Abstract

A theory is developed for the propagation through a nonlinear medium of strong pump and amplified-spontaneous-emission pulses. The theory is based on a solution of the density matrix equations that aims at providing an adequate treatment of the nonlinear polarization of the material without addressing the Taylor expansion over the powers of intensity. The theory has been applied for modeling of three-photon absorption induced upconverted stimulated emission of organic molecules in solvents. Numerical results are presented for the organic chromophore 4-[N-(2-hydroxyethyl)-N-(methyl)amino phenyl]-4-(6-hydroxyhexyl sulfonyl) stilbene dissolved in dimethyl sulfoxide. The results are in good agreement with available experimental results.

© 2004 Optical Society of America

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2003 (1)

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]

2002 (5)

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]

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]

N. Mitkova Dushkina and B. Ullrich, “Intensity dependence of two-photon absorption in CdS measured by photoluminescence excited by femtosecond laser pulses,” Opt. Eng. 41, 2365–2368 (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]

B. N. Jagatap and W. J. Meath, “Contributions of permanent dipole moments to molecular multiphoton excitation cross sections,” J. Opt. Soc. Am. B 19, 2673–2681 (2002).
[CrossRef]

2001 (1)

Y. Luo, P. Macak, P. Norman, C. K. Wang, and H. Ågren, “Ab initio calculations of structure-to-property relations for two-photon absorption of organic molecules,” Nonlinear Opt. 27, 33–46 (2001).

2000 (3)

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]

P. Macak, Y. Luo, and H. Ågren, “Simulations of vibronic profiles in two-photon absorption,” Chem. Phys. Lett. 330, 447–456 (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]

1997 (2)

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]

A. Kummrow, A. Lau, and K. Lenz, “Time-resolved study of ultrafast dephasing processes in solution,” Phys. Rev. A 55, 2310–2320 (1997).
[CrossRef]

1996 (2)

F. Emmerling, M. Lettenberger, and A. Laubereau, “Vibrational dynamics of anthracene in liquid solution studied by picosecond IR/UV spectroscopy with polarization resolution,” J. Phys. Chem. 100, 19, 251–19, 256 (1996).
[CrossRef]

P. Norman, D. Jonsson, O. Vahtras, and H. Ågren, “Non-linear electric and magnetic properties obtained from cubic response functions in the random phase approximation,” J. Chem. Phys. 203, 23–42 (1996).

1992 (1)

M. K. Lawless and R. A. Mathies, “Excited state structure and electronic dephasing time of Nile Blue from absolute resonance Raman intensities,” J. Chem. Phys. 96, 8037–8045 (1992).
[CrossRef]

1991 (1)

J.-Y. Bigot, M. T. Portella, R. W. Schoenlein, C. J. Bardeen, A. Migus, and C. V. Shank, “Non-Markovian dephasing of molecules in solution measured with 3-pulses femtosecond photon echoes,” Phys. Rev. Lett. 66, 1138–1141 (1991).
[CrossRef] [PubMed]

1990 (1)

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

1989 (2)

D. A. Parthenopoulos and P. M. Rentzepis, “3-dimensional optical storage memory,” Science 245, 843–845 (1989).
[CrossRef] [PubMed]

P. C. Becker, H. L. Fragnito, J.-Y. Bigot, C. H. Brito Cruz, R. L. Fork, and C. V. Shank, “Femtosecond photon-echoes from molecules in solution,” Phys. Rev. Lett. 63, 505–507 (1989).
[CrossRef] [PubMed]

1982 (1)

B. Dick and G. Hohlneicher, “Importance of initial and final states as intermediate states in 2-photon spectroscopy of polar molecules,” J. Chem. Phys. 76, 5755–5760 (1982).
[CrossRef]

Ågren, H.

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]

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]

Y. Luo, P. Macak, P. Norman, C. K. Wang, and H. Ågren, “Ab initio calculations of structure-to-property relations for two-photon absorption of organic molecules,” Nonlinear Opt. 27, 33–46 (2001).

P. Macak, Y. Luo, and H. Ågren, “Simulations of vibronic profiles in two-photon absorption,” Chem. Phys. Lett. 330, 447–456 (2000).
[CrossRef]

P. Norman, D. Jonsson, O. Vahtras, and H. Ågren, “Non-linear electric and magnetic properties obtained from cubic response functions in the random phase approximation,” J. Chem. Phys. 203, 23–42 (1996).

