Abstract

The free-carrier absorption cross-section σ of a magnetic colloid composed of magnetite nanoparticles dispersed in oil is obtained by using the Z-scan technique in different experimental conditions of the laser beam. We show that it is possible to obtain σ with picosecond pulsed and millisecond chopped beams with pulse frequencies smaller than about 30 Hz. For higher pulse frequencies, the heating of the colloidal system triggers the appearance of the Soret effect. This effect artificially increases the value of σ calculated from the experimental results. The limits of the different experimental setups are discussed.

© 2012 Optical Society of America

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    [CrossRef]
  31. S. Debrus, J. Lafait, M. May, N. Pinçon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
    [CrossRef]
  32. F. El-Diasty1 and M. Abdel-Baki, “One- and two-photon absorption in transition metal oxide glasses,” J. Appl. Phys. 106, 053521 (2009).
    [CrossRef]
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    [CrossRef]

2011 (2)

F. B. Naranjo, P. K. Kandaswamy, S. Valdueza-Felip, V. Calvo, M. González-Herráez, S. Martín-López, P. Corredera, J. A. Méndez, G. R. Mutta, B. Lacroix, P. Ruterana, and E. Monroy, “Nonlinear absorption of InN/InGaN multiple-quantum-well structures at optical telecommunication wavelengths,” Appl. Phys. Lett. 98, 031902 (2011).
[CrossRef]

G. Fan, S. Qu, Q. Wang, C. Zhao, L. Zhang, and Z. Li, “Pd nanoparticles formation by femtosecond laser irradiation and the nonlinear optical properties at 532 nm using nanosecond laser pulses,” J. Appl. Phys. 109, 023102 (2011).
[CrossRef]

2010 (1)

D. Christodoulides, I. C. Khoo, G. J. Salamo, G. I. Stegeman, and E. W. Van Stryland, “Nonlinear refraction and absorption: mechanisms and magnitudes,” Adv. Opt. Photonics 2, 60–200 (2010).
[CrossRef]

2009 (3)

F. El-Diasty1 and M. Abdel-Baki, “One- and two-photon absorption in transition metal oxide glasses,” J. Appl. Phys. 106, 053521 (2009).
[CrossRef]

Y. P. Han, J. L. Sun, H. A. Ye, W. Z. Wu, and G. Shi, “Nonlinear refraction of silver nanowires from nanosecond to femtosecond laser excitation,” Appl. Phys. B 94, 233–237 (2009).
[CrossRef]

Y. C. Li, S. Z. Kuo, T. H. Wei, J. N. Wang, S. S. Yang, and J. L. Tang, “Control of thermal lensing effect in transparent liquids by femtosecond laser pulses,” Jpn. J. Appl. Phys. 48, 09LF06 (2009).
[CrossRef]

2008 (2)

F. Z. Henari and A. A. Dakhel, “Linear and nonlinear optical properties of gold nanoparticle-Eu oxide composite thin films,” J. Appl. Phys. 104, 033110 (2008).
[CrossRef]

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, “Optical third-order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica,” J. Appl. Phys. 104, 014306 (2008).
[CrossRef]

2007 (2)

2003 (2)

S. Alves, A. Bourdon, and A. M. Figueiredo Neto, “Generalization of the thermal lens model formalism to account for thermodiffusion in a single-beam Z-scan experiment: determination of the Soret coefficient,” J. Opt. Soc. Am. B 20, 713–718 (2003).
[CrossRef]

S. Alves, G. Demouchy, A. Bee, D. Talbot, A. Bourdon, and A. M.Figueiredo Neto, “Investigation of the sign of the Soret coefficient in different ionic and surfacted magnetic colloids using forced Rayleygh scattering and single-beam Z-scan techniques,” Philos. Mag. 83, 2059–2066 (2003).
[CrossRef]

2002 (1)

J. J. Rodrigues, C. H. T. P. Silva, S. C. Zilio, L. Misoguti, and C. R. Mendonça, “Femtosecond Z-scan measurements of nonlinear refraction in amino acid solutions,” Opt. Mater. 20, 153–157 (2002).
[CrossRef]

2000 (2)

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B 70, 587–591 (2000).
[CrossRef]

S. Debrus, J. Lafait, M. May, N. Pinçon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
[CrossRef]

1998 (1)

M. Büchler, P. Schmuki, H. Böhni, T. Stenberg, and T. Mäntylä, “Comparison of the semiconductive properties of sputter-deposited iron oxides with the passive film on iron,” J. Electrochem. Soc. 145, 378–385 (1998).
[CrossRef]

1997 (2)

B. Yu, C. Zhu, F. Gan, X. Wu, G. Zhang, G. Tang, and W. Chen, “Optical nonlinearities of Fe2O3 nanoparticles investigated by Z-scan technique,” Opt. Mater. 8, 249–254 (1997).
[CrossRef]

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. Mater. 6, 251–293 (1997).
[CrossRef]

1994 (3)

W. Zhao and P. Palffy-Muhoray, “Z-Scan measurement of χ(3) using top-hat beams,” Appl. Phys. Lett. 65, 673–675 (1994).
[CrossRef]

L. C. Oliveira and S. C. Zilio, “Single-beam time-resolved Z-scan measurements of slow absorbers,” Appl. Phys. Lett. 65, 2121–2123 (1994).
[CrossRef]

G. P. Banfi, V. Degiorgio, M. Ghigliazza, H. M. Tan, and A. Tomaselli, “Two-photon absorption in semiconductor nanocrystals,” Phys. Rev. B 50, 5699–5702 (1994).
[CrossRef]

1993 (2)

