Abstract

We solve numerically the Maxwell–Bloch equations using an iterative predictor-corrector finite-difference time-domain technique to study the propagation of femtosecond laser pulses in a strong two-photon absorption (TPA) organic molecular medium [4,4-bis(dimethylamino) stilbene]. The hybrid density functional theory is used to calculate electronic structures of the compound. The molecular system is described by a three-level model in an optical regime and has demonstrated a good optical power limiting behavior in a certain intensity region. Thresholds for the breakdown of optical power limiting are observed that are dependent on the input pulse width and, slightly, the propagation distance. The dynamical two-photon absorption cross section is obtained, which is almost a linearly increasing function of the pulse width in the femtosecond time domain. The propagation distance also has an obvious influence on the measurement of the TPA cross section, and nonmonotonic dependence of the TPA cross section on propagation distance is observed. The input pulse width and the thickness of the molecular samples thus should be taken into account when the TPA cross section is measured.

© 2007 Optical Society of America

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  4. G. S. He, J. D. Bhawalkar, C. F. Zhao, C. K. Park, and P. N. Prasad, "Up-conversion dye-doped polymer fiber laser," Appl. Phys. Lett. 68, 3549-3551 (1996).
    [Crossref]
  5. G. S. He, L. X. Yuan, N. Cheng, J. D. Bhawalkar, P. N. Prasad, L. L. Brott, S. J. Clarson, and B. A. Reinhardt, "Nonlinear optical properties of a new chromophore," J. Opt. Soc. Am. B 14, 1079-1087 (1997).
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  6. G. S. He, P. P. Markowicz, T. Lin, and P. N. Prasad, "Observation of stimulated emission by direct three-photon excitation," Nature 415, 767-770 (2002).
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  8. W. F. Sun, Z. X. Wu, Q. Z. Yang, L. Z. Wu, and C. H. Tung, "Reverse saturable absorption of platinum ter/bipyridyl polyphenylacetylide complexes," Appl. Phys. Lett. 82, 850-852 (2003).
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    [Crossref]
  12. G. S. He, T. C. Lin, P. N. Prasad, C. C. Cho, and L. J. Yu, "Optical power limiting and stabilization using a two-photon absorbing neat liquid crystal in isotropic phase," Appl. Phys. Lett. 82, 4717-4719 (2003).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  34. G. S. He, Q. D. Zheng, A. Baev, and P. N. Prasad, "Saturation of multiphoton absorption upon strong and ultrafast infrared laser excitation," J. Appl. Phys. 101, 083108 (2007).
    [Crossref]
  35. R. E. Stratmann, G. E. Scuseria, and M. J. Frisch, "An efficient implementation of time-dependent density-functional theory for the calculation of excitation energies of large molecules," J. Chem. Phys. 109, 8218-8224 (1998).
    [Crossref]
  36. Chengteh Lee, Weitao Yang, and Robert G. Parr, "Development of the Colle-Salvetti correlation-energy formula into a functional of the electron," Phys. Rev. B 37, 785-789 (1988).
    [Crossref]
  37. B. G. Johnson, P. M. Gill, and J. A. Pople, GAUSSIAN 98 (Gaussian Inc., 1998).
  38. P. Baum, S. Lochbrunner, and E. Riedle, "Generation of tunable 7 fs ultraviolet pulses: achromatic phase matching and chirp management," Appl. Phys. B 79, 1027-2032 (2004).
    [Crossref]
  39. N. J. Turro, Modern Molecular Photochemistry (Benjamin, 1978).

2007 (2)

K. Zhao, J. C. Liu, C. K. Wang, and Y. Luo, "Modulation of supercontinuum generation and formation of an attosecond pulse from a generalized two-level medium," J. Phys. B 40, 1523-1534 (2007).
[Crossref]

G. S. He, Q. D. Zheng, A. Baev, and P. N. Prasad, "Saturation of multiphoton absorption upon strong and ultrafast infrared laser excitation," J. Appl. Phys. 101, 083108 (2007).
[Crossref]

2006 (3)

N. Lin, X. Zhao, J. X. Yang, M. H. Jiang, J. C. Liu, C. K. Wang, W. Shi, J. Meng, and J. Weng, "Theoretical study of one-, two-, and three-photon absorption properties for a series of Y-shaped molecules," J. Chem. Phys. 124, 024704 (2006).
[Crossref] [PubMed]