Baev, A.

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]

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]

Bardeen, C. J.

J.-Y. Bigot, M. T. Portella, R. W. Schoenlein, C. J. Bardeen, A. Migus, and C. V. Shank, “Non-Markovian dephasing of molecules in solution measured with 3-pulses femtosecond photon echoes,” Phys. Rev. Lett. 66, 1138–1141 (1991).
[CrossRef] [PubMed]

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]

Becker, P. C.

P. C. Becker, H. L. Fragnito, J.-Y. Bigot, C. H. Brito Cruz, R. L. Fork, and C. V. Shank, “Femtosecond photon-echoes from molecules in solution,” Phys. Rev. Lett. 63, 505–507 (1989).
[CrossRef] [PubMed]

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]

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).
[PubMed]

Bigot, J.-Y.

J.-Y. Bigot, M. T. Portella, R. W. Schoenlein, C. J. Bardeen, A. Migus, and C. V. Shank, “Non-Markovian dephasing of molecules in solution measured with 3-pulses femtosecond photon echoes,” Phys. Rev. Lett. 66, 1138–1141 (1991).
[CrossRef] [PubMed]

P. C. Becker, H. L. Fragnito, J.-Y. Bigot, C. H. Brito Cruz, R. L. Fork, and C. V. Shank, “Femtosecond photon-echoes from molecules in solution,” Phys. Rev. Lett. 63, 505–507 (1989).
[CrossRef] [PubMed]

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).
[CrossRef]

Brito Cruz, C. H.

P. C. Becker, H. L. Fragnito, J.-Y. Bigot, C. H. Brito Cruz, R. L. Fork, and C. V. Shank, “Femtosecond photon-echoes from molecules in solution,” Phys. Rev. Lett. 63, 505–507 (1989).
[CrossRef] [PubMed]

Denk, W.

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

Dick, B.

B. Dick and G. Hohlneicher, “Importance of initial and final states as intermediate states in 2-photon spectroscopy of polar molecules,” J. Chem. Phys. 76, 5755–5760 (1982).
[CrossRef]

Dushkina, N. Mitkova

N. Mitkova Dushkina and B. Ullrich, “Intensity dependence of two-photon absorption in CdS measured by photoluminescence excited by femtosecond laser pulses,” Opt. Eng. 41, 2365–2368 (2002).
[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]

Emmerling, F.

F. Emmerling, M. Lettenberger, and A. Laubereau, “Vibrational dynamics of anthracene in liquid solution studied by picosecond IR/UV spectroscopy with polarization resolution,” J. Phys. Chem. 100, 19, 251–19, 256 (1996).
[CrossRef]

Fork, R. L.

P. C. Becker, H. L. Fragnito, J.-Y. Bigot, C. H. Brito Cruz, R. L. Fork, and C. V. Shank, “Femtosecond photon-echoes from molecules in solution,” Phys. Rev. Lett. 63, 505–507 (1989).
[CrossRef] [PubMed]

Fragnito, H. L.

P. C. Becker, H. L. Fragnito, J.-Y. Bigot, C. H. Brito Cruz, R. L. Fork, and C. V. Shank, “Femtosecond photon-echoes from molecules in solution,” Phys. Rev. Lett. 63, 505–507 (1989).
[CrossRef] [PubMed]

Gel’mukhanov, F.

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]

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]

He, G. S.

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]

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]

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]

Hohlneicher, G.

B. Dick and G. Hohlneicher, “Importance of initial and final states as intermediate states in 2-photon spectroscopy of polar molecules,” J. Chem. Phys. 76, 5755–5760 (1982).
[CrossRef]

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]

Jagatap, B. N.

Jiang, Y.

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]

Jonsson, D.

P. Norman, D. Jonsson, O. Vahtras, and H. Ågren, “Non-linear electric and magnetic properties obtained from cubic response functions in the random phase approximation,” J. Chem. Phys. 203, 23–42 (1996).

Kannan, R.

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]

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]

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]

Kummrow, A.

A. Kummrow, A. Lau, and K. Lenz, “Time-resolved study of ultrafast dephasing processes in solution,” Phys. Rev. A 55, 2310–2320 (1997).
[CrossRef]

Lau, A.

A. Kummrow, A. Lau, and K. Lenz, “Time-resolved study of ultrafast dephasing processes in solution,” Phys. Rev. A 55, 2310–2320 (1997).
[CrossRef]

Laubereau, A.

