Abstract

We demonstrate the effectiveness of a simple method for using Z-scan technique with high repetition rate lasers managing cumulative thermal effects. Following Falconieri [J. Opt. A, 1 (1999) 662], time evolution of Z-scan signal is recorded. We use data time correlation to extrapolate with accuracy the instantaneous nonlinear optical response of the sample. The method employed allows us to clearly evaluate the order of the absorption process underlying the thermo-optical nonlinearities. Using a 76 MHz repetition rate laser with 120 fs pulsewidth we measure third order nonlinearities and thermal properties of CS2 and toluene in accordance with values obtained with low repetition rate light sources.

© 2005 Optical Society of America

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References

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  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 (1990).
    [Crossref]
  2. H. P. Li, C. H. Kam, Y. L. Lam, and W. Ji, “Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals,” Opt. Mat. 15, 237 (2001).
    [Crossref]
  3. K. Y. Tseng, K. S. Wong, and G. K. L. Wong, “Femtosecond time-resolved Z-scan investigations of optical nonlinearities in ZnSe,” Opt. Lett. 21, 180 (1996).
    [Crossref] [PubMed]
  4. M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69, 133 (1999).
    [Crossref]
  5. R. de Nalda, R. del Coso, J. Requejo-Isidro, J. Olivares, A. Suarez-Garcia, J. Solis, and C. N. Afonso, “Limits to the determination of the nonlinear refractive index by the Z-scan method,” J. Opt. Soc. Am. B 19, 289 (2002).
    [Crossref]
  6. S. M. Mian, S. B. McGee, and N. Melikechi, “Experimental and theoretical investigation of thermal lensing effect in mode-locked femtosecond Z-scan experiments,” Opt. Commun. 207, 339 (2002).
    [Crossref]
  7. S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369, 318 (2003).
    [Crossref]
  8. 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. B 78, 433 (2004).
    [Crossref]
  9. M. Falconieri, “Thermo-optical effects in Z-scan measurements using high-repetition-rate lasers,” J. Opt. A-Pure Appl. Opt. 1, 662 (1999).
    [Crossref]
  10. H. Bitto, A. Ruzicic, and J. R. Huber, “Dynamics of selected rovibronic eigenstates in the V-system of carbon-disulfide 12,13CS2,” Chem. Phys. 189, 713 (1994).
    [Crossref]
  11. P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. McDuff, “Single beam Z-scan: measurement techniques and analysis,” J. Nonlinear Opt. Phys. 6, 251 (1997).
    [Crossref]
  12. R. W. Minck, R. W. Terhune, and C. C. Wang, “Nonlinear Optics,” Appl. Opt. 5, 1595 (1966).
    [Crossref] [PubMed]
  13. S. E. Bialkowski, “Thermal, optical and physical properties of common solvents,” (2003), http://www.chem.usu.edu/~sbialkow/Research/Tablevalues.html.

2004 (1)

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. B 78, 433 (2004).
[Crossref]

2003 (2)

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369, 318 (2003).
[Crossref]

S. E. Bialkowski, “Thermal, optical and physical properties of common solvents,” (2003), http://www.chem.usu.edu/~sbialkow/Research/Tablevalues.html.

2002 (2)

R. de Nalda, R. del Coso, J. Requejo-Isidro, J. Olivares, A. Suarez-Garcia, J. Solis, and C. N. Afonso, “Limits to the determination of the nonlinear refractive index by the Z-scan method,” J. Opt. Soc. Am. B 19, 289 (2002).
[Crossref]

S. M. Mian, S. B. McGee, and N. Melikechi, “Experimental and theoretical investigation of thermal lensing effect in mode-locked femtosecond Z-scan experiments,” Opt. Commun. 207, 339 (2002).
[Crossref]

2001 (1)

H. P. Li, C. H. Kam, Y. L. Lam, and W. Ji, “Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals,” Opt. Mat. 15, 237 (2001).
[Crossref]

1999 (2)

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69, 133 (1999).
[Crossref]

M. Falconieri, “Thermo-optical effects in Z-scan measurements using high-repetition-rate lasers,” J. Opt. A-Pure Appl. Opt. 1, 662 (1999).
[Crossref]

1997 (1)

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. McDuff, “Single beam Z-scan: measurement techniques and analysis,” J. Nonlinear Opt. Phys. 6, 251 (1997).
[Crossref]

1996 (1)

1994 (1)

H. Bitto, A. Ruzicic, and J. R. Huber, “Dynamics of selected rovibronic eigenstates in the V-system of carbon-disulfide 12,13CS2,” Chem. Phys. 189, 713 (1994).
[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 (1990).
[Crossref]

1966 (1)

Afonso, C. N.

