Abstract

Multiple diffraction rings appear as a cw laser beam passes through a homeotropic nematic film. The phenomenon is shown to be the result of spatial self-phase modulation that is due to the laser-induced Freedericksz transition.

© 1981 Optical Society of America

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References

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  1. See, for example, Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975), and references therein.
    [Crossref]
  2. These include metal vapor: D. Grischkowsky, Phys. Rev. Lett. 24, 866 (1970); semiconductors: H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, W. Wiegmann, Appl. Phys. Lett. 35, 451 (1979); D. A. B. Miller, M. H. Mozolowski, A. Miller, S. D. Smith, Opt. Commun. 27, 133 (1978); A. Maruani, J-L. Oudar, E. Batifol, D. S. Chemla, Phys. Rev. Lett. 41, 1372 (1978); photorefractive materials: J. Feinberg, R. Hellwarth, J. Opt. Soc. Am. 70, 599A (1980).
    [Crossref]
  3. R. M. Herman, R. J. Serinko, Phys. Rev. A 19, 1757 (1979); B. Ya. Zel’dovich, N. V. Tabiryan, JETP Lett. 30, 478 (1979); B. Ya. Zel’dovich, N. F. Pilipetskii, A. V. Sukhov, N. V. Tabiryan, JETP Lett. 31, 263 (1980); I. C. Khoo, S. L. Zhuang, Appl. Phys. Lett. 37, 3 (1980).
    [Crossref]
  4. A. S. Zolot’ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, L. Chillag, JETP Lett. 32, 158 (1980). According to R. M. Herman, a similar pattern has been observed by A. Saupé.
  5. A. C. Tam, Phys. Rev. A 19, 1971 (1979); G. Brechignac, Ph. Cahuzac, A. Debarre, Opt. Commun. 35, 87 (1980); C. H. Skinner, P. D. Kleiber, Phys. Rev. A 21, 151 (1980); Y. H. Meyer, Opt. Commun. 34, 439 (1980).
    [Crossref]
  6. S. D. Durbin, S. M. Arakelian, Y. R. Shen (to be published).
  7. F. Shimizu, Phys. Rev. Lett. 19, 1097 (1967); T. K. Gustafson, J. P. E. Taran, H. A. Haus, J. R. Lifsitz, P. L. Kelley, Phys. Rev. 177, 306 (1979); M. M. T. Loy, Y. R. Shen, IEEE J. Quantum Electron. QE-9, 409 (1973).
    [Crossref]
  8. More rigorously, the equation should be replaced by Δψ(ρ1) − Δψ(ρ2) k⊥(ρ1 − ρ2) = mπ See the paper by F. Shimizu in Ref. 7.
  9. See, for example, P. Sheng, in Introduction to Liquid Crystals, E. B. Priestley, P. J. Wojtowicz, P. Sheng, eds. (Plenum, New York, 1975), Chap. 8, p. 103.
    [Crossref]
  10. K. Skarp, S. Lagerwall, B. Stebler, Mol. Cryst. Liq. Cryst. 60, 215 (1980).
    [Crossref]

1980 (2)

A. S. Zolot’ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, L. Chillag, JETP Lett. 32, 158 (1980). According to R. M. Herman, a similar pattern has been observed by A. Saupé.

K. Skarp, S. Lagerwall, B. Stebler, Mol. Cryst. Liq. Cryst. 60, 215 (1980).
[Crossref]

1979 (2)

R. M. Herman, R. J. Serinko, Phys. Rev. A 19, 1757 (1979); B. Ya. Zel’dovich, N. V. Tabiryan, JETP Lett. 30, 478 (1979); B. Ya. Zel’dovich, N. F. Pilipetskii, A. V. Sukhov, N. V. Tabiryan, JETP Lett. 31, 263 (1980); I. C. Khoo, S. L. Zhuang, Appl. Phys. Lett. 37, 3 (1980).
[Crossref]

A. C. Tam, Phys. Rev. A 19, 1971 (1979); G. Brechignac, Ph. Cahuzac, A. Debarre, Opt. Commun. 35, 87 (1980); C. H. Skinner, P. D. Kleiber, Phys. Rev. A 21, 151 (1980); Y. H. Meyer, Opt. Commun. 34, 439 (1980).
[Crossref]

1975 (1)

See, for example, Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975), and references therein.
[Crossref]

1970 (1)

