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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 23 — Nov. 10, 2008
  • pp: 19375–19381
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Photonic crystal fiber with a dual-frequency addressable liquid crystal: behavior in the visible wavelength range

A. Lorenz, H.-S. Kitzerow, A. Schwuchow, J. Kobelke, and H. Bartelt  »View Author Affiliations


Optics Express, Vol. 16, Issue 23, pp. 19375-19381 (2008)
http://dx.doi.org/10.1364/OE.16.019375


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Abstract

Wave-guiding in the visible spectral range is investigated for a micro-structured crystal fiber filled with a dual-frequency addressable nematic liquid crystal mixture. The fiber exhibits a solid core surrounded by just 4 rings of cylindrical holes. Control of the liquid crystal alignment by anchoring agents permits relatively low attenuation. Samples with different anchoring conditions at the interface of the silica glass and the liquid crystal show different transmission properties and switching behavior. Polarization dependent and independent fiber optic switching is observed. Due to a dual-frequency addressing scheme, active switching to both states with enhanced and reduced transmission becomes possible for planar anchoring. Even a non-perfect fiber shows reasonable transmission and a variety of interesting effects.

© 2008 Optical Society of America

1. Introduction

Photonic crystal fibers are characterized by a two dimensional holey microstructure and exhibit an extraordinary flexibility of fiber design. Thus, tailoring of the dispersion relation and efficient use of linear and nonlinear optical properties are possible [1

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

-2

2. A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibers (Kluwer Academic Publishers, Boston MA, 2003). [CrossRef]

]. These opportunities have lead to various developments, for example the fabrication of endlessly single mode fibers or the generation of supercontinuum spectra by pulsed light.

The conventional application of optical fibers for telecommunication uses infrared radiation because of low absorption losses of the applied glasses in this spectral range. However, the unique features of photonic crystal fibers make waveguide applications in the visible wavelength range very attractive. In hollow core fibers, for example, the light is guided in air so that absorption losses by the glass become less important. In addition, the high optical nonlinearity, group velocity dispersion or sensibility to external control parameters make photonic crystal fibers suitable for frequency conversion or intensity modulation, thereby enabling active fiber optical devices with limited length, where absorption is negligible.

Liquid crystals are particularly suitable for actively tunable devices, because their optical properties are very sensitive to temperature and electric or magnetic fields. Therefore, the responses to ambient changes can be utilized to fabricate sensors or tunable optic devices with liquid crystals. At visible wavelengths, the tuning possibilities of nematic liquid crystals are very pronounced because their birefringence is larger than in the infrared region. Electrically addressable optical switches and systems with temperature response have already been demonstrated using liquid crystal filled photonic crystal fibers with emphasis on the infrared spectral region [3

3. L. Scolari, T. T. Alkeskjold, J. Riishede, and A. Bjarklev, “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

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]

]. Scolari et al. [3

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

] have investigated a fiber with a dual-frequency addressable (DFA) liquid crystal. In DFA liquid crystals [9

9. H. K. Bücher, R. T. Klingbiel, and J. P. VanMeter: “Frequency-addressed liquid crystal field effect,” Appl. Phys. Lett. 25, 186–188 (1974). [CrossRef]

-10

10. M. Schadt, “Low-Frequency Dielectric Relaxations in Nematics and Dual-Frequency Addressing of Field Effects,” Mol. Cryst. Liq. Cryst. 89, 77–92 (1982). [CrossRef]

], the preferred molecular alignment can be actively aligned by an external a. c. electric field either along the field direction or perpendicular to the field direction, depending on the a. c. frequency. Consequently, advanced tuning possibilities in the infrared spectral region could be demonstrated [3

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

]. However, for visible wavelengths, detailed investigations are still needed.

