Abstract

We report a theoretical investigation of effective four-photon absorption (4PA) process and propose a two-step 4PA model of three-photon-induced excited-state absorption (ESA). Based on three-level rate-equation theory, we find an analytical result for the effective 4PA coefficient that depends on the three-photon absorption (3PA) cross-section, excited-state photophysical properties, and laser pulse duration. We present the analytical theory of the z-dependent nonlinear transmission for straightforwardly yet unambiguously evaluating the 3PA and effective 4PA coefficients simultaneously.

© 2008 Optical Society of America

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  1. D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, "Watersoluble quantum dots for multiphoton fluorescence imaging in vivo," Science 300, 1434 (2003).
    [CrossRef] [PubMed]
  2. G. S. He, P. P. Markowicz, T. C. Lin, and P. N. Prasad, "Observation of stimulated emission by direct three-photon excitation," Nature (London) 415, 767 (2002).
    [CrossRef] [PubMed]
  3. S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, "Finer features for functional microdevices-Micromachines can be created with higher resolution using two-photon absorption," Nature (London) 412, 697 (2001).
    [CrossRef] [PubMed]
  4. G. S. He, K. T. Yong, Q. Zheng, Y. Sahoo, A. Baev, A. I. Ryasnyanskiy, and P. N. Prasad, "Multi-photon excitation properties of CdSe quantum dots solutions and optical limiting behavior in infrared range," Opt. Express 15, 12818 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-20-21818>
    [CrossRef] [PubMed]
  5. D. A. Parthenopoulos and P. M. Rentzepis, "Three-dimensional optical storage memory," Science 245, 843 (1989).
    [CrossRef] [PubMed]
  6. J. D. Bhawalkar, G. S. He, and P. N. Prasad, "Nonlinear multiphoton processes in organic and polymeric materials," Rep. Prog. Phys. 59, 1041 (1996).
    [CrossRef]
  7. Q1. D. S. Correa, L. De Boni, D. T. Balogh, and C. R. Mendonca, "Three- and four-photon excitation of poly(2-methoxy-5-(2�??-ethylhexyloxy)-1,4-phenylenevinylene)(MEH-PPV)," Adv. Mater. 19, 2653 (2007).
    [CrossRef]
  8. F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, "Observation of three-photon enhanced four-photon absorption," Phys. Rev. Lett. 91, 063902 (2003).
    [CrossRef] [PubMed]
  9. H. Matsuda, Y. Fujimoto, S. Ito, Y. Nagasawa, H. Miyasaka, T. Asahi, and H. Masuhara, "Development of nearinfrared 35 fs laser microscope and its application to the detection of three- and four-photon fluorescence of organic microcrystals," J. Phys. Chem. B 110, 1091 (2006).
    [CrossRef] [PubMed]
  10. S. Delysse, P. Filloux, V. Dumarcher, C. Fiorini, and J. M. Nunzi, "Multiphoton absorption in organic dye solutions," Opt. Mater. 9, 347 (1998).
    [CrossRef]
  11. C. G. Lu, Y. P. Cui, W. Huang, B. F. Yun, Z. Y. Wang, G. H. Hu, J. Cui, Z. F. Lu, and Y. Qian, "Vibrational resonance enhanced broadband multiphoton absorption in a triphenylamine derivatives," Appl. Phys. Lett. 91, 121111 (2007).
    [CrossRef]
  12. G. S. He, L. S. Tan, Q. D. Zheng, and P. N. Prasad, "Multiphoton absorbing materials: molecular designs, characterizations, and applications," Chem. Rev. 108, 1245 (2008).
    [CrossRef] [PubMed]
  13. A. Penzkofer and W. Falkenstein, "Three-photon absorption and subsequent excited-state absorption in CdS," Opt. Commun. 16, 247 (1976).
    [CrossRef]
  14. E. Parilov and M. J. Potasek, "Generalized theoretical treatment and numerical method of time-resolved radially dependent laser pulses interacting with multiphoton absorbers," J. Opt. Soc. Am B 23, 1894 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=josab-23-9-1894>
    [CrossRef]
  15. R. L. Sutherland, M. C. Brant, J. Heinrichs, J. E. Slagle, D. G. McLean, and P. A. Fleitz, "Excitedstate characterization and effective three-photon absorption model of two-photon-induced excited-state absorption in organic push-pull charge-transfer chromophores," J. Opt. Soc. Am. B 22, 1939 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=josab-22-9-1939>.
    [CrossRef]
  16. Y. Gao and M. J. Potasek, "Effects of excited-state absorption on two-photon absorbing materials," Appl. Opt. 45, 2521 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=ao-45-11-2521>
    [CrossRef] [PubMed]
  17. M. Fakis, G. Tsigaridas, I. Polyzos, V. Giannetas, P. Persphonis, I. Spiliopoulos, J. Mikroyannidis, "Intensity dependent nonlinear absorption of pyrylium chromophores," Chem. Phys. Lett. 342, 155 (2001).
    [CrossRef]
  18. B. Gu, W. Ji, P. S. Patil, S. M. Dharmaprakash, and H. T. Wang, "Two-photon-induced excited-state absorption: Theory and experiment," Appl. Phys. Lett. 92, 091118 (2008).
    [CrossRef]
  19. B. Gu, W. Ji, P. S. Patil, and S. M. Dharmaprakash, "Ultrafast optical nonlinearities and figures of merit in acceptor-substituted 3,4,5-trimethoxy chalcone derivatives: Structure-property relationships," J. Appl. Phys. 103, 103511 (2008).
    [CrossRef]
  20. M. I. Demchuk, V. S. Konevskii, N. V. Kuleshov, V. P. Mikhailov, P. V. Prokoshin, and K. V. Yumashev, "Nonlinear transmission, ultrafast relaxation and three-photon absorption in reduced SrTiO3," Opt. Commun. 82, 273 (1991).
    [CrossRef]
  21. D. S. Correa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonca, "Z-scan theoretical analysis for three-, four- and five-photon absorption," Opt. Commun. 277, 440 (2007).
    [CrossRef]

