and C. W. Spangler, "Strong cooperative enhancement of two-photon absorption in dendrimers," J. Phys. Chem. B 107, 7540-7543 (2003).
[CrossRef]

M. Kruk, A. Karotki, M. Drobizhev, V. Kuzmitsky, V. Gael, and A. Rebane, "Two-photon absorption of tetraphenylporphin free base," J. Lumin. 105, 45-55 (2003).
[CrossRef]

W. R. Zipfel, R. M. Williams, and W. W. Webb, "Nonlinear magic: multiphoton microscopy in the biosciences," Nat. Biotechnol. 21, 1369-1377 (2003), and references therein.
[CrossRef] [PubMed]

2002

2001

A. Karotki, M. Kruk, M. Drobizhev, A. Rebane, E. Nickel, and C. W. Spangler, "Efficient singlet oxygen generation upon two-photon excitation of new porphyrin with enhanced nonlinear absorption," IEEE J. Sel. Top. Quantum Electron. 7, 971-975 (2001).
[CrossRef]

D. A. Oulianov, I. V. Tomov, A. S. Dvornikov, and P. M. Rentzepis, "Observations on the measurement of two-photon absorption cross-section," Opt. Commun. 191, 235-243 (2001).
[CrossRef]

2000

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

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Röckel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J.-L. Brédas, "Structure-property relationships for two-photon absorbing chromophores: Bis-donor diphenylpolyene and bis(styryl)benzene derivatives," J. Am. Chem. Soc. 122, 9500-9510 (2000).
[CrossRef]

1999

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51-53 (1999).
[CrossRef]

C. W. Spangler, "Recent development in the design of organic materials for optical power limiting," J. Mater. Chem. 9, 2013-2020 (1999), and references therein.
[CrossRef]

J. M. Song, T. Inoue, H. Kawazumi, and T. Ogawa, "Determination of two photon absorption cross section of fluorescein using a mode locked titanium sapphire laser," Anal. Sci. 15, 601-603 (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, 998-1006 (1999).
[CrossRef]

1998

1997

J. D. Bhawalkar, N. D. Kumar, C. F. Zhao, and P. N. Prasad, "Two-photon photodynamic therapy," J. Clin. Laser Med. Surg. 15, 201-204 (1997).
[PubMed]

1996

1995

1989

D. A. Parthenopoulos and P. M. Rentzepis, "Three-dimensional optical storage," Science 245, 843-845 (1989).
[CrossRef] [PubMed]

1987

A. Penzkofer and W. Leupacher, "S0-S1 two photon absorption dynamics of organic dye solutions," Opt. Quantum Electron. 19, 327-349 (1987).
[CrossRef]

S. M. Bachilo and S. L. Bondarev, "Spectral and polarization features of two-photon absorption in retinal and retinyl acetate," J. Appl. Spectrosc. 45, 1078-1083 (1987).
[CrossRef]

1986

A. P. Blokhin, A. V. Povedailo, and V. A. Tolkachev, "Polarization of two-photon excited fluorescence of vapors of complex organic molecules," Opt. Spectrosc. 60, 60-64 (1986).

P. Sperber and A. Penzkofer, "S0-Sn two-photon absorption dynamics of rhodamine dyes," Opt. Quantum Electron. 18, 381-401 (1986).
[CrossRef]

1982

S. Li and C. Y. She, "Two-photon absorption cross-section measurements in common laser dyes at 1.06 ?m," Opt. Acta 29, 281-287 (1982).
[CrossRef]

I. M. Catalano and A. Cingolani, "Multiphoton cross-section measurements with low-power cw laser-induced luminescence," Appl. Opt. 21, 477-480 (1982).
[CrossRef] [PubMed]

1981

I. M. Catalano and A. Cingolani, "Absolute two-photo fluorescence with low-power cw lasers," Appl. Phys. Lett. 38, 745-747 (1981).
[CrossRef]

W. W. Stewart, "Synthesis of 3,6-disulfonated 4-aminonaphthalimides," J. Am. Chem. Soc. 103, 7615-7620 (1981).
[CrossRef]

1980

T. Karstens and K. Kobs, "Rhodamine B and Rhodamine 101 as reference substances for fluorescence quantum yield measurements," J. Phys. Chem. 84, 1871-1872 (1980).
[CrossRef]

1975

G. A. Reynolds and K. H. Drexhage, "New coumarin dyes with rigidized structure for flashlamp-pumped lasers," Chem. Phys. Lett. 13, 222-225 (1975).

1972

J. P. Hermann and J. Ducuing, "Absolute measurement of two-photon cross sections," Phys. Rev. A 5, 2557-2568 (1972).
[CrossRef]

J. P. Hermann and J. Ducuing, "Dispersion of the two-photon cross section in rhodamine dyes," Opt. Commun. 6, 101-105 (1972).
[CrossRef]

D. J. Bradley, M. H. R. Hutchinson, and H. Koetser, "Interactions of picosecond laser pulses with organic molecules. II. Two-photon absorption cross-sections," Proc. R. Soc. Lond. A 329, 105-119 (1972).
[CrossRef]

1971

A. P. Aleksandrov and V. I. Bredikhin, "Measurement of the absolute value of the cross-section for two-photon absorption in anthracene molecules," Opt. Spectrosc. 30, 37-38 (1971).

J. N. Demas and G. A. Crosby, "The measurement of photoluminescence quantum yields. A review," J. Phys. Chem. 75, 991-1024 (1971).
[CrossRef]

1966

M. D. Galanin and Z. A. Chizhikova, "Effective cross sections of two-photon absorption in organic molecules," JETP Lett. 4,27-28 (1966).

1965

W. L. Peticolas, R. Norris, and K. E. Rieckhoff, "Polarization effects in the two-photon excitation of anthracene fluorescence," J. Chem. Phys. 42, 4164-4169 (1965).
[CrossRef]

Abbotto, A.

M. Morone, L. Beverina, A. Abbotto, F. Silvestri, E. Collini, C. Ferrante, R. Bozio, and G. A. Pagani, "Enhancement of two-photon absorption cross-section and singlet-oxygen generation in porphyrins upon ?-functionalization with donor-acceptor substituents," Org. Lett. 8, 2719-2722 (2006).
[CrossRef] [PubMed]

Albota, M. A.

Aleksandrov, A. P.

A. P. Aleksandrov and V. I. Bredikhin, "Measurement of the absolute value of the cross-section for two-photon absorption in anthracene molecules," Opt. Spectrosc. 30, 37-38 (1971).

