Abstract

Nonlinear absorption and nonlinear refraction in the resonant region and the two-photon absorption (TPA) region of hypocrellin A (HA) have been investigated, for the first time to our knowledge, using the Z-scan technique and intensity-dependent transmittance measurement with nanosecond pulses. At 0.53 μm the effective absorption of the triplet state of the normal form of HA is the dominant mechanism causing the reverse saturable absorption. The refractive nonlinearities of HA can be mainly attributed to the thermal effect. With the excitation at 1.06 μm the optical limiting behavior in HA may be caused by the TPA of its ground state. The ground state of HA exhibits a large real part of second-order hyperpolarizability. By establishing the kinetic model for HA, we obtained several nonlinear optical parameters, such as the cross section of TPA, the absorption cross sections of the excited state and the triplet state of the normal form of HA, and the real part of second-order hyperpolarizability of the ground state of HA. The theoretical results are in good agreement with the experimental ones, which not only shows the completeness of the kinetic model but also demonstrates the close relationship between the optical nonlinearities of HA and its dynamic processes. In addition, HA has been proved to be a potential optical limiting material.

© 1998 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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1997

D. S. English, K. Das, J. M. Zenner, W. Zhang, G. A. Kraus, R. C. Larock, and J. W. Petrich, “Hypericin, hypocrellin, and model compound: primary photoprocesses of light-induced antiviral agents,” J. Phys. Chem. A 101, 3235 (1997).
[CrossRef]

K. Das, D. S. English, and J. W. Petrich, “Solvent dependence on the intramolecular excited state proton transfer or hydrogen atom transfer in hypocrellin,” J. Am. Chem. Soc. 119, 2763 (1997).
[CrossRef]

K. Das, D. S. English, and J. W. Petrich, “Deuterium isotope effect on the excited state photophysics of hypocrellin: evidence for proton or hydrogen atom transfer,” J. Phys. Chem. A 101, 3241 (1997).
[CrossRef]

P. Brochard and V. Grolier-Mazza, “Thermal nonlinear refraction in dye solutions: a study of the transient regime,” J. Opt. Soc. Am. B 14, 405 (1997).
[CrossRef]

1996

G. I. Stegeman and W. E. Torruellas, “Nonlinear materials for information processing and communications,” Philos. Trans. R. Soc. London, Ser. A 345, 745 (1996).
[CrossRef]

K. Das, D. S. English, M. J. Fehr, A. V. Smirnov, and J. W. Petrich, “Excited state processes in polycyclic quinones: the light-induced antiviral agent, hypocrellin and a comparison with hypericin,” J. Phys. Chem. 100, 18275 (1996).
[CrossRef]

1995

M. J. Fehr, S. L. Carpenter, Y. Wannemuehler, and J. W. Petrich, “Role of oxygen and photoinduced acidification in the light-dependent antiviral activity of hypocrellin A,” Biochemistry 34, 15845 (1995).
[CrossRef] [PubMed]

G. L. Wood, M. J. Miller, and A. G. Mott, “Investigation of tetrabenzoporphyrin by the Z-scan technique,” Opt. Lett. 20, 973 (1995).
[CrossRef]

1994

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm,” Appl. Phys. Lett. 64, 2773 (1994).
[CrossRef]

Y. Z. Hu, J. Y. An, L. Qin, and L. J. Jiang, “Studies of the triplet state properties of hypocrellin A by nanosecond flash photolysis,” J. Photochem. Photobiol. A 78, 247 (1994).
[CrossRef]

J. Hein, H. Bergner, M. Lenzner, and S. Rentsch, “Determination of real and imaginary part of thiophene oligomers using the Z-scan technique,” Chem. Phys. 179, 543 (1994).
[CrossRef]

1992

Z. Diwu and J. W. Lown, “Photosensitization by anticancer agents, 12. Perylene quinoid pigments, a novel type of singlet oxygen sensitizer,” J. Photochem. Photobiol. A 64, 273 (1992).
[CrossRef]

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

1991

1990

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96 (1990).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

1985

F. Kajzar and J. Messier, “Third-harmonic generation in liquid,” Phys. Rev. A 32, 2352 (1985).
[CrossRef] [PubMed]

1983

R. C. Desai, M. D. Levenson, and J. A. Barker, “Forced Rayleigh scattering: thermal and acoustic effects in phase-conjugate wave-front generation,” Phys. Rev. A 27, 1968 (1983).
[CrossRef]

Alfano, R. R.

