Abstract

The nonlinear optical properties of an azobenzene-containing ionic liquid crystalline polymer were investigated using single beam Z-scan and optical Kerr effect (OKE) techniques. The nonlinear refractive index of electronic origin (3.1×10−19 m2/W) and the nonlinear absorption coefficient (3.63×10−13 m/W) were determined with 800 nm femtosecond laser pulses at a repetition rate of 1 KHz. The corresponding one-photon and two-photon figures of merit are determined to be 6.05 and 0.94, respectively, at irradiance of 50 GW/cm2. The response time of the observed nonlinearities is estimated to be as fast as 300 fs. These experiment results demonstrate that the polymer is a promising candidate for applications in all-optical switching modulators and nonlinear photonic devices.

© 2012 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]

2011

T. C. He, C. S. Wang, C. Z. Zhang, and G. Y. Lu, “Nonlinear optical properties of an azo-based dye irradiated by picosecond and nanosecond laser pulses,” Physica B406(3), 488–493 (2011).
[CrossRef]

2010

T. C. He, C. S. Wang, J. W. Zhang, X. Q. Zhang, and X. M. Lu, “Nonlinear absorption in an azo-containing ion liquid crystal polymer in the different excitation regimes,” Synth. Met.160(17-18), 1896–1901 (2010).
[CrossRef]

X. Q. Zhang, C. S. Wang, X. Pan, S. F. Xiao, Y. Zeng, T. C. He, and X. M. Lu, “Nonlinear optical properties and photoinduced anisotropy of an azobenzene ionic liquid–crystalline polymer,” Opt. Commun.283(1), 146–150 (2010).
[CrossRef]

2009

D. G. Kong, Q. Chang, H. A. Ye, Y. C. Gao, Y. X. Wang, X. R. Zhang, K. Yang, W. Z. Wu, and Y. L. Song, “The fifth-order nonlinearity of CS2,” J. Phys. At. Mol. Opt. Phys.42(6), 065401 (2009).
[CrossRef]

Z. Y. Zhao, T. Q. Jia, J. Lin, Z. G. Wang, and Z. R. Sun, “Femtosecond non-resonant optical nonlinearity of silver chloride nanocrystal doped niobic tellurite glass,” J. Phys. D Appl. Phys.42(4), 045107 (2009).
[CrossRef]

T. Y. Ning, P. Gao, W. L. Wang, H. Lu, W. Y. Fu, Y. L. Zhou, D. X. Zhang, X. D. Bai, E. Wang, and G. Z. Yang, “Nonlinear optical properties of composite films consisting of multi-armed CdS nanorods and ZnO,” Opt. Mater.31(6), 931–935 (2009).
[CrossRef]

Y. M. Chen, J. F. Zhang, Y. X. Wang, X. R. Zhang, K. Yang, C. Zhang, and Y. L. Song, “Third- and fifth-order nonlinearities of heterobimetallic cluster [WOS3Cu3(4-pic)6]·ClO4,” Mater. Chem. Phys.117(1), 66–69 (2009).
[CrossRef]

2008

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(10), 103511 (2008).
[CrossRef]

T. C. He and C. S. Wang, “The study on the nonlinear optical response of Sudan I,” Opt. Commun.281(15-16), 4121–4125 (2008).
[CrossRef]

A. A. Rodriguez-Rosales, O. G. Morales-Saavedra, C. J. Roman-Moreno, and R. Ortega-Martinez, “Variation of nonlinear refractive index in dye-doped liquid crystals by local and nonlocal mechanisms,” Opt. Mater.31(2), 350–360 (2008).
[CrossRef]

T. C. He, L. Zhang, Y. F. Yin, Y. G. Cheng, L. Ding, and Y. J. Mo, “Resonant electronic nonlinearity and laser heating induced nonlinearity of chlorophosphonazo I,” Phys. Lett. A372(21), 3937–3940 (2008).
[CrossRef]

2007

R. S. S. Kumar, S. V. Rao, L. Giribabu, and D. N. Rao, “Femtosecond and nanosecond nonlinear optical properties of alkyl phthalocyanines studied using Z-scan technique,” Chem. Phys. Lett.447(4-6), 274–278 (2007).
[CrossRef]

C. W. Chen, J. L. Tang, K. H. Chung, T. H. Wei, and T. H. Huang, “Negative nonlinear refraction obtained with ultrashort laser pulses,” Opt. Express15(11), 7006–7018 (2007).
[CrossRef] [PubMed]

S. F. Xiao, X. M. Lu, and Q. H. Lu, “Photosensitive liquid-crystalline supramolecules self-assembled from ionic liquid crystal and polyelectrolyte for laser-induced optical anisotropy,” Macromolecules40, 7944–7950 (2007).
[CrossRef]

T. He, Y. Cheng, Y. Du, and Y. Mo, “Z-scan determination of third-order nonlinear optical nonlinearity of three azobenzenes doped polymer films,” Opt. Commun.275(1), 240–244 (2007).
[CrossRef]

2005

2004

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B78(3-4), 433–438 (2004).
[CrossRef]

R. A. Ganeev, A. I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun.231(1-6), 431–436 (2004).
[CrossRef]

2003

Q. Y. Chen, L. Kuang, E. H. Sargent, and Z. Y. Wang, “Ultrafast nonresonant third-order optical nonlinearity of fullerenecontaining polyurethane films at telecommunication wavelengths,” Appl. Phys. Lett.83(11), 2115–2117 (2003).
[CrossRef]