2008

G. S. He, L. S. Tan, Q. D. Zheng, and P. N. Prasad, "Multiphoton absorbing materials: molecular designs, characterizations, and applications," Chem. Rev. 108, 1245 (2008).
[CrossRef] [PubMed]

B. Gu, W. Ji, P. S. Patil, S. M. Dharmaprakash, and H. T. Wang, "Two-photon-induced excited-state absorption: Theory and experiment," Appl. Phys. Lett. 92, 091118 (2008).
[CrossRef]

B. Gu, W. Ji, P. S. Patil, and S. M. Dharmaprakash, "Ultrafast optical nonlinearities and figures of merit in acceptor-substituted 3,4,5-trimethoxy chalcone derivatives: Structure-property relationships," J. Appl. Phys. 103, 103511 (2008).
[CrossRef]

2007

D. S. Correa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonca, "Z-scan theoretical analysis for three-, four- and five-photon absorption," Opt. Commun. 277, 440 (2007).
[CrossRef]

Q1. D. S. Correa, L. De Boni, D. T. Balogh, and C. R. Mendonca, "Three- and four-photon excitation of poly(2-methoxy-5-(2�??-ethylhexyloxy)-1,4-phenylenevinylene)(MEH-PPV)," Adv. Mater. 19, 2653 (2007).
[CrossRef]

C. G. Lu, Y. P. Cui, W. Huang, B. F. Yun, Z. Y. Wang, G. H. Hu, J. Cui, Z. F. Lu, and Y. Qian, "Vibrational resonance enhanced broadband multiphoton absorption in a triphenylamine derivatives," Appl. Phys. Lett. 91, 121111 (2007).
[CrossRef]

G. S. He, K. T. Yong, Q. Zheng, Y. Sahoo, A. Baev, A. I. Ryasnyanskiy, and P. N. Prasad, "Multi-photon excitation properties of CdSe quantum dots solutions and optical limiting behavior in infrared range," Opt. Express 15, 12818 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-20-21818>
[CrossRef] [PubMed]

2006

Y. Gao and M. J. Potasek, "Effects of excited-state absorption on two-photon absorbing materials," Appl. Opt. 45, 2521 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=ao-45-11-2521>
[CrossRef] [PubMed]

H. Matsuda, Y. Fujimoto, S. Ito, Y. Nagasawa, H. Miyasaka, T. Asahi, and H. Masuhara, "Development of nearinfrared 35 fs laser microscope and its application to the detection of three- and four-photon fluorescence of organic microcrystals," J. Phys. Chem. B 110, 1091 (2006).
[CrossRef] [PubMed]

E. Parilov and M. J. Potasek, "Generalized theoretical treatment and numerical method of time-resolved radially dependent laser pulses interacting with multiphoton absorbers," J. Opt. Soc. Am B 23, 1894 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=josab-23-9-1894>
[CrossRef]

2005

2003

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, "Watersoluble quantum dots for multiphoton fluorescence imaging in vivo," Science 300, 1434 (2003).
[CrossRef] [PubMed]

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, "Observation of three-photon enhanced four-photon absorption," Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

2002

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

2001

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, "Finer features for functional microdevices-Micromachines can be created with higher resolution using two-photon absorption," Nature (London) 412, 697 (2001).
[CrossRef] [PubMed]