V. Kimberg, S. Polyutov, F. Gel'mukhanov, H. Ågren, Alexander Baev, Q. D. Zheng, and G. S. He, "Dynamics of cavityless lasing generated by ultrafast multiphoton excitation," Phys. Rev. A 74, 033814 (2006).
[Crossref]

G. S. He, C. G. Lu, Q. D. Zheng, A. Baev, M. Samoc, and P. N. Prasad, "Asymmetric properties between the forward and backward stimulated emission generated by ultrafast three- and four-photon excitation," Phys. Rev. A 73, 033815 (2006).
[Crossref]

2005 (1)

K. Zhao, H. Y. Li, J. C. Liu, C. K. Wang, and Y. Luo, "Dipolar effects on propagation of ultrashort laser pulse in one-dimensional para-nitroaniline (pNA) molecules," J. Phys. B 38, 4235-4245 (2005).
[Crossref]

2004 (3)

X. H. Song, S. Q. Gong, S. Q. Jin, and Z. Z. Xu, "Formation of higher spectral components in a two-level medium driven by two-color ultrashort laser pulses," Phys. Rev. A 69, 015801 (2004).
[Crossref]

Z. Q. Liu, Q. Fang, D. X. Cao, D. Wang, and G. B. Xu, "Triaryl boron-based A-π-A versus triaryl nitrogen-based D-π-D quadrupolar compounds for single- and two-photon excited fluorescence," Org. Lett. 17, 2933-2936 (2004).
[Crossref]

P. Baum, S. Lochbrunner, and E. Riedle, "Generation of tunable 7 fs ultraviolet pulses: achromatic phase matching and chirp management," Appl. Phys. B 79, 1027-2032 (2004).
[Crossref]

2003 (4)

G. S. He, T. C. Lin, P. N. Prasad, C. C. Cho, and L. J. Yu, "Optical power limiting and stabilization using a two-photon absorbing neat liquid crystal in isotropic phase," Appl. Phys. Lett. 82, 4717-4719 (2003).
[Crossref]

C. K. Wang, K. Zhao, Y. Su, X. Zhao, and Y. Luo, "Solvent effects on the electronic structure of a newly synthesized two-photon polymerization initiator," J. Chem. Phys. 119, 1208-1213 (2003).
[Crossref]

W. F. Sun, Z. X. Wu, Q. Z. Yang, L. Z. Wu, and C. H. Tung, "Reverse saturable absorption of platinum ter/bipyridyl polyphenylacetylide complexes," Appl. Phys. Lett. 82, 850-852 (2003).
[Crossref]

Y. Su, Y. H. Wang, and C. K. Wang, "The solvent effect on two-photon absorption of 4,4′-bis (dimethylamino) stilbene," Acta Opt. Sin. 23, 646-650 (2003).

2002 (6)

J. Xiao, Z. Y. Wang, and Z. Z. Xu, "Area evolution of a few-cycle pulse laser in a two-level-atom medium," Phys. Rev. A 65, 031402 (2002).
[Crossref]

F. Gel'mukhanov, A. Baev, P. Macak, Y. Luo, and H. Ågren, "Dynamics of two-photon absorption by molecules and solutions," J. Opt. Soc. Am. A 19, 937-945 (2002)..
[Crossref]

A. Baev, F. Gel'mukhanov, P. Macak, H. Ågren, and Y. Luo, "General theory for pulse propagation in two-photon active media," J. Chem. Phys. 117, 6214-6220 (2002).
[Crossref]

G. S. He, P. P. Markowicz, T. Lin, and P. N. Prasad, "Observation of stimulated emission by direct three-photon excitation," Nature 415, 767-770 (2002).
[Crossref] [PubMed]

P. Salek, O. Vahtras, T. Helgaker, and H. Ågren, "Density-functional theory of linear and nonlinear time-dependent molecular properties," J. Chem. Phys. 117, 9630-9645 (2002).
[Crossref]

P. Cronstrand, Y. Luo, and H. Ågren, "Generalized few-state models for two-photon absorption of conjugated molecules," Chem. Phys. Lett. 352, 262-269 (2002).
[Crossref]

2001 (2)

C. K. Wang, P. Macak, Y. Luo, and H. Ågren, "Effects of π centers and symmetry on two-photon absorption cross sections of organic chromophores," J. Chem. Phys. 114, 9813-9820 (2001).
[Crossref]

A. V. Tarasishin, V. A. Magnitskii, V. A. Shuvaev, and A. M. Zheltikov, "Evolution of ultrashort light pulses in a two-level medium visualized with the finite-difference time domain technique," Opt. Express 8, 452-457 (2001).
[Crossref] [PubMed]

2000 (4)

Q. Wang, C. L. Liu, J. Wang, X. Y. Zhao, and Z. Z. Zha, "The experimental study on two-photon absorption and optical limiting of 4,4′-bis(dimethylamino) stilbene at 532 nm," Acta Opt. Sin. 20, 286-287 (2000).

