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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 21 — Oct. 12, 2009
  • pp: 19298–19310
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Low-loss propagation and continuously tunable birefringence in high-index photonic crystal fibers filled with nematic liquid crystals

Slawomir Ertman, Tomasz R. Wolinski, Dariusz Pysz, Ryszard Buczynski, Edward Nowinowski-Kruszelnicki, and Roman Dabrowski  »View Author Affiliations


Optics Express, Vol. 17, Issue 21, pp. 19298-19310 (2009)
http://dx.doi.org/10.1364/OE.17.019298


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Abstract

Experimental investigations of microstructured fibers filled with liquid crystals (LCs) have so far been performed only by using host fibers made of the silica glass. In this paper, the host photonic crystal fiber (PCF) was made of the PBG08 high-refractive index glass (~1.95) that is much higher than silica glass index (~1.46) and also higher then both ordinary and extraordinary refractive indices of the majority of LCs. As a result, low-loss and index-guiding propagation is observed regardless of the LC molecules orientation. Attenuation of the host PCF was measured to be ~0.15 dB/cm and for the PCF infiltrated with 5CB LC was slightly higher (~0.19 dB/cm), resulting in a significant reduction to ~0.04 dB/cm of the scattering losses caused by the LC. Moreover, an external transverse electric field applied to the effective photonic liquid crystal fiber (PLCF) allowed for continuous phase birefringence tuning from 0 to 2·10−4.

© 2009 OSA

1. Introduction

Photonic crystal fibers (PCFs) have attracted significant interest since the modification of their microstructure allowed for a remarkable control of their key optical properties such as dispersion, birefringence, nonlinearity, along with position and width of the photonic bandgaps (PBGs) in their periodic “photonic-crystal” cladding [1

1. P. St. J. Russell, “Photonic-Crystal Fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006). [CrossRef]

]. In these fibers light can be guided by two different mechanisms: index-guiding (similar to the classical waveguide effect based on total internal reflection) and the photonic bandgap effect. PBG propagation occurs when the effective (average) refractive index of the microstructured cladding is higher than the refractive index of the core, and in this case only selected wavelengths can be guided [1

1. P. St. J. Russell, “Photonic-Crystal Fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006). [CrossRef]

].

Propagation properties of the PCFs can be further dynamically tuned by filling air-holes with substances, those refractive indices are easily influenced by external physical fields [2

2. R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, “Tunable photonic band gap fiber,” Optical Fiber Communication Conference, 466–468 (2002)

,3

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(1-6), 179–184 (2002). [CrossRef]

]. Liquid crystals (LCs) are a very good candidate for making tunable in-fiber devices since they exhibit very high electro-optic and thermo-optic effects. First evidence of photonic band-gap tuning in a PCF filled with a liquid crystal was reported by Larsen et al. in 2003 [4

4. T. Larsen, A. Bjarklev, D. Hermann, and J. Broeng, “Optical devices based on liquid crystal photonic bandgap fibres,” Opt. Express 11(20), 2589–2596 (2003). [CrossRef] [PubMed]

], and similar results were reported by different authors [5

5. T. R. Wolinski, K. Szaniawska, K. Bondarczuk, P. Lesiak, A. W. Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki, and J. Wojcik, “Propagation properties of photonic crystals fibers filled with nematic liquid crystals,” Opto-Electronics Rev. 13(2), 59–64 (2005).

7

7. M. Y. Jeon and J. H. Kim, “Transmission Characteristics in Liquid-Crystal-Infiltrated Photonic Crystal Fibers,” Jpn. J. Appl. Phys. 47(No. 4), 2174–2175 (2008). [CrossRef]

]. Electrical tuning in a hollow-core liquid-crystal photonic crystal fiber was demonstrated in 2004 [8

8. Q. Lu and S. T. Wu, “Electrically tunable liquid-crystal photonic crystal fiber,” Appl. Phys. Lett. 85, 2181–2183 (2005).

] and also in silica glass-core photonic liquid crystals fibers (PLCFs) [9

9. 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(4), 819–821 (2005). [CrossRef]

,10

10. 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 fibers,” Meas. Sci. Technol. 17(5), 985–991 (2006). [CrossRef]

]. In [10

10. 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 fibers,” Meas. Sci. Technol. 17(5), 985–991 (2006). [CrossRef]

] thermal tuning of the PLCF guiding mechanism was presented by using a special low-birefringence LC mixture with the ordinary refractive index lower (in a certain temperature range) than the refractive index of the silica glass. The efficiency of electrical tuning could be significantly improved by using dual-frequency liquid crystals [11

11. L. Scolari, T. Alkeskjold, J. Riishede, A. Bjarklev, D. Hermann, A. Anawati, M. Nielsen, and P. Bassi, “Continuously tunable devices based on electrical control of dual-frequency liquid crystal filled photonic bandgap fibers,” Opt. Express 13(19), 7483–7496 (2005). [CrossRef] [PubMed]

,12

12. A. Lorenz, H.-S. Kitzerow, A. Schwuchow, J. Kobelke, and H. Bartelt, “Photonic crystal fiber with a dual-frequency addressable liquid crystal: behavior in the visible wavelength range,” Opt. Express 16(23), 19375–19381 (2008). [CrossRef]

]. Also, all-optical tuning was demonstrated in a PCF filled with a LC doped either with dyes [13

13. T. Alkeskjold, J. Lægsgaard, A. Bjarklev, D. Hermann, A. Anawati, J. Broeng, J. Li, and S.-T. Wu, “All-optical modulation in dye-doped nematic liquid crystal photonic bandgap fibers,” Opt. Express 12(24), 5857–5871 (2004). [CrossRef] [PubMed]

] or with azobenzene [14

14. V. K. Hsiao and C.-Y. Ko, “Light-controllable photoresponsive liquid-crystal photonic crystal fiber,” Opt. Express 16(17), 12670–12676 (2008). [PubMed]

]. Moreover, frequency tunability of the solid-core photonic crystal fibers filled with nanoparticle-doped liquid crystals has been recently reported [15

15. L. Scolari, S. Gauza, H. Xianyu, L. Zhai, L. Eskildsen, T. T. Alkeskjold, S.-T. Wu, and A. Bjarklev, “Frequency tunability of solid-core photonic crystal fibers filled with nanoparticle-doped liquid crystals,” Opt. Express 17(5), 3754–3764 (2009). [CrossRef] [PubMed]

].

