Abstract

The role of both permanent molecular dipoles and virtual molecular states, for two- and three-photon molecular excitation, is discussed in the context of the two- and three-photon excitation cross sections, with a ten-energy-level giant-dipole molecule as a model. Two types of excitation mechanisms are involved, that which requires permanent dipole moments and that which requires virtual molecular excited states. The results are relevant to the understanding of two- and three-photon excitation processes and for the design of fluorophores with large multiphoton absorption cross sections.

© 2002 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  41. F. Meyers, S. R. Marder, B. M. Pierce, and J. L. Bredas, “Electric field modulated nonlinear optical properties of donor-acceptor polyenes: sum-over-states investigation of the relationship between molecular polarizabilities (α, β, and γ) and bond length alternation,” J. Am. Chem. Soc. 116, 10703–10714 (1994).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  49. J. R. Lakowicz, I. Gryczynski, H. Malak, M. Schrader, P. Engelhardt, H. Kano, and S. W. Hell, “Time-resolved fluorescence spectroscopy and imaging of DNA labeled with DAPI and Hoechst 33342 using three-photon excitation,” Biophys. J. 72, 567–578 (1997).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  53. J. N. Shirley, “Solution of the Schrödinger equation with a Hamiltonian periodic in time,” Phys. Rev. B 138, 979–987 (1965).
    [CrossRef]
  54. R. Pantell, F. Pradere, J. Hanus, M. Schott, and H. Puthoff, “Theoretical and experimental values for two-, three-, and four-photon absorptions,” J. Chem. Phys. 46, 3507–3511 (1967).
    [CrossRef]
  55. R. Gush and H. P. Gush, “Scattering of intense light by a two-level system,” Phys. Rev. A 6, 129–140 (1972).
    [CrossRef]
  56. S. Stenholm, “Saturation effects in RF spectroscopy. I. General theory,” J. Phys. B 5, 878–889 (1972).
    [CrossRef]
  57. J. V. Moloney and W. J. Meath, “Phase and temporal average transition probabilities for a multi-level system in a sinusoidal field,” Mol. Phys. 31, 1537–1548 (1976).
    [CrossRef]
  58. D. L. Andrews and W. A. Ghoul, “Polarisation studies in multiphoton absorption spectroscopy,” J. Chem. Phys. 75, 530–538 (1981).
    [CrossRef]
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2001 (3)

2000 (3)

M. Barzoukas and M. Blanchard-Desce, “Molecular engineering of push-pull dipolar and quadrupolar molecules for two-photon absorption: a multivalence-bond states approach,” J. Chem. Phys. 113, 3951–3959 (2000).
[CrossRef]

Y. Zhou, F. Meng, X. Zhao, D. Xu, and M. Jiang, “Two-photon absorption properties of a new series of 2CTσ chromophores,” Solid State Commun. 116, 605–608 (2000).
[CrossRef]

G. S. He, J. Swiatkiewicz, Y. Jiang, P. N. Prasad, B. A. Reinhardt, L.-S. Tan, and R. Kannan, “Two-photon excitation and optical spatial profile reshaping via a nonlinear absorbing medium,” J. Phys. Chem. A 104, 4805–4810 (2000).
[CrossRef]

1999 (2)

A. Jenei, A. K. Krisch, V. Subramaniam, D. J. Arndt-Jovin, and T. M. Jovin, “Picosecond multiphoton scanning near-field optical microscopy,” Biophys. J. 76, 1092–1100 (1999).
[CrossRef] [PubMed]

R. M. Williams, J. B. Shear, W. R. Zipfel, S. Maiti, and W. W. Webb, “Mucosal mast cell secretion processes imaged using three-photon microscopy of 5-hydroxytryptamine autofluorescence,” Biophys. J. 76, 1835–1846 (1999).
[CrossRef] [PubMed]

1998 (3)

M. A. Albota, C. Xu, and W. W. Webb, “Two-photon fluorescence excitation cross sections of biomolecular probes from 690 to 960 nm,” Appl. Opt. 37, 7352–7356 (1998).
[CrossRef]

M. Albota, D. Beljonne, J.-L. Brédas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Röckel, M. Rumi, G. Subramaniam, W. W. Webb, X.-L. Wu, and C. Xu, “Design of organic molecules with large two-photon absorption cross sections,” Science 281, 1653–1656 (1998).
[CrossRef] [PubMed]

T. Kogej, D. Beljonne, F. Meyers, J. W. Perry, S. R. Marder, and J. L. Brédas, “Mechanisms for enhancement of two-photon absorption in donor-acceptor conjugated chromophores,” Chem. Phys. Lett. 298, 1–6 (1998).
[CrossRef]

1997 (3)

A. E. Kondo and W. J. Meath, “On the spectral and dynamical effects of near-nodal molecule—EMF coupling arising from permanent dipole moments,” Mol. Phys. 92, 805–812 (1997), and references therein.

