Abstract

A simple analytical model is proposed to study the formation of bandgaps in liquid crystal photonic bandgap fibers. The model shows good agreement with full-vectorial plane-wave simulations. Particularly, bandgap splitting is observed due to anisotropy. If the optic axis of the liquid crystal lies perpendicular to the fiber axis, splitting of the fundamental modes of Ex and Ey is also observed.

© 2007 Optical Society of America

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References

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  1. P. St. J. Russell, Science 299, 358 (2003).
    [CrossRef] [PubMed]
  2. B. Bahadur, Liquid Crystals: Applications and Uses, Vol. 1 (World Scientific, 1990).
  3. T. T. Alkeskojld, L. A. Bjarklev, D. S. Hermann, A. Anawati, J. Broeng, J. Li, and S. T. Wu, Opt. Express 12, 5857 (2004).
    [CrossRef]
  4. M. W. Haakestad, T. T. Larsen, M. D. Nielsen, H. E. Engan, and A. Bjarklev, IEEE Photon. Technol. Lett. 17, 819 (2005).
    [CrossRef]
  5. C. L. Xu, W. P. Huang, J. Chrostowski, and S. K. Chaudhuri, J. Lightwave Technol. 12, 1926 (1994).
    [CrossRef]
  6. S. John and K. Busch, J. Lightwave Technol. 17, 1931 (1999).
    [CrossRef]
  7. N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, Opt. Lett. 27, 1592 (2002).
    [CrossRef]
  8. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).
  9. T. Birks, D. Bird, T. Hedley, J. Pottage, and P. Russell, Opt. Express 12, 69 (2004).
    [CrossRef] [PubMed]

2005 (1)

M. W. Haakestad, T. T. Larsen, M. D. Nielsen, H. E. Engan, and A. Bjarklev, IEEE Photon. Technol. Lett. 17, 819 (2005).
[CrossRef]

2004 (2)

2003 (1)

P. St. J. Russell, Science 299, 358 (2003).
[CrossRef] [PubMed]

2002 (1)

1999 (1)

1994 (1)

C. L. Xu, W. P. Huang, J. Chrostowski, and S. K. Chaudhuri, J. Lightwave Technol. 12, 1926 (1994).
[CrossRef]

Abeeluck, A. K.

Alkeskojld, T. T.

Anawati, A.

Bahadur, B.

B. Bahadur, Liquid Crystals: Applications and Uses, Vol. 1 (World Scientific, 1990).

Bird, D.

Birks, T.

Bjarklev, A.

M. W. Haakestad, T. T. Larsen, M. D. Nielsen, H. E. Engan, and A. Bjarklev, IEEE Photon. Technol. Lett. 17, 819 (2005).
[CrossRef]

Bjarklev, L. A.

Broeng, J.

Busch, K.

Chaudhuri, S. K.

C. L. Xu, W. P. Huang, J. Chrostowski, and S. K. Chaudhuri, J. Lightwave Technol. 12, 1926 (1994).
[CrossRef]

Chrostowski, J.

C. L. Xu, W. P. Huang, J. Chrostowski, and S. K. Chaudhuri, J. Lightwave Technol. 12, 1926 (1994).
[CrossRef]

Eggleton, B. J.

Engan, H. E.

M. W. Haakestad, T. T. Larsen, M. D. Nielsen, H. E. Engan, and A. Bjarklev, IEEE Photon. Technol. Lett. 17, 819 (2005).
[CrossRef]

Haakestad, M. W.

M. W. Haakestad, T. T. Larsen, M. D. Nielsen, H. E. Engan, and A. Bjarklev, IEEE Photon. Technol. Lett. 17, 819 (2005).
[CrossRef]

Headley, C.

Hedley, T.

Hermann, D. S.

Huang, W. P.

C. L. Xu, W. P. Huang, J. Chrostowski, and S. K. Chaudhuri, J. Lightwave Technol. 12, 1926 (1994).
[CrossRef]

John, S.

Larsen, T. T.

M. W. Haakestad, T. T. Larsen, M. D. Nielsen, H. E. Engan, and A. Bjarklev, IEEE Photon. Technol. Lett. 17, 819 (2005).
[CrossRef]

Li, J.

Litchinitser, N. M.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Nielsen, M. D.

M. W. Haakestad, T. T. Larsen, M. D. Nielsen, H. E. Engan, and A. Bjarklev, IEEE Photon. Technol. Lett. 17, 819 (2005).
[CrossRef]

Pottage, J.

Russell, P.

Russell, P. St. J.

P. St. J. Russell, Science 299, 358 (2003).
[CrossRef] [PubMed]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Wu, S. T.

Xu, C. L.

C. L. Xu, W. P. Huang, J. Chrostowski, and S. K. Chaudhuri, J. Lightwave Technol. 12, 1926 (1994).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. W. Haakestad, T. T. Larsen, M. D. Nielsen, H. E. Engan, and A. Bjarklev, IEEE Photon. Technol. Lett. 17, 819 (2005).
[CrossRef]

J. Lightwave Technol. (2)

C. L. Xu, W. P. Huang, J. Chrostowski, and S. K. Chaudhuri, J. Lightwave Technol. 12, 1926 (1994).
[CrossRef]

S. John and K. Busch, J. Lightwave Technol. 17, 1931 (1999).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Science (1)

P. St. J. Russell, Science 299, 358 (2003).
[CrossRef] [PubMed]

Other (2)

B. Bahadur, Liquid Crystals: Applications and Uses, Vol. 1 (World Scientific, 1990).

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

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Figures (4)

Fig. 1
Fig. 1

(a) Cross section of the LCPCF. (b) NLC with the optic axis along the z direction. (c) NLC with the optic axis along the y direction.

Fig. 2
Fig. 2

Gap map of the PC cladding with ε a = diag ( n o 2 , n o 2 , n e 2 ) . The arrows indicate the modal cutoffs of an individual NLC rod.

Fig. 3
Fig. 3

Gap map of the PC cladding with ε a = diag ( n o 2 , n o 2 , n e 2 ) obtained by using (a) the full-vectorial model and (b) an approximation that ignores the coupling effect. The arrows indicate the modal cutoffs of an individual cylindrical rod with ε a = n o 2 and ε a = diag ( n o 2 , n o 2 , n e 2 ) .

Fig. 4
Fig. 4

Modal dispersion curves of the fundamental modes as a function of wavelength. Inset: field distributions of E x and E y .

Equations (6)

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2 E x y 2 + x [ 1 n z z 2 x ( n x x 2 E x ) ] + ( n x x 2 k 0 2 β 2 ) E x = 2 E y x y x [ 1 n z z 2 y ( n y y 2 E y ) ] ,
2 E y x 2 + y [ 1 n z z 2 y ( n y y 2 E y ) ] + ( n y y 2 k 0 2 β 2 ) E y = 2 E x x y y [ 1 n z z 2 x ( n x x 2 E x ) ] ,
2 E x y 2 + x [ 1 n z z 2 x ( n x x 2 E x ) ] + ( n x x 2 k 0 2 β 2 ) E x = 0 ,
2 E y x 2 + y [ 1 n z z 2 y ( n x x 2 E y ) ] + ( n x x 2 k 0 2 β 2 ) E y = 0 .
2 E x y 2 + x [ 1 n x x 2 x ( n x x 2 E x ) ] + ( n x x 2 k 0 2 β 2 ) E x = 0 ,
2 E y x 2 + y [ 1 n x x 2 y ( n y y 2 E y ) ] + ( n y y 2 k 0 2 β 2 ) E y = 0 .

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