Abstract

The dispersive characteristics of a photonic crystal fiber enhanced with a liquid crystal core are studied using a planewave expansion method. Numerical results demonstrate that by appropriate design such fibers can function in a single-mode/single-polarization operation, exhibit high- or low- birefringence behavior, or switch between an on-state and an off-state (no guided modes supported). All of the above can be controlled by the application of an external electric field, the specific liquid crystal anchoring conditions and the fiber structural parameters.

© 2006 Optical Society of America

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References

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Appl. Opt. (1)

Appl. Phys. B (1)

S. Lorenz, Ch. Silberhorn, N. Korolkova, R.S. Windeler, and G. Leuchs, "Squeezed light from microstructured fibers: towards free-space quantum cryptography," Appl. Phys. B 73, 855-859 (2001).
[CrossRef]

Appl. Phys. Lett. (3)

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

B. Maune, M. Lon¡car, J. Witzens, M. Hochberg, T. Baehr-Jones, D. Psaltis, A. Scherer, and Y. Qiu, "Liquid-crystal electric tuning of a photonic crystal laser," Appl. Phys. Lett. 85, 360-362 (2004).
[CrossRef]

A. Ferrando and J.J. Miret, "Single-polarization single-mode intraband guidance in supersquare photonic crystal fibers," Appl. Phys. Lett. 78, 3184-3186 (2001).
[CrossRef]

IEEE J. Lightwave Technol. (2)

X. Feng, A.K. Mairaj, D.W. Hewak, and T.M. Monro, "Nonsilica glasses for holey fibers," IEEE J. Lightwave Tech. 23, 2046-2054 (2005).
[CrossRef]

K. Morishita and S. Yutani, "Wavelength-insensitive couplers made of annealed dispersive fibers," IEEE J. Lightwave Technol. 17, 2356-2360 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

E.P. Kosmidou, E.E. Kriezis, and T.D. Tsiboukis, "Analysis of tunable photonic crystal devices comprising liquid crystal materials as defects," IEEE J. Quantum Electron. 41, 657-665 (2005).
[CrossRef]

IEEE Photonics Technol. Lett. (4)

Y. Jeong, B. Yang, B. Lee, H.S. Seo, S. Choi, and K. Oh, "Electrically controllable long-period liquid crystal fiber gratings," IEEE Photonics Technol. Lett. 12, 519-521 (2000).
[CrossRef]

K. Saitoh and M. Koshiba, "Single-polarization single-mode photonic crystal fibers," IEEE Photonics Technol. Lett. 15, 1384-1386 (2003).
[CrossRef]

T.-L. Wu and C.-H. Chao, "A novel ultraflattened dispersion photonic crystal fiber," IEEE Photonics Technol. Lett. 17, 67-69 (2005).
[CrossRef]

L.P. Shen, W.-P. Huang, G.X. Chen, and S.S. Jian, "Design and optimization of photonic crystal fibers for broadband dispersion compensation," IEEE Photonics Technol. Lett. 15, 540-543 (2003).
[CrossRef]

J. Appl. Phys. (1)

J. Li, S.-T. Wu, S. Brugioni, R. Meucci, and S. Faetti, "Infrared refractive indices of liquid crystals," J. Appl. Phys. 97, Art. 073501 (2005).
[CrossRef]

J. Opt. A (1)

B. Zsigri, J. Lægsgaard, and A. Bjarklev, "A novel photonic crystal fibre design for dispersion compensation," J. Opt. A 6, 717-720 (2004).
[CrossRef]

J. Opt. Soc. Am. (1)

JETP (1)

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

Liq. Cryst. (1)

S. Gauza, J. Li, S.-T.Wu, A. Spad³o, R. Da¸browski, Y.-N. Tzeng, and K.-L. Cheng, "High birefringence and high resistivity isothiocyanate-based nematic liquid crystal mixtures," Liq. Cryst. 32, 1077-1085 (2005).
[CrossRef]

Microw. Opt. Tech. Let. (1)

O. Fraz˜ao, J.P. Carvalho, and H.M. Salgado, "Low-loss splice in a microstructured fibre using a conventional fusion splicer," Microw. Opt. Tech. Let. 46, 172-174 (2005).
[CrossRef]

Opt. Express (11)

J. H. Chong and M.K. Rao, "Development of a system for laser splicing photonic crystal fiber," Opt. Express 11, 1365-1370 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-12-1365">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-12-1365</a>.
[CrossRef] [PubMed]

K. Suzuki, H. Kubota, S. Kawanishi, M. Tanaka, and M. Fujita, "Optical properties of a low-loss polarization-maintaining photonic crystal fiber," Opt. Express 9, 676-680 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-676">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-676</a>.
[CrossRef] [PubMed]

X. Feng, T.M. Monro, P. Petropoulos, V. Finazzi, and D. Hewak, "Solid microstructured optical fiber," Opt. Express 11, 2225-2230 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-18-2225">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-18-2225</a>.
[CrossRef] [PubMed]

T.T. Alkeskjold, J. Lægsgaard, A. Bjarklev, D.S. Hermann, J. Broeng, J. Li, and S.-T.Wu, "All-optical modulation in dye-doped nematic liquid crystal photonic bandgap fibers," Opt. Express 12, 5857-5871 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5857">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5857</a>.
[CrossRef] [PubMed]

T.T. Larsen, A. Bjarklev, D.S. Hermann, and J. Broeng, "Optical devices based on liquid crystal photonic bandgap fibers," Opt. Express 11, 2589-2596 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-20-2589">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-20-2589</a>.
[CrossRef] [PubMed]

S.G. Johnson and J.D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173</a>.
[CrossRef] [PubMed]