Ananthavel, S. P.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51-53 (1999).
[CrossRef]

Anderson, H. L.

M. Drobizhev, Y. Stepanenko, Y. Dzenis, A. Karotki, A. Rebane, P. N. Taylor, and H. L. Anderson, "Extremely strong near-IR two-photon absorption in conjugated porphyrin dimers: quantitative description with three-essential-states model," J. Phys. Chem. B 109, 7223-7236 (2005).
[CrossRef]

Bachilo, S. M.

S. M. Bachilo and S. L. Bondarev, "Spectral and polarization features of two-photon absorption in retinal and retinyl acetate," J. Appl. Spectrosc. 45, 1078-1083 (1987).
[CrossRef]

Balaji, J.

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

Banerjee, S.

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

Barlow, S.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Röckel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J.-L. Brédas, "Structure-property relationships for two-photon absorbing chromophores: Bis-donor diphenylpolyene and bis(styryl)benzene derivatives," J. Am. Chem. Soc. 122, 9500-9510 (2000).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51-53 (1999).
[CrossRef]

Beljonne, D.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Röckel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J.-L. Brédas, "Structure-property relationships for two-photon absorbing chromophores: Bis-donor diphenylpolyene and bis(styryl)benzene derivatives," J. Am. Chem. Soc. 122, 9500-9510 (2000).
[CrossRef]

Beverina, L.

M. Morone, L. Beverina, A. Abbotto, F. Silvestri, E. Collini, C. Ferrante, R. Bozio, and G. A. Pagani, "Enhancement of two-photon absorption cross-section and singlet-oxygen generation in porphyrins upon ?-functionalization with donor-acceptor substituents," Org. Lett. 8, 2719-2722 (2006).
[CrossRef] [PubMed]

Bhawalkar, J. D.

J. D. Bhawalkar, N. D. Kumar, C. F. Zhao, and P. N. Prasad, "Two-photon photodynamic therapy," J. Clin. Laser Med. Surg. 15, 201-204 (1997).
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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).
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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).
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Blokhin, A. P.

A. P. Blokhin, A. V. Povedailo, and V. A. Tolkachev, "Polarization of two-photon excited fluorescence of vapors of complex organic molecules," Opt. Spectrosc. 60, 60-64 (1986).

Bondarev, S. L.

S. M. Bachilo and S. L. Bondarev, "Spectral and polarization features of two-photon absorption in retinal and retinyl acetate," J. Appl. Spectrosc. 45, 1078-1083 (1987).
[CrossRef]

Bozio, R.

M. Morone, L. Beverina, A. Abbotto, F. Silvestri, E. Collini, C. Ferrante, R. Bozio, and G. A. Pagani, "Enhancement of two-photon absorption cross-section and singlet-oxygen generation in porphyrins upon ?-functionalization with donor-acceptor substituents," Org. Lett. 8, 2719-2722 (2006).
[CrossRef] [PubMed]

Bradley, D. J.

D. J. Bradley, M. H. R. Hutchinson, and H. Koetser, "Interactions of picosecond laser pulses with organic molecules. II. Two-photon absorption cross-sections," Proc. R. Soc. Lond. A 329, 105-119 (1972).
[CrossRef]

Brédas, J.-L.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Röckel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J.-L. Brédas, "Structure-property relationships for two-photon absorbing chromophores: Bis-donor diphenylpolyene and bis(styryl)benzene derivatives," J. Am. Chem. Soc. 122, 9500-9510 (2000).
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Bredikhin, V. I.

A. P. Aleksandrov and V. I. Bredikhin, "Measurement of the absolute value of the cross-section for two-photon absorption in anthracene molecules," Opt. Spectrosc. 30, 37-38 (1971).

Catalano, I. M.

I. M. Catalano and A. Cingolani, "Multiphoton cross-section measurements with low-power cw laser-induced luminescence," Appl. Opt. 21, 477-480 (1982).
[CrossRef] [PubMed]

I. M. Catalano and A. Cingolani, "Absolute two-photo fluorescence with low-power cw lasers," Appl. Phys. Lett. 38, 745-747 (1981).
[CrossRef]

Chizhikova, Z. A.

M. D. Galanin and Z. A. Chizhikova, "Effective cross sections of two-photon absorption in organic molecules," JETP Lett. 4,27-28 (1966).

Christensson, N.

Chui, Y.

Z. Huang, X. Wang, B. Li, C. Lv, J. Xu, W. Jiang, X. Tao, S. Qian, Y. Chui, and P. Yang, "Two-photon absorption of new multibranched chromophores based on bis(diphenylamino)stilbene," Opt. Mater. 29, 1084-1090 (2007).
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Cingolani, A.

I. M. Catalano and A. Cingolani, "Multiphoton cross-section measurements with low-power cw laser-induced luminescence," Appl. Opt. 21, 477-480 (1982).
[CrossRef] [PubMed]

I. M. Catalano and A. Cingolani, "Absolute two-photo fluorescence with low-power cw lasers," Appl. Phys. Lett. 38, 745-747 (1981).
[CrossRef]

Clay, G. O.

G. O. Clay, C. B. Schaffer, and D. Kleinfeld, "Large two-photon absorptivity of hemoglobin in the infrared range of 780-880 nm," J. Chem. Phys. 126, 025102 (2007).
[CrossRef] [PubMed]

Collini, E.

M. Morone, L. Beverina, A. Abbotto, F. Silvestri, E. Collini, C. Ferrante, R. Bozio, and G. A. Pagani, "Enhancement of two-photon absorption cross-section and singlet-oxygen generation in porphyrins upon ?-functionalization with donor-acceptor substituents," Org. Lett. 8, 2719-2722 (2006).
[CrossRef] [PubMed]

Cremer, C.

Crosby, G. A.

J. N. Demas and G. A. Crosby, "The measurement of photoluminescence quantum yields. A review," J. Phys. Chem. 75, 991-1024 (1971).
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Cumpston, B. H.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51-53 (1999).
[CrossRef]

DeGrado, W. F.

O. S. Finikova, T. Troxler, A. Senes, W. F. DeGrado, R. M. Hochstrasser, and S. A. Vinogradov, "Energy and electron transfer in enhanced two-photon-absorbing systems with triplet cores," J. Phys. Chem. A 111, 6977-6990 (2007).
[CrossRef] [PubMed]

Demas, J. N.

J. N. Demas and G. A. Crosby, "The measurement of photoluminescence quantum yields. A review," J. Phys. Chem. 75, 991-1024 (1971).
[CrossRef]

Denk, W.

Drexhage, K. H.