One of the most interesting features of the PLCFs is the possibility to dynamically tune their polarization properties due to external fields-induced reorientation of LC molecules. Tunable polarizer [16

16. T. T. Alkeskjold and A. Bjarklev, “Electrically controlled broadband liquid crystal photonic bandgap fiber polarimeter,” Opt. Lett. 32(12), 1707–1709 (2007). [CrossRef] [PubMed]

], tunable single polarization operation [17

17. T. R. Woliński, S. Ertman, A. Czapla, P. Lesiak, K. Nowecka, A. W. Domanski, E. Nowinowski-Kruszelnicki, R. Dabrowski, and J. Wójcik, “Polarization effects in photonic liquid crystal fibers,” Meas. Sci. Technol. 18(10), 3061–3069 (2007). [CrossRef]

] and tunable birefringence [11

11. L. Scolari, T. Alkeskjold, J. Riishede, A. Bjarklev, D. Hermann, A. Anawati, M. Nielsen, and P. Bassi, “Continuously tunable devices based on electrical control of dual-frequency liquid crystal filled photonic bandgap fibers,” Opt. Express 13(19), 7483–7496 (2005). [CrossRef] [PubMed]

,18

18. T. R. Woliński, A. Czapla, S. Ertman, M. Tefelska, A. W. Domański, E. Nowinowski-Kruszelnicki, and R. Dąbrowski, “Tunable highly birefringent solid-core photonic liquid crystal fibers,” Opt. Quantum Electron. 39(12-13), 1021–1032 (2007). [CrossRef]

20

20. L. Wei, L. Eskildsen, J. Weirich, L. Scolari, T. T. Alkeskjold, and A. Bjarklev, “Continuously tunable all-in-fiber devices based on thermal and electrical control of negative dielectric anisotropy liquid crystal photonic bandgap fibers,” Appl. Opt. 48(3), 497–503 (2009). [CrossRef] [PubMed]

] have been already obtained in the silica-based PCFs filled with LCs. Thermal birefringence tuning was demonstrated in the highly birefringent PCF selectively filled with liquid crystals [18

18. T. R. Woliński, A. Czapla, S. Ertman, M. Tefelska, A. W. Domański, E. Nowinowski-Kruszelnicki, and R. Dąbrowski, “Tunable highly birefringent solid-core photonic liquid crystal fibers,” Opt. Quantum Electron. 39(12-13), 1021–1032 (2007). [CrossRef]

]. Continuous electric tuning of birefringence was demonstrated in [11

11. L. Scolari, T. Alkeskjold, J. Riishede, A. Bjarklev, D. Hermann, A. Anawati, M. Nielsen, and P. Bassi, “Continuously tunable devices based on electrical control of dual-frequency liquid crystal filled photonic bandgap fibers,” Opt. Express 13(19), 7483–7496 (2005). [CrossRef] [PubMed]

] and in [20

20. L. Wei, L. Eskildsen, J. Weirich, L. Scolari, T. T. Alkeskjold, and A. Bjarklev, “Continuously tunable all-in-fiber devices based on thermal and electrical control of negative dielectric anisotropy liquid crystal photonic bandgap fibers,” Appl. Opt. 48(3), 497–503 (2009). [CrossRef] [PubMed]

], allowing for a relative change of the phase birefringence equal to 3·10−5 and to 5·10−5 respectively. The length of a PLCF sample used in [11

11. L. Scolari, T. Alkeskjold, J. Riishede, A. Bjarklev, D. Hermann, A. Anawati, M. Nielsen, and P. Bassi, “Continuously tunable devices based on electrical control of dual-frequency liquid crystal filled photonic bandgap fibers,” Opt. Express 13(19), 7483–7496 (2005). [CrossRef] [PubMed]

] was 8 mm and birefringence tuning allowed for about a 60-degree phase shift between both orthogonal modes. The sample analyzed in [20

20. L. Wei, L. Eskildsen, J. Weirich, L. Scolari, T. T. Alkeskjold, and A. Bjarklev, “Continuously tunable all-in-fiber devices based on thermal and electrical control of negative dielectric anisotropy liquid crystal photonic bandgap fibers,” Appl. Opt. 48(3), 497–503 (2009). [CrossRef] [PubMed]

] was longer (20 mm) and a phase shift of 250 degree was possible.

A larger tuning range was demonstrated in a 10 mm long tapered microstructured fiber filled with polymer [21

21. C. Kerbage and B. Eggleton, “Numerical analysis and experimental design of tunable birefringence in microstructured optical fiber,” Opt. Express 10(5), 246–255 (2002). [PubMed]

]. In that case, a relative change of birefringence was about 3·10−4 and it allowed for a phase shift of 6π. However, in [21

21. C. Kerbage and B. Eggleton, “Numerical analysis and experimental design of tunable birefringence in microstructured optical fiber,” Opt. Express 10(5), 246–255 (2002). [PubMed]

] the steering was thermal and to reach such a tuning range it was necessary to increase temperature from 20°C to 150°C, which is not the best solution for practical applications.

There was also a number of theoretical works discussing propagation and polarization properties of PCFs filled with LCs, confirming that their properties strongly rely on LC refractive indices and molecular orientation [22

22. C. Zhang, G. Kai, Z. Wang, Y. Liu, T. Sun, S. Yuan, and X. Dong, “Tunable highly birefringent photonic bandgap fibers,” Opt. Lett. 30(20), 2703–2705 (2005). [CrossRef] [PubMed]

26

26. G. Ren, P. Shum, J. Hu, X. Yu, and Y. Gong, “Polarization-Dependent Bandgap Splitting and Mode Guiding in Liquid Crystal Photonic Bandgap Fibers,” J. Lightwave Technol. 26(22), 3650–3659 (2008). [CrossRef]

]. Also, liquid crystal attenuation can play a significant role, especially if a guided mode is penetrating LC-filled holes [27

27. S. Ertman, T. Nasilowski, T. R. Wolinski, and H. Thienpont, “Highly birefringent microstructured fiber selectively filled with lossy material,” Photon. Lett. of Poland 1(1), 13–15 (2009).

].

So far experimental researches (and also most theoretical papers) were focused on silica glass-based PCF filled with LCs. However, the refractive indices of a great majority of LCs are higher than the silica glass refractive index (~1.46), and thus in silica-glass PCFs filled with LCs light is generally propagating due to the photonic band-gap phenomenon. As a result, losses in these PLCFs are in the order of a few or even a few tens dB/cm, and so far only short sections (from few mm to ~5 cm) of the PLCFs have been experimentally investigated [4

4. T. Larsen, A. Bjarklev, D. Hermann, and J. Broeng, “Optical devices based on liquid crystal photonic bandgap fibres,” Opt. Express 11(20), 2589–2596 (2003). [CrossRef] [PubMed]

18

18. T. R. Woliński, A. Czapla, S. Ertman, M. Tefelska, A. W. Domański, E. Nowinowski-Kruszelnicki, and R. Dąbrowski, “Tunable highly birefringent solid-core photonic liquid crystal fibers,” Opt. Quantum Electron. 39(12-13), 1021–1032 (2007). [CrossRef]

].

