Abstract

We carried out Z-scan measurements on lyotropic liquid crystals and on lyotropic liquid crystals doped with ferrofluid. In these experiments, the sample is translated through the focal region of a focused Gaussian laser beam. The dependence of the far-field intensity on sample position due to intensity-dependent optical nonlinearities has been analyzed on the basis of the thermal-lens model of Gordon et al. and the Gaussian decomposition analysis of Sheik-Bahae et al. The thermal-lens model is nonlocal in space and time, whereas the Gaussian decomposition is predicated on a strictly local response. We compare the goodness of fit of the predictions of these models to experimental data, and we discuss limitations of these models in describing Z-scan experiments on systems with nonlocal response.

© 2002 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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  7. D. I. Kovsh, D. J. Hagan, and E. W. Van Stryland, “Numerical modeling of thermal refraction in liquids in the transient regime,” Opt. Express 4, 315327 (1999).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  24. C. P. Bastos dos Santos and A. M. Figueiredo Neto, “Measurement of the coefficient of thermal-expansion of uniaxial and biaxial lyotropic nematics: disk and rods or intrinsically biaxial micelles,” Langmuir 7, 26262629 (1991).
    [CrossRef]
  25. M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 12281235 (1991).
    [CrossRef]

1999 (2)

S. L. Gómez, F. L. S. Cuppo, A. M. Figueiredo Neto, T. Kosa, M. Muramatsu, and R. J. Horowicz, “Z-scan measurement of the nonlinear refractive indices of micellar lyotropic liquid crystals with and without the ferrofluid doping,” Phys. Rev. E 59, 30593063 (1999).
[CrossRef]

D. I. Kovsh, D. J. Hagan, and E. W. Van Stryland, “Numerical modeling of thermal refraction in liquids in the transient regime,” Opt. Express 4, 315327 (1999).
[CrossRef] [PubMed]

1998 (1)

F. Simoni, “Non-linear optics in liquid crystals: basic ideas and perspectives,” Liq. Cryst. 24, 8389 (1998).
[CrossRef]

1996 (3)

A. C. Bento, A. J. Palangana, L. R. Evangelista, M. L. Baesso, J. R. D. Pereira, E. C. da Silva, and A. M. Mansanares, “Geometrical anisotropy dependence of thermal diffusivity in lyotropic nematics: mode mismatched thermal lens measurements,” Appl. Phys. Lett. 68, 33713373 (1996).
[CrossRef]

A. S. Durate, H. L. Fragnito, and E. Palange, “Light induced permanent modifications of the nonlinear optical properties of semiconductor doped glasses,” Solid State Commun. 100, 463466 (1996).
[CrossRef]

D. V. Petrov, A. S. L. Gomes, and C. B. de Araújo, “Reflection of a Gaussian beam from a saturable absorber,” Opt. Commun. 123, 637641 (1996).
[CrossRef]

1994 (2)

L. C. Oliveira and S. C. Zilio, “Single-beam time-resolved z-scan measurements of slow absorbers,” Appl. Phys. Lett. 65, 21212123 (1994).
[CrossRef]

P. Palffy-Muhoray, T. Wei, and W. Zhao, “Z-scan measurements on liquid-crystals: some considerations and results,” Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 251, 1931 (1994).
[CrossRef]

1993 (2)

C. W. Greeff, J. Lu, and M. A. Lee, “Theoretical-study of mechanisms of nonlinear-optical response in liquid-crystals,” Liq. Cryst. 15, 7585 (1993).
[CrossRef]

W. Zhao and P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 16131615 (1993).
[CrossRef]

1991 (4)

C. P. Bastos dos Santos and A. M. Figueiredo Neto, “Measurement of the coefficient of thermal-expansion of uniaxial and biaxial lyotropic nematics: disk and rods or intrinsically biaxial micelles,” Langmuir 7, 26262629 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 12281235 (1991).
[CrossRef]

H. J. Yuan, L. Li, and P. Palffy-Muhoray, “Nonlinear birefringence of nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 199, 223232 (1991).
[CrossRef]