This paper presents experimental results in the visible wavelength range using a photonic crystal fiber drawn from fused silica and a DFA liquid crystal. As response to electric fields, liquid crystal filled photonic crystal fibers can show switching capabilities due to the shifting of transmission bands. In addition, an increase of the transmission at constant shape of the transmission spectrum by applying an electric field with high frequency to a DFA liquid crystal is reported in the present paper. Using perpendicular and planar anchoring conditions at the interfaces between the liquid crystal and the silica glass, different types of alignments inside the holey structure of the fibers are generated. Without the use of anchoring agents, almost no transmission could be detected for visible light. However, using lecithin or 3-glycidoxypropyltrimethoxysilane as anchoring agents leads to reasonable transmission. Tunable waveguides in the visible wavelength region, of the type reported in this paper, are highly interesting e. g. as tunable spectral filters in lab on a chip systems or as sensors with response to electrical fields or temperature changes. If white light is coupled into the fibers, appropriate electric fields change the chromaticity of the output light, for example from white to red and then to green with rising field strength. In addition, tunable filters with polarizing properties and optical broad band switches for the visible spectral region are possible. Respective devices can be combined with white light sources, like supercontinuum sources, or monochromatic sources (visible lasers) and may be integrated in fiber optic systems.

2. Experiments

2.1 Physical properties of the starting materials

By applying electric fields to liquid crystals, their optical axis can be aligned either parallel or perpendicular to the field direction, if the dielectric anisotropy Δε is positive or negative, respectively. For DFA liquid crystals, the sign of Δε depends on the frequency of the a. c. fields. This peculiar behavior is due to the anisotropy of orientational polarization. For liquid crystals consisting of rod-like molecules, the relaxation frequency fc for rotation around axes perpendicular to the long axes of the molecules is smaller than the relaxation frequency for rotation around the molecular axis. If the liquid crystal exhibits sufficiently large components of the permanent dipole moment both parallel and perpendicular to the molecular axes, the dielectric anisotropy Δε as a function of frequency f may change the sign at ffc. If so, the orientation can be actively realigned in either direction by choosing the frequency appropriately. In this study, the DFA liquid crystal mixture ZLI 2461 from Merck was used. ZLI 2461 exhibits positive dielectric anisotropy below the critical frequency fc (≈ 6 kHz) and negative dielectric anisotropy for f > fc.

The photonic crystal fiber is drawn from fused silica and exhibits a solid core surrounded by a two dimensional hexagonal lattice of air holes. The fiber used for the experiments is shown in Fig. 1 (core diameter 11.3 µm, hole diameter d=5.4 µm, spacing Λ=6.7 µm). The bare fiber shows (like conventional optical fibers) a continuous transmission in the spectral region where fused silica is transparent. Light coupled into the core-region can be expected to be guided, because the average effective refractive index of the holey cladding is lower than the refractive index of the core (nsilica ≈ 1.45).

Fig. 1. End face of a photonic crystal fiber (microscopic picture, 100x objective) and attenuation spectrum of the fiber, when filled with air.

2.2 Sample preparation

In order to make use of the anisotropic properties of liquid crystals, it is essential to achieve a well-defined alignment. For this purpose, the inner surfaces of the holey region were coated with 3-glycidoxypropyltrimethoxysilane or lecithin, in order to promote alignment of LC molecules parallel or perpendicular to the surface, respectively. These treatments are known to generate a uniform parallel molecular alignment in liquid crystal-filled capillaries for 3-glycidoxypropyltrimethoxysilane and more complicated radial or escaped radial structures for lecithin. Subsequent to the surface treatment, the holey fibers were filled with the liquid crystal, making use of the capillary forces. For completeness, also fibers with untreated surfaces were studied.

For electric field studies, the fiber samples (length ≈ 20 mm) were sandwiched between two ITO-coated glass-plates (Fig. 2). External fields were applied along the y-direction.

Light was coupled into the sample fibers by using a face to face coupling with a standard telecommunication fiber. This light delivery fiber exhibits a core diameter of 9 µm (slightly smaller than the core diameter of the sample fiber) which allows matching the two cores quite exactly by using an XYZ-positioning stage. Under these conditions, the light is predominantly injected into the core region of the sample fibers. Near field investigations of the free fiber end faces confirmed that the light was confined to the core region. When properly matching the cores of the coupled fibers, a bright region at the end face appeared that was limited to the core, while the cladding regions appeared dark. The light coming from the free end faces of the sample fibers was collected with a microscope equipped with a grating CCD-spectrometer with an appropriate slit.

Fig. 2. Cartoon of a photonic crystal fiber sandwiched between two ITO-coated glass plates with contact electrodes. The fiber is surrounded by transparent glue.

