Abstract

A model for beam propagation through a nonlinear material is developed; the model takes into account inhomogeneous induced refractive-index changes due to the nonlinearity. A focused Gaussian beam of circular cross section, incident upon the sample, emerges as an elliptic Gaussian beam after interaction in this material. The nonlinearity coefficient values derived from a Z scan of photorefractive lithium niobate crystals compare favorably with that found by varying the power P of a Gaussian beam focused at a fixed longitudinal position within the sample and monitoring the far-field beam ellipticity. The nonlinearity coefficient value is used to determine the dopant’s acceptor-to-donor concentration ratio in photorefractive lithium niobate samples.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Cronin-Golomb and A. Yariv, “Optical limiter using photorefractive nonlinearities,” J. Appl. Phys. 57, 4906–4910 (1985).
    [CrossRef]
  2. S. E. Bialkowski, “Application of BaTiO3 beam-fanning optical limiter as an adaptive spatial filter for signal enhancement in pulsed infrared laser-excited photothermal spectroscopy,” Opt. Lett. 14, 1020–1022 (1989).
    [CrossRef] [PubMed]
  3. J. Feinberg, “Self-pumped, continuous-wave phase conjugator using internal reflection,” Opt. Lett. 7, 486–488 (1982).
    [CrossRef] [PubMed]
  4. J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982).
    [CrossRef]
  5. J. Feinberg, “Asymmetric self-defocusing of an optical beam from the photovoltaic effect,” J. Opt. Soc. Am. A 72, 46–51 (1982).
    [CrossRef]
  6. J. J. Liu, P. P. Banerjee, and Q. W. Song, “Role of diffusive, photovoltaic, and thermal effects in beam fanning in LiNbO3,” J. Opt. Soc. Am. B 11, 1688–1693 (1994).
    [CrossRef]
  7. V. V. Voronov, I. R. Dorosh, Yu. S. Kuz’minov, and N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
    [CrossRef]
  8. M. Segev, Y. Ophir, and B. Fischer, “Nonlinear multi two-wave mixing. The fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
    [CrossRef]
  9. G. Zhang, Q. X. Li, P. P. Ho, S. Liu, Z. K. Wu, and R. R. Alfano, “Dependence of specklon size on the laser beam size via photo-induced light scattering in LiNbO3:Fe,” Appl. Opt. 25, 2955–2959 (1986).
    [CrossRef]
  10. E. M. Avakyan, K. G. Belabaev, and S. G. Odoulov, “Polarization-anisotropic light-induced scattering in LiNbO3:Fe crystals,” Sov. Phys. Solid State 25, 1887–1890 (1983).
  11. A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballmann, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
    [CrossRef]
  12. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
    [CrossRef] [PubMed]
  13. Q. W. Song, C.-P. Zhang, and P. J. Talbot, “Anisotropic light-induced scattering and ‘position dispersion’ in KNbO3:Fe crystal,” Opt. Commun. 98, 269–273 (1993).
    [CrossRef]
  14. P. P. Banerjee, R. M. Misra, and M. Maghraoui, “Theoretical and experimental studies of propagation of beams through a finite sample of a cubically nonlinear material,” J. Opt. Soc. Am. B 8, 1072–1080 (1991).
    [CrossRef]
  15. 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]
  16. A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
    [CrossRef]
  17. N. Kukhtarev, G. Dovgalenko, G. Duree, G. Salamo, E. Sharp, B. Wechler, and M. Klein, “Single beam polarization holographic grating recording,” Phys. Rev. Lett. 71, 4330–4332 (1993).
    [CrossRef] [PubMed]
  18. G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. 19, 1637–1645 (1983).
    [CrossRef]
  19. A. M. Prokhorov and Y. S. Kuzminov, Physics and Chemistry of Crystalline Lithium Niobate (Hilger, New York, 1990), Chap. 5, p. 161.

