Abstract

A semiclassical dynamic theory of the nonlinear propagation of a few interacting intense light pulses is applied to study the nonlinear counterpropagation of amplified spontaneous emission (ASE) induced by three-photon absorption of short intense laser pulses in a chromophore solution. Several important results from the modeling are reached for the ASE process developing in the regime of strong saturation. Accounting for ASE in both forward and backward directions with respect to the pump pulse results in a smaller efficiency of nonlinear conversion for the forward ASE compared with the case in which forward emission is considered alone, something that results from the partial repump of the absorbed energy to the backward ASE component; the overall efficiency is nevertheless higher than for the forward emission considered alone. The efficiency of nonlinear conversion of the pump energy to the counterpropagating ASE pulses is strongly dependent on the concentration of active molecules so that a particular combination of concentration versus cell length optimizes the conversion coefficient. Under certain specified conditions, the ASE effect is found to be oscillatory; the origin of oscillations is dynamical competition between stimulated emission and off-resonant absorption. This result can be considered one of the possible explanations of the temporal fluctuations of the forward ASE pulse [Nature 415, 767 (2002)].

© 2005 Optical Society of America

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  1. G. S. He and P. N. Prasad, "Three-photon absorbing materials: characterization and applications," in Nonlinear Optical Transmission and Multiphoton Processes in Organics, A. T. Yeates, K. D. Belfield, F. Kajzar, and C. M. Lawson, eds., Proc. SPIE 5211, 1-12 (2003).
    [CrossRef]
  2. G. S. He, P. P. Markowicz, T.-C. Lin, and P. N. Prasad, "Observation of stimulated emission by direct three-photon excitation," Nature 415, 767-770 (2002).
    [CrossRef] [PubMed]
  3. G. S. He, J. Dai, T.-C. Lin, P. P. Markowicz, and P. N. Prasad, "Ultrashort 1.5-µm laser excited upconverted stimulated emission based on simultaneous three-photon absorption," Opt. Lett. 28, 719-721 (2003).
    [CrossRef] [PubMed]
  4. G. S. He, R. Helgeson, T.-C. Lin, Q. Zheng, F. Wudl, and P. N. Prasad, "One-, two-, and three-photon pumped lasing in a novel liquid dye salt system," IEEE J. Quantum Electron. 39, 1003-1008 (2003).
    [CrossRef]
  5. B. A. Reinhardt, "Two-photon technology: new materials and evolving applications," Photonics Sci. News 4, 21-33 (1999).
  6. A. Baev, F. Gel'mukhanov, O. Rubio-Pons, P. Cronstrand, and H. Ågren, "Upconverted lasing based on many-photon absorption: an all dynamic description," J. Opt. Soc. Am. B 21, 384-396 (2004).
    [CrossRef]
  7. A. Baev, F. Gel'mukhanov, V. Kimberg, and H. Ågren, "Nonlinear propagation of strong multi-mode fields," J. Phys. B 36, 3761-3774 (2003).
    [CrossRef]
  8. A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley, Reading, Mass., 1992).
  9. 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. B 19, 937-945 (2002).
    [CrossRef]
  10. A. Baev, F. Gel'mukhanov, P. Macak, Y. Luo, and H. Ågren, "General theory for pulse propagation in two-photon active media," J. Chem. Phys. 117, 6214-6220 (2002).
    [CrossRef]
  11. M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

2004

2003

G. S. He and P. N. Prasad, "Three-photon absorbing materials: characterization and applications," in Nonlinear Optical Transmission and Multiphoton Processes in Organics, A. T. Yeates, K. D. Belfield, F. Kajzar, and C. M. Lawson, eds., Proc. SPIE 5211, 1-12 (2003).
[CrossRef]

G. S. He, R. Helgeson, T.-C. Lin, Q. Zheng, F. Wudl, and P. N. Prasad, "One-, two-, and three-photon pumped lasing in a novel liquid dye salt system," IEEE J. Quantum Electron. 39, 1003-1008 (2003).
[CrossRef]