An, J. Y.

Y. Z. Hu, J. Y. An, L. Qin, and L. J. Jiang, “Studies of the triplet state properties of hypocrellin A by nanosecond flash photolysis,” J. Photochem. Photobiol. A 78, 247 (1994).
[CrossRef]

Baker, G.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm,” Appl. Phys. Lett. 64, 2773 (1994).
[CrossRef]

Barker, J. A.

R. C. Desai, M. D. Levenson, and J. A. Barker, “Forced Rayleigh scattering: thermal and acoustic effects in phase-conjugate wave-front generation,” Phys. Rev. A 27, 1968 (1983).
[CrossRef]

Bergner, H.

J. Hein, H. Bergner, M. Lenzner, and S. Rentsch, “Determination of real and imaginary part of thiophene oligomers using the Z-scan technique,” Chem. Phys. 179, 543 (1994).
[CrossRef]

Brochard, P.

Carpenter, S. L.

M. J. Fehr, S. L. Carpenter, Y. Wannemuehler, and J. W. Petrich, “Role of oxygen and photoinduced acidification in the light-dependent antiviral activity of hypocrellin A,” Biochemistry 34, 15845 (1995).
[CrossRef] [PubMed]

Cha, M.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm,” Appl. Phys. Lett. 64, 2773 (1994).
[CrossRef]

Das, K.

K. Das, D. S. English, and J. W. Petrich, “Deuterium isotope effect on the excited state photophysics of hypocrellin: evidence for proton or hydrogen atom transfer,” J. Phys. Chem. A 101, 3241 (1997).
[CrossRef]

D. S. English, K. Das, J. M. Zenner, W. Zhang, G. A. Kraus, R. C. Larock, and J. W. Petrich, “Hypericin, hypocrellin, and model compound: primary photoprocesses of light-induced antiviral agents,” J. Phys. Chem. A 101, 3235 (1997).
[CrossRef]

K. Das, D. S. English, and J. W. Petrich, “Solvent dependence on the intramolecular excited state proton transfer or hydrogen atom transfer in hypocrellin,” J. Am. Chem. Soc. 119, 2763 (1997).
[CrossRef]

K. Das, D. S. English, M. J. Fehr, A. V. Smirnov, and J. W. Petrich, “Excited state processes in polycyclic quinones: the light-induced antiviral agent, hypocrellin and a comparison with hypericin,” J. Phys. Chem. 100, 18275 (1996).
[CrossRef]

Desai, R. C.

R. C. Desai, M. D. Levenson, and J. A. Barker, “Forced Rayleigh scattering: thermal and acoustic effects in phase-conjugate wave-front generation,” Phys. Rev. A 27, 1968 (1983).
[CrossRef]

Diwu, Z.

Z. Diwu and J. W. Lown, “Photosensitization by anticancer agents, 12. Perylene quinoid pigments, a novel type of singlet oxygen sensitizer,” J. Photochem. Photobiol. A 64, 273 (1992).
[CrossRef]

Dorsinville, R.

English, D. S.

K. Das, D. S. English, and J. W. Petrich, “Deuterium isotope effect on the excited state photophysics of hypocrellin: evidence for proton or hydrogen atom transfer,” J. Phys. Chem. A 101, 3241 (1997).
[CrossRef]

K. Das, D. S. English, and J. W. Petrich, “Solvent dependence on the intramolecular excited state proton transfer or hydrogen atom transfer in hypocrellin,” J. Am. Chem. Soc. 119, 2763 (1997).
[CrossRef]

D. S. English, K. Das, J. M. Zenner, W. Zhang, G. A. Kraus, R. C. Larock, and J. W. Petrich, “Hypericin, hypocrellin, and model compound: primary photoprocesses of light-induced antiviral agents,” J. Phys. Chem. A 101, 3235 (1997).
[CrossRef]

K. Das, D. S. English, M. J. Fehr, A. V. Smirnov, and J. W. Petrich, “Excited state processes in polycyclic quinones: the light-induced antiviral agent, hypocrellin and a comparison with hypericin,” J. Phys. Chem. 100, 18275 (1996).
[CrossRef]

Etemad, S.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm,” Appl. Phys. Lett. 64, 2773 (1994).
[CrossRef]

Fehr, M. J.