M. Fakis, G. Tsigaridas, I. Polyzos, V. Giannetas, P. Persphonis, I. Spiliopoulos, J. Mikroyannidis, "Intensity dependent nonlinear absorption of pyrylium chromophores," Chem. Phys. Lett. 342, 155 (2001).
[CrossRef]

1998

S. Delysse, P. Filloux, V. Dumarcher, C. Fiorini, and J. M. Nunzi, "Multiphoton absorption in organic dye solutions," Opt. Mater. 9, 347 (1998).
[CrossRef]

1996

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

1991

M. I. Demchuk, V. S. Konevskii, N. V. Kuleshov, V. P. Mikhailov, P. V. Prokoshin, and K. V. Yumashev, "Nonlinear transmission, ultrafast relaxation and three-photon absorption in reduced SrTiO3," Opt. Commun. 82, 273 (1991).
[CrossRef]

1989

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

1976

A. Penzkofer and W. Falkenstein, "Three-photon absorption and subsequent excited-state absorption in CdS," Opt. Commun. 16, 247 (1976).
[CrossRef]

Asahi, T.

H. Matsuda, Y. Fujimoto, S. Ito, Y. Nagasawa, H. Miyasaka, T. Asahi, and H. Masuhara, "Development of nearinfrared 35 fs laser microscope and its application to the detection of three- and four-photon fluorescence of organic microcrystals," J. Phys. Chem. B 110, 1091 (2006).
[CrossRef] [PubMed]

Baev, A.

Bhawalkar, J. D.

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

Brant, M. C.

Bruchez, M. P.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, "Watersoluble quantum dots for multiphoton fluorescence imaging in vivo," Science 300, 1434 (2003).
[CrossRef] [PubMed]

Clark, S. W.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, "Watersoluble quantum dots for multiphoton fluorescence imaging in vivo," Science 300, 1434 (2003).
[CrossRef] [PubMed]

Cui, J.

C. G. Lu, Y. P. Cui, W. Huang, B. F. Yun, Z. Y. Wang, G. H. Hu, J. Cui, Z. F. Lu, and Y. Qian, "Vibrational resonance enhanced broadband multiphoton absorption in a triphenylamine derivatives," Appl. Phys. Lett. 91, 121111 (2007).
[CrossRef]

Cui, Y. P.

C. G. Lu, Y. P. Cui, W. Huang, B. F. Yun, Z. Y. Wang, G. H. Hu, J. Cui, Z. F. Lu, and Y. Qian, "Vibrational resonance enhanced broadband multiphoton absorption in a triphenylamine derivatives," Appl. Phys. Lett. 91, 121111 (2007).
[CrossRef]

Delysse, S.

S. Delysse, P. Filloux, V. Dumarcher, C. Fiorini, and J. M. Nunzi, "Multiphoton absorption in organic dye solutions," Opt. Mater. 9, 347 (1998).
[CrossRef]

Demchuk, M. I.

M. I. Demchuk, V. S. Konevskii, N. V. Kuleshov, V. P. Mikhailov, P. V. Prokoshin, and K. V. Yumashev, "Nonlinear transmission, ultrafast relaxation and three-photon absorption in reduced SrTiO3," Opt. Commun. 82, 273 (1991).
[CrossRef]

Dharmaprakash, S. M.

B. Gu, W. Ji, P. S. Patil, and S. M. Dharmaprakash, "Ultrafast optical nonlinearities and figures of merit in acceptor-substituted 3,4,5-trimethoxy chalcone derivatives: Structure-property relationships," J. Appl. Phys. 103, 103511 (2008).
[CrossRef]

B. Gu, W. Ji, P. S. Patil, S. M. Dharmaprakash, and H. T. Wang, "Two-photon-induced excited-state absorption: Theory and experiment," Appl. Phys. Lett. 92, 091118 (2008).
[CrossRef]

Dumarcher, V.

S. Delysse, P. Filloux, V. Dumarcher, C. Fiorini, and J. M. Nunzi, "Multiphoton absorption in organic dye solutions," Opt. Mater. 9, 347 (1998).
[CrossRef]

Fakis, M.

M. Fakis, G. Tsigaridas, I. Polyzos, V. Giannetas, P. Persphonis, I. Spiliopoulos, J. Mikroyannidis, "Intensity dependent nonlinear absorption of pyrylium chromophores," Chem. Phys. Lett. 342, 155 (2001).
[CrossRef]

Falkenstein, W.

A. Penzkofer and W. Falkenstein, "Three-photon absorption and subsequent excited-state absorption in CdS," Opt. Commun. 16, 247 (1976).
[CrossRef]

Filloux, P.