P. Palffy-Muhoray, H. J. Yuan, L. Li, M. A. Lee, J. R. DeSalvo, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Measurements of 3rd order optical nonlin-earities of nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 207, 291305 (1991).
[CrossRef]

1990 (2)

H. J. Yuan, L. Li, and P. Palffy-Muhoray, “Nonlinear birefringence of nematic liquid crystals,” Proc. SPIE 1307, 363373 (1990).
[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, 760769 (1990).
[CrossRef]

1989 (1)

1984 (1)

1974 (1)

J. R. Whinnery, “Laser measurement of optical-absorption in liquids,” Acc. Chem. Res. 7, 225231 (1974).
[CrossRef]

1973 (1)

1965 (1)

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 38 (1965).
[CrossRef]

1964 (1)

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurements by means of thermal lens effect using HeNe laser (absorption 10−3 to 10−5 cm−1 stimulated Raman scattering ET),” Appl. Phys. Lett. 5, 141143 (1964).
[CrossRef]

Baesso, M. L.

A. C. Bento, A. J. Palangana, L. R. Evangelista, M. L. Baesso, J. R. D. Pereira, E. C. da Silva, and A. M. Mansanares, “Geometrical anisotropy dependence of thermal diffusivity in lyotropic nematics: mode mismatched thermal lens measurements,” Appl. Phys. Lett. 68, 33713373 (1996).
[CrossRef]

Bento, A. C.

A. C. Bento, A. J. Palangana, L. R. Evangelista, M. L. Baesso, J. R. D. Pereira, E. C. da Silva, and A. M. Mansanares, “Geometrical anisotropy dependence of thermal diffusivity in lyotropic nematics: mode mismatched thermal lens measurements,” Appl. Phys. Lett. 68, 33713373 (1996).
[CrossRef]

Carter, C. A.

Cuppo, F. L. S.

S. L. Gómez, F. L. S. Cuppo, A. M. Figueiredo Neto, T. Kosa, M. Muramatsu, and R. J. Horowicz, “Z-scan measurement of the nonlinear refractive indices of micellar lyotropic liquid crystals with and without the ferrofluid doping,” Phys. Rev. E 59, 30593063 (1999).
[CrossRef]

da Silva, E. C.

A. C. Bento, A. J. Palangana, L. R. Evangelista, M. L. Baesso, J. R. D. Pereira, E. C. da Silva, and A. M. Mansanares, “Geometrical anisotropy dependence of thermal diffusivity in lyotropic nematics: mode mismatched thermal lens measurements,” Appl. Phys. Lett. 68, 33713373 (1996).
[CrossRef]

de Araújo, C. B.

D. V. Petrov, A. S. L. Gomes, and C. B. de Araújo, “Reflection of a Gaussian beam from a saturable absorber,” Opt. Commun. 123, 637641 (1996).
[CrossRef]

DeSalvo, J. R.

P. Palffy-Muhoray, H. J. Yuan, L. Li, M. A. Lee, J. R. DeSalvo, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Measurements of 3rd order optical nonlin-earities of nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 207, 291305 (1991).
[CrossRef]

dos Santos, C. P. Bastos

C. P. Bastos dos Santos and A. M. Figueiredo Neto, “Measurement of the coefficient of thermal-expansion of uniaxial and biaxial lyotropic nematics: disk and rods or intrinsically biaxial micelles,” Langmuir 7, 26262629 (1991).
[CrossRef]

Durate, A. S.

A. S. Durate, H. L. Fragnito, and E. Palange, “Light induced permanent modifications of the nonlinear optical properties of semiconductor doped glasses,” Solid State Commun. 100, 463466 (1996).
[CrossRef]

Evangelista, L. R.

A. C. Bento, A. J. Palangana, L. R. Evangelista, M. L. Baesso, J. R. D. Pereira, E. C. da Silva, and A. M. Mansanares, “Geometrical anisotropy dependence of thermal diffusivity in lyotropic nematics: mode mismatched thermal lens measurements,” Appl. Phys. Lett. 68, 33713373 (1996).
[CrossRef]

Figueiredo Neto, A. M.