W. Zhao and P. Palffy-Muhoray, “Z-Scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
[CrossRef]

E. W. Van Stryland, M. Sheik-Bahae, and D. J. Hagan, “Characterization of nonlinear optical absorption and refraction,” Prog. Cryst. Growth Charact. Mater. 27, 279–311 (1993).
[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)

1984 (1)

1974 (1)

J. R. Whinnery, “Laser measurement of optical-absorption in liquids,” Acc. Chem. Res. 7, 225–231 (1974).
[CrossRef]

1966 (1)

J. Tauc, R. Grigorovici, and A. Vancu, “Optical properties and electronic structure of amorphous germanium,” Phys. Status Solidi 15, 627–637 (1966).
[CrossRef]

1964 (1)

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurements by means of thermal lens effect using He-Ne laser,” Appl. Phys. Lett. 5, 141–143 (1964).
[CrossRef]

1879 (1)

Ch. Soret, “Sur l’état d’équilibre que prend au point de vue de sa concentration une dissolution saline primitivement homogène dont deux parties sont portées a des températures différentes,” Arch. Sci. Phys. Nat. 2, 48–61 (1879).

Abdel-Baki, M.

F. El-Diasty1 and M. Abdel-Baki, “One- and two-photon absorption in transition metal oxide glasses,” J. Appl. Phys. 106, 053521 (2009).
[CrossRef]

Alves, S.

Banfi, G. P.

G. P. Banfi, V. Degiorgio, M. Ghigliazza, H. M. Tan, and A. Tomaselli, “Two-photon absorption in semiconductor nanocrystals,” Phys. Rev. B 50, 5699–5702 (1994).
[CrossRef]

Bee, A.

S. Alves, G. Demouchy, A. Bee, D. Talbot, A. Bourdon, and A. M.Figueiredo Neto, “Investigation of the sign of the Soret coefficient in different ionic and surfacted magnetic colloids using forced Rayleygh scattering and single-beam Z-scan techniques,” Philos. Mag. 83, 2059–2066 (2003).
[CrossRef]

Böhni, H.

M. Büchler, P. Schmuki, H. Böhni, T. Stenberg, and T. Mäntylä, “Comparison of the semiconductive properties of sputter-deposited iron oxides with the passive film on iron,” J. Electrochem. Soc. 145, 378–385 (1998).
[CrossRef]

Bourdon, A.

S. Alves, G. Demouchy, A. Bee, D. Talbot, A. Bourdon, and A. M.Figueiredo Neto, “Investigation of the sign of the Soret coefficient in different ionic and surfacted magnetic colloids using forced Rayleygh scattering and single-beam Z-scan techniques,” Philos. Mag. 83, 2059–2066 (2003).
[CrossRef]

S. Alves, A. Bourdon, and A. M. Figueiredo Neto, “Generalization of the thermal lens model formalism to account for thermodiffusion in a single-beam Z-scan experiment: determination of the Soret coefficient,” J. Opt. Soc. Am. B 20, 713–718 (2003).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 1992).

Büchler, M.

M. Büchler, P. Schmuki, H. Böhni, T. Stenberg, and T. Mäntylä, “Comparison of the semiconductive properties of sputter-deposited iron oxides with the passive film on iron,” J. Electrochem. Soc. 145, 378–385 (1998).
[CrossRef]

Calvo, V.

F. B. Naranjo, P. K. Kandaswamy, S. Valdueza-Felip, V. Calvo, M. González-Herráez, S. Martín-López, P. Corredera, J. A. Méndez, G. R. Mutta, B. Lacroix, P. Ruterana, and E. Monroy, “Nonlinear absorption of InN/InGaN multiple-quantum-well structures at optical telecommunication wavelengths,” Appl. Phys. Lett. 98, 031902 (2011).
[CrossRef]

Campos, A. F. C.

Carter, C. A.

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. Mater. 6, 251–293 (1997).
[CrossRef]

Cheang-Wong, J. C.

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, “Optical third-order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica,” J. Appl. Phys. 104, 014306 (2008).
[CrossRef]

Chen, W.

B. Yu, C. Zhu, F. Gan, X. Wu, G. Zhang, G. Tang, and W. Chen, “Optical nonlinearities of Fe2O3 nanoparticles investigated by Z-scan technique,” Opt. Mater. 8, 249–254 (1997).
[CrossRef]

Christodoulides, D.

D. Christodoulides, I. C. Khoo, G. J. Salamo, G. I. Stegeman, and E. W. Van Stryland, “Nonlinear refraction and absorption: mechanisms and magnitudes,” Adv. Opt. Photonics 2, 60–200 (2010).
[CrossRef]

Corredera, P.

F. B. Naranjo, P. K. Kandaswamy, S. Valdueza-Felip, V. Calvo, M. González-Herráez, S. Martín-López, P. Corredera, J. A. Méndez, G. R. Mutta, B. Lacroix, P. Ruterana, and E. Monroy, “Nonlinear absorption of InN/InGaN multiple-quantum-well structures at optical telecommunication wavelengths,” Appl. Phys. Lett. 98, 031902 (2011).
[CrossRef]

Crespo-Sosa, A.

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, “Optical third-order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica,” J. Appl. Phys. 104, 014306 (2008).
[CrossRef]

Dakhel, A. A.

F. Z. Henari and A. A. Dakhel, “Linear and nonlinear optical properties of gold nanoparticle-Eu oxide composite thin films,” J. Appl. Phys. 104, 033110 (2008).
[CrossRef]

de Groot, S. R.

S. R. de Groot, L’Effet Soret, Diffusion Thermique dans les Phases Condensées (North-Holland, 1945).

Debrus, S.