In this paper we use as the host fiber a PCF made of glass with a very high refractive index (~1.95) ensuring index-guiding propagation after filling the fiber with a LC. In this case losses of the host PCF and the PLCF (infiltrated with the 5CB nematic LC) are comparable: 0.15dB/cm and 0.19 dB/cm, respectively. The difference in attenuation of the PCF and the PLCF (equal to 0,04 dB/cm) can be attributed to scattering losses introduced by the LC. Moreover, since light is index-guided any external (electric) field does not introduce changes in transmission spectra of the PLCF and consequently continuous birefringence tuning can be observed.

2. High-index glass host PCF and guest LCs

As the host we used a specially designed photonic crystal fiber that was manufactured at the Institute of Electronics Materials Technology ITME, Warsaw (Poland). According to the ITME internal name system used to distinguish fibers, our fiber is denoted as PCF14(6) and its cross-section is shown in Fig. 1a
Fig. 1 a) Cross section of the PCF14(6) microstructured fiber: the diameter of the fiber is 125.4 μm, the holes diameter is 5.2 μm and the pitch between holes is 7.6 μm; b) dispersion characteristics of the PBG08 glass (material used to fabricate PCF14(6)) and refractive indices of the LCs used in the experiment. The silica-glass refractive index is also presented for a comparison.
. The fiber diameter is 125.4 μm and it consists of six rings of holes with diameters of 5.2 μm and is characterized by the pitch (distance between holes) equal to 7.6 μm. The PCF is made by the stack-and-draw technique from the lead-bismuth-gallate (Pb-Bi-Ga)-based glass designated as PBG08 [28

28. D. Lorenc, M. Aranyosiova, R. Buczyński, R. Stępień, I. Bugar, A. Vincze, and D. Velic, “Nonlinear refractive index of multicomponent glasses designed for fabrication of photonic crystal fibers,” Appl. Phys. B: Lasers Opt 93(2-3), 531–538 (2008). [CrossRef]

]. Chemical composition of the PBG08 glass is as follows: 14.06% SiO2, 39.17% PbO, 27.26% Bi2O3, 14.26% Ga2O3, 5.26% CdO. The transparence window of this glass spreads from 450 nm (UV absorption cutoff) to 4800 nm (multiphonon IR absorption edge) corresponding to its attenuation of the order of 10 dB/m [28

28. D. Lorenc, M. Aranyosiova, R. Buczyński, R. Stępień, I. Bugar, A. Vincze, and D. Velic, “Nonlinear refractive index of multicomponent glasses designed for fabrication of photonic crystal fibers,” Appl. Phys. B: Lasers Opt 93(2-3), 531–538 (2008). [CrossRef]

].

From our point of view the most interesting feature of the PBG08 glass is that it is characterized by a very high refractive index (~1.95). Figure 1b shows dispersion of the PBG08 glass compared to dispersion of the silica glass and also contains wavelength dependence of the refractive indices of three LCs used in our experiments. One of them is a commonly-used and well-characterized 5CB nematic LC: dispersion characteristics of its both refractive indices are well known [29

29. J. Li and S. T. Wu, “Extended Cauchy equations for the refractive indices of liquid crystals,” J. Appl. Phys. 95(3), 896–901 (2004). [CrossRef]

]. Two other LCs (abbreviated as 1658A and 1679) are experimental mixtures synthesized at the Military University of Technology and so far there have been limited data on their refractive indices.

From Fig. 1b it could be noticed that the refractive index of the PBG08 glass is higher than both ordinary and extraordinary indices of the LCs used in this work. It ensures index-guiding propagation for any possible LC molecules orientation. Contrary, by using a silica-glass PCF as a host fiber, PBG propagation would be the only possibility for the same guest LCs independently on their molecular orientation, since the silica-glass refractive index is always lower than both LCs’ refractive indices. This explains the principal advantage of using the high-index PCF for LCs infiltration.

3. Numerical simulations of birefringence tuning in the PCF14(6) filled with 5CB

For simplification we assume that application of the transverse electric field induces the same tilt angle φ for all LC molecules (Fig. 2c). Finally, if the electric field would be strong enough, all the LC molecules should be oriented along the field direction (Fig. 2b).

The proposed model is not strictly convergent with a real situation. In practical cases electric field distribution is not perfectly uniform and LC molecules are not reorienting collectively at the same angle. However, this simplified assumption allowed us to predict qualitatively changes in the phase birefringence induced by the transverse electric field.

Simulations were performed in a wide range of the wavelengths (from 400 to 1900nm) and seven series of calculations were done for the following angles of the LC molecules tilt angles: 0°, 15°, 30°, 45°, 60°, 75° and 90°. Simulations results are presented in Fig. 3
Fig. 3 Numerical simulations of the phase birefringence tuning in the PCF14(6) filled with 5CB induced by collective tilt of the LC molecules. For planar orientation of LC molecules (φ = 0°) fiber is isotropic (non-birefringent).
. As it could be expected, if all the molecules are parallel to the fiber axis (φ = 0°), the fiber is isotropic and consequently its birefringence remains equal to 0 for all wavelengths. When molecules are tilted (by a transverse electric field), birefringence is induced in the fiber and its value is getting higher for increasing tilt angles. It could be also noticed that birefringence is higher for longer wavelengths (reaching 10−4 at 1550 nm when φ = 90°). It means that the process of the continuous LC molecular reorientation results in continuous birefringence tuning of the fiber (from 0 to 10−4 at 1550 nm).

Similar calculations were made for the PCF14(6) filled with the 1679 and 1658A liquid crystal mixtures. Due to limited data on the refractive indices of these LCs, simulations were performed by using a non-dispersion model. We assumed that the refractive index of the host PCF is 1.92 and the ordinary refractive index of the liquid crystal is always equal to 1.52. The value of the extraordinary refractive index for 5CB, 1679 and 1658A was set to be 1.7, 1.8, and 1.88, respectively. Simulations for 5CB infiltration without considering dispersion were performed to confirm that omitting dispersion effects does not lead to significant inaccuracies. A comparison of the phase birefringence of the PCF14(6) filled with the LCs obtained for transverse molecules orientation (φ = 90°) is presented in Fig. 4
Fig. 4 Comparison of the birefringence tuning ranges in PCF14(6) filled with three different liquid crystals 5CB, 1679 and 1658A characterized by different value of an extraordinary refractive index (since for the planar orientation of LC molecules the birefringence of fiber is equal to 0, the tuning range is adequate to the birefringence obtained at the transverse orientation of the LC molecules)
. It could be noticed that the birefringence tuning range for the PCF filled with 1679 (Δn ≈0.28) is about twice higher than for fiber filled with 5CB (Δn ≈0.18). For the PCF filled with 1658A (Δn ≈0.36) the tuning range reaches 8·10−4 and is about five times higher than for the PCF filled with 5CB.