F. Emmerling, M. Lettenberger, and A. Laubereau, “Vibrational dynamics of anthracene in liquid solution studied by picosecond IR/UV spectroscopy with polarization resolution,” J. Phys. Chem. 100, 19, 251–19, 256 (1996).
[CrossRef]

Lawless, M. K.

M. K. Lawless and R. A. Mathies, “Excited state structure and electronic dephasing time of Nile Blue from absolute resonance Raman intensities,” J. Chem. Phys. 96, 8037–8045 (1992).
[CrossRef]

Lenz, K.

A. Kummrow, A. Lau, and K. Lenz, “Time-resolved study of ultrafast dephasing processes in solution,” Phys. Rev. A 55, 2310–2320 (1997).
[CrossRef]

Lettenberger, M.

F. Emmerling, M. Lettenberger, and A. Laubereau, “Vibrational dynamics of anthracene in liquid solution studied by picosecond IR/UV spectroscopy with polarization resolution,” J. Phys. Chem. 100, 19, 251–19, 256 (1996).
[CrossRef]

Lin, T.-C.

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.

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]

Y. Luo, P. Macak, P. Norman, C. K. Wang, and H. Ågren, “Ab initio calculations of structure-to-property relations for two-photon absorption of organic molecules,” Nonlinear Opt. 27, 33–46 (2001).

P. Macak, Y. Luo, and H. Ågren, “Simulations of vibronic profiles in two-photon absorption,” Chem. Phys. Lett. 330, 447–456 (2000).
[CrossRef]

Macak, P.

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]

Y. Luo, P. Macak, P. Norman, C. K. Wang, and H. Ågren, “Ab initio calculations of structure-to-property relations for two-photon absorption of organic molecules,” Nonlinear Opt. 27, 33–46 (2001).

P. Macak, Y. Luo, and H. Ågren, “Simulations of vibronic profiles in two-photon absorption,” Chem. Phys. Lett. 330, 447–456 (2000).
[CrossRef]

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]

Markowicz, P. P.

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]

Mathies, R. A.

M. K. Lawless and R. A. Mathies, “Excited state structure and electronic dephasing time of Nile Blue from absolute resonance Raman intensities,” J. Chem. Phys. 96, 8037–8045 (1992).
[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]

Meath, W. J.

Migus, A.

J.-Y. Bigot, M. T. Portella, R. W. Schoenlein, C. J. Bardeen, A. Migus, and C. V. Shank, “Non-Markovian dephasing of molecules in solution measured with 3-pulses femtosecond photon echoes,” Phys. Rev. Lett. 66, 1138–1141 (1991).
[CrossRef] [PubMed]

Norman, P.

Y. Luo, P. Macak, P. Norman, C. K. Wang, and H. Ågren, “Ab initio calculations of structure-to-property relations for two-photon absorption of organic molecules,” Nonlinear Opt. 27, 33–46 (2001).

P. Norman, D. Jonsson, O. Vahtras, and H. Ågren, “Non-linear electric and magnetic properties obtained from cubic response functions in the random phase approximation,” J. Chem. Phys. 203, 23–42 (1996).

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]

Parthenopoulos, D. A.

D. A. Parthenopoulos and P. M. Rentzepis, “3-dimensional optical storage memory,” Science 245, 843–845 (1989).
[CrossRef] [PubMed]

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]

Portella, M. T.

J.-Y. Bigot, M. T. Portella, R. W. Schoenlein, C. J. Bardeen, A. Migus, and C. V. Shank, “Non-Markovian dephasing of molecules in solution measured with 3-pulses femtosecond photon echoes,” Phys. Rev. Lett. 66, 1138–1141 (1991).
[CrossRef] [PubMed]

Prasad, P. N.

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]

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]

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]

Reinhardt, B. A.

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]

Rentzepis, P. M.

D. A. Parthenopoulos and P. M. Rentzepis, “3-dimensional optical storage memory,” Science 245, 843–845 (1989).
[CrossRef] [PubMed]

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]

Schoenlein, R. W.

J.-Y. Bigot, M. T. Portella, R. W. Schoenlein, C. J. Bardeen, A. Migus, and C. V. Shank, “Non-Markovian dephasing of molecules in solution measured with 3-pulses femtosecond photon echoes,” Phys. Rev. Lett. 66, 1138–1141 (1991).
[CrossRef] [PubMed]

Shank, C. V.