1994 (1)

1993 (2)

N. Kukhtarev, G. Dovgalenko, G. Duree, G. Salamo, E. Sharp, B. Wechler, and M. Klein, “Single beam polarization holographic grating recording,” Phys. Rev. Lett. 71, 4330–4332 (1993).
[CrossRef] [PubMed]

Q. W. Song, C.-P. Zhang, and P. J. Talbot, “Anisotropic light-induced scattering and ‘position dispersion’ in KNbO3:Fe crystal,” Opt. Commun. 98, 269–273 (1993).
[CrossRef]

1991 (1)

1990 (2)

M. Segev, Y. Ophir, and B. Fischer, “Nonlinear multi two-wave mixing. The fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (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, 760 (1990).
[CrossRef]

1989 (2)

1986 (1)

1985 (1)

M. Cronin-Golomb and A. Yariv, “Optical limiter using photorefractive nonlinearities,” J. Appl. Phys. 57, 4906–4910 (1985).
[CrossRef]

1983 (2)

E. M. Avakyan, K. G. Belabaev, and S. G. Odoulov, “Polarization-anisotropic light-induced scattering in LiNbO3:Fe crystals,” Sov. Phys. Solid State 25, 1887–1890 (1983).

G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. 19, 1637–1645 (1983).
[CrossRef]

1982 (3)

J. Feinberg, “Self-pumped, continuous-wave phase conjugator using internal reflection,” Opt. Lett. 7, 486–488 (1982).
[CrossRef] [PubMed]

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982).
[CrossRef]

J. Feinberg, “Asymmetric self-defocusing of an optical beam from the photovoltaic effect,” J. Opt. Soc. Am. A 72, 46–51 (1982).
[CrossRef]

1980 (1)

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz’minov, and N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[CrossRef]

1974 (1)

A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

1966 (1)

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballmann, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Alfano, R. R.

Ashkin, A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballmann, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Avakyan, E. M.

E. M. Avakyan, K. G. Belabaev, and S. G. Odoulov, “Polarization-anisotropic light-induced scattering in LiNbO3:Fe crystals,” Sov. Phys. Solid State 25, 1887–1890 (1983).

Ballmann, A. A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballmann, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Banerjee, P. P.

Belabaev, K. G.

E. M. Avakyan, K. G. Belabaev, and S. G. Odoulov, “Polarization-anisotropic light-induced scattering in LiNbO3:Fe crystals,” Sov. Phys. Solid State 25, 1887–1890 (1983).

Bialkowski, S. E.

Boyd, G. D.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballmann, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Cronin-Golomb, M.

M. Cronin-Golomb and A. Yariv, “Optical limiter using photorefractive nonlinearities,” J. Appl. Phys. 57, 4906–4910 (1985).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982).
[CrossRef]

Dorosh, I. R.

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz’minov, and N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[CrossRef]

Dovgalenko, G.

N. Kukhtarev, G. Dovgalenko, G. Duree, G. Salamo, E. Sharp, B. Wechler, and M. Klein, “Single beam polarization holographic grating recording,” Phys. Rev. Lett. 71, 4330–4332 (1993).
[CrossRef] [PubMed]

Duree, G.

N. Kukhtarev, G. Dovgalenko, G. Duree, G. Salamo, E. Sharp, B. Wechler, and M. Klein, “Single beam polarization holographic grating recording,” Phys. Rev. Lett. 71, 4330–4332 (1993).
[CrossRef] [PubMed]

Dziedzic, J. M.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballmann, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Feinberg, J.

J. Feinberg, “Self-pumped, continuous-wave phase conjugator using internal reflection,” Opt. Lett. 7, 486–488 (1982).
[CrossRef] [PubMed]

J. Feinberg, “Asymmetric self-defocusing of an optical beam from the photovoltaic effect,” J. Opt. Soc. Am. A 72, 46–51 (1982).
[CrossRef]

Fischer, B.

M. Segev, Y. Ophir, and B. Fischer, “Nonlinear multi two-wave mixing. The fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982).
[CrossRef]

Glass, A. M.

A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[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]

Ho, P. P.

Klein, M.

N. Kukhtarev, G. Dovgalenko, G. Duree, G. Salamo, E. Sharp, B. Wechler, and M. Klein, “Single beam polarization holographic grating recording,” Phys. Rev. Lett. 71, 4330–4332 (1993).
[CrossRef] [PubMed]

Kukhtarev, N.

N. Kukhtarev, G. Dovgalenko, G. Duree, G. Salamo, E. Sharp, B. Wechler, and M. Klein, “Single beam polarization holographic grating recording,” Phys. Rev. Lett. 71, 4330–4332 (1993).
[CrossRef] [PubMed]

Kuz’minov, Yu. S.

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz’minov, and N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[CrossRef]

Li, Q. X.

Liu, J. J.

Liu, S.

Maghraoui, M.

Misra, R. M.

Nassau, K.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballmann, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Negran, T. J.

A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

Odoulov, S. G.