Our simulations also indicate that filling the PCF14(6) with LCs does not introduce significant changes in confinement losses (theoretical losses connected with an imaginary part of the effective refractive index), which for both the empty PCF and the filled fiber (PLCF) are almost the same, at the level of 10−9 dB/m. The low level of the confinement losses is connected with the fact that the mode is well located in the core area and, moreover, the mode profile remains almost unchanged in the whole tuning range (Fig. 5
Fig. 5 Central part of the PCF14(6) cross section (a) and calculated mode profiles for X- and Y-polarized modes (b, c) for PCF14(6) filled with 5CB with transverse molecules orientation (φ = 90°) – mode profile is almost the same in whole tuning range.
). In practical cases attenuation of the PLCF will be higher due to material losses of the PBG08 glass and of the LCs.

To complete the theoretical analysis of the PLCFs based on the PCF14(6) a comment on the host fiber dimensions should be made. We decided to use the fiber with a relatively high diameter of holes for several reasons. The first is that the confinement losses of both: the empty PCF and the PCF filled with a LC was very low, so the fundamental mode was well localized in the core and thus the impact of LC scattering was minimized. The second is that filling fiber with bigger holes is easier, and for the PCF14(6) it was possible to fill relatively fast long sections (~up to 60 cm) of the fiber. Finally, reorientation of the LC molecules with an electric field is more effective in large holes.

However, an increase in the diameter of the holes with a constant distance between them is connected with an increasing number of the modes guided in the fiber. Our specially-designed PCF14(6) was optimized to couple the light from a single mode (SM) telecommunication fiber, and thus the fiber was designed to ensure that the profile of the fundamental mode is matching to the mode profile of the standard SM fiber. We numerically increased the diameter of the holes until a highly attenuated fourth-order mode appeared (Fig. 6
Fig. 6 Modes guided in the PCF14(6) fiber: a) fundamental mode; b) second-order mode; c) third-order mode; d) highly attenuated fourth order mode.
). The profiles of the second- and third-order mode have a visible deep in the center of the core, so we assumed that after connecting such a fiber with the SM fiber most of the optical power will be coupled to the fundamental mode. The assumption was confirmed experimentally. In both: the empty PCF14(6) and the LC-filled fiber it was possible to excite only the fundamental mode. However, a very precise alignment of the connected fibers is required.

4. Attenuation measurement

To measure the attenuation of the empty PCF14 and the PCF14(6) filled with the 5CB liquid crystal we decided to use the cut-back technique. In this technique, the output power was measured for the fiber which length was systematically shortened. Attenuation is defined as:
A=1x10log(P(x)P(0))
(1)
where P(0) is the power at the input of the fiber, P(x) is the power measured at the output of the fiber, and x is the length of the fiber. Relation (1) can be also expressed as:
10logP(x)=Ax+10logP(0)
(2)
so attenuation can be calculated by finding the slope of the 10 log P(x) function. Figure 7
Fig. 7 Attenuation measurement of the empty PCF14(6) and the PCF filled with 5CB – attenuation was find as slope coefficients of the 10 log P(x) functions- for the empty PCF it is ~0.15 dB/cm, and ~0.19 dB/cm for the PCF filled with 5CB.
presents the functions plotted for both: the empty PCF14(6) and for the PCF14(6) filled with 5CB, as well as their linear fit expressions. The measured values of attenuation of the empty PCF14(6) is ~0.15 dB/cm, and it increases to ~0.19 dB/cm after infiltration with 5CB (the measurement was performed by using a He-Ne laser operating at the 632.8 nm wavelength).

Due to the fact that confinement losses (for both the empty PCF and the PLCF) were numerically predicted to be very low, the attenuation measurement of the empty fiber can be also treated as the attenuation measurement of the PBG08 glass. An increase of losses after LC infiltration could be explained by the fact that a fraction of the evanescent field (at the PBG08-5CB border) is penetrating the LC-filled holes, this attenuation is higher than for the PBG08 glass. Moreover, thermal fluctuations in LC molecules orientation can also induce extra scattering losses. The difference in the attenuation of the empty PCF and the PLCF (0,04 dB/cm) can be recognized as scattering losses introduced by the LC.

In our measurements described above the samples were manually connected “face-to-face” with the SM fiber by using 3-axis precise translation stages. It means that the linear fit function of (2) can be also used to evaluate coupling losses from the SM fiber to the PCF/PLCF. Since the slope of the function (2) is connected with the fiber attenuation, the y-intercept (10logP(0)) can give information about the optical power coupled to the core P(0). For both: the empty PCF and the 5CB-filled fiber calculated P(0) was almost the same: P(0) ≈102.98 = 955 nW. During our measurements the optical power at the end of the leading-in SM fiber was kept at the constant value of 1200 nW. By comparing this value with the interpolated power coupled to the fiber P(0) we can estimate coupling losses at the level of 1dB.

5. Continuous birefringence tuning with an electric field

To investigate birefringence tuning we have used three different PLCF samples based on the PCF14(6) filled with the 5CB, 1679, and 1658A LCs. Each PLCF sample ~15 cm long was placed between two 12-cm long flat electrodes. The distance between both electrodes was limited by the PCF14(6) diameter and equal to 125 μm. A high-voltage amplifier connected to the electrodes allowed for a continuous change of voltage from 0 to 1500V, with frequency from 500 Hz to 10 kHz. In practice, voltage tuning was limited to about 600V due to electric discharges (to avoid discharges, samples were surrounded with silicon oil), so that maximum intensity of an electric field between 125 μm spaced electrodes was limited to about 5 V/μm. Both ends of the sample were face-to-face connected with low-birefringence, single mode leading-in and leading-out fibers. A tunable laser operating at the 1500-1640 nm range (Tunics Plus) was used as a light source and changes in the output signal were analyzed by the PAT9000B polarimeter (Fig. 8
Fig. 8 Experimental setup used in birefringence tuning measurements.
).

It has been noticed that changes in the electric field led to continuous and repeatable changes in the state of polarization (SOP) at the output of the PLCF sample (Fig. 9
Fig. 9 Electrically induced changes in the state of polarization (SOP) of the PCF14(6) filled with (a) 5CB; (b) 1679; (c) 1658A. Any continuous change in SOP indicates appropriate continuous change in fiber birefringence (measured at 1600nm, frequency of steering voltage fixed to 1 kHz)
). For each sample an increase of electric field resulted in circular traces on the Poincare sphere. It means that continuous phase changes between two polarization components of the guided mode have been electrically induced.