2001

L. Brzozowski and E. H. Sargent, “Azobenzenes for photonic network applications:Third-order nonlinear optical properties,” J. Mater. Sci. Mater. Electron.12(9), 483–489 (2001).
[CrossRef]

1998

R. Rangel-Rojo, S. Yamada, H. Matsuda, and D. Yankelevich, “Large near-resonance third-order nonlinearity in an azobenzenefunctionalized polymer film,” Appl. Phys. Lett.72(9), 1021–1023 (1998).
[CrossRef]

1995

N. Sugimoto, A. Koiwai, S. Hyodo, T. Hioki, and S. Noda, “Nonresonant third-order nonlinear optical susceptibility of CdS clusters encapsulated in zeolite A and X,” Appl. Phys. Lett.66(8), 923–925 (1995).
[CrossRef]

1993

1990

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(4), 760–769 (1990).
[CrossRef]

Agnesi, A.

Baba, M.

R. A. Ganeev, A. I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun.231(1-6), 431–436 (2004).
[CrossRef]

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B78(3-4), 433–438 (2004).
[CrossRef]

Bai, X. D.

T. Y. Ning, P. Gao, W. L. Wang, H. Lu, W. Y. Fu, Y. L. Zhou, D. X. Zhang, X. D. Bai, E. Wang, and G. Z. Yang, “Nonlinear optical properties of composite films consisting of multi-armed CdS nanorods and ZnO,” Opt. Mater.31(6), 931–935 (2009).
[CrossRef]

Brzozowski, L.

L. Brzozowski and E. H. Sargent, “Azobenzenes for photonic network applications:Third-order nonlinear optical properties,” J. Mater. Sci. Mater. Electron.12(9), 483–489 (2001).
[CrossRef]

Chang, Q.

D. G. Kong, Q. Chang, H. A. Ye, Y. C. Gao, Y. X. Wang, X. R. Zhang, K. Yang, W. Z. Wu, and Y. L. Song, “The fifth-order nonlinearity of CS2,” J. Phys. At. Mol. Opt. Phys.42(6), 065401 (2009).
[CrossRef]

Chen, C. H.

Chen, C. W.

Chen, Q. Y.

Q. Y. Chen, L. Kuang, E. H. Sargent, and Z. Y. Wang, “Ultrafast nonresonant third-order optical nonlinearity of fullerenecontaining polyurethane films at telecommunication wavelengths,” Appl. Phys. Lett.83(11), 2115–2117 (2003).
[CrossRef]

Chen, Y. M.

Y. M. Chen, J. F. Zhang, Y. X. Wang, X. R. Zhang, K. Yang, C. Zhang, and Y. L. Song, “Third- and fifth-order nonlinearities of heterobimetallic cluster [WOS3Cu3(4-pic)6]·ClO4,” Mater. Chem. Phys.117(1), 66–69 (2009).
[CrossRef]

Cheng, Y.

T. He, Y. Cheng, Y. Du, and Y. Mo, “Z-scan determination of third-order nonlinear optical nonlinearity of three azobenzenes doped polymer films,” Opt. Commun.275(1), 240–244 (2007).
[CrossRef]

Cheng, Y. G.

T. C. He, L. Zhang, Y. F. Yin, Y. G. Cheng, L. Ding, and Y. J. Mo, “Resonant electronic nonlinearity and laser heating induced nonlinearity of chlorophosphonazo I,” Phys. Lett. A372(21), 3937–3940 (2008).
[CrossRef]

Chung, K. H.

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(10), 103511 (2008).
[CrossRef]

Ding, L.

T. C. He, L. Zhang, Y. F. Yin, Y. G. Cheng, L. Ding, and Y. J. Mo, “Resonant electronic nonlinearity and laser heating induced nonlinearity of chlorophosphonazo I,” Phys. Lett. A372(21), 3937–3940 (2008).
[CrossRef]

Du, Y.

T. He, Y. Cheng, Y. Du, and Y. Mo, “Z-scan determination of third-order nonlinear optical nonlinearity of three azobenzenes doped polymer films,” Opt. Commun.275(1), 240–244 (2007).
[CrossRef]

Fu, W. Y.

T. Y. Ning, P. Gao, W. L. Wang, H. Lu, W. Y. Fu, Y. L. Zhou, D. X. Zhang, X. D. Bai, E. Wang, and G. Z. Yang, “Nonlinear optical properties of composite films consisting of multi-armed CdS nanorods and ZnO,” Opt. Mater.31(6), 931–935 (2009).
[CrossRef]

Fuh, A. Y. G.

Ganeev, R. A.

R. A. Ganeev, A. I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun.231(1-6), 431–436 (2004).
[CrossRef]

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B78(3-4), 433–438 (2004).
[CrossRef]

Gao, P.

T. Y. Ning, P. Gao, W. L. Wang, H. Lu, W. Y. Fu, Y. L. Zhou, D. X. Zhang, X. D. Bai, E. Wang, and G. Z. Yang, “Nonlinear optical properties of composite films consisting of multi-armed CdS nanorods and ZnO,” Opt. Mater.31(6), 931–935 (2009).
[CrossRef]

Gao, Y. C.

D. G. Kong, Q. Chang, H. A. Ye, Y. C. Gao, Y. X. Wang, X. R. Zhang, K. Yang, W. Z. Wu, and Y. L. Song, “The fifth-order nonlinearity of CS2,” J. Phys. At. Mol. Opt. Phys.42(6), 065401 (2009).
[CrossRef]

Giribabu, L.