S. Debrus, J. Lafait, M. May, N. Pinçon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
[CrossRef]

Degiorgio, V.

G. P. Banfi, V. Degiorgio, M. Ghigliazza, H. M. Tan, and A. Tomaselli, “Two-photon absorption in semiconductor nanocrystals,” Phys. Rev. B 50, 5699–5702 (1994).
[CrossRef]

Demouchy, G.

S. Alves, G. Demouchy, A. Bee, D. Talbot, A. Bourdon, and A. M.Figueiredo Neto, “Investigation of the sign of the Soret coefficient in different ionic and surfacted magnetic colloids using forced Rayleygh scattering and single-beam Z-scan techniques,” Philos. Mag. 83, 2059–2066 (2003).
[CrossRef]

Depeyrot, J.

El-Diasty1, F.

F. El-Diasty1 and M. Abdel-Baki, “One- and two-photon absorption in transition metal oxide glasses,” J. Appl. Phys. 106, 053521 (2009).
[CrossRef]

Fan, G.

G. Fan, S. Qu, Q. Wang, C. Zhao, L. Zhang, and Z. Li, “Pd nanoparticles formation by femtosecond laser irradiation and the nonlinear optical properties at 532 nm using nanosecond laser pulses,” J. Appl. Phys. 109, 023102 (2011).
[CrossRef]

Gan, F.

B. Yu, C. Zhu, F. Gan, X. Wu, G. Zhang, G. Tang, and W. Chen, “Optical nonlinearities of Fe2O3 nanoparticles investigated by Z-scan technique,” Opt. Mater. 8, 249–254 (1997).
[CrossRef]

Ghigliazza, M.

G. P. Banfi, V. Degiorgio, M. Ghigliazza, H. M. Tan, and A. Tomaselli, “Two-photon absorption in semiconductor nanocrystals,” Phys. Rev. B 50, 5699–5702 (1994).
[CrossRef]

González-Herráez, M.

F. B. Naranjo, P. K. Kandaswamy, S. Valdueza-Felip, V. Calvo, M. González-Herráez, S. Martín-López, P. Corredera, J. A. Méndez, G. R. Mutta, B. Lacroix, P. Ruterana, and E. Monroy, “Nonlinear absorption of InN/InGaN multiple-quantum-well structures at optical telecommunication wavelengths,” Appl. Phys. Lett. 98, 031902 (2011).
[CrossRef]

Grigorovici, R.

J. Tauc, R. Grigorovici, and A. Vancu, “Optical properties and electronic structure of amorphous germanium,” Phys. Status Solidi 15, 627–637 (1966).
[CrossRef]

Hagan, D. J.

E. W. Van Stryland, M. Sheik-Bahae, and D. J. Hagan, “Characterization of nonlinear optical absorption and refraction,” Prog. Cryst. Growth Charact. Mater. 27, 279–311 (1993).
[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]

Han, Y. P.

Y. P. Han, J. L. Sun, H. A. Ye, W. Z. Wu, and G. Shi, “Nonlinear refraction of silver nanowires from nanosecond to femtosecond laser excitation,” Appl. Phys. B 94, 233–237 (2009).
[CrossRef]

Harris, J. M.

Henari, F. Z.

F. Z. Henari and A. A. Dakhel, “Linear and nonlinear optical properties of gold nanoparticle-Eu oxide composite thin films,” J. Appl. Phys. 104, 033110 (2008).
[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. Mater. 6, 251–293 (1997).
[CrossRef]

Ji, W.

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B 70, 587–591 (2000).
[CrossRef]

Kandaswamy, P. K.

F. B. Naranjo, P. K. Kandaswamy, S. Valdueza-Felip, V. Calvo, M. González-Herráez, S. Martín-López, P. Corredera, J. A. Méndez, G. R. Mutta, B. Lacroix, P. Ruterana, and E. Monroy, “Nonlinear absorption of InN/InGaN multiple-quantum-well structures at optical telecommunication wavelengths,” Appl. Phys. Lett. 98, 031902 (2011).
[CrossRef]

Khoo, I. C.

D. Christodoulides, I. C. Khoo, G. J. Salamo, G. I. Stegeman, and E. W. Van Stryland, “Nonlinear refraction and absorption: mechanisms and magnitudes,” Adv. Opt. Photonics 2, 60–200 (2010).
[CrossRef]

Kuo, S. Z.

Y. C. Li, S. Z. Kuo, T. H. Wei, J. N. Wang, S. S. Yang, and J. L. Tang, “Control of thermal lensing effect in transparent liquids by femtosecond laser pulses,” Jpn. J. Appl. Phys. 48, 09LF06 (2009).
[CrossRef]

Lacroix, B.

F. B. Naranjo, P. K. Kandaswamy, S. Valdueza-Felip, V. Calvo, M. González-Herráez, S. Martín-López, P. Corredera, J. A. Méndez, G. R. Mutta, B. Lacroix, P. Ruterana, and E. Monroy, “Nonlinear absorption of InN/InGaN multiple-quantum-well structures at optical telecommunication wavelengths,” Appl. Phys. Lett. 98, 031902 (2011).
[CrossRef]

Lafait, J.

S. Debrus, J. Lafait, M. May, N. Pinçon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
[CrossRef]

Leite, R. C. C.

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurements by means of thermal lens effect using He-Ne laser,” Appl. Phys. Lett. 5, 141–143 (1964).
[CrossRef]

Li, H. P.

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B 70, 587–591 (2000).
[CrossRef]

Li, Y. C.