The phase difference between two orthogonally polarized components of the fundamental mode after propagation through the highly birefringent fiber can be expressed as:
δϕ=2πλBL
(3)
where B is the phase birefringence of the fiber and L is the length of the fiber. When the electric field is increasing only the phase birefringence is changing in the PLCF placed between electrodes. Assuming that the length of electrodes (LE) is constant, the phase difference induced by the electric field E can express as follows:

Δδϕ(E)=2πλLEΔB(E)
(4)

Since Δδϕ (E) can be easily measured from the Poincare sphere traces (one full circle corresponds to Δδϕ = 2π), any change in the phase birefringence ΔB can be easily calculated by using the following formula:

ΔB(E)=Δδϕ(E)2πλLE
(5)
Fig. 11 Phase birefringence tuning at selected wavelengths in the PCF14(6) filled with 1679.

Tuning of the phase birefringence at selected wavelengths for each of the PLCF samples is presented in Figs. 10
Fig. 10 Phase birefringence tuning at selected wavelengths in the PCF14(6) filled with 5CB
-12
Fig. 12 Phase birefringence tuning at selected wavelengths in the PCF14(6) filled with 1658A.
. It is evident that in each PLCF sample the phase birefringence increases almost linearly with the electric field intensity. In the case of the PLCF with 5CB the tuning range was almost 4·10−5 at 1640 nm wavelength. By comparing this value with numerical simulations (Fig. 3) it could be noticed that application of an electric field with the intensity of 5V/μm corresponds to the 45° tilt of the LC molecules in the “collective tilt” model. Without an electric field orientation of the LC molecules is planar and thus the birefringence of the fiber vanishes. This has been confirmed by a continuous change in the wavelength at different values of the electric field: if the electric field was switched off, the state of polarization (SOP) remained unchanged. However, when the electric field was applied, continuous sweeping of the wavelength resulted in the SOP changes. Relying on our simulations we believe that an increase in the electric field above the 5V/μm would allow for even higher phase birefringence tuning in the PCF14(6) filled with the 5CB LC. Unfortunately, electric discharges prevented us from using higher electric field intensities.

A comparison of the birefringence tuning ranges of all three PLCF samples is presented in Fig. 13
Fig. 13 Comparison of phase birefringence tuning at 1640nm in the PCF14(6) filled with 5CB, 1679 and 1658A. The tuning range is proportional to birefringences of the liquid crystals used: (Δn5CB ≈0.2) < (Δn1679 ≈0.3) < (Δn1658A ≈0.38)
. The tuning range of the PLCF sample filled with 1679 was ~10−4, and for PLCF sample filled with 1658A it was almost 2·10−4. The obtained experimental results are in good agreement with the simulations presented in Fig. 5, confirming that the tuning range depends on the value of LC birefringence.

6. Advantages and disadvantages of using the high-index PCF

The most important consequence of using the high-index PCF as a host for PLCF fabrication is that the light is always index-guided. Consequently, the effective fibers are more broadband with respect to the PLCFs based on silica-glass PCFs, in which only photonic-band-gap propagation is generally possible [4

4. T. Larsen, A. Bjarklev, D. Hermann, and J. Broeng, “Optical devices based on liquid crystal photonic bandgap fibres,” Opt. Express 11(20), 2589–2596 (2003). [CrossRef] [PubMed]

20

20. L. Wei, L. Eskildsen, J. Weirich, L. Scolari, T. T. Alkeskjold, and A. Bjarklev, “Continuously tunable all-in-fiber devices based on thermal and electrical control of negative dielectric anisotropy liquid crystal photonic bandgap fibers,” Appl. Opt. 48(3), 497–503 (2009). [CrossRef] [PubMed]

].

Another outcome of the index-guiding is that the mode field is well localized in the core area and much less penetrates the LC-filled holes than in the case of the silica-based PLCFs. As a consequence impact of the light scattering on the fiber attenuation is smaller. It is worth to emphasize that the attenuation of 0.19 dB/cm obtained for the PCF14(6) filled with 5CB is, to our best knowledge, the lowest attenuation reported so far in microstructured fibers filled with liquid crystals. By taking into account that attenuation of the empty PCF14(6) is 0.15 dB/cm we can evaluate attenuation caused by LC scattering at the level of ~0,04dB/cm. It suggests that total losses of the index guiding PLCF could be further reduced if the attenuation of the host fiber would be smaller.

The use of the high-index host PCF have also a positive impact on the efficiency of the electrically-induced tuning. The external electric field disturbs orientation of the LC molecules, which not only changes the effective refractive indices, but also causes an increase the light scattering. As a result the so-called activation losses (AL) and polarization dependent losses (PDL) are observed in the silica-based PLCFs [9

9. 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(4), 819–821 (2005). [CrossRef]

11

11. L. Scolari, T. Alkeskjold, J. Riishede, A. Bjarklev, D. Hermann, A. Anawati, M. Nielsen, and P. Bassi, “Continuously tunable devices based on electrical control of dual-frequency liquid crystal filled photonic bandgap fibers,” Opt. Express 13(19), 7483–7496 (2005). [CrossRef] [PubMed]

,15

15. L. Scolari, S. Gauza, H. Xianyu, L. Zhai, L. Eskildsen, T. T. Alkeskjold, S.-T. Wu, and A. Bjarklev, “Frequency tunability of solid-core photonic crystal fibers filled with nanoparticle-doped liquid crystals,” Opt. Express 17(5), 3754–3764 (2009). [CrossRef] [PubMed]

17

17. T. R. Woliński, S. Ertman, A. Czapla, P. Lesiak, K. Nowecka, A. W. Domanski, E. Nowinowski-Kruszelnicki, R. Dabrowski, and J. Wójcik, “Polarization effects in photonic liquid crystal fibers,” Meas. Sci. Technol. 18(10), 3061–3069 (2007). [CrossRef]

,20

20. L. Wei, L. Eskildsen, J. Weirich, L. Scolari, T. T. Alkeskjold, and A. Bjarklev, “Continuously tunable all-in-fiber devices based on thermal and electrical control of negative dielectric anisotropy liquid crystal photonic bandgap fibers,” Appl. Opt. 48(3), 497–503 (2009). [CrossRef] [PubMed]

].

To measure AL and PDL for the PLCFs based on the PCF14(6) we have used a broadband halogen light source (with optional broadband polarizer) and a fiber optic spectrometer. As a reference we used transmission recorded for the samples not disturbed by the electric field. Without any polarizer at the input we have not noticed any changes in the spectra with the increasing electric field, so the AL were not observed. Due to a continuous variation of the polarization azimuth at the input of the samples we were able to measure the PDL. Without the electric, the PDL was equal zero, and any increase in the electric field (up to 4V/µm) resulted in the PDL which was evaluated at the level of 1dB. In the other words polarization dependent attenuation was smaller than 0,1 dB/cm.