R. S. S. Kumar, S. V. Rao, L. Giribabu, and D. N. Rao, “Femtosecond and nanosecond nonlinear optical properties of alkyl phthalocyanines studied using Z-scan technique,” Chem. Phys. Lett.447(4-6), 274–278 (2007).
[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(10), 103511 (2008).
[CrossRef]

Hagan, D. J.

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(4), 760–769 (1990).
[CrossRef]

He, T.

T. He, Y. Cheng, Y. Du, and Y. Mo, “Z-scan determination of third-order nonlinear optical nonlinearity of three azobenzenes doped polymer films,” Opt. Commun.275(1), 240–244 (2007).
[CrossRef]

He, T. C.

T. C. He, C. S. Wang, C. Z. Zhang, and G. Y. Lu, “Nonlinear optical properties of an azo-based dye irradiated by picosecond and nanosecond laser pulses,” Physica B406(3), 488–493 (2011).
[CrossRef]

X. Q. Zhang, C. S. Wang, X. Pan, S. F. Xiao, Y. Zeng, T. C. He, and X. M. Lu, “Nonlinear optical properties and photoinduced anisotropy of an azobenzene ionic liquid–crystalline polymer,” Opt. Commun.283(1), 146–150 (2010).
[CrossRef]

T. C. He, C. S. Wang, J. W. Zhang, X. Q. Zhang, and X. M. Lu, “Nonlinear absorption in an azo-containing ion liquid crystal polymer in the different excitation regimes,” Synth. Met.160(17-18), 1896–1901 (2010).
[CrossRef]

T. C. He and C. S. Wang, “The study on the nonlinear optical response of Sudan I,” Opt. Commun.281(15-16), 4121–4125 (2008).
[CrossRef]

T. C. He, L. Zhang, Y. F. Yin, Y. G. Cheng, L. Ding, and Y. J. Mo, “Resonant electronic nonlinearity and laser heating induced nonlinearity of chlorophosphonazo I,” Phys. Lett. A372(21), 3937–3940 (2008).
[CrossRef]

Hioki, T.

N. Sugimoto, A. Koiwai, S. Hyodo, T. Hioki, and S. Noda, “Nonresonant third-order nonlinear optical susceptibility of CdS clusters encapsulated in zeolite A and X,” Appl. Phys. Lett.66(8), 923–925 (1995).
[CrossRef]

Huang, T. H.

Hyodo, S.

N. Sugimoto, A. Koiwai, S. Hyodo, T. Hioki, and S. Noda, “Nonresonant third-order nonlinear optical susceptibility of CdS clusters encapsulated in zeolite A and X,” Appl. Phys. Lett.66(8), 923–925 (1995).
[CrossRef]

Ishizawa, N.

R. A. Ganeev, A. I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun.231(1-6), 431–436 (2004).
[CrossRef]

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B78(3-4), 433–438 (2004).
[CrossRef]

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(10), 103511 (2008).
[CrossRef]

Jia, T. Q.

Z. Y. Zhao, T. Q. Jia, J. Lin, Z. G. Wang, and Z. R. Sun, “Femtosecond non-resonant optical nonlinearity of silver chloride nanocrystal doped niobic tellurite glass,” J. Phys. D Appl. Phys.42(4), 045107 (2009).
[CrossRef]

Koiwai, A.

N. Sugimoto, A. Koiwai, S. Hyodo, T. Hioki, and S. Noda, “Nonresonant third-order nonlinear optical susceptibility of CdS clusters encapsulated in zeolite A and X,” Appl. Phys. Lett.66(8), 923–925 (1995).
[CrossRef]

Kong, D. G.

D. G. Kong, Q. Chang, H. A. Ye, Y. C. Gao, Y. X. Wang, X. R. Zhang, K. Yang, W. Z. Wu, and Y. L. Song, “The fifth-order nonlinearity of CS2,” J. Phys. At. Mol. Opt. Phys.42(6), 065401 (2009).
[CrossRef]

Kuang, L.

Q. Y. Chen, L. Kuang, E. H. Sargent, and Z. Y. Wang, “Ultrafast nonresonant third-order optical nonlinearity of fullerenecontaining polyurethane films at telecommunication wavelengths,” Appl. Phys. Lett.83(11), 2115–2117 (2003).
[CrossRef]

Kumar, R. S. S.

R. S. S. Kumar, S. V. Rao, L. Giribabu, and D. N. Rao, “Femtosecond and nanosecond nonlinear optical properties of alkyl phthalocyanines studied using Z-scan technique,” Chem. Phys. Lett.447(4-6), 274–278 (2007).
[CrossRef]

Kuroda, H.

R. A. Ganeev, A. I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun.231(1-6), 431–436 (2004).
[CrossRef]

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B78(3-4), 433–438 (2004).
[CrossRef]

Lin, H. C.

Lin, J.

Z. Y. Zhao, T. Q. Jia, J. Lin, Z. G. Wang, and Z. R. Sun, “Femtosecond non-resonant optical nonlinearity of silver chloride nanocrystal doped niobic tellurite glass,” J. Phys. D Appl. Phys.42(4), 045107 (2009).
[CrossRef]

Lu, G. Y.

T. C. He, C. S. Wang, C. Z. Zhang, and G. Y. Lu, “Nonlinear optical properties of an azo-based dye irradiated by picosecond and nanosecond laser pulses,” Physica B406(3), 488–493 (2011).
[CrossRef]

Lu, H.