These include metal vapor: D. Grischkowsky, Phys. Rev. Lett. 24, 866 (1970); semiconductors: H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, W. Wiegmann, Appl. Phys. Lett. 35, 451 (1979); D. A. B. Miller, M. H. Mozolowski, A. Miller, S. D. Smith, Opt. Commun. 27, 133 (1978); A. Maruani, J-L. Oudar, E. Batifol, D. S. Chemla, Phys. Rev. Lett. 41, 1372 (1978); photorefractive materials: J. Feinberg, R. Hellwarth, J. Opt. Soc. Am. 70, 599A (1980).
[Crossref]

1967 (1)

F. Shimizu, Phys. Rev. Lett. 19, 1097 (1967); T. K. Gustafson, J. P. E. Taran, H. A. Haus, J. R. Lifsitz, P. L. Kelley, Phys. Rev. 177, 306 (1979); M. M. T. Loy, Y. R. Shen, IEEE J. Quantum Electron. QE-9, 409 (1973).
[Crossref]

Arakelian, S. M.

S. D. Durbin, S. M. Arakelian, Y. R. Shen (to be published).

Chillag, L.

A. S. Zolot’ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, L. Chillag, JETP Lett. 32, 158 (1980). According to R. M. Herman, a similar pattern has been observed by A. Saupé.

Durbin, S. D.

S. D. Durbin, S. M. Arakelian, Y. R. Shen (to be published).

Grischkowsky, D.

These include metal vapor: D. Grischkowsky, Phys. Rev. Lett. 24, 866 (1970); semiconductors: H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, W. Wiegmann, Appl. Phys. Lett. 35, 451 (1979); D. A. B. Miller, M. H. Mozolowski, A. Miller, S. D. Smith, Opt. Commun. 27, 133 (1978); A. Maruani, J-L. Oudar, E. Batifol, D. S. Chemla, Phys. Rev. Lett. 41, 1372 (1978); photorefractive materials: J. Feinberg, R. Hellwarth, J. Opt. Soc. Am. 70, 599A (1980).
[Crossref]

Herman, R. M.

R. M. Herman, R. J. Serinko, Phys. Rev. A 19, 1757 (1979); B. Ya. Zel’dovich, N. V. Tabiryan, JETP Lett. 30, 478 (1979); B. Ya. Zel’dovich, N. F. Pilipetskii, A. V. Sukhov, N. V. Tabiryan, JETP Lett. 31, 263 (1980); I. C. Khoo, S. L. Zhuang, Appl. Phys. Lett. 37, 3 (1980).
[Crossref]

Kitaeva, V. F.

A. S. Zolot’ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, L. Chillag, JETP Lett. 32, 158 (1980). According to R. M. Herman, a similar pattern has been observed by A. Saupé.

Kroo, N.

A. S. Zolot’ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, L. Chillag, JETP Lett. 32, 158 (1980). According to R. M. Herman, a similar pattern has been observed by A. Saupé.

Lagerwall, S.

K. Skarp, S. Lagerwall, B. Stebler, Mol. Cryst. Liq. Cryst. 60, 215 (1980).
[Crossref]

Serinko, R. J.

R. M. Herman, R. J. Serinko, Phys. Rev. A 19, 1757 (1979); B. Ya. Zel’dovich, N. V. Tabiryan, JETP Lett. 30, 478 (1979); B. Ya. Zel’dovich, N. F. Pilipetskii, A. V. Sukhov, N. V. Tabiryan, JETP Lett. 31, 263 (1980); I. C. Khoo, S. L. Zhuang, Appl. Phys. Lett. 37, 3 (1980).
[Crossref]

Shen, Y. R.

See, for example, Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975), and references therein.
[Crossref]

S. D. Durbin, S. M. Arakelian, Y. R. Shen (to be published).

Sheng, P.

See, for example, P. Sheng, in Introduction to Liquid Crystals, E. B. Priestley, P. J. Wojtowicz, P. Sheng, eds. (Plenum, New York, 1975), Chap. 8, p. 103.
[Crossref]

Shimizu, F.

F. Shimizu, Phys. Rev. Lett. 19, 1097 (1967); T. K. Gustafson, J. P. E. Taran, H. A. Haus, J. R. Lifsitz, P. L. Kelley, Phys. Rev. 177, 306 (1979); M. M. T. Loy, Y. R. Shen, IEEE J. Quantum Electron. QE-9, 409 (1973).
[Crossref]

Skarp, K.

K. Skarp, S. Lagerwall, B. Stebler, Mol. Cryst. Liq. Cryst. 60, 215 (1980).
[Crossref]

Sobolev, N. N.

A. S. Zolot’ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, L. Chillag, JETP Lett. 32, 158 (1980). According to R. M. Herman, a similar pattern has been observed by A. Saupé.

Stebler, B.

K. Skarp, S. Lagerwall, B. Stebler, Mol. Cryst. Liq. Cryst. 60, 215 (1980).
[Crossref]

Tam, A. C.

