Abstract

Tunable photonic bandgap (PBG) microstructure fibers, which were filled nematic liquid crystals (NLC), were theoretically investigated based on bandgap theory. By means of the modified plane-wave method, it is found that PBGs shift to the longer wavelength with increasing refractive index of NLC [ny(θ)] for y-polarized light. Fundamental modes are found in these PBG reigns, whose effective mode area, leakage loss and group velocity dispersion (GVD) have been calculated by using the full-vector finite-element method with anisotropic perfectly matched layers. The mode fields become larger with the increase of ny(θ), whereas the leakage loss varies slightly. Moreover, GVD is strongly dependent on ny(θ) and wavelength, which is much larger than the material dispersion of silica.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2005

2004

2003

2002

2001

Abeeluck, A. K.

Alkeskjold, T. T.

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 Photonics Technol. Lett. 17, 819-821 (2005).
[CrossRef]

T. T. Alkeskjold, J. Lægsgaard, A. Bjarklev, D. S. Hermann, A. Anawati, J. Broeng, J. Li, and S. T. Wu, "All-optical modulation in dye-doped nematic liqud crystal photonic bandgap fibers," Opt. Express 12, 5857-5870 (2004).
[CrossRef] [PubMed]

Allan, D. C.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borreill, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Anawati, A.

Bise, R.

Bise, R. T.

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor. "Tunable photonic band gap fiber," in Optical Fiber Communication (Optical Society of America, 2002), pp.466-468.

Bjarklev, A.

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 Photonics Technol. Lett. 17, 819-821 (2005).
[CrossRef]

T. T. Alkeskjold, J. Lægsgaard, A. Bjarklev, D. S. Hermann, A. Anawati, J. Broeng, J. Li, and S. T. Wu, "All-optical modulation in dye-doped nematic liqud crystal photonic bandgap fibers," Opt. Express 12, 5857-5870 (2004).
[CrossRef] [PubMed]

Bolger, J. A.

Borreill, N. F.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borreill, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Botten, L. C.

Bouwmans, G.

Broeng, J.

Choi, S.

de Sterke, C. M.

DiGiovanni, D. J.

Digonnet, M. J.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic-bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

Dong, X. Y.

Du, F.

F. Du, Y.-Q. Lu, and S.-T. Wu, "Electrically tunable liquid-crystal photonic crystal fiber," Appl. Phys. Lett. 85, 2181-2183 (2004).
[CrossRef]

Eggleton, B. J.

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 Photonics Technol. Lett. 17, 819-821 (2005).
[CrossRef]

Fan, S.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic-bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

Feng, X.

Finazzi, V.

Fuerbach, A.

Gallagher, M. T.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borreill, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

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 Photonics Technol. Lett. 17, 819-821 (2005).
[CrossRef]

Hand, D. P.

Headley, C.

Her, T. H.

Hermann, D. S.

Hewak, D.

Jasapara, J.

Joannopoulos, J. D.

Johnson, S. G.

Jones, J. D.

Kai, G. Y.

Kerbage, C.

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor. "Tunable photonic band gap fiber," in Optical Fiber Communication (Optical Society of America, 2002), pp.466-468.

Kim, H. K.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic-bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

Kino, G. S.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic-bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

Knight, J. C.

Koch, K. W.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borreill, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Koshiba, M.

Kranz, K. S.

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor. "Tunable photonic band gap fiber," in Optical Fiber Communication (Optical Society of America, 2002), pp.466-468.

Kwon, M. S.

Lægsgaard, J.

Li, J.

Litchinitser, N. M.

Liu, J. F.

Liu, Y. G.

Lu, Y.-Q.

F. Du, Y.-Q. Lu, and S.-T. Wu, "Electrically tunable liquid-crystal photonic crystal fiber," Appl. Phys. Lett. 85, 2181-2183 (2004).
[CrossRef]

Mangan, B. J.

McPhedran, R. C.

Monro, T. M.

Muller, D.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borreill, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

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 Photonics Technol. Lett. 17, 819-821 (2005).
[CrossRef]

Nulsen, A.

Oh, K.

Oh, Y. H.

Petropoulos, P.

Riishede, J.

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 Photonics Technol. Lett. 17, 819-821 (2005).
[CrossRef]

Russell, P.

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

Russell, P. St.

Saitoh, K.

Scolari, L.

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 Photonics Technol. Lett. 17, 819-821 (2005).
[CrossRef]

Shephard, J. D.

Shin, J.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic-bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

Shin, S. Y.

Smith, C. M.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borreill, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Steel, M. J.

Steinvurzel, P.

Sterke, C. Martijnde

Sun, T. T.

Trevor, D. J.

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor. "Tunable photonic band gap fiber," in Optical Fiber Communication (Optical Society of America, 2002), pp.466-468.