S. Delysse, P. Filloux, V. Dumarcher, C. Fiorini, and J. M. Nunzi, "Multiphoton absorption in organic dye solutions," Opt. Mater. 9, 347 (1998).
[CrossRef]

Fiorini, C.

S. Delysse, P. Filloux, V. Dumarcher, C. Fiorini, and J. M. Nunzi, "Multiphoton absorption in organic dye solutions," Opt. Mater. 9, 347 (1998).
[CrossRef]

Fleitz, P. A.

Fujimoto, Y.

H. Matsuda, Y. Fujimoto, S. Ito, Y. Nagasawa, H. Miyasaka, T. Asahi, and H. Masuhara, "Development of nearinfrared 35 fs laser microscope and its application to the detection of three- and four-photon fluorescence of organic microcrystals," J. Phys. Chem. B 110, 1091 (2006).
[CrossRef] [PubMed]

Gao, Y.

Giannetas, V.

M. Fakis, G. Tsigaridas, I. Polyzos, V. Giannetas, P. Persphonis, I. Spiliopoulos, J. Mikroyannidis, "Intensity dependent nonlinear absorption of pyrylium chromophores," Chem. Phys. Lett. 342, 155 (2001).
[CrossRef]

Gu, B.

B. Gu, W. Ji, P. S. Patil, and S. M. Dharmaprakash, "Ultrafast optical nonlinearities and figures of merit in acceptor-substituted 3,4,5-trimethoxy chalcone derivatives: Structure-property relationships," J. Appl. Phys. 103, 103511 (2008).
[CrossRef]

B. Gu, W. Ji, P. S. Patil, S. M. Dharmaprakash, and H. T. Wang, "Two-photon-induced excited-state absorption: Theory and experiment," Appl. Phys. Lett. 92, 091118 (2008).
[CrossRef]

He, G. S.

G. S. He, L. S. Tan, Q. D. Zheng, and P. N. Prasad, "Multiphoton absorbing materials: molecular designs, characterizations, and applications," Chem. Rev. 108, 1245 (2008).
[CrossRef] [PubMed]

G. S. He, K. T. Yong, Q. Zheng, Y. Sahoo, A. Baev, A. I. Ryasnyanskiy, and P. N. Prasad, "Multi-photon excitation properties of CdSe quantum dots solutions and optical limiting behavior in infrared range," Opt. Express 15, 12818 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-20-21818>
[CrossRef] [PubMed]

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

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

Heinrichs, J.

Hu, G. H.

C. G. Lu, Y. P. Cui, W. Huang, B. F. Yun, Z. Y. Wang, G. H. Hu, J. Cui, Z. F. Lu, and Y. Qian, "Vibrational resonance enhanced broadband multiphoton absorption in a triphenylamine derivatives," Appl. Phys. Lett. 91, 121111 (2007).
[CrossRef]

Huang, W.

C. G. Lu, Y. P. Cui, W. Huang, B. F. Yun, Z. Y. Wang, G. H. Hu, J. Cui, Z. F. Lu, and Y. Qian, "Vibrational resonance enhanced broadband multiphoton absorption in a triphenylamine derivatives," Appl. Phys. Lett. 91, 121111 (2007).
[CrossRef]

Ito, S.

H. Matsuda, Y. Fujimoto, S. Ito, Y. Nagasawa, H. Miyasaka, T. Asahi, and H. Masuhara, "Development of nearinfrared 35 fs laser microscope and its application to the detection of three- and four-photon fluorescence of organic microcrystals," J. Phys. Chem. B 110, 1091 (2006).
[CrossRef] [PubMed]

Ji, W.

B. Gu, W. Ji, P. S. Patil, and S. M. Dharmaprakash, "Ultrafast optical nonlinearities and figures of merit in acceptor-substituted 3,4,5-trimethoxy chalcone derivatives: Structure-property relationships," J. Appl. Phys. 103, 103511 (2008).
[CrossRef]

B. Gu, W. Ji, P. S. Patil, S. M. Dharmaprakash, and H. T. Wang, "Two-photon-induced excited-state absorption: Theory and experiment," Appl. Phys. Lett. 92, 091118 (2008).
[CrossRef]

Kawata, S.

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, "Finer features for functional microdevices-Micromachines can be created with higher resolution using two-photon absorption," Nature (London) 412, 697 (2001).
[CrossRef] [PubMed]

Konevskii, V. S.

M. I. Demchuk, V. S. Konevskii, N. V. Kuleshov, V. P. Mikhailov, P. V. Prokoshin, and K. V. Yumashev, "Nonlinear transmission, ultrafast relaxation and three-photon absorption in reduced SrTiO3," Opt. Commun. 82, 273 (1991).
[CrossRef]

Kuleshov, N. V.