T. Y. Ning, P. Gao, W. L. Wang, H. Lu, W. Y. Fu, Y. L. Zhou, D. X. Zhang, X. D. Bai, E. Wang, and G. Z. Yang, “Nonlinear optical properties of composite films consisting of multi-armed CdS nanorods and ZnO,” Opt. Mater.31(6), 931–935 (2009).
[CrossRef]

Lu, Q. H.

S. F. Xiao, X. M. Lu, and Q. H. Lu, “Photosensitive liquid-crystalline supramolecules self-assembled from ionic liquid crystal and polyelectrolyte for laser-induced optical anisotropy,” Macromolecules40, 7944–7950 (2007).
[CrossRef]

Lu, X. M.

X. Q. Zhang, C. S. Wang, X. Pan, S. F. Xiao, Y. Zeng, T. C. He, and X. M. Lu, “Nonlinear optical properties and photoinduced anisotropy of an azobenzene ionic liquid–crystalline polymer,” Opt. Commun.283(1), 146–150 (2010).
[CrossRef]

T. C. He, C. S. Wang, J. W. Zhang, X. Q. Zhang, and X. M. Lu, “Nonlinear absorption in an azo-containing ion liquid crystal polymer in the different excitation regimes,” Synth. Met.160(17-18), 1896–1901 (2010).
[CrossRef]

S. F. Xiao, X. M. Lu, and Q. H. Lu, “Photosensitive liquid-crystalline supramolecules self-assembled from ionic liquid crystal and polyelectrolyte for laser-induced optical anisotropy,” Macromolecules40, 7944–7950 (2007).
[CrossRef]

Matsuda, H.

R. Rangel-Rojo, S. Yamada, H. Matsuda, and D. Yankelevich, “Large near-resonance third-order nonlinearity in an azobenzenefunctionalized polymer film,” Appl. Phys. Lett.72(9), 1021–1023 (1998).
[CrossRef]

Mo, T. S.

Mo, Y.

T. He, Y. Cheng, Y. Du, and Y. Mo, “Z-scan determination of third-order nonlinear optical nonlinearity of three azobenzenes doped polymer films,” Opt. Commun.275(1), 240–244 (2007).
[CrossRef]

Mo, Y. J.

T. C. He, L. Zhang, Y. F. Yin, Y. G. Cheng, L. Ding, and Y. J. Mo, “Resonant electronic nonlinearity and laser heating induced nonlinearity of chlorophosphonazo I,” Phys. Lett. A372(21), 3937–3940 (2008).
[CrossRef]

Morales-Saavedra, O. G.

A. A. Rodriguez-Rosales, O. G. Morales-Saavedra, C. J. Roman-Moreno, and R. Ortega-Martinez, “Variation of nonlinear refractive index in dye-doped liquid crystals by local and nonlocal mechanisms,” Opt. Mater.31(2), 350–360 (2008).
[CrossRef]

Ning, T. Y.

T. Y. Ning, P. Gao, W. L. Wang, H. Lu, W. Y. Fu, Y. L. Zhou, D. X. Zhang, X. D. Bai, E. Wang, and G. Z. Yang, “Nonlinear optical properties of composite films consisting of multi-armed CdS nanorods and ZnO,” Opt. Mater.31(6), 931–935 (2009).
[CrossRef]

Noda, S.

N. Sugimoto, A. Koiwai, S. Hyodo, T. Hioki, and S. Noda, “Nonresonant third-order nonlinear optical susceptibility of CdS clusters encapsulated in zeolite A and X,” Appl. Phys. Lett.66(8), 923–925 (1995).
[CrossRef]

Ortega-Martinez, R.

A. A. Rodriguez-Rosales, O. G. Morales-Saavedra, C. J. Roman-Moreno, and R. Ortega-Martinez, “Variation of nonlinear refractive index in dye-doped liquid crystals by local and nonlocal mechanisms,” Opt. Mater.31(2), 350–360 (2008).
[CrossRef]

Pan, X.

X. Q. Zhang, C. S. Wang, X. Pan, S. F. Xiao, Y. Zeng, T. C. He, and X. M. Lu, “Nonlinear optical properties and photoinduced anisotropy of an azobenzene ionic liquid–crystalline polymer,” Opt. Commun.283(1), 146–150 (2010).
[CrossRef]

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(10), 103511 (2008).
[CrossRef]

Rangel-Rojo, R.

R. Rangel-Rojo, S. Yamada, H. Matsuda, and D. Yankelevich, “Large near-resonance third-order nonlinearity in an azobenzenefunctionalized polymer film,” Appl. Phys. Lett.72(9), 1021–1023 (1998).
[CrossRef]

Rao, D. N.

R. S. S. Kumar, S. V. Rao, L. Giribabu, and D. N. Rao, “Femtosecond and nanosecond nonlinear optical properties of alkyl phthalocyanines studied using Z-scan technique,” Chem. Phys. Lett.447(4-6), 274–278 (2007).
[CrossRef]

Rao, S. V.

R. S. S. Kumar, S. V. Rao, L. Giribabu, and D. N. Rao, “Femtosecond and nanosecond nonlinear optical properties of alkyl phthalocyanines studied using Z-scan technique,” Chem. Phys. Lett.447(4-6), 274–278 (2007).
[CrossRef]

Reali, G. C.

Rodriguez-Rosales, A. A.

