Abstract

Using the Z-scan technique, we studied the nonlinear absorption and refraction behaviors of a dilute toluene solution of a silicon naphthalocyanine (Si(OSi(n-hexyl)3)2, SiNc) at 532 nanometer with both a 2.8-nanosecond pulse and a 21-nanosecond (HW1/eM) pulse train containing 11 18-picosecond pulses 7 nanosecond apart. A thermal acoustic model and its steady-state approximation account for the heat generated by the nonradiative relaxations subsequent to the absorption. We found that when the steady-state approximation satisfactorily explained the results obtained with a 21-nanosecond pulse train, only the thermal-acoustic model fit the 2.8-nanosecond experimental results, which supports the approximation criterion established by Kovsh et al.

© 2007 Optical Society of America

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2005 (1)

T. H. Wei, T. H. Huang, S. Yang, D. Liu, J. K. Hu and C. W. Chen, "Z-scan study of optical nonlinearity in C60-toluene solution," Mol. Phys. 103, 1847-1857 (2005).

1999 (2)

1998 (1)

T. H. Wei, T. H. Huang, and M. S. Lin, "Signs of nonlinear refraction in chloroaluminum phthalocyanine solution," Appl. Phys. Lett. 72, 2505-2507 (1998).
[CrossRef]

1997 (1)

1996 (3)

T. H. Wei and T. H. Huang, "A study of photophysics using the Z-scan technique: lifetime determination for high-lying excited states," Opt. and Quantum Electron. 28, 1495-1508 (1996).
[CrossRef]

J. Seto, S. Tamura, N. Asai, N. Kishii, Y. Kijima, and N. Matsuzawa, "Macrocyclic functional dyes: Applications to optical disk media, photochemical hole burning and non-linear optics," Pure and Appl. Chem. 68, 1429-1434 (1996).
[CrossRef]

J. W. Perry, K. Mansour, J. Y. S. Lee, X. L. Xu, P.V. Bedwhorth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada,M. Tian, and H. Sasabe, "Organic optical limiter with a strong nonlinear absorptive response," Science 23, 1533-1536 (1996).
[CrossRef]

1995 (1)

1994 (2)

C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, "Dynamic and steady-state behaviors of reverse satura absorption in metallophthalocyanines," Phys. Rev. A 49, 1149-1157 (1994).
[CrossRef] [PubMed]

S. R. Mishra, H. S. Rawat, M. P. Joshi and S. C. Mehendale, "The role of non-linear scattering in optical limiting in C60 solution," J. Phys. B:At. Mol. Phys. 27, 157-163, (1994).
[CrossRef]

1993 (1)

1992 (1)

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. V. Stryland, J. W. Perry, and D. R. Coulter, "Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines," Appl. Phys. B 54, 46-51 (1992).
[CrossRef]

1990 (1)

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, 760-769 (1990).
[CrossRef]

1989 (1)

J. S. Shirk, J. R. Lindle, F. J. Bartoli, C. A. Hoffman, A. H. Kafafi, and A. W. Snow, "Off-resonat third-order optical nonlinearities of meta-substituted phthalocyanines," Appl. Phys. Lett. 55, 1287-1288 (1989).
[CrossRef]

1983 (1)

J. -M. Heritier, "Electrostrictive limit and focusing effects in pulsed photoacoustic detection," Opt. Comm. 44, 267-272 (1983).
[CrossRef]

1980 (1)

J. H. Brannon and D. Madge, "Picosecond laser Photophysics. group 3A phthalocyanines," J. Am. Chem. Soc. 102, 62-65 (1980).
[CrossRef]

Asai, N.

J. Seto, S. Tamura, N. Asai, N. Kishii, Y. Kijima, and N. Matsuzawa, "Macrocyclic functional dyes: Applications to optical disk media, photochemical hole burning and non-linear optics," Pure and Appl. Chem. 68, 1429-1434 (1996).
[CrossRef]

Bartoli, F. J.

J. S. Shirk, J. R. Lindle, F. J. Bartoli, C. A. Hoffman, A. H. Kafafi, and A. W. Snow, "Off-resonat third-order optical nonlinearities of meta-substituted phthalocyanines," Appl. Phys. Lett. 55, 1287-1288 (1989).
[CrossRef]

Bedwhorth, P.V.