3. Results

Filling the fibers with ZLI 2461 (ordinary refractive index no=1.4920 at λ=589 nm, extraordinary refractive index ne=1.6220 at λ=589 nm) changes the transmission spectra to a band-like appearance. Note that the core is now surrounded by an array of cylindrical inclusions with higher refractive index in a background with lower refractive index. According to the ARROW model [11

11. N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. M. de Sterke, “Resonances in microstructured optical waveguides,” Opt. Express 11, 1243–1251 (2003). [CrossRef] [PubMed]

], such arrays of high index cylindrical inclusions exhibit antiresonant reflective guided modes (confined to the core region) and leaky modes. The latter are not confined to the core region and thus not guided. The scattering properties of the single high index rods determine the spectral transmission characteristics of the structure rather than their position and number [12

12. T. P. White, R. C. McPhedran, C. M. de Sterke, N. M. Litchinitser, and B. J. Eggelton, “Resonance and Scattering in microstructured optical fibers,” Opt. Lett. 27, 1977–1979 (2002). [CrossRef]

]. The core of the fiber shown in Fig. 1 is surrounded by two rings of holes which have constant diameters. The outer rings exhibit regularly differing hole sizes. When filled with high index material, especially the first ring determines the transmission characteristics [12

12. T. P. White, R. C. McPhedran, C. M. de Sterke, N. M. Litchinitser, and B. J. Eggelton, “Resonance and Scattering in microstructured optical fibers,” Opt. Lett. 27, 1977–1979 (2002). [CrossRef]

-13

13. H. Bartelt, J. Kirchhof, J. Kobelke, K. Schuster, A. Schwuchow, K. Mörl, U. Röpke, J. Leppert, H. Lehmann, S. Smolka, M. Barth, O. Benson, T. Taccheo, and C. D’Andrea: “Preparation and application of functionalized photonic crystal fibres,” Phys. Status Solidi A 204, 3805–3821 (2007) [CrossRef]

] of the fiber (transmission minima, basic shape of the spectra) while the outer rings help to decrease the confinement loss and influence the shape of the spectra only weakly. Therefore, the fiber shown in Fig. 1 is converted into a tunable waveguide with discrete transmission bands when filled with liquid crystals.

The choice of the liquid crystal material as well as the choice of the anchoring condition at the glass interface determine the transmission properties. The influence of the anchoring agents is in particular essential for the experiments performed in this work. Most of the samples without defined anchoring are hardly waveguides at all, whereas samples with well-defined anchoring show reasonable transmission and different tuning possibilities varying with the type of anchoring. Polarizing microscopy using a monochromatic light source [14

14. G. P. Crawford, J. A. Mitcheltree, E. P. Boyko, W. Fritz, S. Zumer, and J. W. Doane, “K33/K11 determination in nematic liquid crystals: An optical birefringence technique,” Appl. Phys. Lett. 60, 3226–3228 (1992). [CrossRef]

] was applied in order to get an impression on the quality and homogeneity of the anchoring. For this purpose, capillaries with diameters in the range of 40 to 80 µm were treated with lecithin and 3-glycidoxypropyltrimethoxysilane, and subsequently filled with ZLI 2461. Microscopic observations indicate undisturbed alignments. Lecithin was identified to lead to homeotropic anchoring corresponding to an escaped radial director field and 3-glycidoxypropyltrimethoxysilane was identified to lead to a parallel director field.

3.1 Planar anchoring

In the field-off state, the sample shows reasonable transmission. The transmission is enhanced by external fields with f > fc, while the shape of the transmission spectra does essentially not change. Figure 3 shows selected switching possibilities for the transmission of white light. When switching from the field-off state to 380 Vrms for f=10 kHz, the transmission is actively enhanced. The switching time constant is τ1 ≈ 20 ms. When switching off, the transmission passively decreases again with a time constant τ 2 ≈ 80 ms. Switching on 380 Vrms for f=1 kHz reduces the transmission relatively fast, τ 3 ≈ 15 ms. When switching off the 1 kHz field, the transmission first gets a little lower and then grows again, slowly (τ 4 > 160 ms, see Fig. 3(a)). This reappearence of the transmission can be fastened using an a. c. field of high frequency, which obviously enforces the director field to realign to a state of enhanced transmission. When permanently applying 380 Vrms with f=10 kHz and periodically adding a second signal with 380 Vrms and f=1 kHz (Fig. 3(b)), a smaller time constant (τ 5 ≈ 70 ms) is achieved for this transition, while the switching speed for the (low frequency field-induced) transmission decay is reduced. This classical DFA driving scheme [9