A. Baev, F. Gel'mukhanov, V. Kimberg, and H. Ågren, "Nonlinear propagation of strong multi-mode fields," J. Phys. B 36, 3761-3774 (2003).
[CrossRef]

G. S. He, J. Dai, T.-C. Lin, P. P. Markowicz, and P. N. Prasad, "Ultrashort 1.5-µm laser excited upconverted stimulated emission based on simultaneous three-photon absorption," Opt. Lett. 28, 719-721 (2003).
[CrossRef] [PubMed]

2002

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. B 19, 937-945 (2002).
[CrossRef]

A. Baev, F. Gel'mukhanov, P. Macak, Y. Luo, and H. Ågren, "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.-C. Lin, and P. N. Prasad, "Observation of stimulated emission by direct three-photon excitation," Nature 415, 767-770 (2002).
[CrossRef] [PubMed]

1999

B. A. Reinhardt, "Two-photon technology: new materials and evolving applications," Photonics Sci. News 4, 21-33 (1999).

1998

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Ågren, H.

A. Baev, F. Gel'mukhanov, O. Rubio-Pons, P. Cronstrand, and H. Ågren, "Upconverted lasing based on many-photon absorption: an all dynamic description," J. Opt. Soc. Am. B 21, 384-396 (2004).
[CrossRef]

A. Baev, F. Gel'mukhanov, V. Kimberg, and H. Ågren, "Nonlinear propagation of strong multi-mode fields," J. Phys. B 36, 3761-3774 (2003).
[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. B 19, 937-945 (2002).
[CrossRef]

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

Albota, M.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Baev, A.

A. Baev, F. Gel'mukhanov, O. Rubio-Pons, P. Cronstrand, and H. Ågren, "Upconverted lasing based on many-photon absorption: an all dynamic description," J. Opt. Soc. Am. B 21, 384-396 (2004).
[CrossRef]

A. Baev, F. Gel'mukhanov, V. Kimberg, and H. Ågren, "Nonlinear propagation of strong multi-mode fields," J. Phys. B 36, 3761-3774 (2003).
[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. B 19, 937-945 (2002).
[CrossRef]

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

Beljonne, D.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Bredas, J. L.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Cronstrand, P.

Dai, J.

Ehrlich, J. E.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Fu, J. Y.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Gel'mukhanov, F.

A. Baev, F. Gel'mukhanov, O. Rubio-Pons, P. Cronstrand, and H. Ågren, "Upconverted lasing based on many-photon absorption: an all dynamic description," J. Opt. Soc. Am. B 21, 384-396 (2004).
[CrossRef]

A. Baev, F. Gel'mukhanov, V. Kimberg, and H. Ågren, "Nonlinear propagation of strong multi-mode fields," J. Phys. B 36, 3761-3774 (2003).
[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. B 19, 937-945 (2002).
[CrossRef]

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

He, G. S.

He , G. S.

G. S. He and P. N. Prasad, "Three-photon absorbing materials: characterization and applications," in Nonlinear Optical Transmission and Multiphoton Processes in Organics, A. T. Yeates, K. D. Belfield, F. Kajzar, and C. M. Lawson, eds., Proc. SPIE 5211, 1-12 (2003).
[CrossRef]

He, G. S.

G. S. He, R. Helgeson, T.-C. Lin, Q. Zheng, F. Wudl, and P. N. Prasad, "One-, two-, and three-photon pumped lasing in a novel liquid dye salt system," IEEE J. Quantum Electron. 39, 1003-1008 (2003).
[CrossRef]

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

Heikal, A. A.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Helgeson, R.

G. S. He, R. Helgeson, T.-C. Lin, Q. Zheng, F. Wudl, and P. N. Prasad, "One-, two-, and three-photon pumped lasing in a novel liquid dye salt system," IEEE J. Quantum Electron. 39, 1003-1008 (2003).
[CrossRef]

Hess, S. E.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Kimberg, V.