S. Hughes, "Subfemtosecond soft-x-ray generation from a two-level atom: Extreme carrier-wave Rabi flopping," Phys. Rev. A 62, 055401 (2000).
[Crossref]

P. Macak, Y. Luo, P. Norman, and H. Ågren, "Electronic and vibronic contributions to two-photon absorption of molecules with multibranched structures," J. Chem. Phys. 113, 7055-7061 (2000).
[Crossref]

S. Kim, D. McLaughlin, and M. Potasek, "Propagation of the electromagnetic field in optical-limiting reverse-saturable absorbers," Phys. Rev. A 61, 025801 (2000).
[Crossref]

1998 (4)

M. Albota, D. Beijonne, 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. Rockel, 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]

R. E. Stratmann, G. E. Scuseria, and M. J. Frisch, "An efficient implementation of time-dependent density-functional theory for the calculation of excitation energies of large molecules," J. Chem. Phys. 109, 8218-8224 (1998).
[Crossref]

B. G. Johnson, P. M. Gill, and J. A. Pople, GAUSSIAN 98 (Gaussian Inc., 1998).

1997 (1)

1996 (3)

S. Hughes and B. Wherrett, "Multilevel rate-equation analysis to explain the recent observations of limitations to optical limiting dyes," Phys. Rev. A 54, 3546-3552 (1996).
[Crossref] [PubMed]

G. S. He, J. D. Bhawalkar, C. F. Zhao, C. K. Park, and P. N. Prasad, "Up-conversion dye-doped polymer fiber laser," Appl. Phys. Lett. 68, 3549-3551 (1996).
[Crossref]

J. D. Bhawalkar, G. S. He, and P. N. Prasad, "Nonlinear multiphoton processes in organic and polymeric materials," Rep. Prog. Phys. 59, 1041-1070 (1996).
[Crossref]

1995 (2)

1993 (1)

L. W. Tutt and T. F. Boggess, "A review of optical limiting mechanisms and devices using organics, fullerence, semiconductors, and other materials," Prog. Quantum Electron. 17, 299-338 (1993).
[Crossref]

1992 (1)

L. Tutt and A. Kost, "Optical limiting performance of C60 and C70 solution," Nature 356, 225-226 (1992).
[Crossref]

1988 (1)

Chengteh Lee, Weitao Yang, and Robert G. Parr, "Development of the Colle-Salvetti correlation-energy formula into a functional of the electron," Phys. Rev. B 37, 785-789 (1988).
[Crossref]

1978 (1)

N. J. Turro, Modern Molecular Photochemistry (Benjamin, 1978).

Ågren, H.

V. Kimberg, S. Polyutov, F. Gel'mukhanov, H. Ågren, Alexander Baev, Q. D. Zheng, and G. S. He, "Dynamics of cavityless lasing generated by ultrafast multiphoton excitation," Phys. Rev. A 74, 033814 (2006).
[Crossref]

A. Baev, F. Gel'mukhanov, P. Macak, H. Ågren, and Y. Luo, "General theory for pulse propagation in two-photon active media," J. Chem. Phys. 117, 6214-6220 (2002).
[Crossref]

F. Gel'mukhanov, A. Baev, P. Macak, Y. Luo, and H. Ågren, "Dynamics of two-photon absorption by molecules and solutions," J. Opt. Soc. Am. A 19, 937-945 (2002)..
[Crossref]

P. Salek, O. Vahtras, T. Helgaker, and H. Ågren, "Density-functional theory of linear and nonlinear time-dependent molecular properties," J. Chem. Phys. 117, 9630-9645 (2002).
[Crossref]

P. Cronstrand, Y. Luo, and H. Ågren, "Generalized few-state models for two-photon absorption of conjugated molecules," Chem. Phys. Lett. 352, 262-269 (2002).
[Crossref]

C. K. Wang, P. Macak, Y. Luo, and H. Ågren, "Effects of π centers and symmetry on two-photon absorption cross sections of organic chromophores," J. Chem. Phys. 114, 9813-9820 (2001).
[Crossref]

P. Macak, Y. Luo, P. Norman, and H. Ågren, "Electronic and vibronic contributions to two-photon absorption of molecules with multibranched structures," J. Chem. Phys. 113, 7055-7061 (2000).
[Crossref]

Albota, M.