S. L. Gómez, F. L. S. Cuppo, A. M. Figueiredo Neto, T. Kosa, M. Muramatsu, and R. J. Horowicz, “Z-scan measurement of the nonlinear refractive indices of micellar lyotropic liquid crystals with and without the ferrofluid doping,” Phys. Rev. E 59, 30593063 (1999).
[CrossRef]

C. P. Bastos dos Santos and A. M. Figueiredo Neto, “Measurement of the coefficient of thermal-expansion of uniaxial and biaxial lyotropic nematics: disk and rods or intrinsically biaxial micelles,” Langmuir 7, 26262629 (1991).
[CrossRef]

Fragnito, H. L.

A. S. Durate, H. L. Fragnito, and E. Palange, “Light induced permanent modifications of the nonlinear optical properties of semiconductor doped glasses,” Solid State Commun. 100, 463466 (1996).
[CrossRef]

Gomes, A. S. L.

D. V. Petrov, A. S. L. Gomes, and C. B. de Araújo, “Reflection of a Gaussian beam from a saturable absorber,” Opt. Commun. 123, 637641 (1996).
[CrossRef]

Gómez, S. L.

S. L. Gómez, F. L. S. Cuppo, A. M. Figueiredo Neto, T. Kosa, M. Muramatsu, and R. J. Horowicz, “Z-scan measurement of the nonlinear refractive indices of micellar lyotropic liquid crystals with and without the ferrofluid doping,” Phys. Rev. E 59, 30593063 (1999).
[CrossRef]

Gordon, J. P.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 38 (1965).
[CrossRef]

Greeff, C. W.

C. W. Greeff, J. Lu, and M. A. Lee, “Theoretical-study of mechanisms of nonlinear-optical response in liquid-crystals,” Liq. Cryst. 15, 7585 (1993).
[CrossRef]

Hagan, D. J.

D. I. Kovsh, D. J. Hagan, and E. W. Van Stryland, “Numerical modeling of thermal refraction in liquids in the transient regime,” Opt. Express 4, 315327 (1999).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 12281235 (1991).
[CrossRef]

P. Palffy-Muhoray, H. J. Yuan, L. Li, M. A. Lee, J. R. DeSalvo, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Measurements of 3rd order optical nonlin-earities of nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 207, 291305 (1991).
[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, 760769 (1990).
[CrossRef]

Harris, J. M.

Horowicz, R. J.

S. L. Gómez, F. L. S. Cuppo, A. M. Figueiredo Neto, T. Kosa, M. Muramatsu, and R. J. Horowicz, “Z-scan measurement of the nonlinear refractive indices of micellar lyotropic liquid crystals with and without the ferrofluid doping,” Phys. Rev. E 59, 30593063 (1999).
[CrossRef]

Hu, C.

Kosa, T.

S. L. Gómez, F. L. S. Cuppo, A. M. Figueiredo Neto, T. Kosa, M. Muramatsu, and R. J. Horowicz, “Z-scan measurement of the nonlinear refractive indices of micellar lyotropic liquid crystals with and without the ferrofluid doping,” Phys. Rev. E 59, 30593063 (1999).
[CrossRef]

Kovsh, D. I.

Lee, M. A.

C. W. Greeff, J. Lu, and M. A. Lee, “Theoretical-study of mechanisms of nonlinear-optical response in liquid-crystals,” Liq. Cryst. 15, 7585 (1993).
[CrossRef]

P. Palffy-Muhoray, H. J. Yuan, L. Li, M. A. Lee, J. R. DeSalvo, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Measurements of 3rd order optical nonlin-earities of nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 207, 291305 (1991).
[CrossRef]

Leite, R. C. C.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 38 (1965).
[CrossRef]

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurements by means of thermal lens effect using HeNe laser (absorption 10−3 to 10−5 cm−1 stimulated Raman scattering ET),” Appl. Phys. Lett. 5, 141143 (1964).
[CrossRef]

Li, L.

