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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  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]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2007

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

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

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

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

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

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

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

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

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]

1997

1996

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

1993

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

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

1988

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]

Acta Opt. Sin.

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

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]

Appl. Phys. Lett.

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]

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]

Chem. Phys. Lett.

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]

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]

J. Appl. Phys.

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]

J. Chem. Phys.

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]

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]

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]

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]

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]

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. 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]

J. Opt. Soc. Am. A

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]

J. Opt. Soc. Am. B

J. Phys. B

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]

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]

Nature

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]

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

Opt. Express

Opt. Lett.

Org. Lett.

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]

Phys. Rev. A

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]

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]

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]

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]

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

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]

Phys. Rev. B

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]

Prog. Quantum Electron.

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]

Rep. Prog. Phys.

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]

Science

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]

Other

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

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

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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)

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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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