M. Albota, D. Beijonne, 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. Rockel, 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]

Arnold, J. M.

R. W. Ziolkowski, J. M. Arnold, and D. M. Gobny, "Ultrafast pulse interactions with two-level atoms," Phys. Rev. A 52, 3082-3093 (1995).
[Crossref] [PubMed]

Baev, A.

G. S. He, Q. D. Zheng, A. Baev, and P. N. Prasad, "Saturation of multiphoton absorption upon strong and ultrafast infrared laser excitation," J. Appl. Phys. 101, 083108 (2007).
[Crossref]

G. S. He, C. G. Lu, Q. D. Zheng, A. Baev, M. Samoc, and P. N. Prasad, "Asymmetric properties between the forward and backward stimulated emission generated by ultrafast three- and four-photon excitation," Phys. Rev. A 73, 033815 (2006).
[Crossref]

A. Baev, F. Gel'mukhanov, P. Macak, H. Ågren, and Y. Luo, "General theory for pulse propagation in two-photon active media," J. Chem. Phys. 117, 6214-6220 (2002).
[Crossref]

F. Gel'mukhanov, A. Baev, P. Macak, Y. Luo, and H. Ågren, "Dynamics of two-photon absorption by molecules and solutions," J. Opt. Soc. Am. A 19, 937-945 (2002)..
[Crossref]

Baev, Alexander

V. Kimberg, S. Polyutov, F. Gel'mukhanov, H. Ågren, Alexander Baev, Q. D. Zheng, and G. S. He, "Dynamics of cavityless lasing generated by ultrafast multiphoton excitation," Phys. Rev. A 74, 033814 (2006).
[Crossref]

Baum, P.

P. Baum, S. Lochbrunner, and E. Riedle, "Generation of tunable 7 fs ultraviolet pulses: achromatic phase matching and chirp management," Appl. Phys. B 79, 1027-2032 (2004).
[Crossref]

Beijonne, D.

M. Albota, D. Beijonne, 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. Rockel, 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]

Beljonne, D.

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]

Bhatt, J. C.

Bhawalkar, J. D.

G. S. He, L. X. Yuan, N. Cheng, J. D. Bhawalkar, P. N. Prasad, L. L. Brott, S. J. Clarson, and B. A. Reinhardt, "Nonlinear optical properties of a new chromophore," J. Opt. Soc. Am. B 14, 1079-1087 (1997).
[Crossref]

J. D. Bhawalkar, G. S. He, and P. N. Prasad, "Nonlinear multiphoton processes in organic and polymeric materials," Rep. Prog. Phys. 59, 1041-1070 (1996).
[Crossref]

G. S. He, J. D. Bhawalkar, C. F. Zhao, C. K. Park, and P. N. Prasad, "Up-conversion dye-doped polymer fiber laser," Appl. Phys. Lett. 68, 3549-3551 (1996).
[Crossref]

Boggess, T. F.

L. W. Tutt and T. F. Boggess, "A review of optical limiting mechanisms and devices using organics, fullerence, semiconductors, and other materials," Prog. Quantum Electron. 17, 299-338 (1993).
[Crossref]

Brédas, J. L.

M. Albota, D. Beijonne, 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. Rockel, 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]

Brott, L. L.

Cao, D. X.

Z. Q. Liu, Q. Fang, D. X. Cao, D. Wang, and G. B. Xu, "Triaryl boron-based A-π-A versus triaryl nitrogen-based D-π-D quadrupolar compounds for single- and two-photon excited fluorescence," Org. Lett. 17, 2933-2936 (2004).
[Crossref]

Cheng, N.

Cho, C. C.

G. S. He, T. C. Lin, P. N. Prasad, C. C. Cho, and L. J. Yu, "Optical power limiting and stabilization using a two-photon absorbing neat liquid crystal in isotropic phase," Appl. Phys. Lett. 82, 4717-4719 (2003).
[Crossref]

Clarson, S. J.

Cronstrand, P.

P. Cronstrand, Y. Luo, and H. Ågren, "Generalized few-state models for two-photon absorption of conjugated molecules," Chem. Phys. Lett. 352, 262-269 (2002).
[Crossref]

Dillard, A. G.

Ehrlich, J. E.

M. Albota, D. Beijonne, 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. Rockel, 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]

Fang, Q.

