Abstract

We employ the z-scan method to distinguish thermally induced nonlinearities from others by varying the beam waist radius and to determine the thermo-optic coefficient of materials. One can attribute the origin of optical nonlinearities of Chinese tea liquid to laser-heating-induced nonlinear refraction while one irradiates the media with a cw He-Ne laser. We also analyze the influence of position dispersion on optical limiting.

© 1993 Optical Society of America

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References

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  1. M. Sheik-Bahae, A. A. Said, E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
    [Crossref] [PubMed]
  2. H.-J. Zhang, J.-H. Dai, P.-Y. Wang, L.-A. Wu, “Self-focusing and self-trapping in new types of Kerr media with large nonlinearities,” Opt. Lett. 14, 695–696 (1989).
    [Crossref] [PubMed]
  3. M. J. Mran, C. Y. She, R. L. Carman, “Interferometric measurements of nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
    [Crossref]
  4. W. E. Wiliams, M. J. Soileau, W. E. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
    [Crossref]
  5. W. E. Williams, M. J. Soileau, E. W. Van Stryland, “Simple direct measurements of n2,” presented at the 15th Annual Symposium on Optical Materials for High Power Lasers, Boulder, Colo., 1983.
  6. R. L. Carman, A. Mooradian, P. L. Kelley, A. Tufts, “Transient and steady state thermal self-focusing,” Appl. Phys. Lett. 14, 136–139 (1969).
    [Crossref]
  7. D. Weaire, B. S. Wherrett, D. A. B. Miller, S. D. Smith, “Effect of low-power nonlinear refraction on laser-beam propagation in InSb,” Opt. Lett. 4, 331–333 (1974).
    [Crossref]
  8. C. Hu, J. R. Whinnery, “New thermooptical measurement method and a comparison with other methods,” Appl. Opt. 12, 72–79(1973).
    [Crossref] [PubMed]
  9. S. J. Sheldon, L. V. Knight, J. M. Thorne, “Laser-induced thermal lens effect: a new theoretical model,” Appl. Opt. 21, 1663–1669 (1982).
    [Crossref] [PubMed]
  10. R. C. C. Leite, R. S. Moore, S. P. S. Porto, J. R. Whinnery, “Low absorption measurements by means of thermal lens effect using a He–Ne laser,” Appl. Phys. Lett. 5, 141–143 (1964).
    [Crossref]
  11. E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).
  12. E. W. Van Stryland, Y.-Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5, 1980–1988 (1988).
    [Crossref]

1989 (2)

1988 (1)

1985 (1)

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

1984 (1)

W. E. Wiliams, M. J. Soileau, W. E. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
[Crossref]

1982 (1)

1975 (1)

M. J. Mran, C. Y. She, R. L. Carman, “Interferometric measurements of nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
[Crossref]

1974 (1)

1973 (1)

1969 (1)

R. L. Carman, A. Mooradian, P. L. Kelley, A. Tufts, “Transient and steady state thermal self-focusing,” Appl. Phys. Lett. 14, 136–139 (1969).
[Crossref]

1964 (1)

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

Boggess, T. F.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

Carman, R. L.

M. J. Mran, C. Y. She, R. L. Carman, “Interferometric measurements of nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
[Crossref]

R. L. Carman, A. Mooradian, P. L. Kelley, A. Tufts, “Transient and steady state thermal self-focusing,” Appl. Phys. Lett. 14, 136–139 (1969).
[Crossref]

Dai, J.-H.

Guha, S.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

Hagan, D. J.

Hu, C.

Kelley, P. L.

R. L. Carman, A. Mooradian, P. L. Kelley, A. Tufts, “Transient and steady state thermal self-focusing,” Appl. Phys. Lett. 14, 136–139 (1969).
[Crossref]

Knight, L. V.

Leite, R. C. C.

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

Mansour, K.

Miller, D. A. B.

Mooradian, A.

R. L. Carman, A. Mooradian, P. L. Kelley, A. Tufts, “Transient and steady state thermal self-focusing,” Appl. Phys. Lett. 14, 136–139 (1969).
[Crossref]

Moore, R. S.

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

Mran, M. J.

M. J. Mran, C. Y. She, R. L. Carman, “Interferometric measurements of nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
[Crossref]

Porto, S. P. S.

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

Said, A. A.

She, C. Y.

M. J. Mran, C. Y. She, R. L. Carman, “Interferometric measurements of nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
[Crossref]

Sheik-Bahae, M.

Sheldon, S. J.

Smirl, A. L.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

Smith, S. D.

Soileau, M. J.

E. W. Van Stryland, Y.-Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5, 1980–1988 (1988).
[Crossref]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

W. E. Wiliams, M. J. Soileau, W. E. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
[Crossref]

W. E. Williams, M. J. Soileau, E. W. Van Stryland, “Simple direct measurements of n2,” presented at the 15th Annual Symposium on Optical Materials for High Power Lasers, Boulder, Colo., 1983.

Thorne, J. M.

Tufts, A.

R. L. Carman, A. Mooradian, P. L. Kelley, A. Tufts, “Transient and steady state thermal self-focusing,” Appl. Phys. Lett. 14, 136–139 (1969).
[Crossref]

Van Stryland, E. W.

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

E. W. Van Stryland, Y.-Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5, 1980–1988 (1988).
[Crossref]

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

W. E. Williams, M. J. Soileau, E. W. Van Stryland, “Simple direct measurements of n2,” presented at the 15th Annual Symposium on Optical Materials for High Power Lasers, Boulder, Colo., 1983.

