Abstract

A simulation scheme for the transmission spectrum of a photonic crystal fiber infiltrated with a nematic liquid crystal and subject to an external bias is presented. The alignment of the biased liquid crystal is simulated using the finite element method to solve the relevant system of coupled partial differential equations. From the liquid crystal alignment the full tensorial dielectric permittivity in the capillaries is derived. The transmission spectrum for the photonic crystal fiber is obtained by solving the generalized eigenvalue problem deriving from Maxwell’s equations using a vector element based finite element method. We demonstrate results for a splay aligned liquid crystal infiltrated into the capillaries of a four-ring photonic crystal fiber and compare them to corresponding experiments.

© 2009 Optical Society of America

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  1. P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
    [CrossRef] [PubMed]
  2. A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibres, (Kluwer Academic, Dordrecht, 2003).
  3. C. Kerbage, R. S. Windeler, B. J. Eggleton, P. Mach, M. Dolinski, and J. A. Rogers, "Tunable devices based on dynamic positioning of micro-fluids in micro-structured optical fiber," Opt. Commun. 204, 179-184 (2002).
    [CrossRef]
  4. T. T. Larsen, A. Bjarklev, D. S. Hermann and J. Broeng, "Optic devices based on liquid crystal photonic bandgap fibres," Opt. Express 11, 2589-2596 (2003).
    [CrossRef] [PubMed]
  5. T. T. Alkeskjold, J. Lægsgaard, A. Bjarklev, D. S. Hermann, A. Anawati, J. Broeng, J. Li, and S. Wu, "All-optical modulation in dye-doped nematic liquid crystal photonic bandgap fibers," Opt. Express 12, 5857-5871 (2004).
    [CrossRef] [PubMed]
  6. M. W. Haakestad, T. T. Alkeskjold, M. D. Nielsen, L. Scolari, J. Riishede, H. E. Engan and A. Bjarklev, "Electrically tunable photonic bandgap guidance in a liquid crystal filled photonic crystal fiber," IEEE Photon. Technol. Lett. 17, 819-821 (2005).
    [CrossRef]
  7. L. Scolari, T. T. Alkeskjold, J. Riishede, A. Bjarklev, D. Hermann, A. Anawati, M. Nielsen, P. Bassi, "Continuously tunable devices based on electrical control of dual-frequency liquid crystal filled photonic bandgap fibers," Opt. Express 13, 7483-7496 (2005).
    [CrossRef] [PubMed]
  8. T. R. Wolinski, K. Szaniawska, S. Ertman, P. Lesiak, A. W. Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki and J. Wojcik, "Influence of temperature and electrical fields on propagation properties of photonic liquid-crystal fibres," Meas. Sci. Technol. 17, 985-991 (2006).
    [CrossRef]
  9. L. Scolari, T. T. Alkeskjold, A. O. Bjarklev, "Tunable gaussian filter based on tapered liquid crystal photonic bandgap fibre," Electron. Lett. 42, 1270-1271 (2006).
    [CrossRef]
  10. D. Nordegraaf, L. Scolari, J. Lgsgaard, L. Rindorf, and T. T. Alkeskjold, "Electrically and mechanically induced long period gratings in liquid crystal photonic bandgap fibers," Opt. Express 15, 7901-7912 (2007).
    [CrossRef]
  11. T. T. Alkeskjold, L. Scolari, D. Noordegraaf, J. Laegsgaard, J. Weirich, L. Wei, G. Tartarini, P. Bassi, S. Gauza, S. T. Wu, and A. O. Bjarklev, "Integrating liquid crystal based optical devices in photonic crystal fibers," Opt. Quantum Electron. 39, 1009-1019 (2007).
    [CrossRef]
  12. P. D. de Gennes, The Physics of Liquid Crystals, (Clarendon, 1974).
  13. J. Lægsgaard, "Modelling of a biased liquid-crystal capillary waveguide," J. Opt. Soc. Am. B 23, 1843-1851 (2006).
    [CrossRef]
  14. S. V. Burylov, "Equilibrium configuration of a nematic liquid crystal confined to a cylindrical cavity," J. Exp. Theor. Phys. 85, 873-886 (1997).
    [CrossRef]
  15. J. Li and S. T. Wu, "Extended Cauchy equations for the refractive indices of liquid crystals," J. Appl. Phys. 95, 896-901 (2004).
    [CrossRef]
  16. N. M. Litchinitser, S. C. Dunn, P. E. Steinvurzel, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. M. de Sterke, "Application of an ARROW model for designing tunable photonic devices," Opt. Express 12, 5857-5871 (2004).
    [CrossRef]