J.-Y. Bigot, M. T. Portella, R. W. Schoenlein, C. J. Bardeen, A. Migus, and C. V. Shank, “Non-Markovian dephasing of molecules in solution measured with 3-pulses femtosecond photon echoes,” Phys. Rev. Lett. 66, 1138–1141 (1991).
[CrossRef] [PubMed]

P. C. Becker, H. L. Fragnito, J.-Y. Bigot, C. H. Brito Cruz, R. L. Fork, and C. V. Shank, “Femtosecond photon-echoes from molecules in solution,” Phys. Rev. Lett. 63, 505–507 (1989).
[CrossRef] [PubMed]

Strickler, J. H.

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

Swiatkiewicz, J.

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]

Tan, L.-S.

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]

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]

Ullrich, B.

N. Mitkova Dushkina and B. Ullrich, “Intensity dependence of two-photon absorption in CdS measured by photoluminescence excited by femtosecond laser pulses,” Opt. Eng. 41, 2365–2368 (2002).
[CrossRef]

Vahtras, O.

P. Norman, D. Jonsson, O. Vahtras, and H. Ågren, “Non-linear electric and magnetic properties obtained from cubic response functions in the random phase approximation,” J. Chem. Phys. 203, 23–42 (1996).

Wang, C. K.

Y. Luo, P. Macak, P. Norman, C. K. Wang, and H. Ågren, “Ab initio calculations of structure-to-property relations for two-photon absorption of organic molecules,” Nonlinear Opt. 27, 33–46 (2001).

Webb, W. W.

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

Zhao, C. F.

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]

Chem. Phys. Lett. (1)

P. Macak, Y. Luo, and H. Ågren, “Simulations of vibronic profiles in two-photon absorption,” Chem. Phys. Lett. 330, 447–456 (2000).
[CrossRef]

J. Am. Chem. Soc. (1)

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]

J. Chem. Phys. (4)

P. Norman, D. Jonsson, O. Vahtras, and H. Ågren, “Non-linear electric and magnetic properties obtained from cubic response functions in the random phase approximation,” J. Chem. Phys. 203, 23–42 (1996).

M. K. Lawless and R. A. Mathies, “Excited state structure and electronic dephasing time of Nile Blue from absolute resonance Raman intensities,” J. Chem. Phys. 96, 8037–8045 (1992).
[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]

B. Dick and G. Hohlneicher, “Importance of initial and final states as intermediate states in 2-photon spectroscopy of polar molecules,” J. Chem. Phys. 76, 5755–5760 (1982).
[CrossRef]

J. Clin. Laser Med. Surg. (1)

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]

J. Opt. Soc. Am. B (2)

J. Phys. B (1)

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]

J. Phys. Chem. (1)

F. Emmerling, M. Lettenberger, and A. Laubereau, “Vibrational dynamics of anthracene in liquid solution studied by picosecond IR/UV spectroscopy with polarization resolution,” J. Phys. Chem. 100, 19, 251–19, 256 (1996).
[CrossRef]

J. Phys. Chem. A (1)

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]

Nature (1)

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]

Nonlinear Opt. (1)

Y. Luo, P. Macak, P. Norman, C. K. Wang, and H. Ågren, “Ab initio calculations of structure-to-property relations for two-photon absorption of organic molecules,” Nonlinear Opt. 27, 33–46 (2001).

Opt. Eng. (1)

N. Mitkova Dushkina and B. Ullrich, “Intensity dependence of two-photon absorption in CdS measured by photoluminescence excited by femtosecond laser pulses,” Opt. Eng. 41, 2365–2368 (2002).
[CrossRef]

Phys. Rev. A (1)

A. Kummrow, A. Lau, and K. Lenz, “Time-resolved study of ultrafast dephasing processes in solution,” Phys. Rev. A 55, 2310–2320 (1997).
[CrossRef]

Phys. Rev. Lett. (2)

P. C. Becker, H. L. Fragnito, J.-Y. Bigot, C. H. Brito Cruz, R. L. Fork, and C. V. Shank, “Femtosecond photon-echoes from molecules in solution,” Phys. Rev. Lett. 63, 505–507 (1989).
[CrossRef] [PubMed]