A. Baev, F. Gel'mukhanov, V. Kimberg, and H. Ågren, "Nonlinear propagation of strong multi-mode fields," J. Phys. B 36, 3761-3774 (2003).
[CrossRef]

Kogej, T.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Levin, M. D.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Lin, T.-C.

G. S. He, J. Dai, T.-C. Lin, P. P. Markowicz, and P. N. Prasad, "Ultrashort 1.5-µm laser excited upconverted stimulated emission based on simultaneous three-photon absorption," Opt. Lett. 28, 719-721 (2003).
[CrossRef] [PubMed]

G. S. He, R. Helgeson, T.-C. Lin, Q. Zheng, F. Wudl, and P. N. Prasad, "One-, two-, and three-photon pumped lasing in a novel liquid dye salt system," IEEE J. Quantum Electron. 39, 1003-1008 (2003).
[CrossRef]

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

Luo, Y.

A. Baev, F. Gel'mukhanov, P. Macak, Y. Luo, and H. Ågren, "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. B 19, 937-945 (2002).
[CrossRef]

Macak, P.

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. B 19, 937-945 (2002).
[CrossRef]

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

Marder, S. R.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Markowicz, P. P.

McCord-Maughon, D.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Perry, J. W.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Prasad, P. N.

G. S. He, J. Dai, T.-C. Lin, P. P. Markowicz, and P. N. Prasad, "Ultrashort 1.5-µm laser excited upconverted stimulated emission based on simultaneous three-photon absorption," Opt. Lett. 28, 719-721 (2003).
[CrossRef] [PubMed]

G. S. He, R. Helgeson, T.-C. Lin, Q. Zheng, F. Wudl, and P. N. Prasad, "One-, two-, and three-photon pumped lasing in a novel liquid dye salt system," IEEE J. Quantum Electron. 39, 1003-1008 (2003).
[CrossRef]

G. S. He and P. N. Prasad, "Three-photon absorbing materials: characterization and applications," in Nonlinear Optical Transmission and Multiphoton Processes in Organics, A. T. Yeates, K. D. Belfield, F. Kajzar, and C. M. Lawson, eds., Proc. SPIE 5211, 1-12 (2003).
[CrossRef]

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

Reinhardt, B. A.

B. A. Reinhardt, "Two-photon technology: new materials and evolving applications," Photonics Sci. News 4, 21-33 (1999).

Rockel, H.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Rubio-Pons, O.

Rumi, M.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Subramaniam, C.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Webb, W. W.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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, X. L.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Wudl, F.

G. S. He, R. Helgeson, T.-C. Lin, Q. Zheng, F. Wudl, and P. N. Prasad, "One-, two-, and three-photon pumped lasing in a novel liquid dye salt system," IEEE J. Quantum Electron. 39, 1003-1008 (2003).
[CrossRef]

Xu, C.

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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]

Zheng, Q.

G. S. He, R. Helgeson, T.-C. Lin, Q. Zheng, F. Wudl, and P. N. Prasad, "One-, two-, and three-photon pumped lasing in a novel liquid dye salt system," IEEE J. Quantum Electron. 39, 1003-1008 (2003).
[CrossRef]

IEEE J. Quantum Electron.

G. S. He, R. Helgeson, T.-C. Lin, Q. Zheng, F. Wudl, and P. N. Prasad, "One-, two-, and three-photon pumped lasing in a novel liquid dye salt system," IEEE J. Quantum Electron. 39, 1003-1008 (2003).
[CrossRef]

J. Chem. Phys.

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

J. Opt. Soc. Am. B

J. Phys. B

A. Baev, F. Gel'mukhanov, V. Kimberg, and H. Ågren, "Nonlinear propagation of strong multi-mode fields," J. Phys. B 36, 3761-3774 (2003).
[CrossRef]

Nature

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

Opt. Lett.