For a comparison, we present parameters of a current state-of-the art PLCF device based on the silica-host PCF presented in [20

20. L. Wei, L. Eskildsen, J. Weirich, L. Scolari, T. T. Alkeskjold, and A. Bjarklev, “Continuously tunable all-in-fiber devices based on thermal and electrical control of negative dielectric anisotropy liquid crystal photonic bandgap fibers,” Appl. Opt. 48(3), 497–503 (2009). [CrossRef] [PubMed]

]. The device consists of 20-mm section of the PLCF, with insertion losses (normalized to the losses of an empty PCF) are around 1.5 dB in the middle of the bandgap. The device can operate as a tunable waveplate (phase shift tunable from 0 to π) with AL of 0.45 dB and PDL of 0.67 dB. Thus attenuation of the presented PLCF is about 0.75 dB/cm without the electric field and is rising to about 1.3 dB/cm due to the PDL and AL.

However in the context of potential practical applications a simple comparison of attenuations, PDL, AL or birefringence tuning range may be sometimes misleading. Efficiency of connecting of the PLCF with other types of the fibers (especially SM) is also a very important factor and in this area the PLCFs based on the silica-glass PCFs is much more practical. Attenuation of the empty silica-based PCFs is low and they can be effectively used as an leading-in and leading-out fibers for standard devices, which can be also easily spliced to other silica-based fibers.

In contrary, the PCF14(6) based on the PBG08 glass is very lossy (0.15dB/cm) in comparison to standard fibers. It means that a SM fiber should be connected to both ends of the PLCF in order to obtain a device that can be used e.g. in telecommunication systems. However, splicing of the PBG08 glass with the silica glass is a very challenging task since chemical compositions and thermal properties (especially melting temperatures) of both glasses are totally different. Moreover, fusion arc-splicing of the PCF filled with the LC may permanently destroy the LC. Thus some alternative methods of effective fiber connections should be used as e.g. precise capillary connections, gluing with UV curable epoxies or “hot capillary connections” (thermal collapse of capillary made of “soft” glass with melting temperature lower than connected fibers). We are currently testing all the mentioned above methods of connecting the PLCF with leadings and typical losses are in the order of 1dB (similar as for manual “face-to-face” connections - see section 4).

So the main disadvantage of the PLCFs based on the PBG08-glass PCFs is a time consuming procedure of connecting them with other kinds of the fibers. Another issue is a possibility of higher reflections at interfaces due to a high difference in refractive indices. Finally, possibility of a broadband and low-loss operation with continuous tuning of birefringence in a wide range is a very interesting feature, and the index-guiding PLCFs are definitely worthy to pay them more attention.

7. Conclusions

We have demonstrated low-loss propagation in the high-index PCF filled with liquid crystals. The refractive index of the host PCF was about 1.95 and was higher than both ordinary and extraordinary indices of the guest LCs. As a result, low-loss index guiding was possible. The attenuation of the empty PCF was measured to be 0.15 dB/cm and after filling it with 5CB it was only slightly higher reaching 0.19 dB/cm. To our best knowledge, it is the lowest ever reported attenuation value of the PLCF.

Our results suggest that losses could be even lower if the host PCF could be manufactured by using high-index glasses with attenuation lower than for the PBG08 glass. The use of the high-index host PCFs to be infiltrated with LCs seems to be justified not only due to lower losses, but also for much broader operating ranges that are not limited by the presence of photonic bandgaps.

We have also demonstrated continuous and repeatable phase birefringence tuning induced by an external electric field. The most interesting feature of the tuning is that an initially non-birefringent PLCF (without the electric field) becomes dynamically birefringent with an induced phase birefringence proportional to the electric field intensity. Moreover, its birefringence axis is defined by the direction of an electric field, which is especially interesting in the context of potential applications. Such fibers could be used, for example, as all-in-fiber polarization controllers, phase modulators or polarization mode dispersion compensators. The functionality of the PLCFs could be even more extended by using four-electrode steering (similar to V-groove assembled electrodes presented in [16

16. T. T. Alkeskjold and A. Bjarklev, “Electrically controlled broadband liquid crystal photonic bandgap fiber polarimeter,” Opt. Lett. 32(12), 1707–1709 (2007). [CrossRef] [PubMed]

]). Four-electrode steering will allow for a dynamic change in the field direction and it will be possible to make fibers with continuously tunable birefringence and also with switchable birefringence axes.

Acknowledgments

This work was supported by the Polish Ministry of Science and Higher Education under the grants N517 056535 and partially by the European Union in the framework of the European Social Fund through the Warsaw University of Technology Development Program.

References and links

1.

P. St. J. Russell, “Photonic-Crystal Fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006). [CrossRef]

2.

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, “Tunable photonic band gap fiber,” Optical Fiber Communication Conference, 466–468 (2002)

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(1-6), 179–184 (2002). [CrossRef]

4.

T. Larsen, A. Bjarklev, D. Hermann, and J. Broeng, “Optical devices based on liquid crystal photonic bandgap fibres,” Opt. Express 11(20), 2589–2596 (2003). [CrossRef] [PubMed]

5.

T. R. Wolinski, K. Szaniawska, K. Bondarczuk, P. Lesiak, A. W. Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki, and J. Wojcik, “Propagation properties of photonic crystals fibers filled with nematic liquid crystals,” Opto-Electronics Rev. 13(2), 59–64 (2005).

6.

J. Du, Y. Liu, Z. Wang, B. Zou, B. Liu, and X. Dong, “Liquid crystal photonic bandgap fiber: different bandgap transmissions at different temperature ranges,” Appl. Opt. 47(29), 5321–5324 (2008). [CrossRef] [PubMed]

7.

M. Y. Jeon and J. H. Kim, “Transmission Characteristics in Liquid-Crystal-Infiltrated Photonic Crystal Fibers,” Jpn. J. Appl. Phys. 47(No. 4), 2174–2175 (2008). [CrossRef]

8.

Q. Lu and S. T. Wu, “Electrically tunable liquid-crystal photonic crystal fiber,” Appl. Phys. Lett. 85, 2181–2183 (2005).

9.

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(4), 819–821 (2005). [CrossRef]

10.

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 fibers,” Meas. Sci. Technol. 17(5), 985–991 (2006). [CrossRef]

11.

L. Scolari, T. Alkeskjold, J. Riishede, A. Bjarklev, D. Hermann, A. Anawati, M. Nielsen, and P. Bassi, “Continuously tunable devices based on electrical control of dual-frequency liquid crystal filled photonic bandgap fibers,” Opt. Express 13(19), 7483–7496 (2005). [CrossRef] [PubMed]

12.

A. Lorenz, H.-S. Kitzerow, A. Schwuchow, J. Kobelke, and H. Bartelt, “Photonic crystal fiber with a dual-frequency addressable liquid crystal: behavior in the visible wavelength range,” Opt. Express 16(23), 19375–19381 (2008). [CrossRef]

13.

T. Alkeskjold, J. Lægsgaard, A. Bjarklev, D. Hermann, A. Anawati, J. Broeng, J. Li, and S.-T. Wu, “All-optical modulation in dye-doped nematic liquid crystal photonic bandgap fibers,” Opt. Express 12(24), 5857–5871 (2004). [CrossRef] [PubMed]

14.