Y. C. Li, S. Z. Kuo, T. H. Wei, J. N. Wang, S. S. Yang, and J. L. Tang, “Control of thermal lensing effect in transparent liquids by femtosecond laser pulses,” Jpn. J. Appl. Phys. 48, 09LF06 (2009).
[CrossRef]

Li, Z.

G. Fan, S. Qu, Q. Wang, C. Zhao, L. Zhang, and Z. Li, “Pd nanoparticles formation by femtosecond laser irradiation and the nonlinear optical properties at 532 nm using nanosecond laser pulses,” J. Appl. Phys. 109, 023102 (2011).
[CrossRef]

Mäntylä, T.

M. Büchler, P. Schmuki, H. Böhni, T. Stenberg, and T. Mäntylä, “Comparison of the semiconductive properties of sputter-deposited iron oxides with the passive film on iron,” J. Electrochem. Soc. 145, 378–385 (1998).
[CrossRef]

Martín-López, S.

F. B. Naranjo, P. K. Kandaswamy, S. Valdueza-Felip, V. Calvo, M. González-Herráez, S. Martín-López, P. Corredera, J. A. Méndez, G. R. Mutta, B. Lacroix, P. Ruterana, and E. Monroy, “Nonlinear absorption of InN/InGaN multiple-quantum-well structures at optical telecommunication wavelengths,” Appl. Phys. Lett. 98, 031902 (2011).
[CrossRef]

May, M.

S. Debrus, J. Lafait, M. May, N. Pinçon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
[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. Mater. 6, 251–293 (1997).
[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. Mater. 6, 251–293 (1997).
[CrossRef]

Méndez, J. A.

F. B. Naranjo, P. K. Kandaswamy, S. Valdueza-Felip, V. Calvo, M. González-Herráez, S. Martín-López, P. Corredera, J. A. Méndez, G. R. Mutta, B. Lacroix, P. Ruterana, and E. Monroy, “Nonlinear absorption of InN/InGaN multiple-quantum-well structures at optical telecommunication wavelengths,” Appl. Phys. Lett. 98, 031902 (2011).
[CrossRef]

Mendonça, C. R.

J. J. Rodrigues, C. H. T. P. Silva, S. C. Zilio, L. Misoguti, and C. R. Mendonça, “Femtosecond Z-scan measurements of nonlinear refraction in amino acid solutions,” Opt. Mater. 20, 153–157 (2002).
[CrossRef]

Misoguti, L.

J. J. Rodrigues, C. H. T. P. Silva, S. C. Zilio, L. Misoguti, and C. R. Mendonça, “Femtosecond Z-scan measurements of nonlinear refraction in amino acid solutions,” Opt. Mater. 20, 153–157 (2002).
[CrossRef]

Monroy, E.

F. B. Naranjo, P. K. Kandaswamy, S. Valdueza-Felip, V. Calvo, M. González-Herráez, S. Martín-López, P. Corredera, J. A. Méndez, G. R. Mutta, B. Lacroix, P. Ruterana, and E. Monroy, “Nonlinear absorption of InN/InGaN multiple-quantum-well structures at optical telecommunication wavelengths,” Appl. Phys. Lett. 98, 031902 (2011).
[CrossRef]

Moore, R. S.

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurements by means of thermal lens effect using He-Ne laser,” Appl. Phys. Lett. 5, 141–143 (1964).
[CrossRef]

Mutta, G. R.

F. B. Naranjo, P. K. Kandaswamy, S. Valdueza-Felip, V. Calvo, M. González-Herráez, S. Martín-López, P. Corredera, J. A. Méndez, G. R. Mutta, B. Lacroix, P. Ruterana, and E. Monroy, “Nonlinear absorption of InN/InGaN multiple-quantum-well structures at optical telecommunication wavelengths,” Appl. Phys. Lett. 98, 031902 (2011).
[CrossRef]

Naranjo, F. B.

F. B. Naranjo, P. K. Kandaswamy, S. Valdueza-Felip, V. Calvo, M. González-Herráez, S. Martín-López, P. Corredera, J. A. Méndez, G. R. Mutta, B. Lacroix, P. Ruterana, and E. Monroy, “Nonlinear absorption of InN/InGaN multiple-quantum-well structures at optical telecommunication wavelengths,” Appl. Phys. Lett. 98, 031902 (2011).
[CrossRef]

Neto, A. M. Figueiredo

Neto, A. M.Figueiredo

S. Alves, G. Demouchy, A. Bee, D. Talbot, A. Bourdon, and A. M.Figueiredo Neto, “Investigation of the sign of the Soret coefficient in different ionic and surfacted magnetic colloids using forced Rayleygh scattering and single-beam Z-scan techniques,” Philos. Mag. 83, 2059–2066 (2003).
[CrossRef]

Oliveira, L. C.

L. C. Oliveira and S. C. Zilio, “Single-beam time-resolved Z-scan measurements of slow absorbers,” Appl. Phys. Lett. 65, 2121–2123 (1994).
[CrossRef]

Oliver, A.

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, “Optical third-order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica,” J. Appl. Phys. 104, 014306 (2008).
[CrossRef]

Palffy-Muhoray, P.

W. Zhao and P. Palffy-Muhoray, “Z-Scan measurement of χ(3) using top-hat beams,” Appl. Phys. Lett. 65, 673–675 (1994).
[CrossRef]

W. Zhao and P. Palffy-Muhoray, “Z-Scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
[CrossRef]

Pinçon, N.

S. Debrus, J. Lafait, M. May, N. Pinçon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
[CrossRef]

Porel, S.