2007 (2)

T. T. Alkeskjold, L. Scolari, D. Noordegraaf, J. Laegsgaard, J. Weirich, L. Wei, G. Tartarini, P. Bassi, S. Gauza, S. T. Wu, and A. O. Bjarklev, "Integrating liquid crystal based optical devices in photonic crystal fibers," Opt. Quantum Electron. 39, 1009-1019 (2007).
[CrossRef]

D. Nordegraaf, L. Scolari, J. Lgsgaard, L. Rindorf, and T. T. Alkeskjold, "Electrically and mechanically induced long period gratings in liquid crystal photonic bandgap fibers," Opt. Express 15, 7901-7912 (2007).
[CrossRef]

2006 (3)

J. Lægsgaard, "Modelling of a biased liquid-crystal capillary waveguide," J. Opt. Soc. Am. B 23, 1843-1851 (2006).
[CrossRef]

T. R. Wolinski, K. Szaniawska, S. Ertman, P. Lesiak, A. W. Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki and J. Wojcik, "Influence of temperature and electrical fields on propagation properties of photonic liquid-crystal fibres," Meas. Sci. Technol. 17, 985-991 (2006).
[CrossRef]

L. Scolari, T. T. Alkeskjold, A. O. Bjarklev, "Tunable gaussian filter based on tapered liquid crystal photonic bandgap fibre," Electron. Lett. 42, 1270-1271 (2006).
[CrossRef]

2005 (2)

M. W. Haakestad, T. T. Alkeskjold, M. D. Nielsen, L. Scolari, J. Riishede, H. E. Engan and A. Bjarklev, "Electrically tunable photonic bandgap guidance in a liquid crystal filled photonic crystal fiber," IEEE Photon. Technol. Lett. 17, 819-821 (2005).
[CrossRef]

L. Scolari, T. T. Alkeskjold, J. Riishede, A. Bjarklev, D. Hermann, A. Anawati, M. Nielsen, P. Bassi, "Continuously tunable devices based on electrical control of dual-frequency liquid crystal filled photonic bandgap fibers," Opt. Express 13, 7483-7496 (2005).
[CrossRef] [PubMed]

2004 (3)

2003 (2)

2002 (1)

C. Kerbage, R. S. Windeler, B. J. Eggleton, P. Mach, M. Dolinski, and J. A. Rogers, "Tunable devices based on dynamic positioning of micro-fluids in micro-structured optical fiber," Opt. Commun. 204, 179-184 (2002).
[CrossRef]

1997 (1)

S. V. Burylov, "Equilibrium configuration of a nematic liquid crystal confined to a cylindrical cavity," J. Exp. Theor. Phys. 85, 873-886 (1997).
[CrossRef]

Alkeskjold, T. T.

T. T. Alkeskjold, L. Scolari, D. Noordegraaf, J. Laegsgaard, J. Weirich, L. Wei, G. Tartarini, P. Bassi, S. Gauza, S. T. Wu, and A. O. Bjarklev, "Integrating liquid crystal based optical devices in photonic crystal fibers," Opt. Quantum Electron. 39, 1009-1019 (2007).
[CrossRef]

D. Nordegraaf, L. Scolari, J. Lgsgaard, L. Rindorf, and T. T. Alkeskjold, "Electrically and mechanically induced long period gratings in liquid crystal photonic bandgap fibers," Opt. Express 15, 7901-7912 (2007).
[CrossRef]