G. A. Reynolds and K. H. Drexhage, "New coumarin dyes with rigidized structure for flashlamp-pumped lasers," Chem. Phys. Lett. 13, 222-225 (1975).

Drobizhev, M.

N. S. Makarov, A. Rebane, M. Drobizhev, H. Wolleb, and H. Spahni, "Optimizing two-photon absorption for volumetric optical data storage," J. Opt. Soc. Am. B 24, 1874-1885 (2007).
[CrossRef]

M. Drobizhev, N. S. Makarov, Y. Stepanenko, and A. Rebane, "Near-infrared two-photon absorption in phthalocyanines: enhancement of lowest gerade-gerade transition by symmetrical electron-accepting substitution," J. Chem. Phys. 124, 224701 (2006).
[CrossRef] [PubMed]

M. Drobizhev, Y. Stepanenko, Y. Dzenis, A. Karotki, A. Rebane, P. N. Taylor, and H. L. Anderson, "Extremely strong near-IR two-photon absorption in conjugated porphyrin dimers: quantitative description with three-essential-states model," J. Phys. Chem. B 109, 7223-7236 (2005).
[CrossRef]

A. Rebane, N. Christensson, M. Drobizhev, Y. Stepanenko, and C. W. Spangler, "Quantum interference in organic solid," Opt. Express 13, 6033-6038 (2005).
[CrossRef] [PubMed]

M. Kruk, A. Karotki, M. Drobizhev, V. Kuzmitsky, V. Gael, and A. Rebane, "Two-photon absorption of tetraphenylporphin free base," J. Lumin. 105, 45-55 (2003).
[CrossRef]

M. Drobizhev, A. Karotki, Y. Dzenis, A. Rebane, Z. Y. Suo, and C. W. Spangler, "Strong cooperative enhancement of two-photon absorption in dendrimers," J. Phys. Chem. B 107, 7540-7543 (2003).
[CrossRef]

A. Karotki, M. Drobizhev, M. Kruk, C. Spangler, E. Nickel, N. Mamardashvili, and A. Rebane, "Enhancement of two-photon absorption in tetrapyrrolic compounds," J. Opt. Soc. Am. B 20, 321-332 (2003).
[CrossRef]

A. Karotki, M. Kruk, M. Drobizhev, A. Rebane, E. Nickel, and C. W. Spangler, "Efficient singlet oxygen generation upon two-photon excitation of new porphyrin with enhanced nonlinear absorption," IEEE J. Sel. Top. Quantum Electron. 7, 971-975 (2001).
[CrossRef]

Ducuing, J.

J. P. Hermann and J. Ducuing, "Absolute measurement of two-photon cross sections," Phys. Rev. A 5, 2557-2568 (1972).
[CrossRef]

J. P. Hermann and J. Ducuing, "Dispersion of the two-photon cross section in rhodamine dyes," Opt. Commun. 6, 101-105 (1972).
[CrossRef]

Dvornikov, A. S.

D. A. Oulianov, I. V. Tomov, A. S. Dvornikov, and P. M. Rentzepis, "Observations on the measurement of two-photon absorption cross-section," Opt. Commun. 191, 235-243 (2001).
[CrossRef]

Dyer, D. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51-53 (1999).
[CrossRef]

Dzenis, Y.

M. Drobizhev, Y. Stepanenko, Y. Dzenis, A. Karotki, A. Rebane, P. N. Taylor, and H. L. Anderson, "Extremely strong near-IR two-photon absorption in conjugated porphyrin dimers: quantitative description with three-essential-states model," J. Phys. Chem. B 109, 7223-7236 (2005).
[CrossRef]

M. Drobizhev, A. Karotki, Y. Dzenis, A. Rebane, Z. Y. Suo, and C. W. Spangler, "Strong cooperative enhancement of two-photon absorption in dendrimers," J. Phys. Chem. B 107, 7540-7543 (2003).
[CrossRef]

Ehrlich, J. E.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Röckel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J.-L. Brédas, "Structure-property relationships for two-photon absorbing chromophores: Bis-donor diphenylpolyene and bis(styryl)benzene derivatives," J. Am. Chem. Soc. 122, 9500-9510 (2000).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51-53 (1999).
[CrossRef]

Erskine, L. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51-53 (1999).
[CrossRef]

Ferrante, C.

M. Morone, L. Beverina, A. Abbotto, F. Silvestri, E. Collini, C. Ferrante, R. Bozio, and G. A. Pagani, "Enhancement of two-photon absorption cross-section and singlet-oxygen generation in porphyrins upon ?-functionalization with donor-acceptor substituents," Org. Lett. 8, 2719-2722 (2006).
[CrossRef] [PubMed]

Finikova, O. S.

O. S. Finikova, T. Troxler, A. Senes, W. F. DeGrado, R. M. Hochstrasser, and S. A. Vinogradov, "Energy and electron transfer in enhanced two-photon-absorbing systems with triplet cores," J. Phys. Chem. A 111, 6977-6990 (2007).
[CrossRef] [PubMed]

Fischer, A.

Frenz, M.

Friend, C. S.

Gael, V.

M. Kruk, A. Karotki, M. Drobizhev, V. Kuzmitsky, V. Gael, and A. Rebane, "Two-photon absorption of tetraphenylporphin free base," J. Lumin. 105, 45-55 (2003).
[CrossRef]

Galanin, M. D.

M. D. Galanin and Z. A. Chizhikova, "Effective cross sections of two-photon absorption in organic molecules," JETP Lett. 4,27-28 (1966).

Gorohmaru, H.

T. Ishi-i, Y. Taguri, S. Kato, M. Shigeiva, H. Gorohmaru, S. Maeda, and S. Mataka, "Singlet oxygen generation by two-photon excitation of porphyrin derivatives having two-photon-absorbing benzothiadiazole chromophores," J. Mater. Chem. 17, 3341-3346 (2007).
[CrossRef]

Guild, J.

Heikal, A. A.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Röckel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J.-L. Brédas, "Structure-property relationships for two-photon absorbing chromophores: Bis-donor diphenylpolyene and bis(styryl)benzene derivatives," J. Am. Chem. Soc. 122, 9500-9510 (2000).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51-53 (1999).
[CrossRef]

Hermann, J. P.

J. P. Hermann and J. Ducuing, "Absolute measurement of two-photon cross sections," Phys. Rev. A 5, 2557-2568 (1972).
[CrossRef]

J. P. Hermann and J. Ducuing, "Dispersion of the two-photon cross section in rhodamine dyes," Opt. Commun. 6, 101-105 (1972).
[CrossRef]

Hochstrasser, R. M.