Venkataraman, N.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borreill, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Wang, C.

Wang, Z.

West, J. A.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borreill, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

White, T. P.

Windeler, R.

Windeler, R. S.

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor. "Tunable photonic band gap fiber," in Optical Fiber Communication (Optical Society of America, 2002), pp.466-468.

Wu, S. T.

Wu, S.-T.

F. Du, Y.-Q. Lu, and S.-T. Wu, "Electrically tunable liquid-crystal photonic crystal fiber," Appl. Phys. Lett. 85, 2181-2183 (2004).
[CrossRef]

Yuan, S. Z.

Zhang, C. S.

Zhang, W. G.

Appl. Phys. Lett.

F. Du, Y.-Q. Lu, and S.-T. Wu, "Electrically tunable liquid-crystal photonic crystal fiber," Appl. Phys. Lett. 85, 2181-2183 (2004).
[CrossRef]

IEEE J. Quantum Electron.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic-bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

IEEE Photonics Technol. Lett.

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 Photonics Technol. Lett. 17, 819-821 (2005).
[CrossRef]

J. Opt. Soc. Am. B

Nature

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borreill, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

A. Fuerbach, P. Steinvurzel, J. A. Bolger, A. Nulsen, and B. J. Eggleton. "Nonlinear propagation effects in antiresonant high-index inclusion photonic crystal fibers," Opt. Lett. 30, 830-832 (2005).
[CrossRef] [PubMed]

C. S. Zhang, G. Y. Kai, Z. Wang, T. T. Sun, C. Wang,Y. G. Liu, W. G. Zhang, J. F. Liu, S. Z. Yuan, and X. Y. Dong, "Transformation of a transmission mechanism by filling the holes of normal silica-guiding microstructure fibers with nematic liquid crystal," Opt. Lett. 30, 2372-2374 (2005).
[CrossRef] [PubMed]

Z. Wang, G. Y. Kai, Y. G. Liu, J. F. Liu, C. S. Zhang, T. T. Sun, C. Wang, W. G. Zhang, S. Z. Yuan, and X. Y. Dong, "Coupling and decoupling of dual-core photonic bandgap fibers," Opt. Lett. 30, 2542-2544 (2005).
[CrossRef] [PubMed]

Y. H. Oh, M. S. Kwon, S. Y. Shin, S. Choi, and K. Oh, "In-line polarization controller that uses a hollow optical fiber filled with a liquid crystal," Opt. Lett. 29, 2605-2607 (2004).
[CrossRef] [PubMed]

T. P. White, R. C. McPhedran, C. M. de Sterke, L. C. Botten, and M. J. Steel, "Confinement losses in microstructured optical fibers," Opt. Lett. 26, 1660-1662 (2001).
[CrossRef]

N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, "Antiresonant reflecting photonic crystal optical waveguides," Opt. Lett. 27, 1592-1594 (2002).
[CrossRef]

T. P. White, R. C. McPhedran, C. Martijnde Sterke, N. M. Litchinitser, and B. J. Eggleton. "Resonance and scattering in microstructured optical fibers," Opt. Lett. 27, 1977-1979 (2002).
[CrossRef]

Science

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

Other

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor. "Tunable photonic band gap fiber," in Optical Fiber Communication (Optical Society of America, 2002), pp.466-468.

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Figures (6)

Fig. 1
Fig. 1

Cross section of the microstructure fiber.

Fig. 2
Fig. 2

Bandgap map of the NLC-filled MF versus normalized wavelength when the refractive index of the NLC for y-polarized light is 1.635, 1.73, and 1.80.

Fig. 3
Fig. 3

Modal dispersion curve versus normalized wavelength when the refractive index of the NLC for y-polarized light is (a) 1.635 (b), 1.73, and (c) 1.80.

Fig. 4
Fig. 4

Normalized effective mode area as function of normalized wavelength when the refractive index of the NLC for y-polarized light is 1.635, 1.73, 1.80.

Fig. 5
Fig. 5

Normalized leakage loss versus normalized wavelength with a different refractive index of the NLC when the refractive index of the NLC for y-polarized light is 1.635, 1.73, and 1.80; (a) secondary gap region, (b) fundamental gap region.

Fig. 6
Fig. 6

Normalized GVD versus normalized wavelength with different refractive index of NLC when the refractive index of NLC for y-polarized light is 1.635, 1.73, and 1.80; (a) secondary gap region, (b) fundamental gap region.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

× ( [ s ] 1 × E ) k 0 2 ϵ ¯ [ s ] E = 0 ,
E ( x , y , z ) = e ( x , y ) exp ( γ z ) ,
A eff = ( E 2 d x d y ) 2 E 4 d x d y .
L c = 8.686 α .
D w = 2 π c λ 2 d 2 β d ω 2 ,

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