9. H. K. Bücher, R. T. Klingbiel, and J. P. VanMeter: “Frequency-addressed liquid crystal field effect,” Appl. Phys. Lett. 25, 186–188 (1974). [CrossRef]

-10

10. M. Schadt, “Low-Frequency Dielectric Relaxations in Nematics and Dual-Frequency Addressing of Field Effects,” Mol. Cryst. Liq. Cryst. 89, 77–92 (1982). [CrossRef]

], where the high frequency is permanently applied to stabilize one particular state of the liquid crystal cell, demonstrates the typical switching behavior of DFA liquid crystals for white light transmission: The switching contrast is enhanced.

Fig. 3. Transmitted white light intensity versus time (fiber shown as inset in Fig. 1, with ZLI 2461 and planar anchoring).

In addition to changes of the total intensity, fibers with planar anchoring exhibit polarizing capabilities. When coupling white light to a fiber sample, optical near field analysis at the fiber end-face reveals a sudden decrease in the transmission of y-polarized light when external alternating voltages at f=1 kHz above a threshold voltage (≈ 140 V) are applied. The x-polarized part of the optical power gradually decreases with increasing voltage (Fig. 4). The color of the output light changes from white (field-off state) to red (240 Vrms) and then to green (290 Vrms). At 240 Vrms, the contrast of x- and y-polarized light is ≈ 8 dB. The spectra of the transmitted polarized light (Fig. 5) indicate fundamental changes of the transmission properties. The recorded spectrum for E=0 V/m in Fig. 5 could hardly be attributed to bandgap guidance as it seems to follow the source spectrum (broadband transmission), but distinct transmission bands appear above a critical field. At higher field strengths, the band edges in the red spectral region (and in particular the sharp edge around 700 nm) shift to shorter wavelengths with increasing voltage. The spectral distribution observed at f > fc is almost equal to the spectrum of the field-off state. For the field-off state a “broadband transmission” is observed and only with applied fields the band-like appearance of the spectra is generated.

It should be noticed, that by switching from the field-off state to f > fc, the response is polarization independent while switching from the field-off state to f < fc leads to polarization dependent signals. Thus, this device could be applied as an electrical addressable fiber-optical polarizer with well adjustable wavelengths, as an intensity modulator or as a color filter.

Fig. 4. Fiber with planar anchoring: Linearly polarized components of the transmitted white light intensity versus voltage (×: x-polarized, ∇: y-polarized). The insets show near field pictures at 240 Vrms for different polarizations.
Fig. 5. Light source spectrum (×, right scale) and transmitted intensity spectra (left scale) for 0, 144 and 216 Vrms (f=1 kHz) observed for planar anchoring. The spectra were recorded with an ORIEL 77400 CCD grating spectrometer and with a polarizer in x-direction.

3.2 Homeotropic anchoring

The transmission spectra of samples with homeotropic anchoring differ considerably from samples with parallel anchoring. The characteristic sharp edge at λ ≈ 700 nm, seen in the spectra for planar anchoring, is not found for homeotropic anchoring. With increasing voltage, the transmission bands shift to larger wavelength with homeotropic anchoring (Fig. 6), in contrast to the shifting to shorter wavelengths found in samples with parallel anchoring (Fig. 5). The color of the output light changes from yellow (field-off state) to green (192 Vrms and higher voltages). The samples with homeotropic anchoring do not show polarizing capabilities, at least for field strengths up to 300 Vrms.

Fig. 6. Transmitted light intensity spectra for homeotropic anchoring (fiber shown as inset in Fig. 1, filled with ZLI 2461) for 0, 192 and 288 Vrms (f=1 kHz).

4. Conclusions

The influence of the alignment layer on the transmission spectra and their changes with increasing voltage is remarkable. For positive dielectric anisotropy (f < fc), the transmission bands appearing at high field strength are blue-shifted with increasing voltage for planar anchoring and red-shifted for perpendicular anchoring. Detailed theoretical calculations based on a finite element algorithm are currently being performed to understand the complex behavior of the DFA samples in more detail.

Acknowledgments

The authors would like to thank the German Research Foundation (KI 411/4, GRK 1464) for financial support and the company E. Merck (Darmstadt) for the support with liquid crystals.