O. S. Finikova, T. Troxler, A. Senes, W. F. DeGrado, R. M. Hochstrasser, and S. A. Vinogradov, "Energy and electron transfer in enhanced two-photon-absorbing systems with triplet cores," J. Phys. Chem. A 111, 6977-6990 (2007).
[CrossRef] [PubMed]

Hu, Z.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Röckel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J.-L. Brédas, "Structure-property relationships for two-photon absorbing chromophores: Bis-donor diphenylpolyene and bis(styryl)benzene derivatives," J. Am. Chem. Soc. 122, 9500-9510 (2000).
[CrossRef]

Huang, Z.

Z. Huang, X. Wang, B. Li, C. Lv, J. Xu, W. Jiang, X. Tao, S. Qian, Y. Chui, and P. Yang, "Two-photon absorption of new multibranched chromophores based on bis(diphenylamino)stilbene," Opt. Mater. 29, 1084-1090 (2007).
[CrossRef]

Hutchinson, M. H. R.

D. J. Bradley, M. H. R. Hutchinson, and H. Koetser, "Interactions of picosecond laser pulses with organic molecules. II. Two-photon absorption cross-sections," Proc. R. Soc. Lond. A 329, 105-119 (1972).
[CrossRef]

Inoue, T.

J. M. Song, T. Inoue, H. Kawazumi, and T. Ogawa, "Determination of two photon absorption cross section of fluorescein using a mode locked titanium sapphire laser," Anal. Sci. 15, 601-603 (1999).
[CrossRef]

Ishi-i, T.

T. Ishi-i, Y. Taguri, S. Kato, M. Shigeiva, H. Gorohmaru, S. Maeda, and S. Mataka, "Singlet oxygen generation by two-photon excitation of porphyrin derivatives having two-photon-absorbing benzothiadiazole chromophores," J. Mater. Chem. 17, 3341-3346 (2007).
[CrossRef]

Jiang, W.

Z. Huang, X. Wang, B. Li, C. Lv, J. Xu, W. Jiang, X. Tao, S. Qian, Y. Chui, and P. Yang, "Two-photon absorption of new multibranched chromophores based on bis(diphenylamino)stilbene," Opt. Mater. 29, 1084-1090 (2007).
[CrossRef]

Kaatz, P.

Kapoor, R.

Karotki, A.

A. Karotki, M. Khurana, J. R. Lepock, and B. C. Wilson, "Simultaneous two-photon excitation of photofrin in relation to photodynamic therapy," Photochem. Photobiol. 82, 443-452 (2006).
[CrossRef] [PubMed]

M. Drobizhev, Y. Stepanenko, Y. Dzenis, A. Karotki, A. Rebane, P. N. Taylor, and H. L. Anderson, "Extremely strong near-IR two-photon absorption in conjugated porphyrin dimers: quantitative description with three-essential-states model," J. Phys. Chem. B 109, 7223-7236 (2005).
[CrossRef]

M. Drobizhev, A. Karotki, Y. Dzenis, A. Rebane, Z. Y. Suo, and C. W. Spangler, "Strong cooperative enhancement of two-photon absorption in dendrimers," J. Phys. Chem. B 107, 7540-7543 (2003).
[CrossRef]

A. Karotki, M. Drobizhev, M. Kruk, C. Spangler, E. Nickel, N. Mamardashvili, and A. Rebane, "Enhancement of two-photon absorption in tetrapyrrolic compounds," J. Opt. Soc. Am. B 20, 321-332 (2003).
[CrossRef]

M. Kruk, A. Karotki, M. Drobizhev, V. Kuzmitsky, V. Gael, and A. Rebane, "Two-photon absorption of tetraphenylporphin free base," J. Lumin. 105, 45-55 (2003).
[CrossRef]

A. Karotki, M. Kruk, M. Drobizhev, A. Rebane, E. Nickel, and C. W. Spangler, "Efficient singlet oxygen generation upon two-photon excitation of new porphyrin with enhanced nonlinear absorption," IEEE J. Sel. Top. Quantum Electron. 7, 971-975 (2001).
[CrossRef]

Karstens, T.

T. Karstens and K. Kobs, "Rhodamine B and Rhodamine 101 as reference substances for fluorescence quantum yield measurements," J. Phys. Chem. 84, 1871-1872 (1980).
[CrossRef]

Kato, S.

T. Ishi-i, Y. Taguri, S. Kato, M. Shigeiva, H. Gorohmaru, S. Maeda, and S. Mataka, "Singlet oxygen generation by two-photon excitation of porphyrin derivatives having two-photon-absorbing benzothiadiazole chromophores," J. Mater. Chem. 17, 3341-3346 (2007).
[CrossRef]

Kauert, M.

Kawazumi, H.

J. M. Song, T. Inoue, H. Kawazumi, and T. Ogawa, "Determination of two photon absorption cross section of fluorescein using a mode locked titanium sapphire laser," Anal. Sci. 15, 601-603 (1999).
[CrossRef]

Khurana, M.

A. Karotki, M. Khurana, J. R. Lepock, and B. C. Wilson, "Simultaneous two-photon excitation of photofrin in relation to photodynamic therapy," Photochem. Photobiol. 82, 443-452 (2006).
[CrossRef] [PubMed]

Kleinfeld, D.

G. O. Clay, C. B. Schaffer, and D. Kleinfeld, "Large two-photon absorptivity of hemoglobin in the infrared range of 780-880 nm," J. Chem. Phys. 126, 025102 (2007).
[CrossRef] [PubMed]

Kobs, K.

T. Karstens and K. Kobs, "Rhodamine B and Rhodamine 101 as reference substances for fluorescence quantum yield measurements," J. Phys. Chem. 84, 1871-1872 (1980).
[CrossRef]

Koetser, H.

D. J. Bradley, M. H. R. Hutchinson, and H. Koetser, "Interactions of picosecond laser pulses with organic molecules. II. Two-photon absorption cross-sections," Proc. R. Soc. Lond. A 329, 105-119 (1972).
[CrossRef]

Kruk, M.

M. Kruk, A. Karotki, M. Drobizhev, V. Kuzmitsky, V. Gael, and A. Rebane, "Two-photon absorption of tetraphenylporphin free base," J. Lumin. 105, 45-55 (2003).
[CrossRef]

A. Karotki, M. Drobizhev, M. Kruk, C. Spangler, E. Nickel, N. Mamardashvili, and A. Rebane, "Enhancement of two-photon absorption in tetrapyrrolic compounds," J. Opt. Soc. Am. B 20, 321-332 (2003).
[CrossRef]

A. Karotki, M. Kruk, M. Drobizhev, A. Rebane, E. Nickel, and C. W. Spangler, "Efficient singlet oxygen generation upon two-photon excitation of new porphyrin with enhanced nonlinear absorption," IEEE J. Sel. Top. Quantum Electron. 7, 971-975 (2001).
[CrossRef]

Kuebler, S. M.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51-53 (1999).
[CrossRef]

Kumar, G. R.