E. M. Avakyan, K. G. Belabaev, and S. G. Odoulov, “Polarization-anisotropic light-induced scattering in LiNbO3:Fe crystals,” Sov. Phys. Solid State 25, 1887–1890 (1983).

Ophir, Y.

M. Segev, Y. Ophir, and B. Fischer, “Nonlinear multi two-wave mixing. The fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[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]

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

Salamo, G.

N. Kukhtarev, G. Dovgalenko, G. Duree, G. Salamo, E. Sharp, B. Wechler, and M. Klein, “Single beam polarization holographic grating recording,” Phys. Rev. Lett. 71, 4330–4332 (1993).
[CrossRef] [PubMed]

Segev, M.

M. Segev, Y. Ophir, and B. Fischer, “Nonlinear multi two-wave mixing. The fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[CrossRef]

Sharp, E.

N. Kukhtarev, G. Dovgalenko, G. Duree, G. Salamo, E. Sharp, B. Wechler, and M. Klein, “Single beam polarization holographic grating recording,” Phys. Rev. Lett. 71, 4330–4332 (1993).
[CrossRef] [PubMed]

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]

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

Smith, R. G.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballmann, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Song, Q. W.

J. J. Liu, P. P. Banerjee, and Q. W. Song, “Role of diffusive, photovoltaic, and thermal effects in beam fanning in LiNbO3,” J. Opt. Soc. Am. B 11, 1688–1693 (1994).
[CrossRef]

Q. W. Song, C.-P. Zhang, and P. J. Talbot, “Anisotropic light-induced scattering and ‘position dispersion’ in KNbO3:Fe crystal,” Opt. Commun. 98, 269–273 (1993).
[CrossRef]

Talbot, P. J.

Q. W. Song, C.-P. Zhang, and P. J. Talbot, “Anisotropic light-induced scattering and ‘position dispersion’ in KNbO3:Fe crystal,” Opt. Commun. 98, 269–273 (1993).
[CrossRef]

Tkachenko, N. V.

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz’minov, and N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[CrossRef]

Valley, G. C.

G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. 19, 1637–1645 (1983).
[CrossRef]

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (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] [PubMed]

von der Linde, D.

A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

Voronov, V. V.

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz’minov, and N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[CrossRef]

Wechler, B.

N. Kukhtarev, G. Dovgalenko, G. Duree, G. Salamo, E. Sharp, B. Wechler, and M. Klein, “Single beam polarization holographic grating recording,” Phys. Rev. Lett. 71, 4330–4332 (1993).
[CrossRef] [PubMed]

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]

White, J. O.

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982).
[CrossRef]

Wu, Z. K.

Yariv, A.

M. Cronin-Golomb and A. Yariv, “Optical limiter using photorefractive nonlinearities,” J. Appl. Phys. 57, 4906–4910 (1985).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982).
[CrossRef]

Zhang, C.-P.

Q. W. Song, C.-P. Zhang, and P. J. Talbot, “Anisotropic light-induced scattering and ‘position dispersion’ in KNbO3:Fe crystal,” Opt. Commun. 98, 269–273 (1993).
[CrossRef]

Zhang, G.

Appl. Opt. (1)

Appl. Phys. Lett. (3)

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive crystal BaTiO3,” Appl. Phys. Lett. 40, 450–452 (1982).
[CrossRef]

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballmann, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

IEEE J. Quantum Electron. (2)

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]

G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. 19, 1637–1645 (1983).
[CrossRef]

J. Appl. Phys. (1)

M. Cronin-Golomb and A. Yariv, “Optical limiter using photorefractive nonlinearities,” J. Appl. Phys. 57, 4906–4910 (1985).
[CrossRef]

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

J. Feinberg, “Asymmetric self-defocusing of an optical beam from the photovoltaic effect,” J. Opt. Soc. Am. A 72, 46–51 (1982).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (2)

Q. W. Song, C.-P. Zhang, and P. J. Talbot, “Anisotropic light-induced scattering and ‘position dispersion’ in KNbO3:Fe crystal,” Opt. Commun. 98, 269–273 (1993).
[CrossRef]

M. Segev, Y. Ophir, and B. Fischer, “Nonlinear multi two-wave mixing. The fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

N. Kukhtarev, G. Dovgalenko, G. Duree, G. Salamo, E. Sharp, B. Wechler, and M. Klein, “Single beam polarization holographic grating recording,” Phys. Rev. Lett. 71, 4330–4332 (1993).
[CrossRef] [PubMed]

Sov. J. Quantum Electron. (1)

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz’minov, and N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[CrossRef]

Sov. Phys. Solid State (1)

E. M. Avakyan, K. G. Belabaev, and S. G. Odoulov, “Polarization-anisotropic light-induced scattering in LiNbO3:Fe crystals,” Sov. Phys. Solid State 25, 1887–1890 (1983).