A. A. Rodriguez-Rosales, O. G. Morales-Saavedra, C. J. Roman-Moreno, and R. Ortega-Martinez, “Variation of nonlinear refractive index in dye-doped liquid crystals by local and nonlocal mechanisms,” Opt. Mater.31(2), 350–360 (2008).
[CrossRef]

Roman-Moreno, C. J.

A. A. Rodriguez-Rosales, O. G. Morales-Saavedra, C. J. Roman-Moreno, and R. Ortega-Martinez, “Variation of nonlinear refractive index in dye-doped liquid crystals by local and nonlocal mechanisms,” Opt. Mater.31(2), 350–360 (2008).
[CrossRef]

Ryasnyansky, A. I.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B78(3-4), 433–438 (2004).
[CrossRef]

R. A. Ganeev, A. I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun.231(1-6), 431–436 (2004).
[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(4), 760–769 (1990).
[CrossRef]

Sakakibara, S.

R. A. Ganeev, A. I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun.231(1-6), 431–436 (2004).
[CrossRef]

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B78(3-4), 433–438 (2004).
[CrossRef]

Sargent, E. H.

Q. Y. Chen, L. Kuang, E. H. Sargent, and Z. Y. Wang, “Ultrafast nonresonant third-order optical nonlinearity of fullerenecontaining polyurethane films at telecommunication wavelengths,” Appl. Phys. Lett.83(11), 2115–2117 (2003).
[CrossRef]

L. Brzozowski and E. H. Sargent, “Azobenzenes for photonic network applications:Third-order nonlinear optical properties,” J. Mater. Sci. Mater. Electron.12(9), 483–489 (2001).
[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(4), 760–769 (1990).
[CrossRef]

Song, Y. L.

Y. M. Chen, J. F. Zhang, Y. X. Wang, X. R. Zhang, K. Yang, C. Zhang, and Y. L. Song, “Third- and fifth-order nonlinearities of heterobimetallic cluster [WOS3Cu3(4-pic)6]·ClO4,” Mater. Chem. Phys.117(1), 66–69 (2009).
[CrossRef]

D. G. Kong, Q. Chang, H. A. Ye, Y. C. Gao, Y. X. Wang, X. R. Zhang, K. Yang, W. Z. Wu, and Y. L. Song, “The fifth-order nonlinearity of CS2,” J. Phys. At. Mol. Opt. Phys.42(6), 065401 (2009).
[CrossRef]

Sugimoto, N.

N. Sugimoto, A. Koiwai, S. Hyodo, T. Hioki, and S. Noda, “Nonresonant third-order nonlinear optical susceptibility of CdS clusters encapsulated in zeolite A and X,” Appl. Phys. Lett.66(8), 923–925 (1995).
[CrossRef]

Sun, Z. R.

Z. Y. Zhao, T. Q. Jia, J. Lin, Z. G. Wang, and Z. R. Sun, “Femtosecond non-resonant optical nonlinearity of silver chloride nanocrystal doped niobic tellurite glass,” J. Phys. D Appl. Phys.42(4), 045107 (2009).
[CrossRef]

Suzuki, M.

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B78(3-4), 433–438 (2004).
[CrossRef]

R. A. Ganeev, A. I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun.231(1-6), 431–436 (2004).
[CrossRef]

Tang, J. L.

Turu, M.

R. A. Ganeev, A. I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun.231(1-6), 431–436 (2004).
[CrossRef]

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B78(3-4), 433–438 (2004).
[CrossRef]

Van Stryland, E. W.

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(4), 760–769 (1990).
[CrossRef]

Wang, C. S.

T. C. He, C. S. Wang, C. Z. Zhang, and G. Y. Lu, “Nonlinear optical properties of an azo-based dye irradiated by picosecond and nanosecond laser pulses,” Physica B406(3), 488–493 (2011).
[CrossRef]

T. C. He, C. S. Wang, J. W. Zhang, X. Q. Zhang, and X. M. Lu, “Nonlinear absorption in an azo-containing ion liquid crystal polymer in the different excitation regimes,” Synth. Met.160(17-18), 1896–1901 (2010).
[CrossRef]

X. Q. Zhang, C. S. Wang, X. Pan, S. F. Xiao, Y. Zeng, T. C. He, and X. M. Lu, “Nonlinear optical properties and photoinduced anisotropy of an azobenzene ionic liquid–crystalline polymer,” Opt. Commun.283(1), 146–150 (2010).
[CrossRef]

T. C. He and C. S. Wang, “The study on the nonlinear optical response of Sudan I,” Opt. Commun.281(15-16), 4121–4125 (2008).
[CrossRef]

Wang, E.

T. Y. Ning, P. Gao, W. L. Wang, H. Lu, W. Y. Fu, Y. L. Zhou, D. X. Zhang, X. D. Bai, E. Wang, and G. Z. Yang, “Nonlinear optical properties of composite films consisting of multi-armed CdS nanorods and ZnO,” Opt. Mater.31(6), 931–935 (2009).
[CrossRef]

Wang, W. L.

T. Y. Ning, P. Gao, W. L. Wang, H. Lu, W. Y. Fu, Y. L. Zhou, D. X. Zhang, X. D. Bai, E. Wang, and G. Z. Yang, “Nonlinear optical properties of composite films consisting of multi-armed CdS nanorods and ZnO,” Opt. Mater.31(6), 931–935 (2009).
[CrossRef]

Wang, Y. X.