J. R. Lakowicz, I. Gryczynski, H. Malak, M. Schrader, P. Engelhardt, H. Kano, and S. W. Hell, “Time-resolved fluorescence spectroscopy and imaging of DNA labeled with DAPI and Hoechst 33342 using three-photon excitation,” Biophys. J. 72, 567–578 (1997).
[CrossRef] [PubMed]

S. Maiti, J. B. Shear, R. M. Williams, W. R. Zipfel, and W. W. Webb, “Measuring serotonin distribution in live cells with three-photon excitation,” Science 275, 530–532 (1997).
[CrossRef] [PubMed]

1996 (5)

H. Szmacinski, I. Gryczynski, and J. R. Lakowicz, “Three-photon induced fluorescence of the calcium probe Indo-1,” Biophys. J. 70, 547–555 (1996).
[CrossRef] [PubMed]

I. Gryczynski, H. Malak, J. R. Lakowicz, H. C. Cheung, J. Robinson, and P. K. Umeda, “Fluorescence spectral properties of troponin C mutant F22W with one-, two-, and three-photon excitation,” Biophys. J. 71, 3448–3453 (1996).
[CrossRef] [PubMed]

J. B. Shear, E. B. Brown, and W. W. Webb, “Multiphoton-excited fluorescence of fluorogen-labeled neurotransmitters,” Anal. Chem. 68, 1778–1783 (1996).
[CrossRef] [PubMed]

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. Xu, W. Zipfel, J. B. Shear, R. M. Williams, and W. W. Webb, “Multiphoton fluorescence excitation: New spectral window for biological nonlinear microscopy,” Proc. Natl. Acad. Sci. U.S.A. 93, 10763–10768 (1996).
[CrossRef]

1995 (5)

G. S. He, J. D. Bhawalkar, P. N. Prasad, and B. A. Reinhardt, “Three-photon-absorption-induced fluorescence and optical limiting effects in an organic compound,” Opt. Lett. 20, 1524–1526 (1995).
[CrossRef] [PubMed]

I. Gryczynski, H. Malak, and J. R. Lakowicz, “Three-photon induced fluorescence of 2, 5-diphenyloxazole with a femtosecond Ti: sapphire laser,” Chem. Phys. Lett. 245, 30–35 (1995).
[CrossRef]

G. S. He, R. Gvishi, P. N. Prasad, and B. A. Reinhardt, “Two-photon absorption based optical limiting and stabilization in organic molecule-doped solid materials,” Opt. Commun. 117, 133–136 (1995).
[CrossRef]

I. Gryczynski, H. Szmacinski, and J. R. Lakowicz, “On the possibility of calcium imaging using INDO-1 with three-photon excitation,” Photochem. Photobiol. 62, 804–808 (1995).
[CrossRef] [PubMed]

A. P. Davey, E. Bourdin, F. Henari, and W. Blau, “Three photon induced fluorescence from a conjugated organic polymer for infrared frequency upconversion,” Appl. Phys. Lett. 67, 884–885 (1995).
[CrossRef]

1994 (3)

A. E. Kondo, W. J. Meath, S. H. Nilar, and A. J. Thakkar, “Pump-probe studies of the effects of permanent dipoles in one- and two-colour molecular excitations,” Chem. Phys. 186, 375–394 (1994).
[CrossRef]

S. R. Marder, L.-T. Cheng, B. G. Tiemann, A. C. Friedli, M. Blanchard-Desce, J. W. Perry, and J. Skindhoj, “Large first hyperpolarizabilities in push-pull polyenes by tuning of the bond length alternation and aromaticity,” Science 264, 511–514 (1994).
[CrossRef]

F. Meyers, S. R. Marder, B. M. Pierce, and J. L. Bredas, “Electric field modulated nonlinear optical properties of donor-acceptor polyenes: sum-over-states investigation of the relationship between molecular polarizabilities (α, β, and γ) and bond length alternation,” J. Am. Chem. Soc. 116, 10703–10714 (1994).
[CrossRef]

1993 (3)

C. B. Gorman and S. R. Marder, “An investigation of the interrelationships between linear and nonlinear polarizabilities and bond-length alternation in conjugated organic molecules,” Proc. Natl. Acad. Sci. USA 90, 11297–11301 (1993).
[CrossRef] [PubMed]

S. H. Nilar, A. J. Thakkar, A. E. Kondo, and W. J. Meath, “Electronic energies, dipole moment matrix elements, and static polarizabilities and hyperpolarizabilities for some diphenyl molecules,” Can. J. Chem. 71, 1663–1671 (1993).
[CrossRef]

D. L. Andrews and W. J. Meath, “On the role of permanent dipoles in second harmonic generation,” J. Phys. B 26, 4633–4641 (1993).
[CrossRef]