Photonics Sci. News

B. A. Reinhardt, "Two-photon technology: new materials and evolving applications," Photonics Sci. News 4, 21-33 (1999).

Proc. SPIE

G. S. He and P. N. Prasad, "Three-photon absorbing materials: characterization and applications," in Nonlinear Optical Transmission and Multiphoton Processes in Organics, A. T. Yeates, K. D. Belfield, F. Kajzar, and C. M. Lawson, eds., Proc. SPIE 5211, 1-12 (2003).
[CrossRef]

Science

M. Albota, D. Beljonne, J. L. Bredas, 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, C. 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

A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley, Reading, Mass., 1992).

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Figures (12)

Fig. 1
Fig. 1

Energy-level diagram.

Fig. 2
Fig. 2

Conversion coefficient versus concentration. “Right” means simulations for the one-component case and “overall” means simulations for both forward and backward components.

Fig. 3
Fig. 3

Temporal distributions of the (A) R-component intensity at the end of the cell at different concentrations and (B) L-component intensity at the entrance to the cell at different concentrations.

Fig. 4
Fig. 4

ASE intensity dynamics.

Fig. 5
Fig. 5

Three-dimensional dependencies of the R-component intensity under different concentrations: (A) 1×1019 cm-3, (B) 2×1019 cm-3, and (C) 3×1019 cm-3.

Fig. 6
Fig. 6

Illustration of a narrow gain propagation—formation of the L and R components of the ASE.

Fig. 7
Fig. 7

Snapshots of the (A) gain and (B) single R component at different time instants.

Fig. 8
Fig. 8

Snapshots of the (A) gain and (B) and (C) R and L components at different time instants.

Fig. 9
Fig. 9

Simplified model of the ASE.

Fig. 10
Fig. 10

Model oscillations of the ASE at the end of the 10-mm cell for different values of concentration: (A) 1×1019 cm-3, (B) 5×1018 cm-3, and (C) 1×1018 cm-3.

Fig. 11
Fig. 11

Equipotential lines of the frequency, Re Ω.

Fig. 12
Fig. 12

Frequency of the (A) ASE oscillations and (B) damping rate versus the stimulated emission rate at a given α.

Tables (1)

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Table 1 Basic Results of Simulationsa

Equations (19)

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E=ER2 exp(-ιωRt+ιkRz-ιϕR)+EL2×exp(-ιωLt-ιkLz-ιφL)+c.c.,
P=Tr(dρ)=PR exp(-ιωRt+ιkRz-ιφR)+PL exp(-ιωLt-ιkLz-ιφL)+c.c.,
z+1c t-ι2kRΔER=ιkRε0 PR,
-z+1c t-ι2kLΔEL=ιkLε0 PL,
t+Γˆρ=ι[ρ, V],Tr ρ=N,
t+Γαβραβ=δα,βγ>αΓγαργγ+ι γ×(ραγVγβ-Vαγργβ),
ηαβμιγ(rαγGγβμ-Gαγμrγβ)Γαβ-ι(ωμ-ωαβ),μ=L, R,
z+1c t-ι2kRΔER=ιkRε0 βαdβαηαβR,
-z+1c t-ι2kLΔEL=ιkLε0 βαdβαηαβL.
z+1c tIR=ωR Im(ER)*βαdβαηαβR,
-z+1c tIL=ωL Im(EL)*βαdβαηαβL,
t+Γααrαα=β>αΓβαrββ+Wα+WαR+WαL.
Wα=2 Im β[Gαβrβα(1,0)-rαβ(1,0)Gβα],
Wαμ=2 Im β[Gαβμηβαμ-ηαβμGβαμ],
t+Γ1ρ1=ΓNN-pI(ρ1-ρ0),
t+Γ0ρ0=Γ1ρ1+pI(ρ1-ρ0),
z+1c tI=[B(ρ1-ρ0)-α]I=gI.
Ω3-ιΩ2(Γ0+Γ1+2pI)-Ω[Γ0Γ1+(2α¯+Γ0)pI]
+ια¯pIΓ0=0,

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