Y. M. Chen, J. F. Zhang, Y. X. Wang, X. R. Zhang, K. Yang, C. Zhang, and Y. L. Song, “Third- and fifth-order nonlinearities of heterobimetallic cluster [WOS3Cu3(4-pic)6]·ClO4,” Mater. Chem. Phys.117(1), 66–69 (2009).
[CrossRef]

D. G. Kong, Q. Chang, H. A. Ye, Y. C. Gao, Y. X. Wang, X. R. Zhang, K. Yang, W. Z. Wu, and Y. L. Song, “The fifth-order nonlinearity of CS2,” J. Phys. At. Mol. Opt. Phys.42(6), 065401 (2009).
[CrossRef]

Wang, Z. G.

Z. Y. Zhao, T. Q. Jia, J. Lin, Z. G. Wang, and Z. R. Sun, “Femtosecond non-resonant optical nonlinearity of silver chloride nanocrystal doped niobic tellurite glass,” J. Phys. D Appl. Phys.42(4), 045107 (2009).
[CrossRef]

Wang, Z. Y.

Q. Y. Chen, L. Kuang, E. H. Sargent, and Z. Y. Wang, “Ultrafast nonresonant third-order optical nonlinearity of fullerenecontaining polyurethane films at telecommunication wavelengths,” Appl. Phys. Lett.83(11), 2115–2117 (2003).
[CrossRef]

Wei, T. H.

Wei, T.-H.

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(4), 760–769 (1990).
[CrossRef]

Wu, W. Z.

D. G. Kong, Q. Chang, H. A. Ye, Y. C. Gao, Y. X. Wang, X. R. Zhang, K. Yang, W. Z. Wu, and Y. L. Song, “The fifth-order nonlinearity of CS2,” J. Phys. At. Mol. Opt. Phys.42(6), 065401 (2009).
[CrossRef]

Xiao, S. F.

X. Q. Zhang, C. S. Wang, X. Pan, S. F. Xiao, Y. Zeng, T. C. He, and X. M. Lu, “Nonlinear optical properties and photoinduced anisotropy of an azobenzene ionic liquid–crystalline polymer,” Opt. Commun.283(1), 146–150 (2010).
[CrossRef]

S. F. Xiao, X. M. Lu, and Q. H. Lu, “Photosensitive liquid-crystalline supramolecules self-assembled from ionic liquid crystal and polyelectrolyte for laser-induced optical anisotropy,” Macromolecules40, 7944–7950 (2007).
[CrossRef]

Yamada, S.

R. Rangel-Rojo, S. Yamada, H. Matsuda, and D. Yankelevich, “Large near-resonance third-order nonlinearity in an azobenzenefunctionalized polymer film,” Appl. Phys. Lett.72(9), 1021–1023 (1998).
[CrossRef]

Yang, G. Z.

T. Y. Ning, P. Gao, W. L. Wang, H. Lu, W. Y. Fu, Y. L. Zhou, D. X. Zhang, X. D. Bai, E. Wang, and G. Z. Yang, “Nonlinear optical properties of composite films consisting of multi-armed CdS nanorods and ZnO,” Opt. Mater.31(6), 931–935 (2009).
[CrossRef]

Yang, K.

Y. M. Chen, J. F. Zhang, Y. X. Wang, X. R. Zhang, K. Yang, C. Zhang, and Y. L. Song, “Third- and fifth-order nonlinearities of heterobimetallic cluster [WOS3Cu3(4-pic)6]·ClO4,” Mater. Chem. Phys.117(1), 66–69 (2009).
[CrossRef]

D. G. Kong, Q. Chang, H. A. Ye, Y. C. Gao, Y. X. Wang, X. R. Zhang, K. Yang, W. Z. Wu, and Y. L. Song, “The fifth-order nonlinearity of CS2,” J. Phys. At. Mol. Opt. Phys.42(6), 065401 (2009).
[CrossRef]

Yankelevich, D.

R. Rangel-Rojo, S. Yamada, H. Matsuda, and D. Yankelevich, “Large near-resonance third-order nonlinearity in an azobenzenefunctionalized polymer film,” Appl. Phys. Lett.72(9), 1021–1023 (1998).
[CrossRef]

Ye, H. A.

D. G. Kong, Q. Chang, H. A. Ye, Y. C. Gao, Y. X. Wang, X. R. Zhang, K. Yang, W. Z. Wu, and Y. L. Song, “The fifth-order nonlinearity of CS2,” J. Phys. At. Mol. Opt. Phys.42(6), 065401 (2009).
[CrossRef]

Yin, Y. F.

T. C. He, L. Zhang, Y. F. Yin, Y. G. Cheng, L. Ding, and Y. J. Mo, “Resonant electronic nonlinearity and laser heating induced nonlinearity of chlorophosphonazo I,” Phys. Lett. A372(21), 3937–3940 (2008).
[CrossRef]

Zeng, Y.

X. Q. Zhang, C. S. Wang, X. Pan, S. F. Xiao, Y. Zeng, T. C. He, and X. M. Lu, “Nonlinear optical properties and photoinduced anisotropy of an azobenzene ionic liquid–crystalline polymer,” Opt. Commun.283(1), 146–150 (2010).
[CrossRef]

Zhang, C.

Y. M. Chen, J. F. Zhang, Y. X. Wang, X. R. Zhang, K. Yang, C. Zhang, and Y. L. Song, “Third- and fifth-order nonlinearities of heterobimetallic cluster [WOS3Cu3(4-pic)6]·ClO4,” Mater. Chem. Phys.117(1), 66–69 (2009).
[CrossRef]

Zhang, C. Z.