Baba, 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. B 78, 433 (2004).
[Crossref]

Bialkowski, S. E.

S. E. Bialkowski, “Thermal, optical and physical properties of common solvents,” (2003), http://www.chem.usu.edu/~sbialkow/Research/Tablevalues.html.

Bitto, H.

H. Bitto, A. Ruzicic, and J. R. Huber, “Dynamics of selected rovibronic eigenstates in the V-system of carbon-disulfide 12,13CS2,” Chem. Phys. 189, 713 (1994).
[Crossref]

Chapple, P. B.

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. McDuff, “Single beam Z-scan: measurement techniques and analysis,” J. Nonlinear Opt. Phys. 6, 251 (1997).
[Crossref]

Chaux, R.

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369, 318 (2003).
[Crossref]

Couris, S.

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369, 318 (2003).
[Crossref]

de Nalda, R.

del Coso, R.

Falconieri, M.

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69, 133 (1999).
[Crossref]

M. Falconieri, “Thermo-optical effects in Z-scan measurements using high-repetition-rate lasers,” J. Opt. A-Pure Appl. Opt. 1, 662 (1999).
[Crossref]

Faucher, O.

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369, 318 (2003).
[Crossref]

Ganeev, R. A.

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. B 78, 433 (2004).
[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, 760 (1990).
[Crossref]

Hermann, J. A.

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. McDuff, “Single beam Z-scan: measurement techniques and analysis,” J. Nonlinear Opt. Phys. 6, 251 (1997).
[Crossref]

Huber, J. R.

H. Bitto, A. Ruzicic, and J. R. Huber, “Dynamics of selected rovibronic eigenstates in the V-system of carbon-disulfide 12,13CS2,” Chem. Phys. 189, 713 (1994).
[Crossref]

Ishizawa, N.

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. B 78, 433 (2004).
[Crossref]

Ji, W.

H. P. Li, C. H. Kam, Y. L. Lam, and W. Ji, “Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals,” Opt. Mat. 15, 237 (2001).
[Crossref]

Kam, C. H.

H. P. Li, C. H. Kam, Y. L. Lam, and W. Ji, “Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals,” Opt. Mat. 15, 237 (2001).
[Crossref]

Koudoumas, E.

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369, 318 (2003).
[Crossref]

Kuroda, H.

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. B 78, 433 (2004).
[Crossref]

Lam, Y. L.

H. P. Li, C. H. Kam, Y. L. Lam, and W. Ji, “Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals,” Opt. Mat. 15, 237 (2001).
[Crossref]

Lavorel, B.

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369, 318 (2003).
[Crossref]

Li, H. P.

H. P. Li, C. H. Kam, Y. L. Lam, and W. Ji, “Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals,” Opt. Mat. 15, 237 (2001).
[Crossref]

McDuff, R. G.

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. McDuff, “Single beam Z-scan: measurement techniques and analysis,” J. Nonlinear Opt. Phys. 6, 251 (1997).
[Crossref]

McGee, S. B.

S. M. Mian, S. B. McGee, and N. Melikechi, “Experimental and theoretical investigation of thermal lensing effect in mode-locked femtosecond Z-scan experiments,” Opt. Commun. 207, 339 (2002).
[Crossref]

Mckay, T. J.

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. McDuff, “Single beam Z-scan: measurement techniques and analysis,” J. Nonlinear Opt. Phys. 6, 251 (1997).
[Crossref]

Melikechi, N.

S. M. Mian, S. B. McGee, and N. Melikechi, “Experimental and theoretical investigation of thermal lensing effect in mode-locked femtosecond Z-scan experiments,” Opt. Commun. 207, 339 (2002).
[Crossref]

Mian, S. M.

S. M. Mian, S. B. McGee, and N. Melikechi, “Experimental and theoretical investigation of thermal lensing effect in mode-locked femtosecond Z-scan experiments,” Opt. Commun. 207, 339 (2002).
[Crossref]

Michaut, X.

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369, 318 (2003).
[Crossref]

Minck, R. W.

Olivares, J.

Renard, M.

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369, 318 (2003).
[Crossref]

Requejo-Isidro, J.

Ruzicic, A.