H. J. Yuan, L. Li, and P. Palffy-Muhoray, “Nonlinear birefringence of nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 199, 223232 (1991).
[CrossRef]

P. Palffy-Muhoray, H. J. Yuan, L. Li, M. A. Lee, J. R. DeSalvo, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Measurements of 3rd order optical nonlin-earities of nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 207, 291305 (1991).
[CrossRef]

H. J. Yuan, L. Li, and P. Palffy-Muhoray, “Nonlinear birefringence of nematic liquid crystals,” Proc. SPIE 1307, 363373 (1990).
[CrossRef]

Lu, J.

C. W. Greeff, J. Lu, and M. A. Lee, “Theoretical-study of mechanisms of nonlinear-optical response in liquid-crystals,” Liq. Cryst. 15, 7585 (1993).
[CrossRef]

Mansanares, A. M.

A. C. Bento, A. J. Palangana, L. R. Evangelista, M. L. Baesso, J. R. D. Pereira, E. C. da Silva, and A. M. Mansanares, “Geometrical anisotropy dependence of thermal diffusivity in lyotropic nematics: mode mismatched thermal lens measurements,” Appl. Phys. Lett. 68, 33713373 (1996).
[CrossRef]

Moore, R. S.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 38 (1965).
[CrossRef]

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurements by means of thermal lens effect using HeNe laser (absorption 10−3 to 10−5 cm−1 stimulated Raman scattering ET),” Appl. Phys. Lett. 5, 141143 (1964).
[CrossRef]

Muramatsu, M.

S. L. Gómez, F. L. S. Cuppo, A. M. Figueiredo Neto, T. Kosa, M. Muramatsu, and R. J. Horowicz, “Z-scan measurement of the nonlinear refractive indices of micellar lyotropic liquid crystals with and without the ferrofluid doping,” Phys. Rev. E 59, 30593063 (1999).
[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, 21212123 (1994).
[CrossRef]

Palangana, A. J.

A. C. Bento, A. J. Palangana, L. R. Evangelista, M. L. Baesso, J. R. D. Pereira, E. C. da Silva, and A. M. Mansanares, “Geometrical anisotropy dependence of thermal diffusivity in lyotropic nematics: mode mismatched thermal lens measurements,” Appl. Phys. Lett. 68, 33713373 (1996).
[CrossRef]

Palange, E.

A. S. Durate, H. L. Fragnito, and E. Palange, “Light induced permanent modifications of the nonlinear optical properties of semiconductor doped glasses,” Solid State Commun. 100, 463466 (1996).
[CrossRef]

Palffy-Muhoray, P.

P. Palffy-Muhoray, T. Wei, and W. Zhao, “Z-scan measurements on liquid-crystals: some considerations and results,” Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 251, 1931 (1994).
[CrossRef]

W. Zhao and P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 16131615 (1993).
[CrossRef]

P. Palffy-Muhoray, H. J. Yuan, L. Li, M. A. Lee, J. R. DeSalvo, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Measurements of 3rd order optical nonlin-earities of nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 207, 291305 (1991).
[CrossRef]

H. J. Yuan, L. Li, and P. Palffy-Muhoray, “Nonlinear birefringence of nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 199, 223232 (1991).
[CrossRef]

H. J. Yuan, L. Li, and P. Palffy-Muhoray, “Nonlinear birefringence of nematic liquid crystals,” Proc. SPIE 1307, 363373 (1990).
[CrossRef]

Pereira, J. R. D.

A. C. Bento, A. J. Palangana, L. R. Evangelista, M. L. Baesso, J. R. D. Pereira, E. C. da Silva, and A. M. Mansanares, “Geometrical anisotropy dependence of thermal diffusivity in lyotropic nematics: mode mismatched thermal lens measurements,” Appl. Phys. Lett. 68, 33713373 (1996).
[CrossRef]

Petrov, D. V.