Z. Q. Liu, Q. Fang, D. X. Cao, D. Wang, and G. B. Xu, "Triaryl boron-based A-π-A versus triaryl nitrogen-based D-π-D quadrupolar compounds for single- and two-photon excited fluorescence," Org. Lett. 17, 2933-2936 (2004).
[Crossref]

Frisch, M. J.

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G. S. He, J. D. Bhawalkar, C. F. Zhao, C. K. Park, and P. N. Prasad, "Up-conversion dye-doped polymer fiber laser," Appl. Phys. Lett. 68, 3549-3551 (1996).
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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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[Crossref]

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G. S. He, L. X. Yuan, N. Cheng, J. D. Bhawalkar, P. N. Prasad, L. L. Brott, S. J. Clarson, and B. A. Reinhardt, "Nonlinear optical properties of a new chromophore," J. Opt. Soc. Am. B 14, 1079-1087 (1997).
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Riedle, E.

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Song, X. H.

X. H. Song, S. Q. Gong, S. Q. Jin, and Z. Z. Xu, "Formation of higher spectral components in a two-level medium driven by two-color ultrashort laser pulses," Phys. Rev. A 69, 015801 (2004).
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C. K. Wang, K. Zhao, Y. Su, X. Zhao, and Y. Luo, "Solvent effects on the electronic structure of a newly synthesized two-photon polymerization initiator," J. Chem. Phys. 119, 1208-1213 (2003).
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M. Albota, D. Beijonne, 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. Rockel, 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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K. Zhao, J. C. Liu, C. K. Wang, and Y. Luo, "Modulation of supercontinuum generation and formation of an attosecond pulse from a generalized two-level medium," J. Phys. B 40, 1523-1534 (2007).
[Crossref]

N. Lin, X. Zhao, J. X. Yang, M. H. Jiang, J. C. Liu, C. K. Wang, W. Shi, J. Meng, and J. Weng, "Theoretical study of one-, two-, and three-photon absorption properties for a series of Y-shaped molecules," J. Chem. Phys. 124, 024704 (2006).
[Crossref] [PubMed]

K. Zhao, H. Y. Li, J. C. Liu, C. K. Wang, and Y. Luo, "Dipolar effects on propagation of ultrashort laser pulse in one-dimensional para-nitroaniline (pNA) molecules," J. Phys. B 38, 4235-4245 (2005).
[Crossref]

Y. Su, Y. H. Wang, and C. K. Wang, "The solvent effect on two-photon absorption of 4,4′-bis (dimethylamino) stilbene," Acta Opt. Sin. 23, 646-650 (2003).

C. K. Wang, K. Zhao, Y. Su, X. Zhao, and Y. Luo, "Solvent effects on the electronic structure of a newly synthesized two-photon polymerization initiator," J. Chem. Phys. 119, 1208-1213 (2003).
[Crossref]

C. K. Wang, P. Macak, Y. Luo, and H. Ågren, "Effects of π centers and symmetry on two-photon absorption cross sections of organic chromophores," J. Chem. Phys. 114, 9813-9820 (2001).
[Crossref]

Wang, D.

Z. Q. Liu, Q. Fang, D. X. Cao, D. Wang, and G. B. Xu, "Triaryl boron-based A-π-A versus triaryl nitrogen-based D-π-D quadrupolar compounds for single- and two-photon excited fluorescence," Org. Lett. 17, 2933-2936 (2004).
[Crossref]

Wang, J.

Q. Wang, C. L. Liu, J. Wang, X. Y. Zhao, and Z. Z. Zha, "The experimental study on two-photon absorption and optical limiting of 4,4′-bis(dimethylamino) stilbene at 532 nm," Acta Opt. Sin. 20, 286-287 (2000).

Wang, Q.

Q. Wang, C. L. Liu, J. Wang, X. Y. Zhao, and Z. Z. Zha, "The experimental study on two-photon absorption and optical limiting of 4,4′-bis(dimethylamino) stilbene at 532 nm," Acta Opt. Sin. 20, 286-287 (2000).

Wang, Y. H.

Y. Su, Y. H. Wang, and C. K. Wang, "The solvent effect on two-photon absorption of 4,4′-bis (dimethylamino) stilbene," Acta Opt. Sin. 23, 646-650 (2003).

Wang, Z. Y.

J. Xiao, Z. Y. Wang, and Z. Z. Xu, "Area evolution of a few-cycle pulse laser in a two-level-atom medium," Phys. Rev. A 65, 031402 (2002).
[Crossref]

Webb, W. W.

M. Albota, D. Beijonne, 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. Rockel, 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]

Weng, J.