K. Das, D. S. English, M. J. Fehr, A. V. Smirnov, and J. W. Petrich, “Excited state processes in polycyclic quinones: the light-induced antiviral agent, hypocrellin and a comparison with hypericin,” J. Phys. Chem. 100, 18275 (1996).
[CrossRef]

M. J. Fehr, S. L. Carpenter, Y. Wannemuehler, and J. W. Petrich, “Role of oxygen and photoinduced acidification in the light-dependent antiviral activity of hypocrellin A,” Biochemistry 34, 15845 (1995).
[CrossRef] [PubMed]

Grolier-Mazza, V.

Hagan, D. J.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96 (1990).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Hein, J.

J. Hein, H. Bergner, M. Lenzner, and S. Rentsch, “Determination of real and imaginary part of thiophene oligomers using the Z-scan technique,” Chem. Phys. 179, 543 (1994).
[CrossRef]

Hu, Y. Z.

Y. Z. Hu, J. Y. An, L. Qin, and L. J. Jiang, “Studies of the triplet state properties of hypocrellin A by nanosecond flash photolysis,” J. Photochem. Photobiol. A 78, 247 (1994).
[CrossRef]

Jiang, L. J.

Y. Z. Hu, J. Y. An, L. Qin, and L. J. Jiang, “Studies of the triplet state properties of hypocrellin A by nanosecond flash photolysis,” J. Photochem. Photobiol. A 78, 247 (1994).
[CrossRef]

Kajzar, F.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm,” Appl. Phys. Lett. 64, 2773 (1994).
[CrossRef]

F. Kajzar and J. Messier, “Third-harmonic generation in liquid,” Phys. Rev. A 32, 2352 (1985).
[CrossRef] [PubMed]

Kraus, G. A.

D. S. English, K. Das, J. M. Zenner, W. Zhang, G. A. Kraus, R. C. Larock, and J. W. Petrich, “Hypericin, hypocrellin, and model compound: primary photoprocesses of light-induced antiviral agents,” J. Phys. Chem. A 101, 3235 (1997).
[CrossRef]

Larock, R. C.

D. S. English, K. Das, J. M. Zenner, W. Zhang, G. A. Kraus, R. C. Larock, and J. W. Petrich, “Hypericin, hypocrellin, and model compound: primary photoprocesses of light-induced antiviral agents,” J. Phys. Chem. A 101, 3235 (1997).
[CrossRef]

Lawrence, B. L.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm,” Appl. Phys. Lett. 64, 2773 (1994).
[CrossRef]

Lenzner, M.

J. Hein, H. Bergner, M. Lenzner, and S. Rentsch, “Determination of real and imaginary part of thiophene oligomers using the Z-scan technique,” Chem. Phys. 179, 543 (1994).
[CrossRef]

Levenson, M. D.

R. C. Desai, M. D. Levenson, and J. A. Barker, “Forced Rayleigh scattering: thermal and acoustic effects in phase-conjugate wave-front generation,” Phys. Rev. A 27, 1968 (1983).
[CrossRef]

Lown, J. W.

Z. Diwu and J. W. Lown, “Photosensitization by anticancer agents, 12. Perylene quinoid pigments, a novel type of singlet oxygen sensitizer,” J. Photochem. Photobiol. A 64, 273 (1992).
[CrossRef]

Messier, J.

F. Kajzar and J. Messier, “Third-harmonic generation in liquid,” Phys. Rev. A 32, 2352 (1985).
[CrossRef] [PubMed]

Miller, M. J.

Mott, A. G.

Petrich, J. W.