J. W. Perry, K. Mansour, J. Y. S. Lee, X. L. Xu, P.V. Bedwhorth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada,M. Tian, and H. Sasabe, "Organic optical limiter with a strong nonlinear absorptive response," Science 23, 1533-1536 (1996).
[CrossRef]

Brandelik, D. M.

Brannon, J. H.

J. H. Brannon and D. Madge, "Picosecond laser Photophysics. group 3A phthalocyanines," J. Am. Chem. Soc. 102, 62-65 (1980).
[CrossRef]

Brant, M. C.

Brochard, P.

Chen, C. T.

J. W. Perry, K. Mansour, J. Y. S. Lee, X. L. Xu, P.V. Bedwhorth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada,M. Tian, and H. Sasabe, "Organic optical limiter with a strong nonlinear absorptive response," Science 23, 1533-1536 (1996).
[CrossRef]

Chen, C. W.

T. H. Wei, T. H. Huang, S. Yang, D. Liu, J. K. Hu and C. W. Chen, "Z-scan study of optical nonlinearity in C60-toluene solution," Mol. Phys. 103, 1847-1857 (2005).

Coulter, D. R.

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. V. Stryland, J. W. Perry, and D. R. Coulter, "Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines," Appl. Phys. B 54, 46-51 (1992).
[CrossRef]

Fleitz, P. A.

Grolier-Mazza, V.

Habiro, M.

Hagan, D. J.

D. I. Kovsh, S. Yang, D. J. Hagan, and E. W. Van Stryland, "Nonlinear optical beam propagation for optical limiting," Appl. Opt. 38, 5168-5180 (1999).
[CrossRef]

D. I. Kovsh, D. J. Hagan, and E.W. Stryland, "Numerical modeling of thermal refraction in liquids in the transient regime," Opt. Express 4, 315-327 (1999).
[CrossRef] [PubMed]

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. V. Stryland, J. W. Perry, and D. R. Coulter, "Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines," Appl. Phys. B 54, 46-51 (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, 760-769 (1990).
[CrossRef]

Heritier, J. -M.

J. -M. Heritier, "Electrostrictive limit and focusing effects in pulsed photoacoustic detection," Opt. Comm. 44, 267-272 (1983).
[CrossRef]

Hoffman, C. A.

J. S. Shirk, J. R. Lindle, F. J. Bartoli, C. A. Hoffman, A. H. Kafafi, and A. W. Snow, "Off-resonat third-order optical nonlinearities of meta-substituted phthalocyanines," Appl. Phys. Lett. 55, 1287-1288 (1989).
[CrossRef]

Hu, J. K.

T. H. Wei, T. H. Huang, S. Yang, D. Liu, J. K. Hu and C. W. Chen, "Z-scan study of optical nonlinearity in C60-toluene solution," Mol. Phys. 103, 1847-1857 (2005).

Huang, T. H.

T. H. Wei, T. H. Huang, S. Yang, D. Liu, J. K. Hu and C. W. Chen, "Z-scan study of optical nonlinearity in C60-toluene solution," Mol. Phys. 103, 1847-1857 (2005).

T. H. Wei, T. H. Huang, and M. S. Lin, "Signs of nonlinear refraction in chloroaluminum phthalocyanine solution," Appl. Phys. Lett. 72, 2505-2507 (1998).
[CrossRef]

T. H. Wei and T. H. Huang, "A study of photophysics using the Z-scan technique: lifetime determination for high-lying excited states," Opt. and Quantum Electron. 28, 1495-1508 (1996).
[CrossRef]

Joshi, M. P.

S. R. Mishra, H. S. Rawat, M. P. Joshi and S. C. Mehendale, "The role of non-linear scattering in optical limiting in C60 solution," J. Phys. B:At. Mol. Phys. 27, 157-163, (1994).
[CrossRef]

Kafafi, A. H.

J. S. Shirk, J. R. Lindle, F. J. Bartoli, C. A. Hoffman, A. H. Kafafi, and A. W. Snow, "Off-resonat third-order optical nonlinearities of meta-substituted phthalocyanines," Appl. Phys. Lett. 55, 1287-1288 (1989).
[CrossRef]

Kijima, Y.