J.-Y. Bigot, M. T. Portella, R. W. Schoenlein, C. J. Bardeen, A. Migus, and C. V. Shank, “Non-Markovian dephasing of molecules in solution measured with 3-pulses femtosecond photon echoes,” Phys. Rev. Lett. 66, 1138–1141 (1991).
[CrossRef] [PubMed]

Science (2)

D. A. Parthenopoulos and P. M. Rentzepis, “3-dimensional optical storage memory,” Science 245, 843–845 (1989).
[CrossRef] [PubMed]

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

Other (5)

“Two-photon excitation in laser scanning fluorescence microscopy,” in CAN-AM Eastern ’90, R. L. Antos and A. J. Krisiloff, eds., Proc. SPIE 1398, 107–117 (1991).

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

S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford U. Press, New York, 1995).

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T. Helgaker, H. J. Aa. Jensen, P. Jørgensen, J. Olsen, K. Ruud, H. Ågren, T. Andersen, K. L. Bak, V. Bakken, O. Christiansen, P. Dahle, E. K. Dalskov, T. Enevoldsen, H. Heiberg, H. Hettema, D. Jonsson, S. Kirpekar, R. Kobayashi, H. Koch, K. V. Mikkelsen, P. Norman, M. J. Packer, T. Saue, P. R. Taylor, and O. Vahtras, Dalton, an ab initio electronic structure program (release 1.0, 1997), http://www.kjemi.uio.no/software/dalton/dalton.html.

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Figures (9)

Fig. 1
Fig. 1

Structures of the APSS and the reduced molecule.

Fig. 2
Fig. 2

Energy-level diagram.

Fig. 3
Fig. 3

Propagation of the pump pulse through a nonlinear medium of APSS molecules in solution. Initial intensity, 190 GW/cm2; pulse duration (FWHM), 2 ps; wavelength, 1.3 µm; sample length, 10 mm. Input data are collected in Table 3, simulation a.

Fig. 4
Fig. 4

Transmission [Eq. (28)] versus input pump intensity: A, Γ=0.01 eV, parameters from Table 3, simulation a; B, Γ=0.1 eV, parameters from Table 3, simulation f.

Fig. 5
Fig. 5

Propagation of the ASE pulse in the nonlinear medium of APSS molecules in solution. Maximum generated intensity at the end edge, ∼60 MW/cm2; pulse duration, ∼22 ps; wavelength, 553 nm. Input data are collected in Table 3, simulation a. Arrows indicate propagation directions of the ASE front.

Fig. 6
Fig. 6

A, Temporal profiles of ASE intensity Iμ, gain g, and inversion r33-r22 for three values of z. B, same as A on an enlarged scale for z=2 mm. Input parameters are from Table 3, simulation a.

Fig. 7
Fig. 7

Populations r33, r44, and r55 in various points of the medium z. Input data from Table 3, simulation a. r22r33 within graphic accuracy. 3 marks r33 for another set of FC factors (Table 3, simulation d).

Fig. 8
Fig. 8

Temporal distributions of transmitted pump intensity, the ASE intensity, and the inversion at the end edge of the medium, z=1 cm. Top, I0=1.9 GW/cm2; bottom, I0=190 GW/cm2. Inset, temporal profiles of ASE intensity and the gain. Input data are collected in Table 3, simulation a.

Fig. 9
Fig. 9

Change of speed of the gain propagation (dashed curve) and temporal shift Δt (32, solid curve) for I0=1.9 and I0=190 GW/cm2.

Tables (4)

Tables Icon

Table 1 Transition and Permanent Dipole Moments (atomic units) and Excitation Energies, ωe (electron volts), for the APSS Molecule and a Reduced Molecule Calculated at the TD-B3LYP/6-31G** Level

Tables Icon

Table 2 Input Data for Simulations of ASEa

Tables Icon

Table 3 Basic Results of Simulationsa

Tables Icon

Table 4 Excitation Energies of Final State ωe, Third-Order Transition Moment Tzzz, and Three-Photon Probability δ3PL Calculated at the Self-Consistent Field Level with the 6-31G and 6-31G* Basis Setsa

Equations (52)