L. Scolari, T. T. Alkeskjold, A. O. Bjarklev, "Tunable gaussian filter based on tapered liquid crystal photonic bandgap fibre," Electron. Lett. 42, 1270-1271 (2006).
[CrossRef]

M. W. Haakestad, T. T. Alkeskjold, M. D. Nielsen, L. Scolari, J. Riishede, H. E. Engan and A. Bjarklev, "Electrically tunable photonic bandgap guidance in a liquid crystal filled photonic crystal fiber," IEEE Photon. Technol. Lett. 17, 819-821 (2005).
[CrossRef]

L. Scolari, T. T. Alkeskjold, J. Riishede, A. Bjarklev, D. Hermann, A. Anawati, M. Nielsen, P. Bassi, "Continuously tunable devices based on electrical control of dual-frequency liquid crystal filled photonic bandgap fibers," Opt. Express 13, 7483-7496 (2005).
[CrossRef] [PubMed]

T. T. Alkeskjold, J. Lægsgaard, A. Bjarklev, D. S. Hermann, A. Anawati, J. Broeng, J. Li, and S. Wu, "All-optical modulation in dye-doped nematic liquid crystal photonic bandgap fibers," Opt. Express 12, 5857-5871 (2004).
[CrossRef] [PubMed]

Anawati, A.

Bassi, P.

T. T. Alkeskjold, L. Scolari, D. Noordegraaf, J. Laegsgaard, J. Weirich, L. Wei, G. Tartarini, P. Bassi, S. Gauza, S. T. Wu, and A. O. Bjarklev, "Integrating liquid crystal based optical devices in photonic crystal fibers," Opt. Quantum Electron. 39, 1009-1019 (2007).
[CrossRef]

L. Scolari, T. T. Alkeskjold, J. Riishede, A. Bjarklev, D. Hermann, A. Anawati, M. Nielsen, P. Bassi, "Continuously tunable devices based on electrical control of dual-frequency liquid crystal filled photonic bandgap fibers," Opt. Express 13, 7483-7496 (2005).
[CrossRef] [PubMed]

Bjarklev, A.

Bjarklev, A. O.

T. T. Alkeskjold, L. Scolari, D. Noordegraaf, J. Laegsgaard, J. Weirich, L. Wei, G. Tartarini, P. Bassi, S. Gauza, S. T. Wu, and A. O. Bjarklev, "Integrating liquid crystal based optical devices in photonic crystal fibers," Opt. Quantum Electron. 39, 1009-1019 (2007).
[CrossRef]

L. Scolari, T. T. Alkeskjold, A. O. Bjarklev, "Tunable gaussian filter based on tapered liquid crystal photonic bandgap fibre," Electron. Lett. 42, 1270-1271 (2006).
[CrossRef]

Broeng, J.

Burylov, S. V.

S. V. Burylov, "Equilibrium configuration of a nematic liquid crystal confined to a cylindrical cavity," J. Exp. Theor. Phys. 85, 873-886 (1997).
[CrossRef]

Dabrowski, R.

T. R. Wolinski, K. Szaniawska, S. Ertman, P. Lesiak, A. W. Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki and J. Wojcik, "Influence of temperature and electrical fields on propagation properties of photonic liquid-crystal fibres," Meas. Sci. Technol. 17, 985-991 (2006).
[CrossRef]

de Sterke, C. M.

Dolinski, M.

C. Kerbage, R. S. Windeler, B. J. Eggleton, P. Mach, M. Dolinski, and J. A. Rogers, "Tunable devices based on dynamic positioning of micro-fluids in micro-structured optical fiber," Opt. Commun. 204, 179-184 (2002).
[CrossRef]

Domanski, A. W.

T. R. Wolinski, K. Szaniawska, S. Ertman, P. Lesiak, A. W. Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki and J. Wojcik, "Influence of temperature and electrical fields on propagation properties of photonic liquid-crystal fibres," Meas. Sci. Technol. 17, 985-991 (2006).
[CrossRef]

Dunn, S. C.

Eggleton, B. J.