S. Porel, N. Venkatram, D. Narayana Rao, and T. P. Radhakrishnan, “Optical power limiting in the femtosecond regime by silver nanoparticle-embedded polymer film,” J. Appl. Phys. 102, 033107 (2007).
[CrossRef]

Prot, D.

S. Debrus, J. Lafait, M. May, N. Pinçon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
[CrossRef]

Qu, S.

G. Fan, S. Qu, Q. Wang, C. Zhao, L. Zhang, and Z. Li, “Pd nanoparticles formation by femtosecond laser irradiation and the nonlinear optical properties at 532 nm using nanosecond laser pulses,” J. Appl. Phys. 109, 023102 (2011).
[CrossRef]

Radhakrishnan, T. P.

S. Porel, N. Venkatram, D. Narayana Rao, and T. P. Radhakrishnan, “Optical power limiting in the femtosecond regime by silver nanoparticle-embedded polymer film,” J. Appl. Phys. 102, 033107 (2007).
[CrossRef]

Rao, D. Narayana

S. Porel, N. Venkatram, D. Narayana Rao, and T. P. Radhakrishnan, “Optical power limiting in the femtosecond regime by silver nanoparticle-embedded polymer film,” J. Appl. Phys. 102, 033107 (2007).
[CrossRef]

Reyes-Esqueda, J. A.

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, “Optical third-order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica,” J. Appl. Phys. 104, 014306 (2008).
[CrossRef]

Rodrigues, J. J.

J. J. Rodrigues, C. H. T. P. Silva, S. C. Zilio, L. Misoguti, and C. R. Mendonça, “Femtosecond Z-scan measurements of nonlinear refraction in amino acid solutions,” Opt. Mater. 20, 153–157 (2002).
[CrossRef]

Rodríguez-Fernández, L.

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, “Optical third-order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica,” J. Appl. Phys. 104, 014306 (2008).
[CrossRef]

Rosensweig, R. E.

R. E. Rosensweig, Ferrohydrodynamics (Dover, 1997).

Ruterana, P.

F. B. Naranjo, P. K. Kandaswamy, S. Valdueza-Felip, V. Calvo, M. González-Herráez, S. Martín-López, P. Corredera, J. A. Méndez, G. R. Mutta, B. Lacroix, P. Ruterana, and E. Monroy, “Nonlinear absorption of InN/InGaN multiple-quantum-well structures at optical telecommunication wavelengths,” Appl. Phys. Lett. 98, 031902 (2011).
[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]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High sensitivity single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef]

Salamo, G. J.

D. Christodoulides, I. C. Khoo, G. J. Salamo, G. I. Stegeman, and E. W. Van Stryland, “Nonlinear refraction and absorption: mechanisms and magnitudes,” Adv. Opt. Photonics 2, 60–200 (2010).
[CrossRef]

Schmuki, P.

M. Büchler, P. Schmuki, H. Böhni, T. Stenberg, and T. Mäntylä, “Comparison of the semiconductive properties of sputter-deposited iron oxides with the passive film on iron,” J. Electrochem. Soc. 145, 378–385 (1998).
[CrossRef]

Sella, C.

S. Debrus, J. Lafait, M. May, N. Pinçon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
[CrossRef]

Sheik-Bahae, M.

E. W. Van Stryland, M. Sheik-Bahae, and D. J. Hagan, “Characterization of nonlinear optical absorption and refraction,” Prog. Cryst. Growth Charact. Mater. 27, 279–311 (1993).
[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]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High sensitivity single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef]

E. W. Van Stryland and M. Sheik-Bahae, “Z-Scan measurements of optical nonlinearities,” in Characterization Techniques and Tabulations for Organic Nonlinear Material, M. G. Kuzyk and C. W. Dirk, eds. (Marcel Dekker, 1998), 655–692.

Shi, G.

Y. P. Han, J. L. Sun, H. A. Ye, W. Z. Wu, and G. Shi, “Nonlinear refraction of silver nanowires from nanosecond to femtosecond laser excitation,” Appl. Phys. B 94, 233–237 (2009).
[CrossRef]

Silva, C. H. T. P.

J. J. Rodrigues, C. H. T. P. Silva, S. C. Zilio, L. Misoguti, and C. R. Mendonça, “Femtosecond Z-scan measurements of nonlinear refraction in amino acid solutions,” Opt. Mater. 20, 153–157 (2002).
[CrossRef]

Soga, D.

Soret, Ch.

Ch. Soret, “Sur l’état d’équilibre que prend au point de vue de sa concentration une dissolution saline primitivement homogène dont deux parties sont portées a des températures différentes,” Arch. Sci. Phys. Nat. 2, 48–61 (1879).

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. Mater. 6, 251–293 (1997).
[CrossRef]

Stegeman, G. I.

D. Christodoulides, I. C. Khoo, G. J. Salamo, G. I. Stegeman, and E. W. Van Stryland, “Nonlinear refraction and absorption: mechanisms and magnitudes,” Adv. Opt. Photonics 2, 60–200 (2010).
[CrossRef]

Stenberg, T.

M. Büchler, P. Schmuki, H. Böhni, T. Stenberg, and T. Mäntylä, “Comparison of the semiconductive properties of sputter-deposited iron oxides with the passive film on iron,” J. Electrochem. Soc. 145, 378–385 (1998).
[CrossRef]

Sun, J. L.

Y. P. Han, J. L. Sun, H. A. Ye, W. Z. Wu, and G. Shi, “Nonlinear refraction of silver nanowires from nanosecond to femtosecond laser excitation,” Appl. Phys. B 94, 233–237 (2009).
[CrossRef]

Talbot, D.