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

E=E2 exp(-ιωt+ιkz)+Eμ2 exp(-ιωμt+ιkμz-ιφ)+c.c.,
P=Tr(dρ)=βα dβα(t)ραβ=P exp(-ιωt+ιkz)+Pμ exp(-ιωμt+ιkμz-ιφ)+c.c.
z+1ct-ι2kΔE=ιkε0 P,
z+1ct-ι2kμΔEμ=ιkμε0 Pμ.
t+Γˆρ=ι[ρ, V],Tr ρ=[N],V=E·d,
t+Γαβραβ=δα,βγ>αΓγαργγ+ι γ(ραγVγβ-Vαγργβ).
Γαα=β(<α) Γαβ.
1Vαβ=exp(ιωαβt)(Gαβ[exp(-ιωt)+exp(ιωt)]+Gαβμ{exp[-ι(ωμt+φ)]+exp[ι(ωμt+φ)]}).
ραβ=exp(ιωαβt)rαβ+n=1[rαβ(n) exp(-ιnωt)+rβα(n)* exp(ιnωt)]+ηαβ exp[ι(ωμt+φ)]+ηβα*exp[-ι(ωμ+φ)t].
t+ιωαβ+Γαβrαβ
=δαβγ(>α) Γγαrγγ+ιγ{[rαγ(1)+rγα(1)*]Gγβ-Gαγ[rγβ(1)+rβγ(1)*]},
t+ι(ωαβ-ω)+Γαβrαβ(1)
=δαβγ(>α) Γγαrγγ(1)+ιγ{[rαγ+rαγ(2)]Gγβ-Gαγ[rγβ+rγβ(2)]},
t+ι(ωαβ-nω)+Γαβrαβ(n)
=δαβγ(>α) Γγαrγγ(n)+ιγ{[rαγ(n-1)+rαγ(n+1)]Gγβ-Gαγ[rγβ(n-1)+rγβ(n+1)]}.
t-ι(ωμ+φ˙-ωαβ)+Γαβηαβ
ιγ(rαγGγβμ-Gαγμrγβ).
rβα(n)*(-ω)=rαβ(n)(ω),
ηβα*(-ω, -ωμ)=ηαβ(ω, ωμ).
α rαα=N,α rαα(n)=0,n1.
τΓαβ-1,1ω,1|ωαβ|,1(ωαβ2+Γαβ2)1/2.
trαβ=0,αβ;trαβ(n)=0.
ηαβ
ιrαβ(Gββμ-Gααμ)+γ(β) rαγGγβμ-γ(α) GαγμrγβΓαβ-ι(ωμ+φ˙-ωαβ).
P=βα dβαrαβ(1),Pμ=βα dβαηαβ.
z+1ct-ι2kΔE=ιkε0 βα dβαrαβ(1),
z+1ct-ι2kΔEμ=ιkε0 βα dβαηαβ.
z+1ctI=2ω Im βα G˜βαrαβ(1),
z+1ctIμ=gIμ,
g=2ωμIμ-1 Im βα G˜βαμηαβ.
ηαβ=12π02π dφηαβ(φ)1ni=0n-1 ηαβ(φi),
dSiν,Sjν=dSi,Sjν|ν.
Γ51=0.20×1011,Γ52=0.30×1011,
Γ53=0.50×1011,Γ54=9.00×1011,
Γ41=1.66×108,Γ42=1.66×108,
Γ43=3.30×1010,
Γ31=0.01×109,Γ32=1.39×109,
Γ21=2.50×1011.
t+Γααrαα=β>α Γβαrββ+Wα+Wαμ.
Wα=2 Im β[Gαβrβα(1)-rαβ(1)Gβα],
Wαμ=2 Im β[Gαβμηβα-ηαβGβαμ].
γ=12LI02/I2-1I02,σ(3)=γN,
Tabc= Pa,b,c n,m0|μa|mm|μb|nn|μc|f(ωm-2ωf/3)(ωn-ωf/3),
γ=Nπ-12c2ε03λδ3pLΓαβ,δ3PL=135(2δF+3δG),
δF=ijk TiijTkkj,δG=ijk TijkTijk,
l3pl1p1.23×10-2190GW/cm2I2Γ0.01eV29.25DdS1S04
T=J(L)J(0),J(z)= I(z, t)dt,
gkμε0(r33-r22)d322Γ-(r11-r44)d412ΓΩμ2+Γ2.
IthωΓ44Nσ(3)r33τΓ431/3,
Iμ(t*, z)=Iμ(t*, 0)exp[S(t*, z)],
S(t*, z)=0zg[t¯*(z1), z1]dz1,t*=t-zc.
Δt(z)zΔc(z)c2.

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