Van Stryland, W. E.

W. E. Wiliams, M. J. Soileau, W. E. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
[Crossref]

Vanherzeele, H.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

Wang, P.-Y.

Weaire, D.

Wherrett, B. S.

Whinnery, J. R.

C. Hu, J. R. Whinnery, “New thermooptical measurement method and a comparison with other methods,” Appl. Opt. 12, 72–79(1973).
[Crossref] [PubMed]

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

Wiliams, W. E.

W. E. Wiliams, M. J. Soileau, W. E. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
[Crossref]

Williams, W. E.

W. E. Williams, M. J. Soileau, E. W. Van Stryland, “Simple direct measurements of n2,” presented at the 15th Annual Symposium on Optical Materials for High Power Lasers, Boulder, Colo., 1983.

Woodall, M. A.

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

Wu, L.-A.

Wu, Y.-Y.

Zhang, H.-J.

Appl. Opt. (2)

Appl. Phys. Lett. (2)

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

R. L. Carman, A. Mooradian, P. L. Kelley, A. Tufts, “Transient and steady state thermal self-focusing,” Appl. Phys. Lett. 14, 136–139 (1969).
[Crossref]

IEEE J. Quantum Electron. (1)

M. J. Mran, C. Y. She, R. L. Carman, “Interferometric measurements of nonlinear refractive-index coefficient relative to CS2 in laser-system-related materials,” IEEE J. Quantum Electron. QE-11, 259–263 (1975).
[Crossref]

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

Opt. Commun. (1)

W. E. Wiliams, M. J. Soileau, W. E. Van Stryland, “Optical switching and n2 measurements in CS2,” Opt. Commun. 50, 256–260 (1984).
[Crossref]

Opt. Eng. (1)

E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. L. Smirl, S. Guha, T. F. Boggess, “Two photon absorption, nonlinear refraction, and optical limiting in semiconductors,” Opt. Eng. 24, 613–623 (1985).

Opt. Lett. (3)

Other (1)

W. E. Williams, M. J. Soileau, E. W. Van Stryland, “Simple direct measurements of n2,” presented at the 15th Annual Symposium on Optical Materials for High Power Lasers, Boulder, Colo., 1983.

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Figures (4)

Fig. 1
Fig. 1

Measured curves of position dispersion of Chinese tea liquid for different beam waist radii: (a) focal length of focusing lens f = 13 cm, calculated z0 = 0.88 cm, measured Δzp−v = 5.9 cm; (b)f 19.1 cm, calculated z0 1.89 cm, measured Δzp−v = 13.4 cm; (c)f = 30 cm, calculated z0 = 4.67 cm, measured Δzp−v = 24.1 cm; aperture size is 1.0 mm.

Fig. 2
Fig. 2

Measured ΔTp−v as a function of input power of laser Pin under different beam waist radii:●, f = 13 cm; △, f = 19.1 cm; ○, f =30 cm.

Fig. 3
Fig. 3

Experimental setup that we used to measure the optical limiting effect of Chinese tea liquid. D1, D2, detectors; BS, beam splitter; PL, polarizer. The focal length of lenses L1 and L2 is 19.1 cm.

Fig. 4
Fig. 4

Measured response characteristics of the limiter: (a) the nonlinear medium is at the beam waist, (b) the nonlinear medium is at a distance of 3z0 before the beam waist, (c) the nonlinear medium is at a distance of 3z0 after the beam waist.

Equations (17)

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d I / d z = α ( I ) I ,
d ( Δ Φ ) / d z = Δ n ( I ) k ,
Δ n = d n d T Δ T d n d T I τ α / ρ C ,
Δ n = d n d T I w 2 α / 4 K .
E ( z , r , t ) = E 0 ( t ) [ w 0 / w ( z ) ] × exp [ r 2 / w 2 ( z ) ik r 2 / 2 R ( z ) ] × exp [ i Φ ( z , t ) ] ,
Δ Φ ( z , r ) = Δ Φ 0 exp [ 2 r 2 / w 2 ( z ) ] ,
Δ Φ 0 = d n d T P in [ 1 exp ( α L ) ] k / 2 π K ,
E a ( r ) = E ( z , r = 0 ) exp ( α L / 2 ) m = 0 ( i Δ Φ 0 ) m m ! w m 0 w m × exp ( r 2 / w m 2 ik r 2 / 2 R m + i θ m ) ,
P T = c ɛ 0 n 0 π 0 r a | E a ( r ) | 2 r d r ,
T ( z ) = P T P in S exp ( α L ) ,
Δ T p v 1.35 | Δ Φ 0 | , | Δ Φ 0 | π ,
Δ Z p v 5.9 z 0 ,
T ( z , Δ Φ 0 ) = | E a ( z , r = 0 , Δ Φ 0 ) | 2 | E a ( z , r = 0 , Δ Φ 0 = 0 ) | 2 = | ( g + id / d 0 ) 1 + Δ Φ 0 ( z ) ( g + id / d 1 ) 1 | 2 | ( g + id / d 0 ) 1 | 2 .
T ( z , Δ Φ 0 ) 1 4 Δ Φ 0 x x 2 + 9 ,
x p , v = ± 3 ,
Δ z p v = 6 z 0 .
Δ T p v = 8 | x p , v | x p , v 2 + 9 Δ Φ 0 = 1.33 Δ Φ 0 .

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