N. M. Litchinitser, S. C. Dunn, P. E. Steinvurzel, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. M. de Sterke, "Application of an ARROW model for designing tunable photonic devices," Opt. Express 12, 5857-5871 (2004).
[CrossRef]

C. Kerbage, R. S. Windeler, B. J. Eggleton, P. Mach, M. Dolinski, and J. A. Rogers, "Tunable devices based on dynamic positioning of micro-fluids in micro-structured optical fiber," Opt. Commun. 204, 179-184 (2002).
[CrossRef]

Engan, H. E.

M. W. Haakestad, T. T. Alkeskjold, M. D. Nielsen, L. Scolari, J. Riishede, H. E. Engan and A. Bjarklev, "Electrically tunable photonic bandgap guidance in a liquid crystal filled photonic crystal fiber," IEEE Photon. Technol. Lett. 17, 819-821 (2005).
[CrossRef]

Ertman, S.

T. R. Wolinski, K. Szaniawska, S. Ertman, P. Lesiak, A. W. Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki and J. Wojcik, "Influence of temperature and electrical fields on propagation properties of photonic liquid-crystal fibres," Meas. Sci. Technol. 17, 985-991 (2006).
[CrossRef]

Gauza, S.

T. T. Alkeskjold, L. Scolari, D. Noordegraaf, J. Laegsgaard, J. Weirich, L. Wei, G. Tartarini, P. Bassi, S. Gauza, S. T. Wu, and A. O. Bjarklev, "Integrating liquid crystal based optical devices in photonic crystal fibers," Opt. Quantum Electron. 39, 1009-1019 (2007).
[CrossRef]

Haakestad, M. W.

M. W. Haakestad, T. T. Alkeskjold, M. D. Nielsen, L. Scolari, J. Riishede, H. E. Engan and A. Bjarklev, "Electrically tunable photonic bandgap guidance in a liquid crystal filled photonic crystal fiber," IEEE Photon. Technol. Lett. 17, 819-821 (2005).
[CrossRef]

Hermann, D.

Hermann, D. S.

Kerbage, C.

C. Kerbage, R. S. Windeler, B. J. Eggleton, P. Mach, M. Dolinski, and J. A. Rogers, "Tunable devices based on dynamic positioning of micro-fluids in micro-structured optical fiber," Opt. Commun. 204, 179-184 (2002).
[CrossRef]

Laegsgaard, J.

T. T. Alkeskjold, L. Scolari, D. Noordegraaf, J. Laegsgaard, J. Weirich, L. Wei, G. Tartarini, P. Bassi, S. Gauza, S. T. Wu, and A. O. Bjarklev, "Integrating liquid crystal based optical devices in photonic crystal fibers," Opt. Quantum Electron. 39, 1009-1019 (2007).
[CrossRef]

Lægsgaard, J.

Larsen, T. T.

Lesiak, P.

T. R. Wolinski, K. Szaniawska, S. Ertman, P. Lesiak, A. W. Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki and J. Wojcik, "Influence of temperature and electrical fields on propagation properties of photonic liquid-crystal fibres," Meas. Sci. Technol. 17, 985-991 (2006).
[CrossRef]

Lgsgaard, J.

Li, J.

Litchinitser, N. M.

Mach, P.

C. Kerbage, R. S. Windeler, B. J. Eggleton, P. Mach, M. Dolinski, and J. A. Rogers, "Tunable devices based on dynamic positioning of micro-fluids in micro-structured optical fiber," Opt. Commun. 204, 179-184 (2002).
[CrossRef]

McPhedran, R. C.

Nielsen, M.

Nielsen, M. D.

M. W. Haakestad, T. T. Alkeskjold, M. D. Nielsen, L. Scolari, J. Riishede, H. E. Engan and A. Bjarklev, "Electrically tunable photonic bandgap guidance in a liquid crystal filled photonic crystal fiber," IEEE Photon. Technol. Lett. 17, 819-821 (2005).
[CrossRef]

Noordegraaf, D.