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

Kumar, N. D.

J. D. Bhawalkar, N. D. Kumar, C. F. Zhao, and P. N. Prasad, "Two-photon photodynamic therapy," J. Clin. Laser Med. Surg. 15, 201-204 (1997).
[PubMed]

Kuzmitsky, V.

M. Kruk, A. Karotki, M. Drobizhev, V. Kuzmitsky, V. Gael, and A. Rebane, "Two-photon absorption of tetraphenylporphin free base," J. Lumin. 105, 45-55 (2003).
[CrossRef]

Lee, I.-Y. S.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51-53 (1999).
[CrossRef]

Lepock, J. R.

A. Karotki, M. Khurana, J. R. Lepock, and B. C. Wilson, "Simultaneous two-photon excitation of photofrin in relation to photodynamic therapy," Photochem. Photobiol. 82, 443-452 (2006).
[CrossRef] [PubMed]

Leupacher, W.

A. Penzkofer and W. Leupacher, "S0-S1 two photon absorption dynamics of organic dye solutions," Opt. Quantum Electron. 19, 327-349 (1987).
[CrossRef]

Li, B.

Z. Huang, X. Wang, B. Li, C. Lv, J. Xu, W. Jiang, X. Tao, S. Qian, Y. Chui, and P. Yang, "Two-photon absorption of new multibranched chromophores based on bis(diphenylamino)stilbene," Opt. Mater. 29, 1084-1090 (2007).
[CrossRef]

Li, S.

S. Li and C. Y. She, "Two-photon absorption cross-section measurements in common laser dyes at 1.06 ?m," Opt. Acta 29, 281-287 (1982).
[CrossRef]

Lv, C.

Z. Huang, X. Wang, B. Li, C. Lv, J. Xu, W. Jiang, X. Tao, S. Qian, Y. Chui, and P. Yang, "Two-photon absorption of new multibranched chromophores based on bis(diphenylamino)stilbene," Opt. Mater. 29, 1084-1090 (2007).
[CrossRef]

Maeda, S.

T. Ishi-i, Y. Taguri, S. Kato, M. Shigeiva, H. Gorohmaru, S. Maeda, and S. Mataka, "Singlet oxygen generation by two-photon excitation of porphyrin derivatives having two-photon-absorbing benzothiadiazole chromophores," J. Mater. Chem. 17, 3341-3346 (2007).
[CrossRef]

Maiti, S.

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

Makarov, N. S.

N. S. Makarov, A. Rebane, M. Drobizhev, H. Wolleb, and H. Spahni, "Optimizing two-photon absorption for volumetric optical data storage," J. Opt. Soc. Am. B 24, 1874-1885 (2007).
[CrossRef]

M. Drobizhev, N. S. Makarov, Y. Stepanenko, and A. Rebane, "Near-infrared two-photon absorption in phthalocyanines: enhancement of lowest gerade-gerade transition by symmetrical electron-accepting substitution," J. Chem. Phys. 124, 224701 (2006).
[CrossRef] [PubMed]

Mamardashvili, N.

Marder, S. R.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Röckel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J.-L. Brédas, "Structure-property relationships for two-photon absorbing chromophores: Bis-donor diphenylpolyene and bis(styryl)benzene derivatives," J. Am. Chem. Soc. 122, 9500-9510 (2000).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51-53 (1999).
[CrossRef]

Mataka, S.

T. Ishi-i, Y. Taguri, S. Kato, M. Shigeiva, H. Gorohmaru, S. Maeda, and S. Mataka, "Singlet oxygen generation by two-photon excitation of porphyrin derivatives having two-photon-absorbing benzothiadiazole chromophores," J. Mater. Chem. 17, 3341-3346 (2007).
[CrossRef]

McCord-Maughon, D.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Röckel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J.-L. Brédas, "Structure-property relationships for two-photon absorbing chromophores: Bis-donor diphenylpolyene and bis(styryl)benzene derivatives," J. Am. Chem. Soc. 122, 9500-9510 (2000).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51-53 (1999).
[CrossRef]

Morone, M.

M. Morone, L. Beverina, A. Abbotto, F. Silvestri, E. Collini, C. Ferrante, R. Bozio, and G. A. Pagani, "Enhancement of two-photon absorption cross-section and singlet-oxygen generation in porphyrins upon ?-functionalization with donor-acceptor substituents," Org. Lett. 8, 2719-2722 (2006).
[CrossRef] [PubMed]

Nickel, E.

A. Karotki, M. Drobizhev, M. Kruk, C. Spangler, E. Nickel, N. Mamardashvili, and A. Rebane, "Enhancement of two-photon absorption in tetrapyrrolic compounds," J. Opt. Soc. Am. B 20, 321-332 (2003).
[CrossRef]

A. Karotki, M. Kruk, M. Drobizhev, A. Rebane, E. Nickel, and C. W. Spangler, "Efficient singlet oxygen generation upon two-photon excitation of new porphyrin with enhanced nonlinear absorption," IEEE J. Sel. Top. Quantum Electron. 7, 971-975 (2001).
[CrossRef]

Norris, R.

W. L. Peticolas, R. Norris, and K. E. Rieckhoff, "Polarization effects in the two-photon excitation of anthracene fluorescence," J. Chem. Phys. 42, 4164-4169 (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]

Ogawa, T.

J. M. Song, T. Inoue, H. Kawazumi, and T. Ogawa, "Determination of two photon absorption cross section of fluorescein using a mode locked titanium sapphire laser," Anal. Sci. 15, 601-603 (1999).
[CrossRef]

Oulianov, D. A.

D. A. Oulianov, I. V. Tomov, A. S. Dvornikov, and P. M. Rentzepis, "Observations on the measurement of two-photon absorption cross-section," Opt. Commun. 191, 235-243 (2001).
[CrossRef]

Pagani, G. A.

