Abstract

The wave-front curvature of an incident laser beam can modify the spatial phase modulation of the beam, and hence the diffraction of the beam, traversing a liquid-crystal film. It is shown both theoretically and experimentally that this explains the anomalous fine structure in the diffraction ring pattern observed with laser intensities above the Freederickscz transition threshold.

© 1984 Optical Society of America

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References

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  1. See, for example, the Optical Physics Technical Group session, Spatial Interference Rings: Conical Emission, in the 1983 Annual Meeting of Optical Society of America, New Orleans, La., 1983[ J. Opt. Soc. Am. 73, 1880 (1983)].
  2. S. D. Durbin, S. M. Arakelian, Y. R. Shen, Phys. Rev. Lett. 47, 1411 (1981);B. Ya Zel'dovich, N. T. Tabiryan, Yu. S. Chilingaryan, Sov. Phys. JETP 54, 32 (1981);A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, L. Csillag, JETP Lett. 32, 158 (1980);I. C. Khoo, Phys. Rev. A 23, 2078 (1981).
    [CrossRef]
  3. S. D. Durbin, S. M. Arakelian, Y. R. Shen, Opt. Lett. 6, 411 (1981).
    [PubMed]
  4. L. Csillag, I. Janossy, V. F. Kitaeva, N. Kroo, N. N. Sobolev, Mol. Cryst. Liq. Cryst. 84, 125 (1982).
    [CrossRef]
  5. P. D. McWane, Nature 211, 1081 (1966).
    [CrossRef]
  6. See, for instance, S. Chandrasekhar, Liquid Crystals (Cambridge U. Press, Cambridge, 1977), Chap. 3.
  7. A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, A. P. Sukhorukov, L. Csillag, Sov. Phys. JETP 56, 786 (1982), Fig. 3.

1982

L. Csillag, I. Janossy, V. F. Kitaeva, N. Kroo, N. N. Sobolev, Mol. Cryst. Liq. Cryst. 84, 125 (1982).
[CrossRef]

A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, A. P. Sukhorukov, L. Csillag, Sov. Phys. JETP 56, 786 (1982), Fig. 3.

1981

S. D. Durbin, S. M. Arakelian, Y. R. Shen, Opt. Lett. 6, 411 (1981).
[PubMed]

S. D. Durbin, S. M. Arakelian, Y. R. Shen, Phys. Rev. Lett. 47, 1411 (1981);B. Ya Zel'dovich, N. T. Tabiryan, Yu. S. Chilingaryan, Sov. Phys. JETP 54, 32 (1981);A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, L. Csillag, JETP Lett. 32, 158 (1980);I. C. Khoo, Phys. Rev. A 23, 2078 (1981).
[CrossRef]

1966

P. D. McWane, Nature 211, 1081 (1966).
[CrossRef]

Arakelian, S. M.

S. D. Durbin, S. M. Arakelian, Y. R. Shen, Phys. Rev. Lett. 47, 1411 (1981);B. Ya Zel'dovich, N. T. Tabiryan, Yu. S. Chilingaryan, Sov. Phys. JETP 54, 32 (1981);A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, L. Csillag, JETP Lett. 32, 158 (1980);I. C. Khoo, Phys. Rev. A 23, 2078 (1981).
[CrossRef]

S. D. Durbin, S. M. Arakelian, Y. R. Shen, Opt. Lett. 6, 411 (1981).
[PubMed]

Chandrasekhar, S.

See, for instance, S. Chandrasekhar, Liquid Crystals (Cambridge U. Press, Cambridge, 1977), Chap. 3.

Csillag, L.

A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, A. P. Sukhorukov, L. Csillag, Sov. Phys. JETP 56, 786 (1982), Fig. 3.

L. Csillag, I. Janossy, V. F. Kitaeva, N. Kroo, N. N. Sobolev, Mol. Cryst. Liq. Cryst. 84, 125 (1982).
[CrossRef]

Durbin, S. D.

S. D. Durbin, S. M. Arakelian, Y. R. Shen, Phys. Rev. Lett. 47, 1411 (1981);B. Ya Zel'dovich, N. T. Tabiryan, Yu. S. Chilingaryan, Sov. Phys. JETP 54, 32 (1981);A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, L. Csillag, JETP Lett. 32, 158 (1980);I. C. Khoo, Phys. Rev. A 23, 2078 (1981).
[CrossRef]

S. D. Durbin, S. M. Arakelian, Y. R. Shen, Opt. Lett. 6, 411 (1981).
[PubMed]

Janossy, I.

L. Csillag, I. Janossy, V. F. Kitaeva, N. Kroo, N. N. Sobolev, Mol. Cryst. Liq. Cryst. 84, 125 (1982).
[CrossRef]

Kitaeva, V. F.