J. Seto, S. Tamura, N. Asai, N. Kishii, Y. Kijima, and N. Matsuzawa, "Macrocyclic functional dyes: Applications to optical disk media, photochemical hole burning and non-linear optics," Pure and Appl. Chem. 68, 1429-1434 (1996).
[CrossRef]

Kishii, N.

J. Seto, S. Tamura, N. Asai, N. Kishii, Y. Kijima, and N. Matsuzawa, "Macrocyclic functional dyes: Applications to optical disk media, photochemical hole burning and non-linear optics," Pure and Appl. Chem. 68, 1429-1434 (1996).
[CrossRef]

Kovsh, D. I.

Kuwano, A.

Lee, J. Y. S.

J. W. Perry, K. Mansour, J. Y. S. Lee, X. L. Xu, P.V. Bedwhorth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada,M. Tian, and H. Sasabe, "Organic optical limiter with a strong nonlinear absorptive response," Science 23, 1533-1536 (1996).
[CrossRef]

Li, C.

C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, "Dynamic and steady-state behaviors of reverse satura absorption in metallophthalocyanines," Phys. Rev. A 49, 1149-1157 (1994).
[CrossRef] [PubMed]

Lin, M. S.

T. H. Wei, T. H. Huang, and M. S. Lin, "Signs of nonlinear refraction in chloroaluminum phthalocyanine solution," Appl. Phys. Lett. 72, 2505-2507 (1998).
[CrossRef]

Lindle, J. R.

J. S. Shirk, J. R. Lindle, F. J. Bartoli, C. A. Hoffman, A. H. Kafafi, and A. W. Snow, "Off-resonat third-order optical nonlinearities of meta-substituted phthalocyanines," Appl. Phys. Lett. 55, 1287-1288 (1989).
[CrossRef]

Liu, D.

T. H. Wei, T. H. Huang, S. Yang, D. Liu, J. K. Hu and C. W. Chen, "Z-scan study of optical nonlinearity in C60-toluene solution," Mol. Phys. 103, 1847-1857 (2005).

Madge, D.

J. H. Brannon and D. Madge, "Picosecond laser Photophysics. group 3A phthalocyanines," J. Am. Chem. Soc. 102, 62-65 (1980).
[CrossRef]

Mansour, K.

J. W. Perry, K. Mansour, J. Y. S. Lee, X. L. Xu, P.V. Bedwhorth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada,M. Tian, and H. Sasabe, "Organic optical limiter with a strong nonlinear absorptive response," Science 23, 1533-1536 (1996).
[CrossRef]

Marder, S. R.

J. W. Perry, K. Mansour, J. Y. S. Lee, X. L. Xu, P.V. Bedwhorth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada,M. Tian, and H. Sasabe, "Organic optical limiter with a strong nonlinear absorptive response," Science 23, 1533-1536 (1996).
[CrossRef]

Matsuzawa, N.

J. Seto, S. Tamura, N. Asai, N. Kishii, Y. Kijima, and N. Matsuzawa, "Macrocyclic functional dyes: Applications to optical disk media, photochemical hole burning and non-linear optics," Pure and Appl. Chem. 68, 1429-1434 (1996).
[CrossRef]

Mclean, D. G.

Mehendale, S. C.

S. R. Mishra, H. S. Rawat, M. P. Joshi and S. C. Mehendale, "The role of non-linear scattering in optical limiting in C60 solution," J. Phys. B:At. Mol. Phys. 27, 157-163, (1994).
[CrossRef]

Miles, P.

J. W. Perry, K. Mansour, J. Y. S. Lee, X. L. Xu, P.V. Bedwhorth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada,M. Tian, and H. Sasabe, "Organic optical limiter with a strong nonlinear absorptive response," Science 23, 1533-1536 (1996).
[CrossRef]

Mishra, S. R.

S. R. Mishra, H. S. Rawat, M. P. Joshi and S. C. Mehendale, "The role of non-linear scattering in optical limiting in C60 solution," J. Phys. B:At. Mol. Phys. 27, 157-163, (1994).
[CrossRef]

Ng, D.