T. C. He, C. S. Wang, C. Z. Zhang, and G. Y. Lu, “Nonlinear optical properties of an azo-based dye irradiated by picosecond and nanosecond laser pulses,” Physica B406(3), 488–493 (2011).
[CrossRef]

Zhang, D. X.

T. Y. Ning, P. Gao, W. L. Wang, H. Lu, W. Y. Fu, Y. L. Zhou, D. X. Zhang, X. D. Bai, E. Wang, and G. Z. Yang, “Nonlinear optical properties of composite films consisting of multi-armed CdS nanorods and ZnO,” Opt. Mater.31(6), 931–935 (2009).
[CrossRef]

Zhang, J. F.

Y. M. Chen, J. F. Zhang, Y. X. Wang, X. R. Zhang, K. Yang, C. Zhang, and Y. L. Song, “Third- and fifth-order nonlinearities of heterobimetallic cluster [WOS3Cu3(4-pic)6]·ClO4,” Mater. Chem. Phys.117(1), 66–69 (2009).
[CrossRef]

Zhang, J. W.

T. C. He, C. S. Wang, J. W. Zhang, X. Q. Zhang, and X. M. Lu, “Nonlinear absorption in an azo-containing ion liquid crystal polymer in the different excitation regimes,” Synth. Met.160(17-18), 1896–1901 (2010).
[CrossRef]

Zhang, L.

T. C. He, L. Zhang, Y. F. Yin, Y. G. Cheng, L. Ding, and Y. J. Mo, “Resonant electronic nonlinearity and laser heating induced nonlinearity of chlorophosphonazo I,” Phys. Lett. A372(21), 3937–3940 (2008).
[CrossRef]

Zhang, X. Q.

T. C. He, C. S. Wang, J. W. Zhang, X. Q. Zhang, and X. M. Lu, “Nonlinear absorption in an azo-containing ion liquid crystal polymer in the different excitation regimes,” Synth. Met.160(17-18), 1896–1901 (2010).
[CrossRef]

X. Q. Zhang, C. S. Wang, X. Pan, S. F. Xiao, Y. Zeng, T. C. He, and X. M. Lu, “Nonlinear optical properties and photoinduced anisotropy of an azobenzene ionic liquid–crystalline polymer,” Opt. Commun.283(1), 146–150 (2010).
[CrossRef]

Zhang, X. R.

D. G. Kong, Q. Chang, H. A. Ye, Y. C. Gao, Y. X. Wang, X. R. Zhang, K. Yang, W. Z. Wu, and Y. L. Song, “The fifth-order nonlinearity of CS2,” J. Phys. At. Mol. Opt. Phys.42(6), 065401 (2009).
[CrossRef]

Y. M. Chen, J. F. Zhang, Y. X. Wang, X. R. Zhang, K. Yang, C. Zhang, and Y. L. Song, “Third- and fifth-order nonlinearities of heterobimetallic cluster [WOS3Cu3(4-pic)6]·ClO4,” Mater. Chem. Phys.117(1), 66–69 (2009).
[CrossRef]

Zhao, Z. Y.

Z. Y. Zhao, T. Q. Jia, J. Lin, Z. G. Wang, and Z. R. Sun, “Femtosecond non-resonant optical nonlinearity of silver chloride nanocrystal doped niobic tellurite glass,” J. Phys. D Appl. Phys.42(4), 045107 (2009).
[CrossRef]

Zhou, Y. L.

T. Y. Ning, P. Gao, W. L. Wang, H. Lu, W. Y. Fu, Y. L. Zhou, D. X. Zhang, X. D. Bai, E. Wang, and G. Z. Yang, “Nonlinear optical properties of composite films consisting of multi-armed CdS nanorods and ZnO,” Opt. Mater.31(6), 931–935 (2009).
[CrossRef]

Appl. Phys. B

R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, and H. Kuroda, “Nonlinear refraction in CS2,” Appl. Phys. B78(3-4), 433–438 (2004).
[CrossRef]

Appl. Phys. Lett.

N. Sugimoto, A. Koiwai, S. Hyodo, T. Hioki, and S. Noda, “Nonresonant third-order nonlinear optical susceptibility of CdS clusters encapsulated in zeolite A and X,” Appl. Phys. Lett.66(8), 923–925 (1995).
[CrossRef]

Q. Y. Chen, L. Kuang, E. H. Sargent, and Z. Y. Wang, “Ultrafast nonresonant third-order optical nonlinearity of fullerenecontaining polyurethane films at telecommunication wavelengths,” Appl. Phys. Lett.83(11), 2115–2117 (2003).
[CrossRef]

R. Rangel-Rojo, S. Yamada, H. Matsuda, and D. Yankelevich, “Large near-resonance third-order nonlinearity in an azobenzenefunctionalized polymer film,” Appl. Phys. Lett.72(9), 1021–1023 (1998).
[CrossRef]

Chem. Phys. Lett.