N. Lin, X. Zhao, J. X. Yang, M. H. Jiang, J. C. Liu, C. K. Wang, W. Shi, J. Meng, and J. Weng, "Theoretical study of one-, two-, and three-photon absorption properties for a series of Y-shaped molecules," J. Chem. Phys. 124, 024704 (2006).
[Crossref] [PubMed]

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S. Hughes and B. Wherrett, "Multilevel rate-equation analysis to explain the recent observations of limitations to optical limiting dyes," Phys. Rev. A 54, 3546-3552 (1996).
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W. F. Sun, Z. X. Wu, Q. Z. Yang, L. Z. Wu, and C. H. Tung, "Reverse saturable absorption of platinum ter/bipyridyl polyphenylacetylide complexes," Appl. Phys. Lett. 82, 850-852 (2003).
[Crossref]

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M. Albota, D. Beijonne, 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. Rockel, 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]

Wu, Z. X.

W. F. Sun, Z. X. Wu, Q. Z. Yang, L. Z. Wu, and C. H. Tung, "Reverse saturable absorption of platinum ter/bipyridyl polyphenylacetylide complexes," Appl. Phys. Lett. 82, 850-852 (2003).
[Crossref]

Xiao, J.

J. Xiao, Z. Y. Wang, and Z. Z. Xu, "Area evolution of a few-cycle pulse laser in a two-level-atom medium," Phys. Rev. A 65, 031402 (2002).
[Crossref]

Xu, C.

M. Albota, D. Beijonne, 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. Rockel, 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]

Xu, G. B.

Z. Q. Liu, Q. Fang, D. X. Cao, D. Wang, and G. B. Xu, "Triaryl boron-based A-π-A versus triaryl nitrogen-based D-π-D quadrupolar compounds for single- and two-photon excited fluorescence," Org. Lett. 17, 2933-2936 (2004).
[Crossref]

Xu, G. C.

Xu, Z. Z.

X. H. Song, S. Q. Gong, S. Q. Jin, and Z. Z. Xu, "Formation of higher spectral components in a two-level medium driven by two-color ultrashort laser pulses," Phys. Rev. A 69, 015801 (2004).
[Crossref]

J. Xiao, Z. Y. Wang, and Z. Z. Xu, "Area evolution of a few-cycle pulse laser in a two-level-atom medium," Phys. Rev. A 65, 031402 (2002).
[Crossref]

Yang, J. X.

N. Lin, X. Zhao, J. X. Yang, M. H. Jiang, J. C. Liu, C. K. Wang, W. Shi, J. Meng, and J. Weng, "Theoretical study of one-, two-, and three-photon absorption properties for a series of Y-shaped molecules," J. Chem. Phys. 124, 024704 (2006).
[Crossref] [PubMed]

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W. F. Sun, Z. X. Wu, Q. Z. Yang, L. Z. Wu, and C. H. Tung, "Reverse saturable absorption of platinum ter/bipyridyl polyphenylacetylide complexes," Appl. Phys. Lett. 82, 850-852 (2003).
[Crossref]

Yang, Weitao

Chengteh Lee, Weitao Yang, and Robert G. Parr, "Development of the Colle-Salvetti correlation-energy formula into a functional of the electron," Phys. Rev. B 37, 785-789 (1988).
[Crossref]

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G. S. He, T. C. Lin, P. N. Prasad, C. C. Cho, and L. J. Yu, "Optical power limiting and stabilization using a two-photon absorbing neat liquid crystal in isotropic phase," Appl. Phys. Lett. 82, 4717-4719 (2003).
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Yuan, L. X.

Zha, Z. Z.

Q. Wang, C. L. Liu, J. Wang, X. Y. Zhao, and Z. Z. Zha, "The experimental study on two-photon absorption and optical limiting of 4,4′-bis(dimethylamino) stilbene at 532 nm," Acta Opt. Sin. 20, 286-287 (2000).

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G. S. He, J. D. Bhawalkar, C. F. Zhao, C. K. Park, and P. N. Prasad, "Up-conversion dye-doped polymer fiber laser," Appl. Phys. Lett. 68, 3549-3551 (1996).
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K. Zhao, J. C. Liu, C. K. Wang, and Y. Luo, "Modulation of supercontinuum generation and formation of an attosecond pulse from a generalized two-level medium," J. Phys. B 40, 1523-1534 (2007).
[Crossref]

K. Zhao, H. Y. Li, J. C. Liu, C. K. Wang, and Y. Luo, "Dipolar effects on propagation of ultrashort laser pulse in one-dimensional para-nitroaniline (pNA) molecules," J. Phys. B 38, 4235-4245 (2005).
[Crossref]

C. K. Wang, K. Zhao, Y. Su, X. Zhao, and Y. Luo, "Solvent effects on the electronic structure of a newly synthesized two-photon polymerization initiator," J. Chem. Phys. 119, 1208-1213 (2003).
[Crossref]

Zhao, X.