S. Alves, G. Demouchy, A. Bee, D. Talbot, A. Bourdon, and A. M.Figueiredo Neto, “Investigation of the sign of the Soret coefficient in different ionic and surfacted magnetic colloids using forced Rayleygh scattering and single-beam Z-scan techniques,” Philos. Mag. 83, 2059–2066 (2003).
[CrossRef]

Tan, H. M.

G. P. Banfi, V. Degiorgio, M. Ghigliazza, H. M. Tan, and A. Tomaselli, “Two-photon absorption in semiconductor nanocrystals,” Phys. Rev. B 50, 5699–5702 (1994).
[CrossRef]

Tang, G.

B. Yu, C. Zhu, F. Gan, X. Wu, G. Zhang, G. Tang, and W. Chen, “Optical nonlinearities of Fe2O3 nanoparticles investigated by Z-scan technique,” Opt. Mater. 8, 249–254 (1997).
[CrossRef]

Tang, J. L.

Y. C. Li, S. Z. Kuo, T. H. Wei, J. N. Wang, S. S. Yang, and J. L. Tang, “Control of thermal lensing effect in transparent liquids by femtosecond laser pulses,” Jpn. J. Appl. Phys. 48, 09LF06 (2009).
[CrossRef]

Tang, S. H.

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B 70, 587–591 (2000).
[CrossRef]

Tauc, J.

J. Tauc, R. Grigorovici, and A. Vancu, “Optical properties and electronic structure of amorphous germanium,” Phys. Status Solidi 15, 627–637 (1966).
[CrossRef]

Tomaselli, A.

G. P. Banfi, V. Degiorgio, M. Ghigliazza, H. M. Tan, and A. Tomaselli, “Two-photon absorption in semiconductor nanocrystals,” Phys. Rev. B 50, 5699–5702 (1994).
[CrossRef]

Torres-Torres, C.

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, “Optical third-order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica,” J. Appl. Phys. 104, 014306 (2008).
[CrossRef]

Tourinho, F. A.

Valdueza-Felip, S.

F. B. Naranjo, P. K. Kandaswamy, S. Valdueza-Felip, V. Calvo, M. González-Herráez, S. Martín-López, P. Corredera, J. A. Méndez, G. R. Mutta, B. Lacroix, P. Ruterana, and E. Monroy, “Nonlinear absorption of InN/InGaN multiple-quantum-well structures at optical telecommunication wavelengths,” Appl. Phys. Lett. 98, 031902 (2011).
[CrossRef]

Van Stryland, E. W.

D. Christodoulides, I. C. Khoo, G. J. Salamo, G. I. Stegeman, and E. W. Van Stryland, “Nonlinear refraction and absorption: mechanisms and magnitudes,” Adv. Opt. Photonics 2, 60–200 (2010).
[CrossRef]

E. W. Van Stryland, M. Sheik-Bahae, and D. J. Hagan, “Characterization of nonlinear optical absorption and refraction,” Prog. Cryst. Growth Charact. Mater. 27, 279–311 (1993).
[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]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High sensitivity single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
[CrossRef]

E. W. Van Stryland and M. Sheik-Bahae, “Z-Scan measurements of optical nonlinearities,” in Characterization Techniques and Tabulations for Organic Nonlinear Material, M. G. Kuzyk and C. W. Dirk, eds. (Marcel Dekker, 1998), 655–692.

Vancu, A.

J. Tauc, R. Grigorovici, and A. Vancu, “Optical properties and electronic structure of amorphous germanium,” Phys. Status Solidi 15, 627–637 (1966).
[CrossRef]

Venkatram, N.

S. Porel, N. Venkatram, D. Narayana Rao, and T. P. Radhakrishnan, “Optical power limiting in the femtosecond regime by silver nanoparticle-embedded polymer film,” J. Appl. Phys. 102, 033107 (2007).
[CrossRef]

Venturini, J.

S. Debrus, J. Lafait, M. May, N. Pinçon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
[CrossRef]

Wang, J. N.

Y. C. Li, S. Z. Kuo, T. H. Wei, J. N. Wang, S. S. Yang, and J. L. Tang, “Control of thermal lensing effect in transparent liquids by femtosecond laser pulses,” Jpn. J. Appl. Phys. 48, 09LF06 (2009).
[CrossRef]

Wang, Q.

G. Fan, S. Qu, Q. Wang, C. Zhao, L. Zhang, and Z. Li, “Pd nanoparticles formation by femtosecond laser irradiation and the nonlinear optical properties at 532 nm using nanosecond laser pulses,” J. Appl. Phys. 109, 023102 (2011).
[CrossRef]

Wei, T. H.

Y. C. Li, S. Z. Kuo, T. H. Wei, J. N. Wang, S. S. Yang, and J. L. Tang, “Control of thermal lensing effect in transparent liquids by femtosecond laser pulses,” Jpn. J. Appl. Phys. 48, 09LF06 (2009).
[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]

Whinnery, J. R.

J. R. Whinnery, “Laser measurement of optical-absorption in liquids,” Acc. Chem. Res. 7, 225–231 (1974).
[CrossRef]

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurements by means of thermal lens effect using He-Ne laser,” Appl. Phys. Lett. 5, 141–143 (1964).
[CrossRef]

Wu, W. Z.

Y. P. Han, J. L. Sun, H. A. Ye, W. Z. Wu, and G. Shi, “Nonlinear refraction of silver nanowires from nanosecond to femtosecond laser excitation,” Appl. Phys. B 94, 233–237 (2009).
[CrossRef]

Wu, X.

