Abstract

The stop-band characteristics of waves in cholesteric-liquid-crystal half-space are investigated using the exact wave solution, the Floquet theorem, and the corresponding Brillouin diagram. The other half-space is filled with a uniform dielectric medium. By appropriate choice of the dielectric constant of the uniform medium and the angle of incidence of the incoming plane wave, the stop band may split into two or three stop bands.

© 1973 Optical Society of America

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References

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  1. H. de Vries, Acta Crystallogr. 4, 219 (1951).
    [Crossref]
  2. G. H. Conners, J. Opt. Soc. Am. 58, 875 (1968).
    [Crossref]
  3. J. Adams, W. Haas, and J. Dailey, J. Appl. Phys. 42, 4096 (1971).
    [Crossref]
  4. Groupe des Cristaux Liquides, La Recherche (Paris) 2, 435 (1971).
  5. Liquid Crystals and Their Applications, edited by T. Kallard (Optosonic Press, New York, 1970).
  6. J. L. Fergason, Mol. Cryst. Liq. Cryst. 1, 293 (1966).
    [Crossref]
  7. D. Taupin, J. Phys. (Paris) 30, 4 (1969).
    [Crossref]
  8. D. W. Berreman and T. J. Scheffer, Phys. Rev. Lett. 25, 577 (1970).
    [Crossref]
  9. E. I. Kats, Zh. Eksp. Teor. Fiz. 59, 1854 (1970) [Sov. Phys.-JETP 32, 1004 (1970)].
  10. R. Dreher, G. Meier, and A. Saupe, Mol. Cryst. Liq. Cryst. 13, 17 (1971).
    [Crossref]
  11. A. S. Marathay, Opt. Commun. 3, 369 (1971).
    [Crossref]
  12. T. Tamir, H. C. Wang, and A. A. Oliner, IEEE Trans. Antennas Propag. 12, 323 (1964).
  13. C. Elachi, IEEE Trans. Antennas Propag. 20, 534 (1972).
    [Crossref]
  14. C. Yeh, K. F. Casey, and Z. A. Kaprielian, IEEE Trans. Microwave Theory Tech. 13, 297 (1965).
    [Crossref]

1972 (1)

C. Elachi, IEEE Trans. Antennas Propag. 20, 534 (1972).
[Crossref]

1971 (4)

J. Adams, W. Haas, and J. Dailey, J. Appl. Phys. 42, 4096 (1971).
[Crossref]

Groupe des Cristaux Liquides, La Recherche (Paris) 2, 435 (1971).

R. Dreher, G. Meier, and A. Saupe, Mol. Cryst. Liq. Cryst. 13, 17 (1971).
[Crossref]

A. S. Marathay, Opt. Commun. 3, 369 (1971).
[Crossref]

1970 (2)

D. W. Berreman and T. J. Scheffer, Phys. Rev. Lett. 25, 577 (1970).
[Crossref]

E. I. Kats, Zh. Eksp. Teor. Fiz. 59, 1854 (1970) [Sov. Phys.-JETP 32, 1004 (1970)].

1969 (1)

D. Taupin, J. Phys. (Paris) 30, 4 (1969).
[Crossref]

1968 (1)

1966 (1)

J. L. Fergason, Mol. Cryst. Liq. Cryst. 1, 293 (1966).
[Crossref]

1965 (1)

C. Yeh, K. F. Casey, and Z. A. Kaprielian, IEEE Trans. Microwave Theory Tech. 13, 297 (1965).
[Crossref]

1964 (1)

T. Tamir, H. C. Wang, and A. A. Oliner, IEEE Trans. Antennas Propag. 12, 323 (1964).

1951 (1)

H. de Vries, Acta Crystallogr. 4, 219 (1951).
[Crossref]

Adams, J.

J. Adams, W. Haas, and J. Dailey, J. Appl. Phys. 42, 4096 (1971).
[Crossref]

Berreman, D. W.

D. W. Berreman and T. J. Scheffer, Phys. Rev. Lett. 25, 577 (1970).
[Crossref]

Casey, K. F.

C. Yeh, K. F. Casey, and Z. A. Kaprielian, IEEE Trans. Microwave Theory Tech. 13, 297 (1965).
[Crossref]

Conners, G. H.

Dailey, J.

J. Adams, W. Haas, and J. Dailey, J. Appl. Phys. 42, 4096 (1971).
[Crossref]

de Vries, H.

H. de Vries, Acta Crystallogr. 4, 219 (1951).
[Crossref]

Dreher, R.

R. Dreher, G. Meier, and A. Saupe, Mol. Cryst. Liq. Cryst. 13, 17 (1971).
[Crossref]

Elachi, C.

C. Elachi, IEEE Trans. Antennas Propag. 20, 534 (1972).
[Crossref]

Fergason, J. L.

J. L. Fergason, Mol. Cryst. Liq. Cryst. 1, 293 (1966).
[Crossref]

Haas, W.

J. Adams, W. Haas, and J. Dailey, J. Appl. Phys. 42, 4096 (1971).
[Crossref]

Kaprielian, Z. A.

C. Yeh, K. F. Casey, and Z. A. Kaprielian, IEEE Trans. Microwave Theory Tech. 13, 297 (1965).
[Crossref]

Kats, E. I.

E. I. Kats, Zh. Eksp. Teor. Fiz. 59, 1854 (1970) [Sov. Phys.-JETP 32, 1004 (1970)].

Marathay, A. S.

A. S. Marathay, Opt. Commun. 3, 369 (1971).
[Crossref]

Meier, G.

R. Dreher, G. Meier, and A. Saupe, Mol. Cryst. Liq. Cryst. 13, 17 (1971).
[Crossref]

Oliner, A. A.