Other (1)

A. M. Prokhorov and Y. S. Kuzminov, Physics and Chemistry of Crystalline Lithium Niobate (Hilger, New York, 1990), Chap. 5, p. 161.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Typical Z-scan graph, drawn by solution of Eq. (1) and propagation of the Gaussian beam a distance D behind the sample.

Fig. 2
Fig. 2

Z-scan setup for a thick sample. The thick lines represent the path of the rays, described as the locus of the 1/e points of the Gaussian beam. The dotted lines show the ray path in the absence of the medium. The circular symmetry of the Gaussian beam is assumed throughout the sample.

Fig. 3
Fig. 3

Plot of ellipticity as a function of displacement s for the same parameters as in Fig. 1 but for P=0.2 mW.

Fig. 4
Fig. 4

Typical beam pattern at D=0.5 m for P=0.05 mW, f0=20 cm, and s=19.5 cm for Fe-doped LiNbO3 crystal.

Fig. 5
Fig. 5

Experimental (triangles) and theoretical (curve) variation of the beam ellipticity on the observation plane as a function of scan distance. Here P=0.2 mW, D=0.5 m, and f0=10 cm. On comparison, n2=-1.4×10-12 m2/V2.

Fig. 6
Fig. 6

(a) Theoretically and (b) experimentally obtained P-scan graph for D=0.5 m for f0=20 cm and s=19.5 cm for the Fe-doped LiNbO3 crystal; plot (a) was drawn with n2=-4×10-11 m2/V2 to provide the best match with the experimental results in (b).

Fig. 7
Fig. 7

Theoretically obtained P-scan graphs for D=1 m, f0=20 cm, n2=-4.0×10-11 m2/V2, and three different positions of the crystal, s. (a) s<f0; (b) s>f0.

Fig. 8
Fig. 8

Propagation of beam corresponding to wx inside a crystal with n2=-4×10-11 m2/V2 for three different values of incident beam power and wy: (a) s=16.0 cm, (b) s=25.0 cm; f0=20 cm, ne=2.2.

Fig. 9
Fig. 9

Theoretically obtained P-scan graphs for D=1 m, f0=20 cm, n2=1.4×10-12 m2/V2, and several different positions of the crystal, s. (a) s<f0, (b) s>f0.

Fig. 10
Fig. 10

Propagation of beam corresponding to wx inside a crystal with n2=4×10-11 m2/V2 for three different values of incident beam power and wy: (a) s=16.0 cm, (b) s=24.0 cm; f0=20 cm, ne=2.2.

Tables (1)

Tables Icon

Table 1 Experimental Results for Effective Nonlinearities (n2) of the 12 Crystals

Equations (19)

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

d2wxdz2=λ02ne2π2wx3-8n2ηPπnewx2wy,
d2wydz2=λ02ne2π2wy3.
n2-12 ne3r33 kαγRNAμeβND,
wy2(z)=w021+z2zRy2,zRy=neπw02λ0.
wx2(z)=w021+z2zRx2,
zRx=neπw02λ0 1+4nen2ηπPλ02.
Δq=Δz+q2find(Δz),
E(x, y, z)=a(z)exp-x2wx2exp-y2wy2.
Δqx=Δz+qx2findx,Δqy=Δz+qy2findy.
n=ne+n2|E|2ne-2n2a2(z)x2wx2+y2wy2,
findx=newx24n2xa2(z)Δz,findy=newy24n2ya2(z)Δz.
dqxdz=1+4n2xa(z)qx2newx2,
dqydz=1+4n2ya(z)qy2newy2.
1Rx2 dRxdz=ne2π2wx4-λ02Rx2(neπwx2Rx)2-4n2xa2newx2,
1Ry2 dRydz=ne2π2wy4-λ02Ry2(neπwy2Ry)2-4n2ya2newy2,
d2wxdz2=λ02ne2π2wx3-4n2xa2newx,
d2wydz2=λ02ne2π2wy3-4n2ya2newy.
d2wxdz2=λ02ne2π2wx3-8n2xPηπnewx2wy,
d2wydz2=λ02ne2π2wy3-8n2yPηπnewy2wx.

Metrics