T. T. Alkeskjold, L. Scolari, D. Noordegraaf, J. Laegsgaard, J. Weirich, L. Wei, G. Tartarini, P. Bassi, S. Gauza, S. T. Wu, and A. O. Bjarklev, "Integrating liquid crystal based optical devices in photonic crystal fibers," Opt. Quantum Electron. 39, 1009-1019 (2007).
[CrossRef]

Nordegraaf, D.

Nowinowski-Kruszelnicki, E.

T. R. Wolinski, K. Szaniawska, S. Ertman, P. Lesiak, A. W. Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki and J. Wojcik, "Influence of temperature and electrical fields on propagation properties of photonic liquid-crystal fibres," Meas. Sci. Technol. 17, 985-991 (2006).
[CrossRef]

Riishede, J.

L. Scolari, T. T. Alkeskjold, J. Riishede, A. Bjarklev, D. Hermann, A. Anawati, M. Nielsen, P. Bassi, "Continuously tunable devices based on electrical control of dual-frequency liquid crystal filled photonic bandgap fibers," Opt. Express 13, 7483-7496 (2005).
[CrossRef] [PubMed]

M. W. Haakestad, T. T. Alkeskjold, M. D. Nielsen, L. Scolari, J. Riishede, H. E. Engan and A. Bjarklev, "Electrically tunable photonic bandgap guidance in a liquid crystal filled photonic crystal fiber," IEEE Photon. Technol. Lett. 17, 819-821 (2005).
[CrossRef]

Rindorf, L.

Rogers, J. A.

C. Kerbage, R. S. Windeler, B. J. Eggleton, P. Mach, M. Dolinski, and J. A. Rogers, "Tunable devices based on dynamic positioning of micro-fluids in micro-structured optical fiber," Opt. Commun. 204, 179-184 (2002).
[CrossRef]

Russell, P. St. J.

P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

Scolari, L.

D. Nordegraaf, L. Scolari, J. Lgsgaard, L. Rindorf, and T. T. Alkeskjold, "Electrically and mechanically induced long period gratings in liquid crystal photonic bandgap fibers," Opt. Express 15, 7901-7912 (2007).
[CrossRef]

T. T. Alkeskjold, L. Scolari, D. Noordegraaf, J. Laegsgaard, J. Weirich, L. Wei, G. Tartarini, P. Bassi, S. Gauza, S. T. Wu, and A. O. Bjarklev, "Integrating liquid crystal based optical devices in photonic crystal fibers," Opt. Quantum Electron. 39, 1009-1019 (2007).
[CrossRef]

L. Scolari, T. T. Alkeskjold, A. O. Bjarklev, "Tunable gaussian filter based on tapered liquid crystal photonic bandgap fibre," Electron. Lett. 42, 1270-1271 (2006).
[CrossRef]

M. W. Haakestad, T. T. Alkeskjold, M. D. Nielsen, L. Scolari, J. Riishede, H. E. Engan and A. Bjarklev, "Electrically tunable photonic bandgap guidance in a liquid crystal filled photonic crystal fiber," IEEE Photon. Technol. Lett. 17, 819-821 (2005).
[CrossRef]

L. Scolari, T. T. Alkeskjold, J. Riishede, A. Bjarklev, D. Hermann, A. Anawati, M. Nielsen, P. Bassi, "Continuously tunable devices based on electrical control of dual-frequency liquid crystal filled photonic bandgap fibers," Opt. Express 13, 7483-7496 (2005).
[CrossRef] [PubMed]

Steinvurzel, P. E.

Szaniawska, K.

T. R. Wolinski, K. Szaniawska, S. Ertman, P. Lesiak, A. W. Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki and J. Wojcik, "Influence of temperature and electrical fields on propagation properties of photonic liquid-crystal fibres," Meas. Sci. Technol. 17, 985-991 (2006).
[CrossRef]

Tartarini, G.

T. T. Alkeskjold, L. Scolari, D. Noordegraaf, J. Laegsgaard, J. Weirich, L. Wei, G. Tartarini, P. Bassi, S. Gauza, S. T. Wu, and A. O. Bjarklev, "Integrating liquid crystal based optical devices in photonic crystal fibers," Opt. Quantum Electron. 39, 1009-1019 (2007).
[CrossRef]

Wei, L.