J. W. Perry, K. Mansour, J. Y. S. Lee, X. L. Xu, P.V. Bedwhorth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada,M. Tian, and H. Sasabe, "Organic optical limiter with a strong nonlinear absorptive response," Science 23, 1533-1536 (1996).
[CrossRef]

Perry, J. W.

J. W. Perry, K. Mansour, J. Y. S. Lee, X. L. Xu, P.V. Bedwhorth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada,M. Tian, and H. Sasabe, "Organic optical limiter with a strong nonlinear absorptive response," Science 23, 1533-1536 (1996).
[CrossRef]

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. V. Stryland, J. W. Perry, and D. R. Coulter, "Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines," Appl. Phys. B 54, 46-51 (1992).
[CrossRef]

Pottenger, T.

Rawat, H. S.

S. R. Mishra, H. S. Rawat, M. P. Joshi and S. C. Mehendale, "The role of non-linear scattering in optical limiting in C60 solution," J. Phys. B:At. Mol. Phys. 27, 157-163, (1994).
[CrossRef]

Said, A. A.

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, 760-769 (1990).
[CrossRef]

Sasabe, H.

J. W. Perry, K. Mansour, J. Y. S. Lee, X. L. Xu, P.V. Bedwhorth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada,M. Tian, and H. Sasabe, "Organic optical limiter with a strong nonlinear absorptive response," Science 23, 1533-1536 (1996).
[CrossRef]

Sence, M. J.

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. V. Stryland, J. W. Perry, and D. R. Coulter, "Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines," Appl. Phys. B 54, 46-51 (1992).
[CrossRef]

Seto, J.

J. Seto, S. Tamura, N. Asai, N. Kishii, Y. Kijima, and N. Matsuzawa, "Macrocyclic functional dyes: Applications to optical disk media, photochemical hole burning and non-linear optics," Pure and Appl. Chem. 68, 1429-1434 (1996).
[CrossRef]

Sheik-Bahae, M.

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, 760-769 (1990).
[CrossRef]

Shirk, J. S.

J. S. Shirk, J. R. Lindle, F. J. Bartoli, C. A. Hoffman, A. H. Kafafi, and A. W. Snow, "Off-resonat third-order optical nonlinearities of meta-substituted phthalocyanines," Appl. Phys. Lett. 55, 1287-1288 (1989).
[CrossRef]

Snow, A. W.

J. S. Shirk, J. R. Lindle, F. J. Bartoli, C. A. Hoffman, A. H. Kafafi, and A. W. Snow, "Off-resonat third-order optical nonlinearities of meta-substituted phthalocyanines," Appl. Phys. Lett. 55, 1287-1288 (1989).
[CrossRef]

Stryland, E. W. V.

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. V. Stryland, J. W. Perry, and D. R. Coulter, "Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines," Appl. Phys. B 54, 46-51 (1992).
[CrossRef]

Stryland, E.W.

Sutherland, R. L.

Takane, N.

Tamura, S.

J. Seto, S. Tamura, N. Asai, N. Kishii, Y. Kijima, and N. Matsuzawa, "Macrocyclic functional dyes: Applications to optical disk media, photochemical hole burning and non-linear optics," Pure and Appl. Chem. 68, 1429-1434 (1996).
[CrossRef]

Tian, M.

J. W. Perry, K. Mansour, J. Y. S. Lee, X. L. Xu, P.V. Bedwhorth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada,M. Tian, and H. Sasabe, "Organic optical limiter with a strong nonlinear absorptive response," Science 23, 1533-1536 (1996).
[CrossRef]

Tomiyama, T.

Van Stryland, E. W.

D. I. Kovsh, S. Yang, D. J. Hagan, and E. W. Van Stryland, "Nonlinear optical beam propagation for optical limiting," Appl. Opt. 38, 5168-5180 (1999).
[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, 760-769 (1990).
[CrossRef]

Wada, T.

J. W. Perry, K. Mansour, J. Y. S. Lee, X. L. Xu, P.V. Bedwhorth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada,M. Tian, and H. Sasabe, "Organic optical limiter with a strong nonlinear absorptive response," Science 23, 1533-1536 (1996).
[CrossRef]

Wang, H.