H. Bitto, A. Ruzicic, and J. R. Huber, “Dynamics of selected rovibronic eigenstates in the V-system of carbon-disulfide 12,13CS2,” Chem. Phys. 189, 713 (1994).
[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. B 78, 433 (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, 760 (1990).
[Crossref]

Sakakibara, S.

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. B 78, 433 (2004).
[Crossref]

Salvetti, G.

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69, 133 (1999).
[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 (1990).
[Crossref]

Solis, J.

Staromlynska, J.

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. McDuff, “Single beam Z-scan: measurement techniques and analysis,” J. Nonlinear Opt. Phys. 6, 251 (1997).
[Crossref]

Stryland, E. W. Van.

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]

Suarez-Garcia, A.

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. B 78, 433 (2004).
[Crossref]

Terhune, R. W.

Tseng, K. Y.

Turu, 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. B 78, 433 (2004).
[Crossref]

Wang, C. C.

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, 760 (1990).
[Crossref]

Wong, G. K. L.

Wong, K. S.

Appl. Opt. (1)

Appl. Phys. B (2)

M. Falconieri and G. Salvetti, “Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,” Appl. Phys. B 69, 133 (1999).
[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. B 78, 433 (2004).
[Crossref]

Chem. Phys. (1)

H. Bitto, A. Ruzicic, and J. R. Huber, “Dynamics of selected rovibronic eigenstates in the V-system of carbon-disulfide 12,13CS2,” Chem. Phys. 189, 713 (1994).
[Crossref]

Chem. Phys. Lett. (1)

S. Couris, M. Renard, O. Faucher, B. Lavorel, R. Chaux, E. Koudoumas, and X. Michaut, “An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan techniques,” Chem. Phys. Lett. 369, 318 (2003).
[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 (1990).
[Crossref]

J. Nonlinear Opt. Phys. (1)

P. B. Chapple, J. Staromlynska, J. A. Hermann, T. J. Mckay, and R. G. McDuff, “Single beam Z-scan: measurement techniques and analysis,” J. Nonlinear Opt. Phys. 6, 251 (1997).
[Crossref]

J. Opt. A-Pure Appl. Opt. (1)

M. Falconieri, “Thermo-optical effects in Z-scan measurements using high-repetition-rate lasers,” J. Opt. A-Pure Appl. Opt. 1, 662 (1999).
[Crossref]

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

Opt. Commun. (1)

S. M. Mian, S. B. McGee, and N. Melikechi, “Experimental and theoretical investigation of thermal lensing effect in mode-locked femtosecond Z-scan experiments,” Opt. Commun. 207, 339 (2002).
[Crossref]

Opt. Lett. (1)

Opt. Mat. (1)

H. P. Li, C. H. Kam, Y. L. Lam, and W. Ji, “Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals,” Opt. Mat. 15, 237 (2001).
[Crossref]

Other (1)

S. E. Bialkowski, “Thermal, optical and physical properties of common solvents,” (2003), http://www.chem.usu.edu/~sbialkow/Research/Tablevalues.html.

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Figures (4)

Fig. 1.
Fig. 1.

Experimental apparatus. L1, L2, L3 and L4 are lenses, Ch is a chopper, BS is a beam splitter, Pd1 and Pd2 are Si photodiodes for closed- and open-aperture Z-scan, respectively.

Fig. 2.
Fig. 2.

(a) Normalized traces measured at prefocal and postfocal z positions of the transmittance curve for a CS2 sample. Open symbols are experimental data. Red and black curves are fits obtained using Eq. (1) and a single exponential, respectively. Filled symbols are extrapolated values. (b) Z-scan profiles at different times, including that at t = 0 (thick black line), as reconstructed by the fitting procedure. In the inset, the open-aperture profile (dots) and its fit (red line) are shown.

Fig. 3.
Fig. 3.

Temperature evolution of a liquid sample calculated at the center of the heating source.

Fig. 4.
Fig. 4.

Time evolution of prefocal and postfocal traces for a sample of Ge nanocrystals and a bare SiO2 layer.

Tables (1)

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Table 1. Summary of the results and comparison with values taken from the literature

Equations (2)

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I ζ t I ζ 0 = 1 + ϑ ( q ) q 1 ( 1 + ζ 2 ) q 1 tan 1 ( 2 [ ( 2 q + 1 ) 2 + ζ 2 ] t c ( ζ ) 2 qt + 2 q + 1 + ζ 2 ) ,
ϑ ( 2 ) = P 2 d c βL λκ dn dT 2 πw 0 2 ,

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