M. Morone, L. Beverina, A. Abbotto, F. Silvestri, E. Collini, C. Ferrante, R. Bozio, and G. A. Pagani, "Enhancement of two-photon absorption cross-section and singlet-oxygen generation in porphyrins upon ?-functionalization with donor-acceptor substituents," Org. Lett. 8, 2719-2722 (2006).
[CrossRef] [PubMed]

Parker, T. C.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Röckel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J.-L. Brédas, "Structure-property relationships for two-photon absorbing chromophores: Bis-donor diphenylpolyene and bis(styryl)benzene derivatives," J. Am. Chem. Soc. 122, 9500-9510 (2000).
[CrossRef]

Parta, A.

Parthenopoulos, D. A.

D. A. Parthenopoulos and P. M. Rentzepis, "Three-dimensional optical storage," Science 245, 843-845 (1989).
[CrossRef] [PubMed]

Penzkofer, A.

A. Penzkofer and W. Leupacher, "S0-S1 two photon absorption dynamics of organic dye solutions," Opt. Quantum Electron. 19, 327-349 (1987).
[CrossRef]

P. Sperber and A. Penzkofer, "S0-Sn two-photon absorption dynamics of rhodamine dyes," Opt. Quantum Electron. 18, 381-401 (1986).
[CrossRef]

Perry, J. W.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Röckel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J.-L. Brédas, "Structure-property relationships for two-photon absorbing chromophores: Bis-donor diphenylpolyene and bis(styryl)benzene derivatives," J. Am. Chem. Soc. 122, 9500-9510 (2000).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51-53 (1999).
[CrossRef]

Peticolas, W. L.

W. L. Peticolas, R. Norris, and K. E. Rieckhoff, "Polarization effects in the two-photon excitation of anthracene fluorescence," J. Chem. Phys. 42, 4164-4169 (1965).
[CrossRef]

Phillip, R.

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

Povedailo, A. V.

A. P. Blokhin, A. V. Povedailo, and V. A. Tolkachev, "Polarization of two-photon excited fluorescence of vapors of complex organic molecules," Opt. Spectrosc. 60, 60-64 (1986).

Prasad, P. N.

J. D. Bhawalkar, N. D. Kumar, C. F. Zhao, and P. N. Prasad, "Two-photon photodynamic therapy," J. Clin. Laser Med. Surg. 15, 201-204 (1997).
[PubMed]

Qian, S.

Z. Huang, X. Wang, B. Li, C. Lv, J. Xu, W. Jiang, X. Tao, S. Qian, Y. Chui, and P. Yang, "Two-photon absorption of new multibranched chromophores based on bis(diphenylamino)stilbene," Opt. Mater. 29, 1084-1090 (2007).
[CrossRef]

Qin, J.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51-53 (1999).
[CrossRef]

Rebane, A.

N. S. Makarov, A. Rebane, M. Drobizhev, H. Wolleb, and H. Spahni, "Optimizing two-photon absorption for volumetric optical data storage," J. Opt. Soc. Am. B 24, 1874-1885 (2007).
[CrossRef]

M. Drobizhev, N. S. Makarov, Y. Stepanenko, and A. Rebane, "Near-infrared two-photon absorption in phthalocyanines: enhancement of lowest gerade-gerade transition by symmetrical electron-accepting substitution," J. Chem. Phys. 124, 224701 (2006).
[CrossRef] [PubMed]

M. Drobizhev, Y. Stepanenko, Y. Dzenis, A. Karotki, A. Rebane, P. N. Taylor, and H. L. Anderson, "Extremely strong near-IR two-photon absorption in conjugated porphyrin dimers: quantitative description with three-essential-states model," J. Phys. Chem. B 109, 7223-7236 (2005).
[CrossRef]

A. Rebane, N. Christensson, M. Drobizhev, Y. Stepanenko, and C. W. Spangler, "Quantum interference in organic solid," Opt. Express 13, 6033-6038 (2005).
[CrossRef] [PubMed]

M. Kruk, A. Karotki, M. Drobizhev, V. Kuzmitsky, V. Gael, and A. Rebane, "Two-photon absorption of tetraphenylporphin free base," J. Lumin. 105, 45-55 (2003).
[CrossRef]

M. Drobizhev, A. Karotki, Y. Dzenis, A. Rebane, Z. Y. Suo, and C. W. Spangler, "Strong cooperative enhancement of two-photon absorption in dendrimers," J. Phys. Chem. B 107, 7540-7543 (2003).
[CrossRef]

A. Karotki, M. Drobizhev, M. Kruk, C. Spangler, E. Nickel, N. Mamardashvili, and A. Rebane, "Enhancement of two-photon absorption in tetrapyrrolic compounds," J. Opt. Soc. Am. B 20, 321-332 (2003).
[CrossRef]

A. Karotki, M. Kruk, M. Drobizhev, A. Rebane, E. Nickel, and C. W. Spangler, "Efficient singlet oxygen generation upon two-photon excitation of new porphyrin with enhanced nonlinear absorption," IEEE J. Sel. Top. Quantum Electron. 7, 971-975 (2001).
[CrossRef]

Rentzepis, P. M.

D. A. Oulianov, I. V. Tomov, A. S. Dvornikov, and P. M. Rentzepis, "Observations on the measurement of two-photon absorption cross-section," Opt. Commun. 191, 235-243 (2001).
[CrossRef]

D. A. Parthenopoulos and P. M. Rentzepis, "Three-dimensional optical storage," Science 245, 843-845 (1989).
[CrossRef] [PubMed]

Reynolds, G. A.

G. A. Reynolds and K. H. Drexhage, "New coumarin dyes with rigidized structure for flashlamp-pumped lasers," Chem. Phys. Lett. 13, 222-225 (1975).

Ricka, J.

Rieckhoff, K. E.

W. L. Peticolas, R. Norris, and K. E. Rieckhoff, "Polarization effects in the two-photon excitation of anthracene fluorescence," J. Chem. Phys. 42, 4164-4169 (1965).
[CrossRef]

Rockel, H.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51-53 (1999).
[CrossRef]

Röckel, H.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Röckel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J.-L. Brédas, "Structure-property relationships for two-photon absorbing chromophores: Bis-donor diphenylpolyene and bis(styryl)benzene derivatives," J. Am. Chem. Soc. 122, 9500-9510 (2000).
[CrossRef]

Rumi, M.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Röckel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J.-L. Brédas, "Structure-property relationships for two-photon absorbing chromophores: Bis-donor diphenylpolyene and bis(styryl)benzene derivatives," J. Am. Chem. Soc. 122, 9500-9510 (2000).
[CrossRef]

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Rockel, M. Rumi, X.-L. Wu, S. R. Marder, and J. W. Perry, "Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication," Nature 398, 51-53 (1999).
[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]

Schaffer, C. B.