V. K. Hsiao and C.-Y. Ko, “Light-controllable photoresponsive liquid-crystal photonic crystal fiber,” Opt. Express 16(17), 12670–12676 (2008). [PubMed]

15.

L. Scolari, S. Gauza, H. Xianyu, L. Zhai, L. Eskildsen, T. T. Alkeskjold, S.-T. Wu, and A. Bjarklev, “Frequency tunability of solid-core photonic crystal fibers filled with nanoparticle-doped liquid crystals,” Opt. Express 17(5), 3754–3764 (2009). [CrossRef] [PubMed]

16.

T. T. Alkeskjold and A. Bjarklev, “Electrically controlled broadband liquid crystal photonic bandgap fiber polarimeter,” Opt. Lett. 32(12), 1707–1709 (2007). [CrossRef] [PubMed]

17.

T. R. Woliński, S. Ertman, A. Czapla, P. Lesiak, K. Nowecka, A. W. Domanski, E. Nowinowski-Kruszelnicki, R. Dabrowski, and J. Wójcik, “Polarization effects in photonic liquid crystal fibers,” Meas. Sci. Technol. 18(10), 3061–3069 (2007). [CrossRef]

18.

T. R. Woliński, A. Czapla, S. Ertman, M. Tefelska, A. W. Domański, E. Nowinowski-Kruszelnicki, and R. Dąbrowski, “Tunable highly birefringent solid-core photonic liquid crystal fibers,” Opt. Quantum Electron. 39(12-13), 1021–1032 (2007). [CrossRef]

19.

S. Ertman, A. Czapla, T. R. Woliński, T. Nasiłowski, H. Thienpont, E. Nowinowski-Kruszelnicki, and R. Dąbrowski, “Light propagation in highly birefringent photonic liquid crystal fibers,” Opto-Electronics Review 17(2), 150–155 (2009). [CrossRef]

20.

L. Wei, L. Eskildsen, J. Weirich, L. Scolari, T. T. Alkeskjold, and A. Bjarklev, “Continuously tunable all-in-fiber devices based on thermal and electrical control of negative dielectric anisotropy liquid crystal photonic bandgap fibers,” Appl. Opt. 48(3), 497–503 (2009). [CrossRef] [PubMed]

21.

C. Kerbage and B. Eggleton, “Numerical analysis and experimental design of tunable birefringence in microstructured optical fiber,” Opt. Express 10(5), 246–255 (2002). [PubMed]

22.

C. Zhang, G. Kai, Z. Wang, Y. Liu, T. Sun, S. Yuan, and X. Dong, “Tunable highly birefringent photonic bandgap fibers,” Opt. Lett. 30(20), 2703–2705 (2005). [CrossRef] [PubMed]

23.

D. C. Zografopoulos, E. E. Kriezis, and T. D. Tsiboukis, “Photonic crystal-liquid crystal fibers for single-polarization or high-birefringence guidance,” Opt. Express 14(2), 914–925 (2006). [CrossRef] [PubMed]

24.

J. Sun and C. C. Chan, “Effect of liquid crystal alignment on bandgap formation in photonic bandgap fibers,” Opt. Lett. 32(14), 1989–1991 (2007). [CrossRef] [PubMed]

25.

G. Tartarini, M. Pansera, T. Tanggaard Alkeskjold, A. Bjarklev, and P. Bassi,“Polarization Properties of Elliptical-Hole Liquid Crystal Photonic Bandgap Fibers,” J. Lightwave Technol. 25(9), 2522–2530 (2007). [CrossRef]

26.

G. Ren, P. Shum, J. Hu, X. Yu, and Y. Gong, “Polarization-Dependent Bandgap Splitting and Mode Guiding in Liquid Crystal Photonic Bandgap Fibers,” J. Lightwave Technol. 26(22), 3650–3659 (2008). [CrossRef]

27.

S. Ertman, T. Nasilowski, T. R. Wolinski, and H. Thienpont, “Highly birefringent microstructured fiber selectively filled with lossy material,” Photon. Lett. of Poland 1(1), 13–15 (2009).

28.

D. Lorenc, M. Aranyosiova, R. Buczyński, R. Stępień, I. Bugar, A. Vincze, and D. Velic, “Nonlinear refractive index of multicomponent glasses designed for fabrication of photonic crystal fibers,” Appl. Phys. B: Lasers Opt 93(2-3), 531–538 (2008). [CrossRef]

29.

J. Li and S. T. Wu, “Extended Cauchy equations for the refractive indices of liquid crystals,” J. Appl. Phys. 95(3), 896–901 (2004). [CrossRef]

30.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,” Opt. Fiber Technol. 6(2), 181–191 (2000). [CrossRef]

31.

S. Ertman, T. R. Woliński, A. Czapla, K. Nowecka, E. Nowinowski-Kruszelnicki, and J. Wójcik, “Liquid crystal molecular orientation in photonic liquid crystal fibers with photopolymer layers,” Proc. SPIE 6587, 658706 (2007). [CrossRef]

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(230.3720) Optical devices : Liquid-crystal devices
(260.1440) Physical optics : Birefringence
(260.2110) Physical optics : Electromagnetic optics
(060.5295) Fiber optics and optical communications : Photonic crystal fibers

ToC Category:
Photonic Crystal Fibers

History
Original Manuscript: July 13, 2009
Revised Manuscript: September 16, 2009
Manuscript Accepted: September 16, 2009
Published: October 9, 2009

Citation
Slawomir Ertman, Tomasz R. Wolinski, Dariusz Pysz, Ryszard Buczynski, Edward Nowinowski-Kruszelnicki, and Roman Dabrowski, "Low-loss propagation and continuously tunable birefringence in high-index photonic crystal fibers filled with nematic liquid crystals," Opt. Express 17, 19298-19310 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-21-19298