M. I. Demchuk, V. S. Konevskii, N. V. Kuleshov, V. P. Mikhailov, P. V. Prokoshin, and K. V. Yumashev, "Nonlinear transmission, ultrafast relaxation and three-photon absorption in reduced SrTiO3," Opt. Commun. 82, 273 (1991).
[CrossRef]

Larson, D. R.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, "Watersoluble quantum dots for multiphoton fluorescence imaging in vivo," Science 300, 1434 (2003).
[CrossRef] [PubMed]

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 (London) 415, 767 (2002).
[CrossRef] [PubMed]

Liu, M.

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, "Observation of three-photon enhanced four-photon absorption," Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

Lu, C. G.

C. G. Lu, Y. P. Cui, W. Huang, B. F. Yun, Z. Y. Wang, G. H. Hu, J. Cui, Z. F. Lu, and Y. Qian, "Vibrational resonance enhanced broadband multiphoton absorption in a triphenylamine derivatives," Appl. Phys. Lett. 91, 121111 (2007).
[CrossRef]

Lu, Z. F.

C. G. Lu, Y. P. Cui, W. Huang, B. F. Yun, Z. Y. Wang, G. H. Hu, J. Cui, Z. F. Lu, and Y. Qian, "Vibrational resonance enhanced broadband multiphoton absorption in a triphenylamine derivatives," Appl. Phys. Lett. 91, 121111 (2007).
[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 (London) 415, 767 (2002).
[CrossRef] [PubMed]

Masuhara, H.

H. Matsuda, Y. Fujimoto, S. Ito, Y. Nagasawa, H. Miyasaka, T. Asahi, and H. Masuhara, "Development of nearinfrared 35 fs laser microscope and its application to the detection of three- and four-photon fluorescence of organic microcrystals," J. Phys. Chem. B 110, 1091 (2006).
[CrossRef] [PubMed]

Matsuda, H.

H. Matsuda, Y. Fujimoto, S. Ito, Y. Nagasawa, H. Miyasaka, T. Asahi, and H. Masuhara, "Development of nearinfrared 35 fs laser microscope and its application to the detection of three- and four-photon fluorescence of organic microcrystals," J. Phys. Chem. B 110, 1091 (2006).
[CrossRef] [PubMed]

McLean, D. G.

Mikhailov, V. P.

M. I. Demchuk, V. S. Konevskii, N. V. Kuleshov, V. P. Mikhailov, P. V. Prokoshin, and K. V. Yumashev, "Nonlinear transmission, ultrafast relaxation and three-photon absorption in reduced SrTiO3," Opt. Commun. 82, 273 (1991).
[CrossRef]

Mikroyannidis, J.

M. Fakis, G. Tsigaridas, I. Polyzos, V. Giannetas, P. Persphonis, I. Spiliopoulos, J. Mikroyannidis, "Intensity dependent nonlinear absorption of pyrylium chromophores," Chem. Phys. Lett. 342, 155 (2001).
[CrossRef]

Miyasaka, H.

H. Matsuda, Y. Fujimoto, S. Ito, Y. Nagasawa, H. Miyasaka, T. Asahi, and H. Masuhara, "Development of nearinfrared 35 fs laser microscope and its application to the detection of three- and four-photon fluorescence of organic microcrystals," J. Phys. Chem. B 110, 1091 (2006).
[CrossRef] [PubMed]

Nagasawa, Y.

H. Matsuda, Y. Fujimoto, S. Ito, Y. Nagasawa, H. Miyasaka, T. Asahi, and H. Masuhara, "Development of nearinfrared 35 fs laser microscope and its application to the detection of three- and four-photon fluorescence of organic microcrystals," J. Phys. Chem. B 110, 1091 (2006).
[CrossRef] [PubMed]

Nunzi, J. M.

S. Delysse, P. Filloux, V. Dumarcher, C. Fiorini, and J. M. Nunzi, "Multiphoton absorption in organic dye solutions," Opt. Mater. 9, 347 (1998).
[CrossRef]

Parilov, E.

E. Parilov and M. J. Potasek, "Generalized theoretical treatment and numerical method of time-resolved radially dependent laser pulses interacting with multiphoton absorbers," J. Opt. Soc. Am B 23, 1894 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=josab-23-9-1894>
[CrossRef]

Parthenopoulos, D. A.

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

Patil, P. S.

B. Gu, W. Ji, P. S. Patil, and S. M. Dharmaprakash, "Ultrafast optical nonlinearities and figures of merit in acceptor-substituted 3,4,5-trimethoxy chalcone derivatives: Structure-property relationships," J. Appl. Phys. 103, 103511 (2008).
[CrossRef]

B. Gu, W. Ji, P. S. Patil, S. M. Dharmaprakash, and H. T. Wang, "Two-photon-induced excited-state absorption: Theory and experiment," Appl. Phys. Lett. 92, 091118 (2008).
[CrossRef]

Penzkofer, A.