D. V. Petrov, A. S. L. Gomes, and C. B. de Araújo, “Reflection of a Gaussian beam from a saturable absorber,” Opt. Commun. 123, 637641 (1996).
[CrossRef]

Porto, S. P. S.

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 38 (1965).
[CrossRef]

Said, A. A.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 12281235 (1991).
[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, 760769 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity single-beam n2 measurements,” Opt. Lett. 14, 955957 (1989).
[CrossRef] [PubMed]

Sheik-Bahae, M.

P. Palffy-Muhoray, H. J. Yuan, L. Li, M. A. Lee, J. R. DeSalvo, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Measurements of 3rd order optical nonlin-earities of nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 207, 291305 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 12281235 (1991).
[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, 760769 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity single-beam n2 measurements,” Opt. Lett. 14, 955957 (1989).
[CrossRef] [PubMed]

Simoni, F.

F. Simoni, “Non-linear optics in liquid crystals: basic ideas and perspectives,” Liq. Cryst. 24, 8389 (1998).
[CrossRef]

Soileau, M. J.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 12281235 (1991).
[CrossRef]

Van Stryland, E. W.

D. I. Kovsh, D. J. Hagan, and E. W. Van Stryland, “Numerical modeling of thermal refraction in liquids in the transient regime,” Opt. Express 4, 315327 (1999).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 12281235 (1991).
[CrossRef]

P. Palffy-Muhoray, H. J. Yuan, L. Li, M. A. Lee, J. R. DeSalvo, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Measurements of 3rd order optical nonlin-earities of nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 207, 291305 (1991).
[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, 760769 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity single-beam n2 measurements,” Opt. Lett. 14, 955957 (1989).
[CrossRef] [PubMed]

Wei, T.

P. Palffy-Muhoray, T. Wei, and W. Zhao, “Z-scan measurements on liquid-crystals: some considerations and results,” Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 251, 1931 (1994).
[CrossRef]

Wei, T. H.

P. Palffy-Muhoray, H. J. Yuan, L. Li, M. A. Lee, J. R. DeSalvo, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Measurements of 3rd order optical nonlin-earities of nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 207, 291305 (1991).
[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, 760769 (1990).
[CrossRef]

Whinnery, J. R.

J. R. Whinnery, “Laser measurement of optical-absorption in liquids,” Acc. Chem. Res. 7, 225231 (1974).
[CrossRef]

C. Hu and J. R. Whinnery, “New thermooptical measurement method and a comparison with other methods,” Appl. Opt. 12, 7279 (1973).
[CrossRef] [PubMed]

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 38 (1965).
[CrossRef]

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurements by means of thermal lens effect using HeNe laser (absorption 10−3 to 10−5 cm−1 stimulated Raman scattering ET),” Appl. Phys. Lett. 5, 141143 (1964).
[CrossRef]

Yuan, H. J.

H. J. Yuan, L. Li, and P. Palffy-Muhoray, “Nonlinear birefringence of nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 199, 223232 (1991).
[CrossRef]

P. Palffy-Muhoray, H. J. Yuan, L. Li, M. A. Lee, J. R. DeSalvo, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Measurements of 3rd order optical nonlin-earities of nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 207, 291305 (1991).
[CrossRef]

H. J. Yuan, L. Li, and P. Palffy-Muhoray, “Nonlinear birefringence of nematic liquid crystals,” Proc. SPIE 1307, 363373 (1990).
[CrossRef]

Zhao, W.

P. Palffy-Muhoray, T. Wei, and W. Zhao, “Z-scan measurements on liquid-crystals: some considerations and results,” Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 251, 1931 (1994).
[CrossRef]

W. Zhao and P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 16131615 (1993).
[CrossRef]

Zilio, S. C.