L. Csillag, I. Janossy, V. F. Kitaeva, N. Kroo, N. N. Sobolev, Mol. Cryst. Liq. Cryst. 84, 125 (1982).
[CrossRef]

A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, A. P. Sukhorukov, L. Csillag, Sov. Phys. JETP 56, 786 (1982), Fig. 3.

Kroo, N.

A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, A. P. Sukhorukov, L. Csillag, Sov. Phys. JETP 56, 786 (1982), Fig. 3.

L. Csillag, I. Janossy, V. F. Kitaeva, N. Kroo, N. N. Sobolev, Mol. Cryst. Liq. Cryst. 84, 125 (1982).
[CrossRef]

McWane, P. D.

P. D. McWane, Nature 211, 1081 (1966).
[CrossRef]

Shen, Y. R.

S. D. Durbin, S. M. Arakelian, Y. R. Shen, Phys. Rev. Lett. 47, 1411 (1981);B. Ya Zel'dovich, N. T. Tabiryan, Yu. S. Chilingaryan, Sov. Phys. JETP 54, 32 (1981);A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, L. Csillag, JETP Lett. 32, 158 (1980);I. C. Khoo, Phys. Rev. A 23, 2078 (1981).
[CrossRef]

S. D. Durbin, S. M. Arakelian, Y. R. Shen, Opt. Lett. 6, 411 (1981).
[PubMed]

Sobolev, N. N.

L. Csillag, I. Janossy, V. F. Kitaeva, N. Kroo, N. N. Sobolev, Mol. Cryst. Liq. Cryst. 84, 125 (1982).
[CrossRef]

A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, A. P. Sukhorukov, L. Csillag, Sov. Phys. JETP 56, 786 (1982), Fig. 3.

Sukhorukov, A. P.

A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, A. P. Sukhorukov, L. Csillag, Sov. Phys. JETP 56, 786 (1982), Fig. 3.

Zolot'ko, A. S.

A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, A. P. Sukhorukov, L. Csillag, Sov. Phys. JETP 56, 786 (1982), Fig. 3.

Mol. Cryst. Liq. Cryst.

L. Csillag, I. Janossy, V. F. Kitaeva, N. Kroo, N. N. Sobolev, Mol. Cryst. Liq. Cryst. 84, 125 (1982).
[CrossRef]

Nature

P. D. McWane, Nature 211, 1081 (1966).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

S. D. Durbin, S. M. Arakelian, Y. R. Shen, Phys. Rev. Lett. 47, 1411 (1981);B. Ya Zel'dovich, N. T. Tabiryan, Yu. S. Chilingaryan, Sov. Phys. JETP 54, 32 (1981);A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, L. Csillag, JETP Lett. 32, 158 (1980);I. C. Khoo, Phys. Rev. A 23, 2078 (1981).
[CrossRef]

Sov. Phys. JETP

A. S. Zolot'ko, V. F. Kitaeva, N. Kroo, N. N. Sobolev, A. P. Sukhorukov, L. Csillag, Sov. Phys. JETP 56, 786 (1982), Fig. 3.

Other

See, for example, the Optical Physics Technical Group session, Spatial Interference Rings: Conical Emission, in the 1983 Annual Meeting of Optical Society of America, New Orleans, La., 1983[ J. Opt. Soc. Am. 73, 1880 (1983)].

See, for instance, S. Chandrasekhar, Liquid Crystals (Cambridge U. Press, Cambridge, 1977), Chap. 3.

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Figures (3)

Fig. 1
Fig. 1

Calculated phase Φ/2π as a function of the reduced radial coordinate r/W for an incident laser intensity I(r = 0) = 4.48I0, where I0 is the plane-wave Freederickscz threshold.

Fig. 2
Fig. 2

Calculated far-field intensity distribution for a divergent beam (R = 6 cm) traversing the sample. The dotted curve refers to the experimental data. The intensity has been arbitrarily normalized to that at the center of the diffraction pattern.

Fig. 3
Fig. 3

Calculated far-field intensity distribution for a convergent beam (R = −6 cm) traversing the sample. The dotted curve refers to the experimental data. The intensity has been arbitrarily normalized to that at the center of the diffraction pattern.

Equations (4)

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I ( α ) | 0 d r r J 0 ( k 0 α r ) exp [ ( r / W ) 2 + i Φ ( r ) ] | 2 ,
Φ ( r ) = k 0 [ r 2 / 2 R + 0 d δ n ( r , z ) d z ] ,
δ n ( r , z ) = [ n o 2 cos 2 θ ( r , z ) + n e m 2 sin 2 θ ( r , z ) ] 1 / 2 n o ,
d 2 θ 1 / d r 2 + ( 1 / r ) d θ 1 / d r + ( π / d ) 2 { [ ( I / I 0 ) × exp ( 2 r 2 / W 2 ) 1 ] θ 1 a θ 1 3 } = 0 .

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