C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, "Dynamic and steady-state behaviors of reverse satura absorption in metallophthalocyanines," Phys. Rev. A 49, 1149-1157 (1994).
[CrossRef] [PubMed]

Wang, Y.

C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, "Dynamic and steady-state behaviors of reverse satura absorption in metallophthalocyanines," Phys. Rev. A 49, 1149-1157 (1994).
[CrossRef] [PubMed]

Watanabe, I.

Wei, T. H.

T. H. Wei, T. H. Huang, S. Yang, D. Liu, J. K. Hu and C. W. Chen, "Z-scan study of optical nonlinearity in C60-toluene solution," Mol. Phys. 103, 1847-1857 (2005).

T. H. Wei, T. H. Huang, and M. S. Lin, "Signs of nonlinear refraction in chloroaluminum phthalocyanine solution," Appl. Phys. Lett. 72, 2505-2507 (1998).
[CrossRef]

T. H. Wei and T. H. Huang, "A study of photophysics using the Z-scan technique: lifetime determination for high-lying excited states," Opt. and Quantum Electron. 28, 1495-1508 (1996).
[CrossRef]

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. V. Stryland, J. W. Perry, and D. R. Coulter, "Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines," Appl. Phys. B 54, 46-51 (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, 760-769 (1990).
[CrossRef]

Xu, X. L.

J. W. Perry, K. Mansour, J. Y. S. Lee, X. L. Xu, P.V. Bedwhorth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada,M. Tian, and H. Sasabe, "Organic optical limiter with a strong nonlinear absorptive response," Science 23, 1533-1536 (1996).
[CrossRef]

Yang, M.

C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, "Dynamic and steady-state behaviors of reverse satura absorption in metallophthalocyanines," Phys. Rev. A 49, 1149-1157 (1994).
[CrossRef] [PubMed]

Yang, S.

T. H. Wei, T. H. Huang, S. Yang, D. Liu, J. K. Hu and C. W. Chen, "Z-scan study of optical nonlinearity in C60-toluene solution," Mol. Phys. 103, 1847-1857 (2005).

D. I. Kovsh, S. Yang, D. J. Hagan, and E. W. Van Stryland, "Nonlinear optical beam propagation for optical limiting," Appl. Opt. 38, 5168-5180 (1999).
[CrossRef]

Zhang, L.

C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, "Dynamic and steady-state behaviors of reverse satura absorption in metallophthalocyanines," Phys. Rev. A 49, 1149-1157 (1994).
[CrossRef] [PubMed]

Appl. Opt. (2)

Appl. Phys. B (1)

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. V. Stryland, J. W. Perry, and D. R. Coulter, "Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines," Appl. Phys. B 54, 46-51 (1992).
[CrossRef]

Appl. Phys. Lett. (2)

J. S. Shirk, J. R. Lindle, F. J. Bartoli, C. A. Hoffman, A. H. Kafafi, and A. W. Snow, "Off-resonat third-order optical nonlinearities of meta-substituted phthalocyanines," Appl. Phys. Lett. 55, 1287-1288 (1989).
[CrossRef]

T. H. Wei, T. H. Huang, and M. S. Lin, "Signs of nonlinear refraction in chloroaluminum phthalocyanine solution," Appl. Phys. Lett. 72, 2505-2507 (1998).
[CrossRef]

At. Mol. Phys. (1)

S. R. Mishra, H. S. Rawat, M. P. Joshi and S. C. Mehendale, "The role of non-linear scattering in optical limiting in C60 solution," J. Phys. B:At. Mol. Phys. 27, 157-163, (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

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, 760-769 (1990).
[CrossRef]

J. Am. Chem. Soc. (1)

J. H. Brannon and D. Madge, "Picosecond laser Photophysics. group 3A phthalocyanines," J. Am. Chem. Soc. 102, 62-65 (1980).
[CrossRef]

J. Opt. Soc. Am. B (1)

Mol. Phys. (1)

T. H. Wei, T. H. Huang, S. Yang, D. Liu, J. K. Hu and C. W. Chen, "Z-scan study of optical nonlinearity in C60-toluene solution," Mol. Phys. 103, 1847-1857 (2005).