A. C. Tam, Phys. Rev. A 19, 1971 (1979); G. Brechignac, Ph. Cahuzac, A. Debarre, Opt. Commun. 35, 87 (1980); C. H. Skinner, P. D. Kleiber, Phys. Rev. A 21, 151 (1980); Y. H. Meyer, Opt. Commun. 34, 439 (1980).
[Crossref]

Zolot’ko, A. S.

A. S. Zolot’ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, L. Chillag, JETP Lett. 32, 158 (1980). According to R. M. Herman, a similar pattern has been observed by A. Saupé.

JETP Lett. (1)

A. S. Zolot’ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, L. Chillag, JETP Lett. 32, 158 (1980). According to R. M. Herman, a similar pattern has been observed by A. Saupé.

Mol. Cryst. Liq. Cryst. (1)

K. Skarp, S. Lagerwall, B. Stebler, Mol. Cryst. Liq. Cryst. 60, 215 (1980).
[Crossref]

Phys. Rev. A (2)

R. M. Herman, R. J. Serinko, Phys. Rev. A 19, 1757 (1979); B. Ya. Zel’dovich, N. V. Tabiryan, JETP Lett. 30, 478 (1979); B. Ya. Zel’dovich, N. F. Pilipetskii, A. V. Sukhov, N. V. Tabiryan, JETP Lett. 31, 263 (1980); I. C. Khoo, S. L. Zhuang, Appl. Phys. Lett. 37, 3 (1980).
[Crossref]

A. C. Tam, Phys. Rev. A 19, 1971 (1979); G. Brechignac, Ph. Cahuzac, A. Debarre, Opt. Commun. 35, 87 (1980); C. H. Skinner, P. D. Kleiber, Phys. Rev. A 21, 151 (1980); Y. H. Meyer, Opt. Commun. 34, 439 (1980).
[Crossref]

Phys. Rev. Lett. (2)

These include metal vapor: D. Grischkowsky, Phys. Rev. Lett. 24, 866 (1970); semiconductors: H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, W. Wiegmann, Appl. Phys. Lett. 35, 451 (1979); D. A. B. Miller, M. H. Mozolowski, A. Miller, S. D. Smith, Opt. Commun. 27, 133 (1978); A. Maruani, J-L. Oudar, E. Batifol, D. S. Chemla, Phys. Rev. Lett. 41, 1372 (1978); photorefractive materials: J. Feinberg, R. Hellwarth, J. Opt. Soc. Am. 70, 599A (1980).
[Crossref]

F. Shimizu, Phys. Rev. Lett. 19, 1097 (1967); T. K. Gustafson, J. P. E. Taran, H. A. Haus, J. R. Lifsitz, P. L. Kelley, Phys. Rev. 177, 306 (1979); M. M. T. Loy, Y. R. Shen, IEEE J. Quantum Electron. QE-9, 409 (1973).
[Crossref]

Prog. Quantum Electron. (1)

See, for example, Y. R. Shen, Prog. Quantum Electron. 4, 1 (1975), and references therein.
[Crossref]

Other (3)

S. D. Durbin, S. M. Arakelian, Y. R. Shen (to be published).

More rigorously, the equation should be replaced by Δψ(ρ1) − Δψ(ρ2) k⊥(ρ1 − ρ2) = mπ See the paper by F. Shimizu in Ref. 7.

See, for example, P. Sheng, in Introduction to Liquid Crystals, E. B. Priestley, P. J. Wojtowicz, P. Sheng, eds. (Plenum, New York, 1975), Chap. 8, p. 103.
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Typical diffraction ring pattern. The photo is developed to reduce the relative intensity of the central region.

Fig. 2
Fig. 2

The number of observed rings N as a function of laser intensity I is shown by the filled circles. The open circles show the prediction from simultaneous birefringence measurements, and the solid line is the theoretical curve.

Fig. 3
Fig. 3

Half-angle βm of outermost ring as a function of laser intensity.

Fig. 4
Fig. 4

Profile of induced phase retardation. Light diffracted at ρ1 and ρ2 has the same wave vector and interferes.

Equations (5)

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Δ ψ ( ρ ) = 2 π λ d / 2 d / 2 Δ n ( ρ , z ) d z ,
Δ ψ ( ρ ) = Δ ψ 0 exp ( 2 ρ 2 / a 2 ) ,
N Δ ψ 0 / 2 π .
β m ( d Δ ψ d ρ ) max / ( 2 π / λ ) .
E ( ρ ) = ( ρ ) exp [ i k z z + i Δ ψ ( ρ ) ] .

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