L. C. Oliveira and S. C. Zilio, “Single-beam time-resolved z-scan measurements of slow absorbers,” Appl. Phys. Lett. 65, 21212123 (1994).
[CrossRef]

Acc. Chem. Res. (1)

J. R. Whinnery, “Laser measurement of optical-absorption in liquids,” Acc. Chem. Res. 7, 225231 (1974).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (4)

A. C. Bento, A. J. Palangana, L. R. Evangelista, M. L. Baesso, J. R. D. Pereira, E. C. da Silva, and A. M. Mansanares, “Geometrical anisotropy dependence of thermal diffusivity in lyotropic nematics: mode mismatched thermal lens measurements,” Appl. Phys. Lett. 68, 33713373 (1996).
[CrossRef]

R. C. C. Leite, R. S. Moore, and J. R. Whinnery, “Low absorption measurements by means of thermal lens effect using HeNe laser (absorption 10−3 to 10−5 cm−1 stimulated Raman scattering ET),” Appl. Phys. Lett. 5, 141143 (1964).
[CrossRef]

W. Zhao and P. Palffy-Muhoray, “Z-scan technique using top-hat beams,” Appl. Phys. Lett. 63, 16131615 (1993).
[CrossRef]

L. C. Oliveira and S. C. Zilio, “Single-beam time-resolved z-scan measurements of slow absorbers,” Appl. Phys. Lett. 65, 21212123 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760769 (1990).
[CrossRef]

J. Appl. Phys. (1)

J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36, 38 (1965).
[CrossRef]

Langmuir (1)

C. P. Bastos dos Santos and A. M. Figueiredo Neto, “Measurement of the coefficient of thermal-expansion of uniaxial and biaxial lyotropic nematics: disk and rods or intrinsically biaxial micelles,” Langmuir 7, 26262629 (1991).
[CrossRef]

Liq. Cryst. (2)

F. Simoni, “Non-linear optics in liquid crystals: basic ideas and perspectives,” Liq. Cryst. 24, 8389 (1998).
[CrossRef]

C. W. Greeff, J. Lu, and M. A. Lee, “Theoretical-study of mechanisms of nonlinear-optical response in liquid-crystals,” Liq. Cryst. 15, 7585 (1993).
[CrossRef]

Mol. Cryst. Liq. Cryst. (2)

H. J. Yuan, L. Li, and P. Palffy-Muhoray, “Nonlinear birefringence of nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 199, 223232 (1991).
[CrossRef]

P. Palffy-Muhoray, H. J. Yuan, L. Li, M. A. Lee, J. R. DeSalvo, T. H. Wei, M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, “Measurements of 3rd order optical nonlin-earities of nematic liquid crystals,” Mol. Cryst. Liq. Cryst. 207, 291305 (1991).
[CrossRef]

Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A (1)

P. Palffy-Muhoray, T. Wei, and W. Zhao, “Z-scan measurements on liquid-crystals: some considerations and results,” Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 251, 1931 (1994).
[CrossRef]

Opt. Commun. (1)

D. V. Petrov, A. S. L. Gomes, and C. B. de Araújo, “Reflection of a Gaussian beam from a saturable absorber,” Opt. Commun. 123, 637641 (1996).
[CrossRef]

Opt. Eng. (1)

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, and E. W. van Stryland, “Nonlinear refraction and optical limiting in thick media,” Opt. Eng. 30, 12281235 (1991).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. E (1)

S. L. Gómez, F. L. S. Cuppo, A. M. Figueiredo Neto, T. Kosa, M. Muramatsu, and R. J. Horowicz, “Z-scan measurement of the nonlinear refractive indices of micellar lyotropic liquid crystals with and without the ferrofluid doping,” Phys. Rev. E 59, 30593063 (1999).
[CrossRef]

Proc. SPIE (1)

H. J. Yuan, L. Li, and P. Palffy-Muhoray, “Nonlinear birefringence of nematic liquid crystals,” Proc. SPIE 1307, 363373 (1990).
[CrossRef]

Solid State Commun. (1)

A. S. Durate, H. L. Fragnito, and E. Palange, “Light induced permanent modifications of the nonlinear optical properties of semiconductor doped glasses,” Solid State Commun. 100, 463466 (1996).
[CrossRef]

Other (3)

A. M. Figueiredo Neto, Y. Galerne, A. M. Levelut, and L. Liébert, Physics of Complex and Supermolecular Fluids, Exxon Monograph Series, S. A. Safran and N. A. Clark, eds. (Wiley, New York, 1987), p. 347.