Opt. and Quantum Electron. (1)

T. H. Wei and T. H. Huang, "A study of photophysics using the Z-scan technique: lifetime determination for high-lying excited states," Opt. and Quantum Electron. 28, 1495-1508 (1996).
[CrossRef]

Opt. Comm. (1)

J. -M. Heritier, "Electrostrictive limit and focusing effects in pulsed photoacoustic detection," Opt. Comm. 44, 267-272 (1983).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, "Dynamic and steady-state behaviors of reverse satura absorption in metallophthalocyanines," Phys. Rev. A 49, 1149-1157 (1994).
[CrossRef] [PubMed]

Pure and Appl. Chem. (1)

J. Seto, S. Tamura, N. Asai, N. Kishii, Y. Kijima, and N. Matsuzawa, "Macrocyclic functional dyes: Applications to optical disk media, photochemical hole burning and non-linear optics," Pure and Appl. Chem. 68, 1429-1434 (1996).
[CrossRef]

Science (1)

J. W. Perry, K. Mansour, J. Y. S. Lee, X. L. Xu, P.V. Bedwhorth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada,M. Tian, and H. Sasabe, "Organic optical limiter with a strong nonlinear absorptive response," Science 23, 1533-1536 (1996).
[CrossRef]

Other (7)

D. R. Lide. in CRC Handbook of Chemistry and Physics, 77th ed., D. R. Lide and et al, eds. (CRC Press, Boca Raton, 1996), pp. 6-128.

D. Landau and E. M. Lifshitz, in Course of theoretical physics (Pergamon Press), Vol. 6.

C. Jensen, in High Power Dye Lasers, F. J. Durate, eds. (Springer-Verlag, Berlin, 1991), pp. 48.

A. Seilmeier and W. Kaiser, in Ultrashort Laser Pulses 2nd ed., W. Kaiser, eds. (Springer-Verlag, Berlin, 1993), pp. 305.

J. W. Perry, L. R. Khundkar, D. L. Coulter, D. Alvarez, Jr., S. R. Marder, T. H. Wei, M. J. Sence, E. W. Van Stryland, and D. J. Hagan, in Organic Molecules for Nonlinear Optics and Photonics, NATO ASI Series E, J. Messier, F. Kajzar, and P. Prasad, eds, (Kluwer, Dordrecht, 1991), Vol. 194, pp. 369-382.

A. A. Said, T. Xia, D. J. Hagan, A. Wajsgrus. S. Yang, D. Kovsh and E. W. Van Stryland, in Conference on Nonlinear Optical Liquids, Proc. SPIE-2853, (1996).

C. W. Chang, M. S. thesis, National Chung Cheng University, pp. 28, (1999).

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Figures (7)

Fig. 1.
Fig. 1.

The Z-scan experimental setup. D4, D5, and D6 are photodetectors. BS1 and BS2 are beam splitters. A sample placed on a motion control stage can be moved from -z to +z.

Fig. 2.
Fig. 2.

The temporal profile of the full pulse envelope. The numbers above spikes mark their order.

Fig. 3.
Fig. 3.

A five-energy-band model for SiNc-toluene: upward-pointing arrows, wiggly lines, and downward-pointing arrows indicate optical excitation, non-radiative relaxation and radiative relaxation, respectively. ∣ ν) refers to vibrational eigenstate. τ denotes lifetime (ISC ≡intersystem crossing, IC ≡internal conversion, and f ≡fluorescence).

Fig. 4.
Fig. 4.

The Z-scan curves for 21-ns pulse trains with an energy level of 0.8 μJ. (a) NT: triangles stand for the experimental result without an aperture, and the solid line for the theoretical simulation. (b) NT a : squares stand for the experimental result with an aperture, the solid line for the theoretical fit with Eqs. (16) and (18), and the dashed line for the theoretical fit with Eq. (19) alone. (c) NT d : dots stand for the experimental result with an aperture, the solid line for the theoretical fit with Eqs. (16) and (18), and the dashed line for the theoretical fit with Eq. (19) alone.

Fig. 5.
Fig. 5.