T. Tamir, H. C. Wang, and A. A. Oliner, IEEE Trans. Antennas Propag. 12, 323 (1964).

Saupe, A.

R. Dreher, G. Meier, and A. Saupe, Mol. Cryst. Liq. Cryst. 13, 17 (1971).
[Crossref]

Scheffer, T. J.

D. W. Berreman and T. J. Scheffer, Phys. Rev. Lett. 25, 577 (1970).
[Crossref]

Tamir, T.

T. Tamir, H. C. Wang, and A. A. Oliner, IEEE Trans. Antennas Propag. 12, 323 (1964).

Taupin, D.

D. Taupin, J. Phys. (Paris) 30, 4 (1969).
[Crossref]

Wang, H. C.

T. Tamir, H. C. Wang, and A. A. Oliner, IEEE Trans. Antennas Propag. 12, 323 (1964).

Yeh, C.

C. Yeh, K. F. Casey, and Z. A. Kaprielian, IEEE Trans. Microwave Theory Tech. 13, 297 (1965).
[Crossref]

Acta Crystallogr. (1)

H. de Vries, Acta Crystallogr. 4, 219 (1951).
[Crossref]

Groupe des Cristaux Liquides, La Recherche (Paris) (1)

Groupe des Cristaux Liquides, La Recherche (Paris) 2, 435 (1971).

IEEE Trans. Antennas Propag. (2)

T. Tamir, H. C. Wang, and A. A. Oliner, IEEE Trans. Antennas Propag. 12, 323 (1964).

C. Elachi, IEEE Trans. Antennas Propag. 20, 534 (1972).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

C. Yeh, K. F. Casey, and Z. A. Kaprielian, IEEE Trans. Microwave Theory Tech. 13, 297 (1965).
[Crossref]

J. Appl. Phys. (1)

J. Adams, W. Haas, and J. Dailey, J. Appl. Phys. 42, 4096 (1971).
[Crossref]

J. Opt. Soc. Am. (1)

J. Phys. (Paris) (1)

D. Taupin, J. Phys. (Paris) 30, 4 (1969).
[Crossref]

Mol. Cryst. Liq. Cryst. (2)

J. L. Fergason, Mol. Cryst. Liq. Cryst. 1, 293 (1966).
[Crossref]

R. Dreher, G. Meier, and A. Saupe, Mol. Cryst. Liq. Cryst. 13, 17 (1971).
[Crossref]

Opt. Commun. (1)

A. S. Marathay, Opt. Commun. 3, 369 (1971).
[Crossref]

Phys. Rev. Lett. (1)

D. W. Berreman and T. J. Scheffer, Phys. Rev. Lett. 25, 577 (1970).
[Crossref]

Zh. Eksp. Teor. Fiz. (1)

E. I. Kats, Zh. Eksp. Teor. Fiz. 59, 1854 (1970) [Sov. Phys.-JETP 32, 1004 (1970)].

Other (1)

Liquid Crystals and Their Applications, edited by T. Kallard (Optosonic Press, New York, 1970).

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Figures (4)

Fig. 1
Fig. 1

Geometry of the problem.

Fig. 2
Fig. 2

Brillouin diagrams for waves in cholesteric liquid crystals.

Fig. 3
Fig. 3

Sketch of the Brillouin diagram near an interaction region. The dashed line corresponds to the imaginary part of κ. The continuous line corresponds to the real part of κ.

Fig. 4
Fig. 4

Interaction region (dark area) as a function of sin2θ for various values of η, ¯, 3. The y and x are defined in the figure and do not correspond to the spatial coordinates.

Tables (1)

Tables Icon

Table I Characteristic parameters.

Equations (18)

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( z ) = ¯ + η cos K z η sin K z 0 η sin K z ¯ η cos K z 0 0 0 3 ,
E ( i ) = E e i k ( sin θ x + cos θ z ) ,
E ( CLC ) = n = n = + E n e i ( k sin θ i x + i κ n z ) ,
D n E x n + η [ E x , n + 1 + E x , n 1 + i E y , n + 1 i E y , n 1 ] = 0 ,
D n E y n η [ E y , n + 1 + E y , n 1 + i E x , n + 1 i E x , n 1 ] = 0 , E z n = C n E x n ,
D n = 2 ¯ 2 κ n 2 / ( ω 2 c 2 k 2 sin 2 θ 3 ) , D n = 2 ( ¯ + k 2 sin 2 θ + κ n 2 ω 2 / c 2 ) , C n = k κ n sin θ ( ω 2 / c 2 ) 3 k 2 sin 2 θ ,
E x n / E x 0 , E y n / E x 0 , E z n / E x 0
κ n = ± α 1 ω / c ,
κ n = ± α 2 ω / c ,
α 1 = ¯ [ 1 ( / 3 ) sin 2 θ ] 1 2
α 2 = ¯ ( 1 ( / ¯ ) sin 2 θ ) 1 2 .
κ = κ 0 ( 1 + η a ) , ω = ω 0 ( 1 + η b ) ,
at intersection point 1 b 2 a 2 = 1 / ( 4 ¯ α 2 2 ) 2 ,
at intersection point 2 b 2 a 2 = 1 / ( 4 ¯ ) 2 ,
( b a ) [ b + ( α 2 / α 1 ) a ] = 1 / ( 4 ¯ α 2 ) 2 ,
( b a ) [ b + ( α 2 / α 1 ) a ] = 1 / ( 4 ¯ α 2 ) 2 ,
1 2 [ Δ ω ω | 1 + Δ ω ω | 3 ] > 1 α 1 + α 2 1 2 α 2 ,
1 2 [ Δ ω ω | 1 + Δ ω ω | 3 ] > 1 2 α 1 1 α 1 + α 2 .