A. Penzkofer and W. Falkenstein, "Three-photon absorption and subsequent excited-state absorption in CdS," Opt. Commun. 16, 247 (1976).
[CrossRef]

Persphonis, P.

M. Fakis, G. Tsigaridas, I. Polyzos, V. Giannetas, P. Persphonis, I. Spiliopoulos, J. Mikroyannidis, "Intensity dependent nonlinear absorption of pyrylium chromophores," Chem. Phys. Lett. 342, 155 (2001).
[CrossRef]

Polyakov, S.

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, "Observation of three-photon enhanced four-photon absorption," Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

Polyzos, I.

M. Fakis, G. Tsigaridas, I. Polyzos, V. Giannetas, P. Persphonis, I. Spiliopoulos, J. Mikroyannidis, "Intensity dependent nonlinear absorption of pyrylium chromophores," Chem. Phys. Lett. 342, 155 (2001).
[CrossRef]

Potasek, M. J.

E. Parilov and M. J. Potasek, "Generalized theoretical treatment and numerical method of time-resolved radially dependent laser pulses interacting with multiphoton absorbers," J. Opt. Soc. Am B 23, 1894 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=josab-23-9-1894>
[CrossRef]

Y. Gao and M. J. Potasek, "Effects of excited-state absorption on two-photon absorbing materials," Appl. Opt. 45, 2521 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=ao-45-11-2521>
[CrossRef] [PubMed]

Prasad, P. N.

G. S. He, L. S. Tan, Q. D. Zheng, and P. N. Prasad, "Multiphoton absorbing materials: molecular designs, characterizations, and applications," Chem. Rev. 108, 1245 (2008).
[CrossRef] [PubMed]

G. S. He, K. T. Yong, Q. Zheng, Y. Sahoo, A. Baev, A. I. Ryasnyanskiy, and P. N. Prasad, "Multi-photon excitation properties of CdSe quantum dots solutions and optical limiting behavior in infrared range," Opt. Express 15, 12818 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-20-21818>
[CrossRef] [PubMed]

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

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

Prokoshin, P. V.

M. I. Demchuk, V. S. Konevskii, N. V. Kuleshov, V. P. Mikhailov, P. V. Prokoshin, and K. V. Yumashev, "Nonlinear transmission, ultrafast relaxation and three-photon absorption in reduced SrTiO3," Opt. Commun. 82, 273 (1991).
[CrossRef]

Qian, Y.

C. G. Lu, Y. P. Cui, W. Huang, B. F. Yun, Z. Y. Wang, G. H. Hu, J. Cui, Z. F. Lu, and Y. Qian, "Vibrational resonance enhanced broadband multiphoton absorption in a triphenylamine derivatives," Appl. Phys. Lett. 91, 121111 (2007).
[CrossRef]

Rentzepis, P. M.

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

Ryasnyanskiy, A. I.

Sahoo, Y.

Slagle, J. E.

Spiliopoulos, I.

M. Fakis, G. Tsigaridas, I. Polyzos, V. Giannetas, P. Persphonis, I. Spiliopoulos, J. Mikroyannidis, "Intensity dependent nonlinear absorption of pyrylium chromophores," Chem. Phys. Lett. 342, 155 (2001).
[CrossRef]

Stegeman, G.

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, "Observation of three-photon enhanced four-photon absorption," Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

Sun, H. B.

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, "Finer features for functional microdevices-Micromachines can be created with higher resolution using two-photon absorption," Nature (London) 412, 697 (2001).
[CrossRef] [PubMed]

Sutherland, R. L.

Takada, K.

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, "Finer features for functional microdevices-Micromachines can be created with higher resolution using two-photon absorption," Nature (London) 412, 697 (2001).
[CrossRef] [PubMed]

Tan, L. S.

G. S. He, L. S. Tan, Q. D. Zheng, and P. N. Prasad, "Multiphoton absorbing materials: molecular designs, characterizations, and applications," Chem. Rev. 108, 1245 (2008).
[CrossRef] [PubMed]

Tanaka, T.

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, "Finer features for functional microdevices-Micromachines can be created with higher resolution using two-photon absorption," Nature (London) 412, 697 (2001).
[CrossRef] [PubMed]

Tsigaridas, G.

M. Fakis, G. Tsigaridas, I. Polyzos, V. Giannetas, P. Persphonis, I. Spiliopoulos, J. Mikroyannidis, "Intensity dependent nonlinear absorption of pyrylium chromophores," Chem. Phys. Lett. 342, 155 (2001).
[CrossRef]

Wang, H. T.