N. Lin, X. Zhao, J. X. Yang, M. H. Jiang, J. C. Liu, C. K. Wang, W. Shi, J. Meng, and J. Weng, "Theoretical study of one-, two-, and three-photon absorption properties for a series of Y-shaped molecules," J. Chem. Phys. 124, 024704 (2006).
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C. K. Wang, K. Zhao, Y. Su, X. Zhao, and Y. Luo, "Solvent effects on the electronic structure of a newly synthesized two-photon polymerization initiator," J. Chem. Phys. 119, 1208-1213 (2003).
[Crossref]

Zhao, X. Y.

Q. Wang, C. L. Liu, J. Wang, X. Y. Zhao, and Z. Z. Zha, "The experimental study on two-photon absorption and optical limiting of 4,4′-bis(dimethylamino) stilbene at 532 nm," Acta Opt. Sin. 20, 286-287 (2000).

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[Crossref]

V. Kimberg, S. Polyutov, F. Gel'mukhanov, H. Ågren, Alexander Baev, Q. D. Zheng, and G. S. He, "Dynamics of cavityless lasing generated by ultrafast multiphoton excitation," Phys. Rev. A 74, 033814 (2006).
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Q. Wang, C. L. Liu, J. Wang, X. Y. Zhao, and Z. Z. Zha, "The experimental study on two-photon absorption and optical limiting of 4,4′-bis(dimethylamino) stilbene at 532 nm," Acta Opt. Sin. 20, 286-287 (2000).

Y. Su, Y. H. Wang, and C. K. Wang, "The solvent effect on two-photon absorption of 4,4′-bis (dimethylamino) stilbene," Acta Opt. Sin. 23, 646-650 (2003).

Appl. Phys. B (1)

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G. S. He, J. D. Bhawalkar, C. F. Zhao, C. K. Park, and P. N. Prasad, "Up-conversion dye-doped polymer fiber laser," Appl. Phys. Lett. 68, 3549-3551 (1996).
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W. F. Sun, Z. X. Wu, Q. Z. Yang, L. Z. Wu, and C. H. Tung, "Reverse saturable absorption of platinum ter/bipyridyl polyphenylacetylide complexes," Appl. Phys. Lett. 82, 850-852 (2003).
[Crossref]

G. S. He, T. C. Lin, P. N. Prasad, C. C. Cho, and L. J. Yu, "Optical power limiting and stabilization using a two-photon absorbing neat liquid crystal in isotropic phase," Appl. Phys. Lett. 82, 4717-4719 (2003).
[Crossref]

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P. Cronstrand, Y. Luo, and H. Ågren, "Generalized few-state models for two-photon absorption of conjugated molecules," Chem. Phys. Lett. 352, 262-269 (2002).
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G. S. He, Q. D. Zheng, A. Baev, and P. N. Prasad, "Saturation of multiphoton absorption upon strong and ultrafast infrared laser excitation," J. Appl. Phys. 101, 083108 (2007).
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[Crossref]

K. Zhao, J. C. Liu, C. K. Wang, and Y. Luo, "Modulation of supercontinuum generation and formation of an attosecond pulse from a generalized two-level medium," J. Phys. B 40, 1523-1534 (2007).
[Crossref]

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Z. Q. Liu, Q. Fang, D. X. Cao, D. Wang, and G. B. Xu, "Triaryl boron-based A-π-A versus triaryl nitrogen-based D-π-D quadrupolar compounds for single- and two-photon excited fluorescence," Org. Lett. 17, 2933-2936 (2004).
[Crossref]

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[Crossref]

G. S. He, C. G. Lu, Q. D. Zheng, A. Baev, M. Samoc, and P. N. Prasad, "Asymmetric properties between the forward and backward stimulated emission generated by ultrafast three- and four-photon excitation," Phys. Rev. A 73, 033815 (2006).
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J. Xiao, Z. Y. Wang, and Z. Z. Xu, "Area evolution of a few-cycle pulse laser in a two-level-atom medium," Phys. Rev. A 65, 031402 (2002).
[Crossref]

X. H. Song, S. Q. Gong, S. Q. Jin, and Z. Z. Xu, "Formation of higher spectral components in a two-level medium driven by two-color ultrashort laser pulses," Phys. Rev. A 69, 015801 (2004).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Evolution of electric fields as propagation distances with different input peak amplitudes F 0 , (i) 2.5 × 10 7 V cm , (ii) 4.0 × 10 7 V cm , and (iii) 5.5 × 10 7 V cm with the pulse widths fixed to be 5 fs .