The Z-scan curve for 21-ns pulse trains with an energy level of 1.4 μJ. (a) NT: triangles stand for the experimental result without an aperture, and the solid line for the theoretical simulation. (b) NT a : squares stand for the experimental result with an aperture, the solid line for the theoretical fit with Eqs. (16) and (18), and the dashed line for the theoretical fit with Eq. (19) alone. (c) NTd: dots stand for the experimental result with an aperture, the solid line for the theoretical fit with Eqs. (16) and (18), and the dashed line for the theoretical fit with Eq. (19) alone.

Fig. 6.
Fig. 6.

The Z-scan curve for 2.8-ns pulses with an energy level of 1.4 μJ. (a) NT: triangles stand for the experimental result without an aperture, and the solid line for the theoretical simulation. (b) NT a : squares stand for the experimental result with an aperture, the solid line for the theoretical fit with Eqs. (16) and (18), and the dashed line for the theoretical fit with Eq. (19) alone. (c) NT d : dots stand for the experimental result with an aperture, the solid line for the theoretical fit with Eqs. (16) and (18), and the dashed line for the theoretical fit with Eq. (19) alone.

Fig. 7.
Fig. 7.

The Z-scan curve for 2.8-ns pulses with an energy level of 2.5 μJ. (a) NT: triangles stand for the experimental result without an aperture, and the solid line for the theoretical simulation. (b) NT a : squares stand for the experimental result with an aperture, the solid line for the theoretical fit with Eqs. (16) and (18), and the dashed line for the theoretical fit with Eq. (19) alone. (c) NT d : dots stand for the experimental result with an aperture, the solid line for the theoretical fit with Eqs. (16) and (18), and the dashed line for the theoretical fit with Eq. (19) alone.

Equations (19)

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I 0 = I z r , t = I 00 ( n ) × [ w 0 2 w 2 ( z ) ] × exp [ 2 r 2 w 2 ( z ) ] × exp [ ( t n × 7 ns τ ) 2 ]
ϕ 0 = ϕ ( z , r , t ) = kr 2 2 R ( z ) .
I 00 ( n ) = 2 ε ( n ) π 3 2 w 0 2 τ .
ε ( n ) = ε ( 0 ) × exp [ ( n × 7 ns τ env ) 2 ] .
ε ( n ) = ε t × exp [ ( n × 7 ns τ env ) 2 ] m = 5 5 exp [ ( m × 7 ns τ e n v ) ] .
I 0 = I z r , t = I 00 × [ w 0 2 w 2 ( z ) ] × exp [ 2 r 2 w 2 ( z ) ] × exp [ ( t τ ) 2 ]
dI dz ' = [ ( σa ) S 0 N S 0 + ( σa ) S 1 N S 1 + ( σa ) T 1 ] I βN S 0 I 2
dz ' = [ ( σr ) S 0 N S 0 + ( σr ) S 1 N S 1 + ( σr ) T 1 N T 1 ] I + γ N S 0 I + kn 2 I + k Δ n therm ,
dN S 0 dt = ( σa ) S 0 N S 0 I ħω βN S 0 I 2 2 ħω + N S 1 τ f + N T 1 τ T 1 ,
dN S 1 dt = ( σa ) S 0 N S 0 I ħω + βN S 0 I 2 2 ħω N S 1 τ f N S 1 τ ISC ,
dN T 1 dt = N S 1 τ ISC N T 1 τ T 1 .
dQ dt = ( σa ) S 0 N S 0 I ħω × ħ ( ω ω S 1 ) + ( σa ) S 1 N S 1 I + βN S 0 I 2 2 ħω × ħ ( 2 ω ω S 1 ) + ( σa ) T 1 N T 1 I ,
Δ θ = 1 ρC p t dQ dt ' dt ' .
Δθ n = 1 ρC p dQ n dt ' dt ' ,
Δ θ = 5 n 1 Δ θ n .
2 ( Δρ ) t 2 v s 2 2 ( Δ ρ ) = v s 2 2 ( Δθ ) γ e 2 nc 2 I ,
Δn therm = ( n θ ) ρ Δ θ + ( n ρ ) θ Δ ρ .
Δ n therm γ e 2 Δ ρ .
Δ n therm e 2 n Δ θ + γ e 2 4 n 2 cv s 2 I .

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