B. Gu, W. Ji, P. S. Patil, S. M. Dharmaprakash, and H. T. Wang, "Two-photon-induced excited-state absorption: Theory and experiment," Appl. Phys. Lett. 92, 091118 (2008).
[CrossRef]

Wang, Z. Y.

C. G. Lu, Y. P. Cui, W. Huang, B. F. Yun, Z. Y. Wang, G. H. Hu, J. Cui, Z. F. Lu, and Y. Qian, "Vibrational resonance enhanced broadband multiphoton absorption in a triphenylamine derivatives," Appl. Phys. Lett. 91, 121111 (2007).
[CrossRef]

Webb, W. W.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, "Watersoluble quantum dots for multiphoton fluorescence imaging in vivo," Science 300, 1434 (2003).
[CrossRef] [PubMed]

Williams, R. M.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, "Watersoluble quantum dots for multiphoton fluorescence imaging in vivo," Science 300, 1434 (2003).
[CrossRef] [PubMed]

Wise, F. W.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, "Watersoluble quantum dots for multiphoton fluorescence imaging in vivo," Science 300, 1434 (2003).
[CrossRef] [PubMed]

Yong, K. T.

Yoshino, F.

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, "Observation of three-photon enhanced four-photon absorption," Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

Yumashev, K. V.

M. I. Demchuk, V. S. Konevskii, N. V. Kuleshov, V. P. Mikhailov, P. V. Prokoshin, and K. V. Yumashev, "Nonlinear transmission, ultrafast relaxation and three-photon absorption in reduced SrTiO3," Opt. Commun. 82, 273 (1991).
[CrossRef]

Yun, B. F.

C. G. Lu, Y. P. Cui, W. Huang, B. F. Yun, Z. Y. Wang, G. H. Hu, J. Cui, Z. F. Lu, and Y. Qian, "Vibrational resonance enhanced broadband multiphoton absorption in a triphenylamine derivatives," Appl. Phys. Lett. 91, 121111 (2007).
[CrossRef]

Zheng, Q.

Zheng, Q. D.

G. S. He, L. S. Tan, Q. D. Zheng, and P. N. Prasad, "Multiphoton absorbing materials: molecular designs, characterizations, and applications," Chem. Rev. 108, 1245 (2008).
[CrossRef] [PubMed]

Zipfel, W. R.

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, "Watersoluble quantum dots for multiphoton fluorescence imaging in vivo," Science 300, 1434 (2003).
[CrossRef] [PubMed]

Adv. Mater.

Q1. D. S. Correa, L. De Boni, D. T. Balogh, and C. R. Mendonca, "Three- and four-photon excitation of poly(2-methoxy-5-(2�??-ethylhexyloxy)-1,4-phenylenevinylene)(MEH-PPV)," Adv. Mater. 19, 2653 (2007).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

C. G. Lu, Y. P. Cui, W. Huang, B. F. Yun, Z. Y. Wang, G. H. Hu, J. Cui, Z. F. Lu, and Y. Qian, "Vibrational resonance enhanced broadband multiphoton absorption in a triphenylamine derivatives," Appl. Phys. Lett. 91, 121111 (2007).
[CrossRef]

B. Gu, W. Ji, P. S. Patil, S. M. Dharmaprakash, and H. T. Wang, "Two-photon-induced excited-state absorption: Theory and experiment," Appl. Phys. Lett. 92, 091118 (2008).
[CrossRef]

Chem. Phys. Lett.

M. Fakis, G. Tsigaridas, I. Polyzos, V. Giannetas, P. Persphonis, I. Spiliopoulos, J. Mikroyannidis, "Intensity dependent nonlinear absorption of pyrylium chromophores," Chem. Phys. Lett. 342, 155 (2001).
[CrossRef]

Chem. Rev.

G. S. He, L. S. Tan, Q. D. Zheng, and P. N. Prasad, "Multiphoton absorbing materials: molecular designs, characterizations, and applications," Chem. Rev. 108, 1245 (2008).
[CrossRef] [PubMed]

J. Appl. Phys.

B. Gu, W. Ji, P. S. Patil, and S. M. Dharmaprakash, "Ultrafast optical nonlinearities and figures of merit in acceptor-substituted 3,4,5-trimethoxy chalcone derivatives: Structure-property relationships," J. Appl. Phys. 103, 103511 (2008).
[CrossRef]

J. Opt. Soc. Am B

E. Parilov and M. J. Potasek, "Generalized theoretical treatment and numerical method of time-resolved radially dependent laser pulses interacting with multiphoton absorbers," J. Opt. Soc. Am B 23, 1894 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=josab-23-9-1894>
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. Chem. B

H. Matsuda, Y. Fujimoto, S. Ito, Y. Nagasawa, H. Miyasaka, T. Asahi, and H. Masuhara, "Development of nearinfrared 35 fs laser microscope and its application to the detection of three- and four-photon fluorescence of organic microcrystals," J. Phys. Chem. B 110, 1091 (2006).
[CrossRef] [PubMed]

Nature (London)

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

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, "Finer features for functional microdevices-Micromachines can be created with higher resolution using two-photon absorption," Nature (London) 412, 697 (2001).
[CrossRef] [PubMed]

Opt. Commun.