T. T. Alkeskjold, L. Scolari, D. Noordegraaf, J. Laegsgaard, J. Weirich, L. Wei, G. Tartarini, P. Bassi, S. Gauza, S. T. Wu, and A. O. Bjarklev, "Integrating liquid crystal based optical devices in photonic crystal fibers," Opt. Quantum Electron. 39, 1009-1019 (2007).
[CrossRef]

Weirich, J.

T. T. Alkeskjold, L. Scolari, D. Noordegraaf, J. Laegsgaard, J. Weirich, L. Wei, G. Tartarini, P. Bassi, S. Gauza, S. T. Wu, and A. O. Bjarklev, "Integrating liquid crystal based optical devices in photonic crystal fibers," Opt. Quantum Electron. 39, 1009-1019 (2007).
[CrossRef]

White, T. P.

Windeler, R. S.

C. Kerbage, R. S. Windeler, B. J. Eggleton, P. Mach, M. Dolinski, and J. A. Rogers, "Tunable devices based on dynamic positioning of micro-fluids in micro-structured optical fiber," Opt. Commun. 204, 179-184 (2002).
[CrossRef]

Wojcik, J.

T. R. Wolinski, K. Szaniawska, S. Ertman, P. Lesiak, A. W. Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki and J. Wojcik, "Influence of temperature and electrical fields on propagation properties of photonic liquid-crystal fibres," Meas. Sci. Technol. 17, 985-991 (2006).
[CrossRef]

Wolinski, T. R.

T. R. Wolinski, K. Szaniawska, S. Ertman, P. Lesiak, A. W. Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki and J. Wojcik, "Influence of temperature and electrical fields on propagation properties of photonic liquid-crystal fibres," Meas. Sci. Technol. 17, 985-991 (2006).
[CrossRef]

Wu, S.

Wu, S. T.

T. T. Alkeskjold, L. Scolari, D. Noordegraaf, J. Laegsgaard, J. Weirich, L. Wei, G. Tartarini, P. Bassi, S. Gauza, S. T. Wu, and A. O. Bjarklev, "Integrating liquid crystal based optical devices in photonic crystal fibers," Opt. Quantum Electron. 39, 1009-1019 (2007).
[CrossRef]

J. Li and S. T. Wu, "Extended Cauchy equations for the refractive indices of liquid crystals," J. Appl. Phys. 95, 896-901 (2004).
[CrossRef]

Electron. Lett. (1)

L. Scolari, T. T. Alkeskjold, A. O. Bjarklev, "Tunable gaussian filter based on tapered liquid crystal photonic bandgap fibre," Electron. Lett. 42, 1270-1271 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. W. Haakestad, T. T. Alkeskjold, M. D. Nielsen, L. Scolari, J. Riishede, H. E. Engan and A. Bjarklev, "Electrically tunable photonic bandgap guidance in a liquid crystal filled photonic crystal fiber," IEEE Photon. Technol. Lett. 17, 819-821 (2005).
[CrossRef]

J. Appl. Phys. (1)

J. Li and S. T. Wu, "Extended Cauchy equations for the refractive indices of liquid crystals," J. Appl. Phys. 95, 896-901 (2004).
[CrossRef]

J. Exp. Theor. Phys. (1)

S. V. Burylov, "Equilibrium configuration of a nematic liquid crystal confined to a cylindrical cavity," J. Exp. Theor. Phys. 85, 873-886 (1997).
[CrossRef]

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

Meas. Sci. Technol. (1)

T. R. Wolinski, K. Szaniawska, S. Ertman, P. Lesiak, A. W. Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki and J. Wojcik, "Influence of temperature and electrical fields on propagation properties of photonic liquid-crystal fibres," Meas. Sci. Technol. 17, 985-991 (2006).
[CrossRef]

Opt. Commun. (1)

C. Kerbage, R. S. Windeler, B. J. Eggleton, P. Mach, M. Dolinski, and J. A. Rogers, "Tunable devices based on dynamic positioning of micro-fluids in micro-structured optical fiber," Opt. Commun. 204, 179-184 (2002).
[CrossRef]