K. Das, D. S. English, and J. W. Petrich, “Deuterium isotope effect on the excited state photophysics of hypocrellin: evidence for proton or hydrogen atom transfer,” J. Phys. Chem. A 101, 3241 (1997).
[CrossRef]

D. S. English, K. Das, J. M. Zenner, W. Zhang, G. A. Kraus, R. C. Larock, and J. W. Petrich, “Hypericin, hypocrellin, and model compound: primary photoprocesses of light-induced antiviral agents,” J. Phys. Chem. A 101, 3235 (1997).
[CrossRef]

K. Das, D. S. English, and J. W. Petrich, “Solvent dependence on the intramolecular excited state proton transfer or hydrogen atom transfer in hypocrellin,” J. Am. Chem. Soc. 119, 2763 (1997).
[CrossRef]

K. Das, D. S. English, M. J. Fehr, A. V. Smirnov, and J. W. Petrich, “Excited state processes in polycyclic quinones: the light-induced antiviral agent, hypocrellin and a comparison with hypericin,” J. Phys. Chem. 100, 18275 (1996).
[CrossRef]

M. J. Fehr, S. L. Carpenter, Y. Wannemuehler, and J. W. Petrich, “Role of oxygen and photoinduced acidification in the light-dependent antiviral activity of hypocrellin A,” Biochemistry 34, 15845 (1995).
[CrossRef] [PubMed]

Qin, L.

Y. Z. Hu, J. Y. An, L. Qin, and L. J. Jiang, “Studies of the triplet state properties of hypocrellin A by nanosecond flash photolysis,” J. Photochem. Photobiol. A 78, 247 (1994).
[CrossRef]

Rentsch, S.

J. Hein, H. Bergner, M. Lenzner, and S. Rentsch, “Determination of real and imaginary part of thiophene oligomers using the Z-scan technique,” Chem. Phys. 179, 543 (1994).
[CrossRef]

Said, A. A.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Sheik-Bahae, M.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96 (1990).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Smirnov, A. V.

K. Das, D. S. English, M. J. Fehr, A. V. Smirnov, and J. W. Petrich, “Excited state processes in polycyclic quinones: the light-induced antiviral agent, hypocrellin and a comparison with hypericin,” J. Phys. Chem. 100, 18275 (1996).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman and W. E. Torruellas, “Nonlinear materials for information processing and communications,” Philos. Trans. R. Soc. London, Ser. A 345, 745 (1996).
[CrossRef]

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm,” Appl. Phys. Lett. 64, 2773 (1994).
[CrossRef]

Torruellas, W. E.

G. I. Stegeman and W. E. Torruellas, “Nonlinear materials for information processing and communications,” Philos. Trans. R. Soc. London, Ser. A 345, 745 (1996).
[CrossRef]

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm,” Appl. Phys. Lett. 64, 2773 (1994).
[CrossRef]

Van Stryland, E. W.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption,” Phys. Rev. Lett. 65, 96 (1990).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Wang, J.

Wannemuehler, Y.

M. J. Fehr, S. L. Carpenter, Y. Wannemuehler, and J. W. Petrich, “Role of oxygen and photoinduced acidification in the light-dependent antiviral activity of hypocrellin A,” Biochemistry 34, 15845 (1995).
[CrossRef] [PubMed]

Wei, T. H.

A. A. Said, M. Sheik-Bahae, D. J. Hagan, T. H. Wei, J. Wang, J. Young, and E. W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B 9, 405 (1992).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Wood, G. L.

Yang, L.

Yang, N. L.

Young, J.

Zenner, J. M.

D. S. English, K. Das, J. M. Zenner, W. Zhang, G. A. Kraus, R. C. Larock, and J. W. Petrich, “Hypericin, hypocrellin, and model compound: primary photoprocesses of light-induced antiviral agents,” J. Phys. Chem. A 101, 3235 (1997).
[CrossRef]

Zhang, W.

D. S. English, K. Das, J. M. Zenner, W. Zhang, G. A. Kraus, R. C. Larock, and J. W. Petrich, “Hypericin, hypocrellin, and model compound: primary photoprocesses of light-induced antiviral agents,” J. Phys. Chem. A 101, 3235 (1997).
[CrossRef]

Zou, W. K.