In situations where the medium presents a slow (ms) thermal response, Oliveira and Zilio4 proposed a time-resolved signal-detection scheme to eliminate any parasitic linear effects. The data-acquisition setup measures the transmitted intensity at t=0 {I(z, 0)} and t=τ (≫tc, a characteristic relaxation time) {I(z, τ)} and evaluates the ratio I(z, 0)/I(z, τ).

D. R. Lide, ed., CRC Handbook of Chemistry and Physics, 78th ed. (CRC Press, Boca Raton, Fla., 1997).

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Figures (4)

Fig. 1
Fig. 1

(a) Z-scan curve from Eq. (2), the Sheik-Bahae formalism (SBF) with ΔΦ0=-0.2; (b) Z-scan curve from Eq. (14), the Thermal-lens model (TLM). θ=0.1.

Fig. 2
Fig. 2

Typical Z-scan results with the different lyotropic mixtures. The solid curve corresponds to the SBF fitting [Eq. (2)] and the dotted curve to the TLM [Eq. (13) with t10tco]. (a) Undoped mixture; (b) ferrofluid-doped mixture (c1); (c) ferrofluid-doped mixture (c2); (d) ferrofluid-doped mixture (c3).

Fig. 3
Fig. 3

Typical time-dependent transmittance at a fixed z (ferrofluid-doped mixture with c2). The solid curve is a fitting to Eq. (13).

Fig. 4
Fig. 4

Beam-waist dependence of the nonlinear index γ. Undoped mixture. Incident power of 238 mW.

Tables (3)

Tables Icon

Table 1 Nonlinear Refractive Index (n2) in the SBF Framework, Thermal Conductivity (κ), and Thermo-optic Coefficient (n/T) in the TLM Framework, of the Different Lyotropic Samples Investigated

Tables Icon

Table 2 Nonlinear Optical Phase Shifts (ΔΦ0 and θ) and Their Ratio

Tables Icon

Table 3 Fit χ2 of SBF and TLM Expressions to Experimental Z-Scan Data

Equations (30)

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n=no+12n2E2=no+γI,
α=αo+α2E2=αo+βI,
TNSBF(z)1+ΔΦo 4x(1+x2)(9+x2),
ΔΦo=2πΔndλ=2πγIodλ=2πdλ n2εocnoIo,
ΔTpvSBF=0.406|ΔΦo|.
|ΔzpvSBF|=1.717zo,
TNSBF(z)=I(z, )I(, ).
I(, )=I(z, 0),
TNSBF(z)=I(z, )I(z, 0).
TNTLM(z, t)
=I(z, t)I(z, 0)=11+θ1+tc/2t2x1+x2+θ1+tc/2t211+x2,
tc=w24D,
θ=αo Pdλκ nT,
TNTLM(z, t)11+θ1+tc/2t2x1+x2.
tc=wo2(1+x2)4D=tco(1+x2),
TNTLM(z, t)=1+θ1+(1+x2)tco/2t2x1+x2-1.
TNTLM(z)11+θ 2x1+x2.
ΔpvTLM2|θ|.
|ΔzpvTLM|2zo.
|ΔΦ|=ΔTpv0.406
|θ|=ΔTpv2
to=w24D1 ms.
ΔΦ=2πdλ n2εocnoIo.
θ=2πdλ n2εocnoIo=παowo2d2λκ nTIo.
ΔT=αo ItCp,
Δn=αoCp nTIt,
ΔT(r, t)=Aωo28k Ei-2r2wo2-Ei-2r28Dt+wo2,
D=wo24tco.
n2=cnoγ=εocnoαo4κ nTwo2,
αoκ nT=εocno4 n2w2.

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