R. S. S. Kumar, S. V. Rao, L. Giribabu, and D. N. Rao, “Femtosecond and nanosecond nonlinear optical properties of alkyl phthalocyanines studied using Z-scan technique,” Chem. Phys. Lett.447(4-6), 274–278 (2007).
[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(4), 760–769 (1990).
[CrossRef]

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(10), 103511 (2008).
[CrossRef]

J. Mater. Sci. Mater. Electron.

L. Brzozowski and E. H. Sargent, “Azobenzenes for photonic network applications:Third-order nonlinear optical properties,” J. Mater. Sci. Mater. Electron.12(9), 483–489 (2001).
[CrossRef]

J. Phys. At. Mol. Opt. Phys.

D. G. Kong, Q. Chang, H. A. Ye, Y. C. Gao, Y. X. Wang, X. R. Zhang, K. Yang, W. Z. Wu, and Y. L. Song, “The fifth-order nonlinearity of CS2,” J. Phys. At. Mol. Opt. Phys.42(6), 065401 (2009).
[CrossRef]

J. Phys. D Appl. Phys.

Z. Y. Zhao, T. Q. Jia, J. Lin, Z. G. Wang, and Z. R. Sun, “Femtosecond non-resonant optical nonlinearity of silver chloride nanocrystal doped niobic tellurite glass,” J. Phys. D Appl. Phys.42(4), 045107 (2009).
[CrossRef]

Macromolecules

S. F. Xiao, X. M. Lu, and Q. H. Lu, “Photosensitive liquid-crystalline supramolecules self-assembled from ionic liquid crystal and polyelectrolyte for laser-induced optical anisotropy,” Macromolecules40, 7944–7950 (2007).
[CrossRef]

Mater. Chem. Phys.

Y. M. Chen, J. F. Zhang, Y. X. Wang, X. R. Zhang, K. Yang, C. Zhang, and Y. L. Song, “Third- and fifth-order nonlinearities of heterobimetallic cluster [WOS3Cu3(4-pic)6]·ClO4,” Mater. Chem. Phys.117(1), 66–69 (2009).
[CrossRef]

Opt. Commun.

T. He, Y. Cheng, Y. Du, and Y. Mo, “Z-scan determination of third-order nonlinear optical nonlinearity of three azobenzenes doped polymer films,” Opt. Commun.275(1), 240–244 (2007).
[CrossRef]

T. C. He and C. S. Wang, “The study on the nonlinear optical response of Sudan I,” Opt. Commun.281(15-16), 4121–4125 (2008).
[CrossRef]

R. A. Ganeev, A. I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, and H. Kuroda, “Two- and three-photon absorption in CS2,” Opt. Commun.231(1-6), 431–436 (2004).
[CrossRef]

X. Q. Zhang, C. S. Wang, X. Pan, S. F. Xiao, Y. Zeng, T. C. He, and X. M. Lu, “Nonlinear optical properties and photoinduced anisotropy of an azobenzene ionic liquid–crystalline polymer,” Opt. Commun.283(1), 146–150 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Mater.

A. A. Rodriguez-Rosales, O. G. Morales-Saavedra, C. J. Roman-Moreno, and R. Ortega-Martinez, “Variation of nonlinear refractive index in dye-doped liquid crystals by local and nonlocal mechanisms,” Opt. Mater.31(2), 350–360 (2008).
[CrossRef]

T. Y. Ning, P. Gao, W. L. Wang, H. Lu, W. Y. Fu, Y. L. Zhou, D. X. Zhang, X. D. Bai, E. Wang, and G. Z. Yang, “Nonlinear optical properties of composite films consisting of multi-armed CdS nanorods and ZnO,” Opt. Mater.31(6), 931–935 (2009).
[CrossRef]

Phys. Lett. A

T. C. He, L. Zhang, Y. F. Yin, Y. G. Cheng, L. Ding, and Y. J. Mo, “Resonant electronic nonlinearity and laser heating induced nonlinearity of chlorophosphonazo I,” Phys. Lett. A372(21), 3937–3940 (2008).
[CrossRef]

Physica B

T. C. He, C. S. Wang, C. Z. Zhang, and G. Y. Lu, “Nonlinear optical properties of an azo-based dye irradiated by picosecond and nanosecond laser pulses,” Physica B406(3), 488–493 (2011).
[CrossRef]

Synth. Met.

T. C. He, C. S. Wang, J. W. Zhang, X. Q. Zhang, and X. M. Lu, “Nonlinear absorption in an azo-containing ion liquid crystal polymer in the different excitation regimes,” Synth. Met.160(17-18), 1896–1901 (2010).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) The molecular structure of the polymer. (b)UV-vis absorption spectrum of the polymer in chloroform solution.

Fig. 2
Fig. 2

(a) Normalized open-aperture Z-scan curve excited by the amplified kilohertz laser with irradiance of 50 GW/cm2 at 800 nm. The solid curve is the theoretical fit. (b) The relation of 2PA coefficient β versus I00.

Fig. 3
Fig. 3

(a) The divided Z-scan experiment curve measured at 50 GW/cm2. The solid curve is the theoretical fit. (b) Intensity dependence of ΔZp-v/z0, the distance of the normalized peak and valley transmittance of the divided closed-aperture Z-scan data, and ΔTp-v, the difference between the peak and valley transmittance of the normalized divided closed-aperture Z-scan data.

Fig. 4
Fig. 4

Time-resolved optical Kerr response of the polymer solution under a pump intensity of 60 GW/cm2. The inset is the OKE signal of CS2 measured under the same conditions. The solid curve is the theoretical fit.

Fig. 5
Fig. 5

Normalized closed-aperture Z-scan curves excited by the high repetition rate (80 MHz) Ti:sapphire laser at various excitation irradiances, and the solid lines are the best-fit curves calculated by Z-scan theory.

Equations (2)

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

T(z)= 1 π q 0 + ln( 1+ q 0 exp( x 2 ) ) dx,
T(z)=1 4xΔ ϕ 0 ( x 2 +9)( x 2 +1) ,

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