B. Yu, C. Zhu, F. Gan, X. Wu, G. Zhang, G. Tang, and W. Chen, “Optical nonlinearities of Fe2O3 nanoparticles investigated by Z-scan technique,” Opt. Mater. 8, 249–254 (1997).
[CrossRef]

Yang, S. S.

Y. C. Li, S. Z. Kuo, T. H. Wei, J. N. Wang, S. S. Yang, and J. L. Tang, “Control of thermal lensing effect in transparent liquids by femtosecond laser pulses,” Jpn. J. Appl. Phys. 48, 09LF06 (2009).
[CrossRef]

Ye, H. A.

Y. P. Han, J. L. Sun, H. A. Ye, W. Z. Wu, and G. Shi, “Nonlinear refraction of silver nanowires from nanosecond to femtosecond laser excitation,” Appl. Phys. B 94, 233–237 (2009).
[CrossRef]

Yin, M.

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B 70, 587–591 (2000).
[CrossRef]

Yu, B.

B. Yu, C. Zhu, F. Gan, X. Wu, G. Zhang, G. Tang, and W. Chen, “Optical nonlinearities of Fe2O3 nanoparticles investigated by Z-scan technique,” Opt. Mater. 8, 249–254 (1997).
[CrossRef]

Zhang, G.

B. Yu, C. Zhu, F. Gan, X. Wu, G. Zhang, G. Tang, and W. Chen, “Optical nonlinearities of Fe2O3 nanoparticles investigated by Z-scan technique,” Opt. Mater. 8, 249–254 (1997).
[CrossRef]

Zhang, L.

G. Fan, S. Qu, Q. Wang, C. Zhao, L. Zhang, and Z. Li, “Pd nanoparticles formation by femtosecond laser irradiation and the nonlinear optical properties at 532 nm using nanosecond laser pulses,” J. Appl. Phys. 109, 023102 (2011).
[CrossRef]

Zhao, C.

G. Fan, S. Qu, Q. Wang, C. Zhao, L. Zhang, and Z. Li, “Pd nanoparticles formation by femtosecond laser irradiation and the nonlinear optical properties at 532 nm using nanosecond laser pulses,” J. Appl. Phys. 109, 023102 (2011).
[CrossRef]

Zhao, W.

W. Zhao and P. Palffy-Muhoray, “Z-Scan measurement of χ(3) using top-hat beams,” Appl. Phys. Lett. 65, 673–675 (1994).
[CrossRef]

W. Zhao and P. Palffy-Muhoray, “Z-Scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
[CrossRef]

Zhu, C.

B. Yu, C. Zhu, F. Gan, X. Wu, G. Zhang, G. Tang, and W. Chen, “Optical nonlinearities of Fe2O3 nanoparticles investigated by Z-scan technique,” Opt. Mater. 8, 249–254 (1997).
[CrossRef]

Zilio, S. C.

J. J. Rodrigues, C. H. T. P. Silva, S. C. Zilio, L. Misoguti, and C. R. Mendonça, “Femtosecond Z-scan measurements of nonlinear refraction in amino acid solutions,” Opt. Mater. 20, 153–157 (2002).
[CrossRef]

L. C. Oliveira and S. C. Zilio, “Single-beam time-resolved Z-scan measurements of slow absorbers,” Appl. Phys. Lett. 65, 2121–2123 (1994).
[CrossRef]

Acc. Chem. Res. (1)

J. R. Whinnery, “Laser measurement of optical-absorption in liquids,” Acc. Chem. Res. 7, 225–231 (1974).
[CrossRef]

Adv. Opt. Photonics (1)

D. Christodoulides, I. C. Khoo, G. J. Salamo, G. I. Stegeman, and E. W. Van Stryland, “Nonlinear refraction and absorption: mechanisms and magnitudes,” Adv. Opt. Photonics 2, 60–200 (2010).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (2)

Y. P. Han, J. L. Sun, H. A. Ye, W. Z. Wu, and G. Shi, “Nonlinear refraction of silver nanowires from nanosecond to femtosecond laser excitation,” Appl. Phys. B 94, 233–237 (2009).
[CrossRef]

M. Yin, H. P. Li, S. H. Tang, and W. Ji, “Determination of nonlinear absorption and refraction by single Z-scan method,” Appl. Phys. B 70, 587–591 (2000).
[CrossRef]

Appl. Phys. Lett. (5)

L. C. Oliveira and S. C. Zilio, “Single-beam time-resolved Z-scan measurements of slow absorbers,” Appl. Phys. Lett. 65, 2121–2123 (1994).
[CrossRef]

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurements by means of thermal lens effect using He-Ne laser,” Appl. Phys. Lett. 5, 141–143 (1964).
[CrossRef]

W. Zhao and P. Palffy-Muhoray, “Z-Scan measurement of χ(3) using top-hat beams,” Appl. Phys. Lett. 65, 673–675 (1994).
[CrossRef]

W. Zhao and P. Palffy-Muhoray, “Z-Scan technique using top-hat beams,” Appl. Phys. Lett. 63, 1613–1615 (1993).
[CrossRef]

F. B. Naranjo, P. K. Kandaswamy, S. Valdueza-Felip, V. Calvo, M. González-Herráez, S. Martín-López, P. Corredera, J. A. Méndez, G. R. Mutta, B. Lacroix, P. Ruterana, and E. Monroy, “Nonlinear absorption of InN/InGaN multiple-quantum-well structures at optical telecommunication wavelengths,” Appl. Phys. Lett. 98, 031902 (2011).
[CrossRef]

Arch. Sci. Phys. Nat. (1)

Ch. Soret, “Sur l’état d’équilibre que prend au point de vue de sa concentration une dissolution saline primitivement homogène dont deux parties sont portées a des températures différentes,” Arch. Sci. Phys. Nat. 2, 48–61 (1879).