K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, "Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion," Opt. Express 11, 843-852 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-843">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-843</a>.
[CrossRef] [PubMed]

A. Ferrando, E. Silvestre, and P. Andr´es, "Designing the properties of dispersion-flattened photonic crystal fibers," Opt. Express 9, 687-697 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687</a>.
[CrossRef] [PubMed]

K.P. Hansen, "Dispersion flattened hybrid-core nonlinear photonic crystal fiber," Opt. Express 11, 1503-1509 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1503">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1503</a>.
[CrossRef] [PubMed]

M. D. Nielsen, C. Jacobsen, N.A. Mortensen, J.R. Folkenberg, and H.R. Simonsen, "Low-loss photonic crystal fibers for transmission systems and their dispersion properties," Opt. Express 12, 1372-1376 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1372">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1372</a>.
[CrossRef] [PubMed]

T. Ritari, J. Tuominen, H. Ludvigsen, J.C. Petersen, T. Sørensen, T.P. Hansen, and H.R. Simonsen, "Gas sensing using air-guiding photonic bandgap fibers," Opt. Express 12, 4080-4087 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-4080">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-4080</a>.
[CrossRef] [PubMed]

Opt. Fiber Techn. (1)

J. Broeng, D. Mogilevtsev, S. Barkou, and A. Bjarklev, "Photonic crystal fibers: a new class of optical waveguides," Opt. Fiber Techn. 5, 305-330 (1999).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

G.P. Crawford, D.W. Allender, and J.W. Doane, "Surface elastic and molecular-anchoring properties of nematic liquid crystals confined to cylindrical cavities," Phys. Rev. A 45, 8693-8710 (1992).
[CrossRef] [PubMed]

Other (3)

S.G. Johnson and J.D. Joannopoulos, "The MIT Photonic-Bands Package," <a href="http://ab-initio.mit.edu/mpb/">http://ab-initio.mit.edu/mpb/</a>.

B. Bahadur, Liquid crystals: applications and uses, vol. 1 (World Scientific Publishing, 1990).
[CrossRef]

M.J. Weber, Handbook of optical materials (CRC Press, 2003).

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Figures (12)

Fig. 1.
Fig. 1.

Cross-sectional view of the proposed type of PC-LC fiber: hole-to-hole spacing Λ, hole radius r, and central defect core diameter dc . The figure corresponds to parameters r = 0.2Λ, and dc = Λ.

Fig. 2.
Fig. 2.

Dispersion curve for the degenerate HEx and HEy modes of a triangular lattice PCF with r = 0.2Λ and ng = 1.68. The notations nFSM eff and n(eff) (1) refer to the effective indices of the FSM mode and the first higher order mode, respectively.

Fig. 3.
Fig. 3.

The planar-polar director profile at the strong (a) and the weak (b) anchoring limit.

Fig. 4.
Fig. 4.

Layout for arbitrarily controlling the orientation of the nematic director profile in the xOy plane: for instance, uniform x-parallel alignment (Vx = V 0, Vy = 0), and uniform y-parallel alignment (Vy =V 0, Vx = 0).

Fig. 5.
Fig. 5.

Dispersion curves for the fundamental HEx and HEy modes and radiation line for the PC-LC fiber of Fig. 4 in the planar polar weak anchoring limit case for rdef - 0.5Λ and r = 0.2Λ. As noticed, the fiber exhibits both endlessly single-mode and single-polarization behavior.

Fig. 6.
Fig. 6.

Modal intensity profiles at Λ/λ = 1.5 for the fundamental y- and x-polarized modes for the dispersion curves of Fig. 5: a) HEy mode for rdef = 0.5Λ, b) HEx mode for rdef = 0.5Λ. The air hole radius is r = 0.2Λ. The HEy mode, which senses a homogenous core of ne = 1.68, shows a regular hexagonal profile. On the contrary, the HEX mode radiates into the cladding.

Fig. 7.
Fig. 7.

Dispersion curves for the fundamental HEx and HEy modes and radiation line for the planar polar weak anchoring limit case. HEx mode curves correspond to different rdef values.

Fig. 8.
Fig. 8.

Modal intensity profiles at Λ/λ = 1.5 for the fundamental x-polarized mode for different radii of the defect core: a) rdef = 0.1 Λ, b) rdef = 0.15Λ, c) rdef = 0.2Λ, and d) rdef - 0.25Λ. The radius of the air holes is kept constant at r = 0.2Λ.

Fig. 9.
Fig. 9.

Modal birefringence of the fundamental HEx and HEy modes for rdef = 0.1Λ, 0.15Λ, 0.2Λ, and 0.25λ.

Fig. 10.
Fig. 10.

Modal dispersion curves for (a) ng = 1.67 and (b) ng = 1.69. The parameters used in both cases are r = 0.2Λ, rdef = 0.4Λ, no = 1.5, and ne = 1.68.

Fig. 11.
Fig. 11.

The escaped - radial profile at the strong (a) and the weak (b) anchoring limit.

Fig. 12.
Fig. 12.

Dispersion curves for the axial director profile case for rdef = 0.5Λ and r = 0.2Λ. The fiber operates in an off-state since all supported modes are evanescent.

Equations (5)

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

2 ψ r ϕ r 2 + 1 r ψ r ϕ r + 1 r 2 2 ψ r ϕ ϕ 2 = 0 ,
ψ r ϕ = π 2 tan 1 [ ( R 2 + γr 2 ) ( R 2 γr 2 ) tan ϕ ] ,
n eff , x core = n e [ 1 ( 2 r def Λ ) 2 ] + n o ( 2 r def Λ ) 2 , λ > > Λ .
ψ r ϕ = 0 ,
θ ( r ) = π 2 2 tan 1 ( r R tan ( a 2 ) ) ,

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