1991 (1)

1990 (2)

M. A. Kmetic and W. J. Meath, “Perturbative correction to the rotating-wave approximations for two-level molecules and effects of permanent dipoles on single-photon and multiphoton spectra,” Phys. Rev. A 41, 1556–1568 (1990).
[CrossRef] [PubMed]

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

1989 (1)

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

1987 (2)

A. E. Stiegman, V. M. Miskowski, J. W. Perry, and D. R. Coulter, “A series of donor–acceptor molecules of the form NH2(C6H4)(C☰C)n(C6H4)NO2. Unusual effects of varying n,” J. Am. Chem. Soc. 109, 5884–5886 (1987).
[CrossRef]

T. Hattori and T. Kobayashi, “Bloch–Siegert shift in giant dipole molecules,” Phys. Rev. A 35, 2733–2736 (1987).
[CrossRef] [PubMed]

1986 (1)

T. Kobayashi, M. Terauchi, and H. Uchiki, “Lasing properties and gain spectrum of 4-diethylamino-4-nitrostilbene with a giant dipole,” Chem. Phys. Lett. 126, 143–148 (1986).
[CrossRef]

1985 (1)

M. A. Kmetic and W. J. Meath, “Permanent dipole moments and multi-photon resonances,” Phys. Lett. 108A, 340–343 (1985).
[CrossRef]

1984 (1)

W. J. Meath and E. A. Power, “On the importance of permanent moments in multiphoton absorption using perturbation theory,” J. Phys. B 17, 763–781 (1984).
[CrossRef]

1983 (1)

G. F. Thomas and W. J. Meath, “Multi-photon vibrational resonances with modulation effects, using HeXe, NeAr and NeXe as models—Erratum,” Mol. Phys. 48, 649–650 (1983).

1982 (2)

B. Dick and G. Hohlneicher, “Importance of initial and final states as intermediate states in two-photon spectroscopy of polar molecules,” J. Chem. Phys. 76, 5755–5760 (1982).
[CrossRef]

G. F. Thomas and W. J. Meath, “Multi-photon vibrational resonances with modulation effects, using HeXe, NeAr and NeXe as models,” Mol. Phys. 46, 743–755 (1982).
[CrossRef]

1981 (1)

D. L. Andrews and W. A. Ghoul, “Polarisation studies in multiphoton absorption spectroscopy,” J. Chem. Phys. 75, 530–538 (1981).
[CrossRef]

1979 (2)

R. R. Birge and B. M. Pierce, “A theoretical analysis of the two-photon properties of linear polyenes and the visual chromophores,” J. Chem. Phys. 70, 165–178 (1979).
[CrossRef]

T. Kobayashi, E. O. Degenkolb, and P. M. Rentzepis, “Lifetime measurements of 4-diethylamino-4-nitrostilbene fluorescence by picosecond optical amplifications,” J. Appl. Phys. 50, 3118–3121 (1979).
[CrossRef]

1977 (1)

J. L. Oudar and D. S. Chemla, “Hyperpolarizabilities of the nitroanilines and their relations to the excited state dipole moment,” J. Chem. Phys. 66, 2664–2668 (1977).
[CrossRef]

1976 (1)

J. V. Moloney and W. J. Meath, “Phase and temporal average transition probabilities for a multi-level system in a sinusoidal field,” Mol. Phys. 31, 1537–1548 (1976).
[CrossRef]

1972 (2)

R. Gush and H. P. Gush, “Scattering of intense light by a two-level system,” Phys. Rev. A 6, 129–140 (1972).
[CrossRef]

S. Stenholm, “Saturation effects in RF spectroscopy. I. General theory,” J. Phys. B 5, 878–889 (1972).
[CrossRef]

1967 (1)

R. Pantell, F. Pradere, J. Hanus, M. Schott, and H. Puthoff, “Theoretical and experimental values for two-, three-, and four-photon absorptions,” J. Chem. Phys. 46, 3507–3511 (1967).
[CrossRef]

1965 (1)

J. N. Shirley, “Solution of the Schrödinger equation with a Hamiltonian periodic in time,” Phys. Rev. B 138, 979–987 (1965).
[CrossRef]

1964 (1)

S. Singh and L. T. Bradley, “Three-photon absorption in napthalene crystals by laser excitation,” Phys. Rev. Lett. 12, 612–614 (1964).
[CrossRef]

1931 (1)

M. Göppert-Mayer, “Uber Elementarakte mit zwei Quantensprüngen,” Ann. Phys. (Leipzig) 9, 273–295 (1931).
[CrossRef]

Albota, M.

M. Albota, D. Beljonne, J.-L. Brédas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Röckel, M. Rumi, G. Subramaniam, W. W. Webb, X.-L. Wu, and C. Xu, “Design of organic molecules with large two-photon absorption cross sections,” Science 281, 1653–1656 (1998).
[CrossRef] [PubMed]

Albota, M. A.