G. O. Clay, C. B. Schaffer, and D. Kleinfeld, "Large two-photon absorptivity of hemoglobin in the infrared range of 780-880 nm," J. Chem. Phys. 126, 025102 (2007).
[CrossRef] [PubMed]

Senes, A.

O. S. Finikova, T. Troxler, A. Senes, W. F. DeGrado, R. M. Hochstrasser, and S. A. Vinogradov, "Energy and electron transfer in enhanced two-photon-absorbing systems with triplet cores," J. Phys. Chem. A 111, 6977-6990 (2007).
[CrossRef] [PubMed]

Sengupta, P.

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

She, C. Y.

S. Li and C. Y. She, "Two-photon absorption cross-section measurements in common laser dyes at 1.06 ?m," Opt. Acta 29, 281-287 (1982).
[CrossRef]

Shelton, D. P.

Shigeiva, M.

T. Ishi-i, Y. Taguri, S. Kato, M. Shigeiva, H. Gorohmaru, S. Maeda, and S. Mataka, "Singlet oxygen generation by two-photon excitation of porphyrin derivatives having two-photon-absorbing benzothiadiazole chromophores," J. Mater. Chem. 17, 3341-3346 (2007).
[CrossRef]

Silvestri, F.

M. Morone, L. Beverina, A. Abbotto, F. Silvestri, E. Collini, C. Ferrante, R. Bozio, and G. A. Pagani, "Enhancement of two-photon absorption cross-section and singlet-oxygen generation in porphyrins upon ?-functionalization with donor-acceptor substituents," Org. Lett. 8, 2719-2722 (2006).
[CrossRef] [PubMed]

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]

Song, J. M.

J. M. Song, T. Inoue, H. Kawazumi, and T. Ogawa, "Determination of two photon absorption cross section of fluorescein using a mode locked titanium sapphire laser," Anal. Sci. 15, 601-603 (1999).
[CrossRef]

Spahni, H.

Spangler, C.

Spangler, C. W.

A. Rebane, N. Christensson, M. Drobizhev, Y. Stepanenko, and C. W. Spangler, "Quantum interference in organic solid," Opt. Express 13, 6033-6038 (2005).
[CrossRef] [PubMed]

M. Drobizhev, A. Karotki, Y. Dzenis, A. Rebane, Z. Y. Suo, and C. W. Spangler, "Strong cooperative enhancement of two-photon absorption in dendrimers," J. Phys. Chem. B 107, 7540-7543 (2003).
[CrossRef]

A. Karotki, M. Kruk, M. Drobizhev, A. Rebane, E. Nickel, and C. W. Spangler, "Efficient singlet oxygen generation upon two-photon excitation of new porphyrin with enhanced nonlinear absorption," IEEE J. Sel. Top. Quantum Electron. 7, 971-975 (2001).
[CrossRef]

C. W. Spangler, "Recent development in the design of organic materials for optical power limiting," J. Mater. Chem. 9, 2013-2020 (1999), and references therein.
[CrossRef]

Sperber, P.

P. Sperber and A. Penzkofer, "S0-Sn two-photon absorption dynamics of rhodamine dyes," Opt. Quantum Electron. 18, 381-401 (1986).
[CrossRef]

Stelzer, E. H. K.

Stepanenko, Y.

M. Drobizhev, N. S. Makarov, Y. Stepanenko, and A. Rebane, "Near-infrared two-photon absorption in phthalocyanines: enhancement of lowest gerade-gerade transition by symmetrical electron-accepting substitution," J. Chem. Phys. 124, 224701 (2006).
[CrossRef] [PubMed]

M. Drobizhev, Y. Stepanenko, Y. Dzenis, A. Karotki, A. Rebane, P. N. Taylor, and H. L. Anderson, "Extremely strong near-IR two-photon absorption in conjugated porphyrin dimers: quantitative description with three-essential-states model," J. Phys. Chem. B 109, 7223-7236 (2005).
[CrossRef]

A. Rebane, N. Christensson, M. Drobizhev, Y. Stepanenko, and C. W. Spangler, "Quantum interference in organic solid," Opt. Express 13, 6033-6038 (2005).
[CrossRef] [PubMed]

Stewart, W. W.

W. W. Stewart, "Synthesis of 3,6-disulfonated 4-aminonaphthalimides," J. Am. Chem. Soc. 103, 7615-7620 (1981).
[CrossRef]

Stoller, P. C.

Suo, Z. Y.

M. Drobizhev, A. Karotki, Y. Dzenis, A. Rebane, Z. Y. Suo, and C. W. Spangler, "Strong cooperative enhancement of two-photon absorption in dendrimers," J. Phys. Chem. B 107, 7540-7543 (2003).
[CrossRef]

Taguri, Y.

T. Ishi-i, Y. Taguri, S. Kato, M. Shigeiva, H. Gorohmaru, S. Maeda, and S. Mataka, "Singlet oxygen generation by two-photon excitation of porphyrin derivatives having two-photon-absorbing benzothiadiazole chromophores," J. Mater. Chem. 17, 3341-3346 (2007).
[CrossRef]

Tao, X.

Z. Huang, X. Wang, B. Li, C. Lv, J. Xu, W. Jiang, X. Tao, S. Qian, Y. Chui, and P. Yang, "Two-photon absorption of new multibranched chromophores based on bis(diphenylamino)stilbene," Opt. Mater. 29, 1084-1090 (2007).
[CrossRef]

Taylor, P. N.

M. Drobizhev, Y. Stepanenko, Y. Dzenis, A. Karotki, A. Rebane, P. N. Taylor, and H. L. Anderson, "Extremely strong near-IR two-photon absorption in conjugated porphyrin dimers: quantitative description with three-essential-states model," J. Phys. Chem. B 109, 7223-7236 (2005).
[CrossRef]

Thayumanavan, S.

M. Rumi, J. E. Ehrlich, A. A. Heikal, J. W. Perry, S. Barlow, Z. Hu, D. McCord-Maughon, T. C. Parker, H. Röckel, S. Thayumanavan, S. R. Marder, D. Beljonne, and J.-L. Brédas, "Structure-property relationships for two-photon absorbing chromophores: Bis-donor diphenylpolyene and bis(styryl)benzene derivatives," J. Am. Chem. Soc. 122, 9500-9510 (2000).
[CrossRef]

Tian, P.

Tolkachev, V. A.

A. P. Blokhin, A. V. Povedailo, and V. A. Tolkachev, "Polarization of two-photon excited fluorescence of vapors of complex organic molecules," Opt. Spectrosc. 60, 60-64 (1986).