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References

  1. P. St. J. Russell, “Photonic-Crystal Fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006). [CrossRef]
  2. R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, “Tunable photonic band gap fiber,” Optical Fiber Communication Conference, 466–468 (2002)
  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(1-6), 179–184 (2002). [CrossRef]
  4. T. Larsen, A. Bjarklev, D. Hermann, and J. Broeng, “Optical devices based on liquid crystal photonic bandgap fibres,” Opt. Express 11(20), 2589–2596 (2003). [CrossRef] [PubMed]
  5. T. R. Wolinski, K. Szaniawska, K. Bondarczuk, P. Lesiak, A. W. Domanski, R. Dabrowski, E. Nowinowski-Kruszelnicki, and J. Wojcik, “Propagation properties of photonic crystals fibers filled with nematic liquid crystals,” Opto-Electronics Rev. 13(2), 59–64 (2005).
  6. J. Du, Y. Liu, Z. Wang, B. Zou, B. Liu, and X. Dong, “Liquid crystal photonic bandgap fiber: different bandgap transmissions at different temperature ranges,” Appl. Opt. 47(29), 5321–5324 (2008). [CrossRef] [PubMed]
  7. M. Y. Jeon and J. H. Kim, “Transmission Characteristics in Liquid-Crystal-Infiltrated Photonic Crystal Fibers,” Jpn. J. Appl. Phys. 47(No. 4), 2174–2175 (2008). [CrossRef]
  8. Q. Lu and S. T. Wu, “Electrically tunable liquid-crystal photonic crystal fiber,” Appl. Phys. Lett. 85, 2181–2183 (2005).
  9. 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(4), 819–821 (2005). [CrossRef]
  10. 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 fibers,” Meas. Sci. Technol. 17(5), 985–991 (2006). [CrossRef]
  11. L. Scolari, T. Alkeskjold, J. Riishede, A. Bjarklev, D. Hermann, A. Anawati, M. Nielsen, and P. Bassi, “Continuously tunable devices based on electrical control of dual-frequency liquid crystal filled photonic bandgap fibers,” Opt. Express 13(19), 7483–7496 (2005). [CrossRef] [PubMed]
  12. A. Lorenz, H.-S. Kitzerow, A. Schwuchow, J. Kobelke, and H. Bartelt, “Photonic crystal fiber with a dual-frequency addressable liquid crystal: behavior in the visible wavelength range,” Opt. Express 16(23), 19375–19381 (2008). [CrossRef]
  13. T. Alkeskjold, J. Lægsgaard, A. Bjarklev, D. Hermann, A. Anawati, J. Broeng, J. Li, and S.-T. Wu, “All-optical modulation in dye-doped nematic liquid crystal photonic bandgap fibers,” Opt. Express 12(24), 5857–5871 (2004). [CrossRef] [PubMed]
  14. V. K. Hsiao and C.-Y. Ko, “Light-controllable photoresponsive liquid-crystal photonic crystal fiber,” Opt. Express 16(17), 12670–12676 (2008). [PubMed]
  15. L. Scolari, S. Gauza, H. Xianyu, L. Zhai, L. Eskildsen, T. T. Alkeskjold, S.-T. Wu, and A. Bjarklev, “Frequency tunability of solid-core photonic crystal fibers filled with nanoparticle-doped liquid crystals,” Opt. Express 17(5), 3754–3764 (2009). [CrossRef] [PubMed]
  16. T. T. Alkeskjold and A. Bjarklev, “Electrically controlled broadband liquid crystal photonic bandgap fiber polarimeter,” Opt. Lett. 32(12), 1707–1709 (2007). [CrossRef] [PubMed]
  17. T. R. Woliński, S. Ertman, A. Czapla, P. Lesiak, K. Nowecka, A. W. Domanski, E. Nowinowski-Kruszelnicki, R. Dabrowski, and J. Wójcik, “Polarization effects in photonic liquid crystal fibers,” Meas. Sci. Technol. 18(10), 3061–3069 (2007). [CrossRef]
  18. T. R. Woliński, A. Czapla, S. Ertman, M. Tefelska, A. W. Domański, E. Nowinowski-Kruszelnicki, and R. Dąbrowski, “Tunable highly birefringent solid-core photonic liquid crystal fibers,” Opt. Quantum Electron. 39(12-13), 1021–1032 (2007). [CrossRef]
  19. S. Ertman, A. Czapla, T. R. Woliński, T. Nasiłowski, H. Thienpont, E. Nowinowski-Kruszelnicki, and R. Dąbrowski, “Light propagation in highly birefringent photonic liquid crystal fibers,” Opto-Electronics Review 17(2), 150–155 (2009). [CrossRef]
  20. L. Wei, L. Eskildsen, J. Weirich, L. Scolari, T. T. Alkeskjold, and A. Bjarklev, “Continuously tunable all-in-fiber devices based on thermal and electrical control of negative dielectric anisotropy liquid crystal photonic bandgap fibers,” Appl. Opt. 48(3), 497–503 (2009). [CrossRef] [PubMed]
  21. C. Kerbage and B. Eggleton, “Numerical analysis and experimental design of tunable birefringence in microstructured optical fiber,” Opt. Express 10(5), 246–255 (2002). [PubMed]
  22. C. Zhang, G. Kai, Z. Wang, Y. Liu, T. Sun, S. Yuan, and X. Dong, “Tunable highly birefringent photonic bandgap fibers,” Opt. Lett. 30(20), 2703–2705 (2005). [CrossRef] [PubMed]
  23. D. C. Zografopoulos, E. E. Kriezis, and T. D. Tsiboukis, “Photonic crystal-liquid crystal fibers for single-polarization or high-birefringence guidance,” Opt. Express 14(2), 914–925 (2006). [CrossRef] [PubMed]
  24. J. Sun and C. C. Chan, “Effect of liquid crystal alignment on bandgap formation in photonic bandgap fibers,” Opt. Lett. 32(14), 1989–1991 (2007). [CrossRef] [PubMed]
  25. G. Tartarini, M. Pansera, T. Tanggaard Alkeskjold, A. Bjarklev, and P. Bassi,“Polarization Properties of Elliptical-Hole Liquid Crystal Photonic Bandgap Fibers,” J. Lightwave Technol. 25(9), 2522–2530 (2007). [CrossRef]
  26. G. Ren, P. Shum, J. Hu, X. Yu, and Y. Gong, “Polarization-Dependent Bandgap Splitting and Mode Guiding in Liquid Crystal Photonic Bandgap Fibers,” J. Lightwave Technol. 26(22), 3650–3659 (2008). [CrossRef]
  27. S. Ertman, T. Nasilowski, T. R. Wolinski, and H. Thienpont, “Highly birefringent microstructured fiber selectively filled with lossy material,” Photon. Lett. of Poland 1(1), 13–15 (2009).
  28. D. Lorenc, M. Aranyosiova, R. Buczyński, R. Stępień, I. Bugar, A. Vincze, and D. Velic, “Nonlinear refractive index of multicomponent glasses designed for fabrication of photonic crystal fibers,” Appl. Phys. B: Lasers Opt 93(2-3), 531–538 (2008). [CrossRef]
  29. J. Li and S. T. Wu, “Extended Cauchy equations for the refractive indices of liquid crystals,” J. Appl. Phys. 95(3), 896–901 (2004). [CrossRef]
  30. F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,” Opt. Fiber Technol. 6(2), 181–191 (2000). [CrossRef]
  31. S. Ertman, T. R. Woliński, A. Czapla, K. Nowecka, E. Nowinowski-Kruszelnicki, and J. Wójcik, “Liquid crystal molecular orientation in photonic liquid crystal fibers with photopolymer layers,” Proc. SPIE 6587, 658706 (2007). [CrossRef]

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