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. Appl. Phys. (6)

G. Fan, S. Qu, Q. Wang, C. Zhao, L. Zhang, and Z. Li, “Pd nanoparticles formation by femtosecond laser irradiation and the nonlinear optical properties at 532 nm using nanosecond laser pulses,” J. Appl. Phys. 109, 023102 (2011).
[CrossRef]

F. Z. Henari and A. A. Dakhel, “Linear and nonlinear optical properties of gold nanoparticle-Eu oxide composite thin films,” J. Appl. Phys. 104, 033110 (2008).
[CrossRef]

C. Torres-Torres, J. A. Reyes-Esqueda, J. C. Cheang-Wong, A. Crespo-Sosa, L. Rodríguez-Fernández, and A. Oliver, “Optical third-order nonlinearity by nanosecond and picosecond pulses in Cu nanoparticles in ion-implanted silica,” J. Appl. Phys. 104, 014306 (2008).
[CrossRef]

S. Debrus, J. Lafait, M. May, N. Pinçon, D. Prot, C. Sella, and J. Venturini, “Z-scan determination of the third-order optical nonlinearity of gold:silica nanocomposites,” J. Appl. Phys. 88, 4469–4475 (2000).
[CrossRef]

F. El-Diasty1 and M. Abdel-Baki, “One- and two-photon absorption in transition metal oxide glasses,” J. Appl. Phys. 106, 053521 (2009).
[CrossRef]

S. Porel, N. Venkatram, D. Narayana Rao, and T. P. Radhakrishnan, “Optical power limiting in the femtosecond regime by silver nanoparticle-embedded polymer film,” J. Appl. Phys. 102, 033107 (2007).
[CrossRef]

J. Electrochem. Soc. (1)

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Figures (5)

Fig. 1.
Fig. 1.

(a) Absorbance spectrum of the ferrofluid ϕ = 0.36 % and L = 50 μm . (b) Plot of ( E f α 0 ) 1 / 2 as a function of E f , where E f is the incident photon energy and α 0 the linear absorption coefficient: ϕ = 0.36 % .

Fig. 2.
Fig. 2.

Open-aperture ZS normalized transmittance as a function of the z -position of the sample. τ = 100 ps , f = 20 Hz , E p = 3.3 μJ . The solid line is a fit with Eq. (4).

Fig. 3.
Fig. 3.

Fitting parameter σ of Eq. (4) as a function of the time interval between pulses that, in the case of pulses with time interval Δ t = 50 ms , represents the free-carrier absorption cross section of the magnetic colloid. (open circles) femtosecond pulses; (black dots) picosecond pulses; (triangles) millisecond pulses.

Fig. 4.
Fig. 4.

Sequence of transmitted pulses at the far field, after passing through the sample, as a function of time, in different sample positions. Millisecond time-scale experiment. τ = 17 ms .

Fig. 5.
Fig. 5.

(a) Normalized transmittance with the sample at the focus, defined as Γ * = Γ ( z = 0 , t ) / Γ ( z = 0 , t = 0 ) as a function of time. τ = 280 fs and pulse frequencies f of 80 Hz (black dots), 3 kHz (squares), and 10 kHz (open circles). (b) Relaxation of Γ * measured with single pulses of τ = 280 fs . Sample initially illuminated with pulses of 3 kHz (squares) and 10 kHz (open circles).

Tables (1)

Tables Icon

Table 1. Values of Effective Nonlinear Optical Absorption ( β eff ) in Different Experimental Conditions, Assuming the TPA Phenomenon a

Equations (13)

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n = n 0 + n 2 I α = α 0 + β I ,
α = α 0 + β I + σ N ,
d I d z = ( α 0 + σ N ) I , d N d t = α 0 h ν I ( t ) , d F d z = ( α 0 + σ α 0 2 h ν F ) F ,
F out ( z , r ) = F in ( z , r ) e α 0 L 1 + α 0 σ 2 h ν F in ( z , r ) L eff ,
Γ n ( z ) = ln [ 1 + p ( z ) ] p ( z ) , p ( z ) = α 0 σ 2 h ν F 0 L eff ( 1 + z 2 / z 0 2 ) ,
Γ n ( z ) = E out ( z ) / E in e α 0 L ,
I ( z , r , t ) = I 0 w 0 2 w 2 ( z ) exp [ 2 r 2 w 2 ( z ) 4 ln 2 τ 2 t 2 ] ,
F in ( z , r ) = + I ( z , r , t ) d t = F 0 w 0 2 w 2 ( z ) e 2 r 2 w 2 ( z ) ,
E in = 0 2 π 0 + F in ( r , z ) r d r d θ = F 0 π w 0 2 2 .
F in F out d F ( α 0 + σ α 0 2 h ν F ) F = 0 L d z , 1 α 0 ln | ( σ α 0 2 h ν F out + α 0 ) ( σ α 0 2 h ν F in + α 0 ) F in F out | = L , F out ( z , r ) = F in ( z , r ) e α 0 L 1 + α 0 σ 2 h ν F in ( z , r ) L eff ,
E out = 0 2 π 0 + F out ( r , z ) r d r d θ = F 0 π w 0 2 2 e α 0 L ln | 1 + p ( z ) | p ( z ) ,
Γ n ( z ) = ln | 1 + p ( z ) | p ( z ) .
I ( z , r , t ) = { I 0 w 0 2 w 2 ( z ) exp [ 2 r 2 w 2 ( z ) ] if | t | τ 2 , 0 if | t | > τ 2 ,

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