Appl. Phys. Lett.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, and F. Kajzar, “Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm,” Appl. Phys. Lett. 64, 2773 (1994).
[CrossRef]

Biochemistry

M. J. Fehr, S. L. Carpenter, Y. Wannemuehler, and J. W. Petrich, “Role of oxygen and photoinduced acidification in the light-dependent antiviral activity of hypocrellin A,” Biochemistry 34, 15845 (1995).
[CrossRef] [PubMed]

Chem. Phys.

J. Hein, H. Bergner, M. Lenzner, and S. Rentsch, “Determination of real and imaginary part of thiophene oligomers using the Z-scan technique,” Chem. Phys. 179, 543 (1994).
[CrossRef]

IEEE J. Quantum Electron.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

J. Am. Chem. Soc.

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Figures (11)

Fig. 1
Fig. 1

Two-dimensional structures of (A) the normal form and (B) the tautomer of HA; (C) kinetic scheme for HA in solutions of low viscosity. N and T denote the normal form and tautomer of HA respectively, kPT is the backproton transfer rate, and kisc is the intersystem crossing rate of the excited state of the normal form.

Fig. 2
Fig. 2

Experimental configuration for Z-scan and intensity-dependent transmittance measurement.

Fig. 3
Fig. 3

Typical (A) open-aperture, (B) closed-aperture, and (C) divided Z-scan data for HA at 0.53 μm. The solid curves are the theoretic fits of the experimental data. I0=0.052 GW/cm2.

Fig. 4
Fig. 4

Linear absorption spectrum of a 5-mm-thick HA solution in ethanol of 7.7×10-5 M concentration.

Fig. 5
Fig. 5

Measured (circles) and computed (curve) αeff versus I0 at 0.53 μm. The theoretical curve is obtained with σ1=1.13×10-16 cm2 and σT=8.15×10-17 cm2.

Fig. 6
Fig. 6

Typical (A) open-aperture, (B) closed-aperture, and (C) divided Z-scan data for HA at 1.06 μm. The curves are the theoretic fits of the experimental data. I0=8.9 GW/cm2.

Fig. 7
Fig. 7

Plot of T0/T versus I0 for HA with the theoretical fit (curve) at 1.06 μm.

Fig. 8
Fig. 8

Refractive-index change versus the peak irradiance I0 at 1.06 μm. The line represents a third-order nonlinearity.

Fig. 9
Fig. 9

Kinetic model of HA with the excitation in its resonant region.

Fig. 10
Fig. 10

(A) Time evolution of the population densities of S0 (solid curve), S1 (dashed curve), and T1 (dash–dot curve); (B) Time evolution of total absorption coefficient α (solid curve), absorption coefficients of S0 (σ0N0, dashed curve), S1 (σ1N1, dotted curve), and T1 (σTNT, dash–dot curve). λex=0.53 μm, I0=0.052 GW/cm2.

Fig. 11
Fig. 11

Averaged refractive-index changes induced by electronic effect (solid curves) and thermal effect (dash–dot curve) as functions of pulse duration (FWHM) for a fluence of 0.50 J/cm2.

Tables (3)

Tables Icon

Table 1 Nonlinear Parameters of Hypocrellin A at 1.06 μm Extracted from Z-Scan Data

Tables Icon

Table 2 Absorption Cross Sections of S1 and T1

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Table 3 Physical Parameters of Ethanol Used in Numerical Computations

Equations (14)

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

T=1πq0(z) - ln[1+q0(z)exp(-τ2)]dτ,
q0(z)=α2I0Leff/(1+z2/z02),
T0/T=πq0(0)- ln[1+q0(0)exp(-τ2)]dτ.
N0t=-σ0N0ω I+(kr+kic)N1+kTSNT,
N1t=σ0N0ω I-N1τ1,
NTt=kiscN1-kTSNT,
Ni=0Ldz-dt02π rNiIdr0Ldz-dt02π rIdr,
Iz=-αI,
T(z)=2π-dt0rI(L, r, t, z)drE0 exp(-α0L),
αeff=σ0N0+σ1N1+σTNT.
Δn0=2Δnqss -[fdiff(r=0, τ)+fac(r=0, τ, m)]exp(-τ2)dτ- exp(-τ2)dτ,
Δnqss=-12 αeffF0ρ0Cp dndT,
α2=σ2N00.
χR(3)=χR(3)+L(4)ε0 N00γS0(3),

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