A. Penzkofer and W. Falkenstein, "Three-photon absorption and subsequent excited-state absorption in CdS," Opt. Commun. 16, 247 (1976).
[CrossRef]

M. I. Demchuk, V. S. Konevskii, N. V. Kuleshov, V. P. Mikhailov, P. V. Prokoshin, and K. V. Yumashev, "Nonlinear transmission, ultrafast relaxation and three-photon absorption in reduced SrTiO3," Opt. Commun. 82, 273 (1991).
[CrossRef]

D. S. Correa, L. De Boni, L. Misoguti, I. Cohanoschi, F. E. Hernandez, and C. R. Mendonca, "Z-scan theoretical analysis for three-, four- and five-photon absorption," Opt. Commun. 277, 440 (2007).
[CrossRef]

Opt. Express

Opt. Mater.

S. Delysse, P. Filloux, V. Dumarcher, C. Fiorini, and J. M. Nunzi, "Multiphoton absorption in organic dye solutions," Opt. Mater. 9, 347 (1998).
[CrossRef]

Phys. Rev. Lett.

F. Yoshino, S. Polyakov, M. Liu, and G. Stegeman, "Observation of three-photon enhanced four-photon absorption," Phys. Rev. Lett. 91, 063902 (2003).
[CrossRef] [PubMed]

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 (1996).
[CrossRef]

Science

D. R. Larson, W. R. Zipfel, R. M. Williams, S. W. Clark, M. P. Bruchez, F. W. Wise, and W. W. Webb, "Watersoluble quantum dots for multiphoton fluorescence imaging in vivo," Science 300, 1434 (2003).
[CrossRef] [PubMed]

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

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Figures (2)

Fig. 1.
Fig. 1.

Schematic diagram of (a) one-step four-photon absorption and (b) two-step four-photon absorption.

Fig. 2.
Fig. 2.

Pulse-width dependence of effective 4PA coefficient for τ e=1 ps. The circles are numerical simulations, while the solid line is the analytical result. The effective 4PA coefficient is normalized to σ e α 3 τ e/3h̄ω.

Tables (1)

Tables Icon

Table 1. Coefficient amn when 0≤p 0π and 0≤h 0π.

Equations (17)

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

I z = σ 3 N S 0 I 3 σ e N S 1 I .
N S 0 t = σ 3 N S 0 I 3 3 h ¯ ω + N S 1 τ e ,
N S 1 t = σ 3 N S 0 I 3 3 h ¯ ω σ e N S 1 I h - ω N S 1 τ e + N S h τ h ,
N S h t = σ e N S 1 I h ¯ ω N S h τ h ,
N = N S 0 + N S 1 + N S h ,
N S 1 t = σ 3 N I 3 3 h ¯ ω N S 1 τ e .
N S 1 ( t ) = σ 3 N 3 h ¯ ω t I 3 ( t ) exp [ ( ( t t ) τ e ) ] dt .
N S 1 ( t ) = σ 3 N 3 h ¯ ω F ( t ) I 3 ( t ) ,
F ( t ) = 1 I 3 ( t ) t I 3 ( t ) exp [ ( ( t t ) τ e ) ] dt .
F = + F ( t ) I 4 ( t ) dt + I 4 ( t ) dt
d I ( r , z , t ) dz = [ α 3 I 2 ( r , z , t ) + α 4 I 3 ( r , z , t ) ] I ( r , z , t ) ,
α 4 = σ e α 3 3 h ¯ ω 2 π τ + exp ( t 2 τ 2 ) { t exp ( 3 t 2 τ 2 ) exp ( t t τ e ) dt } dt .
α 4 = σ e α 3 τ e 3 h ¯ ω 0.54 ( τ τ e ) 3 1 + 0.54 ( τ τ e ) 3
I c = 3 h ¯ ω N S 1 c α 3 τ e 3 ,
T ( z , p , h ) = m = 0 4 n = 0 4 a mn p m h n .
T ( z , p ) = m = 0 4 a m 0 p m ,
T ( z , h ) = n = 0 4 a 0 n h n .

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