Tomov, I. V.

D. A. Oulianov, I. V. Tomov, A. S. Dvornikov, and P. M. Rentzepis, "Observations on the measurement of two-photon absorption cross-section," Opt. Commun. 191, 235-243 (2001).
[CrossRef]

Troxler, T.

O. S. Finikova, T. Troxler, A. Senes, W. F. DeGrado, R. M. Hochstrasser, and S. A. Vinogradov, "Energy and electron transfer in enhanced two-photon-absorbing systems with triplet cores," J. Phys. Chem. A 111, 6977-6990 (2007).
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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the experimental setup. PH1, PH2 – laser beam alignment pinholes; L1 – focusing lens; FW – neutral density filter wheel; M1 – spherical mirror, LN CCD – liquid nitrogen-cooled CCD detector.

Fig. 2.
Fig. 2.

Variation of the excitation pulse parameters with OPA tuning in signal (red), second harmonic of idler (orange) and second harmonic of signal (green) range of wavelengths. (a) - pulse duration FWHM; (b) - beam diameter in vertical (circles) and horizontal (squares) direction; (c) Combined correction function, (d) autocorrelation function of the laser pulse at 1160 nm (black line) and the corresponding Gaussian fit (red line), (e) vertical section of spatial beam profile at 1160 nm (black line) and the corresponding Gaussian fit (red line).

Fig. 3.
Fig. 3.

Corrected fluorescence spectra measured with a Perkin-Elmer LS 50B spectrofluorimeter. 9-Chloroanthracene (Aldrich), 9,10-Dichloroanthracene (Aldrich), 4,4’-Bis-(diphenylamino)stilbene (BDPAS, MPA Technologies), Perylene (Aldrich), Coumarin 540A (Exciton), Coumarin 485 (Exciton), Fluorescein (Aldrich), Lucifer Yellow (Lucifer Yellow CH ammonium salt, Molecular Probes), Rhodamine 6G (Rhodamine 590, Exciton), Rhodamine B (Rhodamine 610, Exciton), Tetraphenyl-porphine (5,10,15,20-Tetraphenyl-21H,23H-porphine Aldrich), Zn-tetra-tert-butyl Pc (Zn 2,9,16,23-tetra-tert-butyl-29H,31H-phthalocyanine (Aldrich), Zn-tetrakis-(phenylthio)-Pc (Zn 2,9,16,23-tetrakis-(phenylthio)-29H,31H-phthalocyanine Aldrich), Si-Nc dioctyloxide (Silicon 2,3-naphthalocyanine dioctyloxide Aldrich), Styryl 9M (Aldrich).

Fig. 4.
Fig. 4.

(a–h). 2PA spectra (dark blue circles, left vertical-axis) and molar extinction (magenta line, right vertical axis). Large dark blue circles are absolute cross sections at selected wavelengths measured here. Other symbols are the literature data with corresponding references shown in inset. For Fluorescein, 2PA spectrum is shown both in linear (4g) and log (4h) scales.

Fig. 4.
Fig. 4.

(i-p). 2PA spectra (dark blue circles, left vertical-axis) and molar extinction (magenta line, right vertical axis). Large dark blue circles are absolute cross sections at selected wavelengths measured here. Other symbols are the literature data with corresponding references shown in inset.

Tables (5)

Tables Icon

Table 1. Two-photon cross sections (GM) of the dyes at selected wavelengths (nm). The relative error of numbers shown here is ±15%.

Tables Icon

Table 2. Comparison of 2PA cross sections of Fluorescein, Rhodamine 6G, and Rhodamine B with the literature data.

Tables Icon

Table 3. Two-photon cross sections (GM) of the dyes at selected wavelengths (nm). The relative error of numbers shown here is ±15% (first five compounds).

Tables Icon

Table 4. Two-photon cross sections (GM) of the dyes at selected wavelengths (nm). The relative error of numbers shown here is ±15% (second five compounds).

Tables Icon

Table 5. Two-photon cross sections (GM) of the dyes at selected wavelengths (nm). The relative error of numbers shown here is ±15% (last five compounds).

Equations (16)

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

F 1 = N 1 T λ min λ max η ( λ ) φ ( λ ) d λ ,
N 1 = ( 1 10 OD ) h v 1 I 1 ( x , y ) dxdy ,
F 1 = ( 1 10 OD ) W 1 T h v 1 λ min λ max η ( λ ) φ ( λ ) d λ .
F 2 = N 2 T g λ min λ max η ( λ ) φ ( λ ) d λ ,
N 2 = 1 2 σ 2 lC ( h v 2 ) 2 I 2 2 ( x , y , t ) dxdy dt ,
I 2 = I 2 ( 0 ) exp ( 4 ln 2 t 2 τ 2 ) exp ( 4 ln 2 x 2 Δ x 2 ) exp ( 4 ln 2 y 2 Δ y 2 ) ,
W 2 = g pulse I 2 ( x , y , t ) dx dy dt = 1 8 ( π ln 2 ) 3 2 g I 2 ( 0 ) τ Δ x Δ y ,
I 2 ( 0 ) = 8 ( ln 2 π ) 3 2 W 2 τ Δ x Δ y g .
N 2 = 2 ( ln 2 π ) 3 2 σ 2 lC ( h v 2 ) 2 τ Δ x Δ y g 2 W 2 2 .
F 2 = 2 ( ln 2 π ) 3 2 σ 2 lC W 2 2 T ( h v 2 ) 2 τ Δ x Δ y g λ min λ max η ( λ ) φ ( λ ) d λ .
σ 2 = 1 2 ( π ln 2 ) 3 2 W 1 W 2 2 ( h v 2 ) 2 h v 1 F 2 F 1 σ 1 g τ Δ x Δ y ( 1 10 OD ) ln 10 OD .
F ( λ ) = A σ 2 ( λ ) W 2 ( λ ) ( h v ) 2 τ ( λ ) Δ x ( λ ) Δ y ( λ ) ,
A 2 PA ( λ ) = F ( λ ) W 2 ( λ ) ( h v ) 2 τ ( λ ) Δ x ( λ ) Δ y ( λ ~ ) .
C ( λ ) = τ ( λ ) Δ x ( λ ) Δ y ( λ ) .
σ 2 , s = F 2 , s ( λ reg ) C r φ r ( λ reg ) F 2 , r ( λ reg ) C s φ s ( λ reg ) σ 2 , r ,
A 2 PA , s ( λ ) = F 2 , s ( λ ) F 2 , r ( λ ) A 2 PA , r ( λ ) ,

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