Andrews, D. L.

D. L. Andrews and W. J. Meath, “On the role of permanent dipoles in second harmonic generation,” J. Phys. B 26, 4633–4641 (1993).
[CrossRef]

D. L. Andrews and W. A. Ghoul, “Polarisation studies in multiphoton absorption spectroscopy,” J. Chem. Phys. 75, 530–538 (1981).
[CrossRef]

Arndt-Jovin, D. J.

A. Jenei, A. K. Krisch, V. Subramaniam, D. J. Arndt-Jovin, and T. M. Jovin, “Picosecond multiphoton scanning near-field optical microscopy,” Biophys. J. 76, 1092–1100 (1999).
[CrossRef] [PubMed]

Barzoukas, M.

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[CrossRef] [PubMed]

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M. Albota, D. Beljonne, J.-L. Brédas, J. E. Ehrlich, J.-Y. Fu, A. A. Heikal, S. E. Hess, T. Kogej, M. D. Levin, S. R. Marder, D. McCord-Maughon, J. W. Perry, H. Röckel, M. Rumi, G. Subramaniam, W. W. Webb, X.-L. Wu, and C. Xu, “Design of organic molecules with large two-photon absorption cross sections,” Science 281, 1653–1656 (1998).
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[CrossRef]

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T. Kogej, D. Beljonne, F. Meyers, J. W. Perry, S. R. Marder, and J. L. Brédas, “Mechanisms for enhancement of two-photon absorption in donor-acceptor conjugated chromophores,” Chem. Phys. Lett. 298, 1–6 (1998).
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C. Xu, W. Zipfel, J. B. Shear, R. M. Williams, and W. W. Webb, “Multiphoton fluorescence excitation: New spectral window for biological nonlinear microscopy,” Proc. Natl. Acad. Sci. U.S.A. 93, 10763–10768 (1996).
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Anal. Chem. (1)

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Can. J. Chem. (1)

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Chem. Phys. (1)

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Tables (2)

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Table 1 Two-Photon Cross Sections σ(2), in Units of 10-50 cm4 s, for the 1f Transitions of the Model Moleculea

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Table 2 Three-Photon Cross Sections σ(3), and Its Various Components as Defined in Text, in Units of 10-83 cm6 s2, for the 1f Transitions of the Model Moleculea

Equations (20)

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dPf(n)dt=Rf(n)=2E2n|M(n)|222n2 sin(ωf1-nω)t(ωf1-nω),
M(2)=p (μfp·eˆ)(μp1·eˆ)(Ep1-ω),
M(3)=p,q (μfp·eˆ)(μpq·eˆ)(μq1·eˆ)(Ep1-2ω)(Eq1-ω),
σ(n)(peak)=Rf(n)(nω=Ef1)Fn=2n+1πnn-2ωncnΓ|M(n)(ωf1=nω)|2,
σ(n)(peak)=2n+1πnαnt0n-2a02nΓ×[Eωn|M(n)(ωf1=nω)|2]au,
M(2)=(df·eˆ)(μf1·eˆ)(Ef1-ω)+p1,f (μfp·eˆ)(μp1·eˆ)(Ep1-ω)=Md(2)+Mv(2),
σ(2)=σd(2)+σv(2)+σdv(2),
M(3)=M(3)(2-level)+ΔM(3),
M(3)(2-level)=Mdf(3)(2-level)+Mv(3)(2-level),
Mdf(3)(2-level)=(df·eˆ)2(μf1·eˆ)2Eω3,
Mv(3)(2-level)=-(μf1·eˆ)34Eω3,
ΔM(3)=ΔMd(3)+ΔMμ(3),
ΔMd(3)=(df·eˆ)Eω p1,f (μfp·eˆ)(μp1·eˆ)(Ep1-Eω)+p1,f (dp·eˆ)(μfp·eˆ)(μp1·eˆ)(Ep1-2Eω)(Ep1-Eω),
ΔMμ(3)=(μf1·eˆ)2Eω p1,f|μfp·e|2(Ep1-2Eω)-|μ1p·eˆ|2(Ep1-Eω)+p1,fq1,fpq (μfp·eˆ)(μpq·eˆ)(μq1·eˆ)(Ep1-2Eω)(Eq1-Eω),
σ(3)=σ(3)(2-level)+σΔM(3)+σ2,ΔM(3),
σ(3)(2-level)=σdf(3)+σv(3)+σdf,v(3).
M(3)=Md(3)+Mμ(3),
Md(3)=Mdf(3)(2-level)+ΔMd(3),
Mμ(3)=Mv(3)(2-level)+ΔMμ(3).
σ(3)=σd(3)+σμ(3)+σd,μ(3),

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