Fig. 2
Fig. 2

Population difference ρ 11 ρ 33 at 0.014 μ m induced by the 5 fs pulses with three different input peak amplitudes of fields.

Fig. 3
Fig. 3

Output peak amplitude F out at z = 7.0 μ m versus the input peak amplitude F 0 of the 5 fs pulses. The short-dot curve is guided for the case without absorption of the medium.

Fig. 4
Fig. 4

Output single pulse energy fluence A out ( mJ cm 2 ) versus input single pulse energy fluence A in ( mJ cm 2 ) , for 5 fs pulse at propagation distances 7.0 μ m (square) and 10.5 μ m (circle), and for 15 fs pulse at propagation distance 7.0 μ m (triangle). The short-dot curve is guided for the case without absorption of the medium.

Fig. 5
Fig. 5

Inverse transmission as a function of the input peak intensity for 5, 10, 15, and 20 fs pulses at propagation distance 7.0 μ m . Symbols show results of strict numerical simulations. The solid curves denote the fit according to Eq. (7) with β = β 0 = const for obtaining the TPA cross section. The fit based on linear dependence of β on intensity [Eq. (9)] for the 5 fs pulse is depicted by dashed curve ( β 0 = 7.6 × 10 9 cm W , ξ = 2.58 × 10 21 cm 3 W 2 ).

Fig. 6
Fig. 6

Dependence of TPA cross section σ tp on pulse width τ p and the propagation distance.

Equations (18)

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

ρ ̇ m n = i [ H , ρ ] m n γ m n ( ρ m n ρ m n 0 ) ,
u 1 t = ω 21 v 1 + E ( μ 22 μ 11 ) v 1 + E ( μ 23 v 3 + μ 13 v 2 ) γ 12 ( u 1 u 1 0 ) ,
v 1 t = ω 21 u 1 E ( μ 22 μ 11 ) u 1 E ( μ 23 u 3 μ 13 u 2 ) 2 E μ 12 ( ρ 11 ρ 22 ) γ 12 ( v 1 v 1 0 ) ,
u 2 t = ω 32 v 2 + E ( μ 33 μ 22 ) v 2 E ( μ 13 v 1 + μ 12 v 3 ) γ 23 ( u 2 u 2 0 ) ,
v 2 t = ω 32 u 2 E ( μ 33 μ 22 ) u 2 E ( μ 13 u 1 μ 12 u 3 ) 2 E μ 23 ( ρ 22 ρ 33 ) γ 23 ( v 2 v 2 0 ) ,
u 3 t = ω 31 v 3 + E ( μ 33 μ 11 ) v 3 + E ( μ 23 v 1 μ 12 v 2 ) γ 13 ( u 3 u 3 0 ) ,
v 3 t = ω 31 u 3 E ( μ 33 μ 11 ) u 3 E ( μ 23 u 1 μ 12 u 2 ) 2 E μ 23 ( ρ 11 ρ 33 ) γ 13 ( v 3 v 3 0 ) ,
ρ 11 t = E ( μ 12 v 1 + μ 13 v 3 ) γ 11 ( ρ 11 ρ 11 0 ) ,
ρ 22 t = E ( μ 12 v 1 μ 23 v 2 ) γ 22 ( ρ 22 ρ 22 0 ) ,
ρ 33 t = E ( μ 13 v 3 + μ 23 v 2 ) γ 33 ( ρ 33 ρ 33 0 ) ,
E x z = μ 0 H y t ,
H y z = P x t ε 0 E x t ,
P x = N μ ̂ x = N tr ( μ ̂ x ρ ̂ ) ,
d I d z + α I + β I 2 = 0 ,
I ( z ) = α I ( 0 ) exp ( α z ) α + β I ( 0 ) ( 1 exp ( α z ) ) .
1 T ( z ) = I ( 0 ) I ( z ) = exp ( α z ) + [ exp ( α z ) 1 ] β I ( 0 ) α ,
h ν β = σ tp N ,
β = β 0 ξ I ( 0 ) ,

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