Opt. Express (5)

Opt. Quantum Electron. (1)

T. T. Alkeskjold, L. Scolari, D. Noordegraaf, J. Laegsgaard, J. Weirich, L. Wei, G. Tartarini, P. Bassi, S. Gauza, S. T. Wu, and A. O. Bjarklev, "Integrating liquid crystal based optical devices in photonic crystal fibers," Opt. Quantum Electron. 39, 1009-1019 (2007).
[CrossRef]

Science (1)

P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

Other (2)

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibres, (Kluwer Academic, Dordrecht, 2003).

P. D. de Gennes, The Physics of Liquid Crystals, (Clarendon, 1974).

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Figures (11)

Fig. 1.
Fig. 1.

Schematic illustration of the photonic crystal fiber with four rings of LC infiltrated capillaries and placed between two electrodes. The fiber is surrounded by air. Inset: The director vector for a splay aligned LC

Fig. 2.
Fig. 2.

Schematic illustration of the director vector expressed by the cylinder like coordinates θ and ϕ.

Fig. 3.
Fig. 3.

The iterative solution process for the system of coupled partial differential equations

Fig. 4.
Fig. 4.

The meshed computational domain. (a) The structure has been reduced to a quarter of its original size (b) the mesh for a single capillary

Fig. 5.
Fig. 5.

Cross section plot of ∣Ey ∣ for an applied voltage of 150V over (a) the whole computational domain, (b) the truncated domain to illustrate the voltage drop around the capillaries

Fig. 6.
Fig. 6.

The vector-components nx ,ny ,nz of the director for a) no bias, b) for 100V and c) 150V applied bias.

Fig. 7.
Fig. 7.

Average integrated relative director change depending on the different rings of the fiber. The various curves reflect different voltages

Fig. 8.
Fig. 8.

Maximum δ n for the different capillaries compared to the average variation, taken over all capillaries

Fig. 9.
Fig. 9.

The simulated transmission spectrum for an applied bias of 0V and 100V and 150V

Fig. 10.
Fig. 10.

The experimental transmission spectrum for 0Vrms, 100Vrms and 150Vrms potential difference

Fig. 11.
Fig. 11.

The dispersion curves of the bandgap guided modes for 0V, 100V and 150V. The black line shows the dispersion curve for silica

Tables (2)

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Table 1. The K-constants and dielectric constants for MDA-00-3969, measured at room temperature (22° C)

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Table 2. The Cauchy coefficients for MDA-00-3969 and the Sellmeier coefficients for the silica material at room temperature

Equations (13)

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F [ n ] = F 0 + F el = Ω d Ω ( k 1 2 ( · n ) 2 + k 2 2 ( n · × n ) 2 + k 3 2 ( n × × n ) 2 ) Ω d Ω ( 1 2 D E )
e ̂ r = ( cos φ sin φ ) e ̂ φ = ( sin φ cos φ )
( n x n y n z ) = ( cos ϕ sin θ cos φ sin ϕ sin θ sin φ cos ϕ sin θ sin φ + sin ϕ sin θ cos φ cos θ )
· D = · ε Φ = 0
ε ij = ε δ ij + Δε n i n j ( i , j = 1,2,3 )
δ n ̂ = Ω n ̂ v n ̂ 0 Ω dxdy n ̂ 0
ε o = n o 2 ε e = n e 2
ε ij = ε o δ ij + Δε n i n j ( i , j = 1,2,3 )
n e ( λ ) = A e + B e λ 2 + C e λ 4
n o ( λ ) = A o + B o λ 2 + C o λ 4
n 2 ( λ ) = 1 + i = 1 3 B i λ 2 λ 2 C i
p i = Ω d Ω ( E i out · E 1 inc 2 + E i out · E 2 inc 2 ) Ω d Ω E i out 2 ( Ω d Ω E 1 inc 2 + E 2 inc 2 )
λ m = 2 d m + 1 / 2 n 2 2 n 1 2

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