References and links

1.

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

2.

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibers (Kluwer Academic Publishers, Boston MA, 2003). [CrossRef]

3.

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

4.

F. M. Cox, A. Argyros, and M. C. J. Large, “Liquid-filled hollow core microstructured polymer optical fiber,” Opt. Express 14, 4135–4140 (2006). [CrossRef] [PubMed]

5.

T. T. Alkeskjold, J. Lægsgaard, A. Bjarklev, D. S. Hermann, J. Broeng, J. Li, S. Gauza, and S.-T. Wu, “Highly tunable large-core single-mode liquid-crystal photonic bandgap fiber,” Appl. Opt. 45, 2261–2264 (2006). [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.

H. Matthias, A. Lorenz, and H.-S. Kitzerow, “Tuneable photonic crystals obtained by liquid crystal infiltration,” Phys. Status Solidi A 11, 3754–3767 (2007).

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.

H. K. Bücher, R. T. Klingbiel, and J. P. VanMeter: “Frequency-addressed liquid crystal field effect,” Appl. Phys. Lett. 25, 186–188 (1974). [CrossRef]

10.

M. Schadt, “Low-Frequency Dielectric Relaxations in Nematics and Dual-Frequency Addressing of Field Effects,” Mol. Cryst. Liq. Cryst. 89, 77–92 (1982). [CrossRef]

11.

N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. M. de Sterke, “Resonances in microstructured optical waveguides,” Opt. Express 11, 1243–1251 (2003). [CrossRef] [PubMed]

12.

T. P. White, R. C. McPhedran, C. M. de Sterke, N. M. Litchinitser, and B. J. Eggelton, “Resonance and Scattering in microstructured optical fibers,” Opt. Lett. 27, 1977–1979 (2002). [CrossRef]

13.

H. Bartelt, J. Kirchhof, J. Kobelke, K. Schuster, A. Schwuchow, K. Mörl, U. Röpke, J. Leppert, H. Lehmann, S. Smolka, M. Barth, O. Benson, T. Taccheo, and C. D’Andrea: “Preparation and application of functionalized photonic crystal fibres,” Phys. Status Solidi A 204, 3805–3821 (2007) [CrossRef]

14.

G. P. Crawford, J. A. Mitcheltree, E. P. Boyko, W. Fritz, S. Zumer, and J. W. Doane, “K33/K11 determination in nematic liquid crystals: An optical birefringence technique,” Appl. Phys. Lett. 60, 3226–3228 (1992). [CrossRef]

15.

S. Kralj and S. Žumer, “The stability diagram of a nematic liquid crystal confined to a cylindrical cavity,” Liq. Cryst. 15, 521–527 (1993). [CrossRef]

OCIS Codes
(160.3710) Materials : Liquid crystals
(230.3990) Optical devices : Micro-optical devices
(230.7370) Optical devices : Waveguides
(260.1440) Physical optics : Birefringence
(060.5295) Fiber optics and optical communications : Photonic crystal fibers

ToC Category:
Photonic Crystal Fibers

History
Original Manuscript: September 12, 2008
Revised Manuscript: October 13, 2008
Manuscript Accepted: October 14, 2008
Published: November 7, 2008

Citation
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, 19375-19381 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-23-19375


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References

  1. P. St. J. Russell, "Photonic Crystal Fibers," J. Lightwave Technol. 24, 4729-4749 (2006). [CrossRef]
  2. A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibers (Kluwer Academic Publishers, Boston MA, 2003). [CrossRef]
  3. L. Scolari, T. T. Alkeskjold, J. Riishede, and A. Bjarklev, "Continuously tunable devices based on electrical control of dual-frequency liquid crystal filled photonic bandgap fibers," Opt. Express 13, 7483-7496 (2005). [CrossRef] [PubMed]
  4. F. M. Cox, A. Argyros, and M. C. J. Large, "Liquid-filled hollow core microstructured polymer optical fiber," Opt. Express 14, 4135-4140 (2006). [CrossRef] [PubMed]
  5. T. T. Alkeskjold, J. Lægsgaard, A. Bjarklev, D. S. Hermann, J. Broeng, J. Li, S. Gauza, and S.-T. Wu, "Highly tunable large-core single-mode liquid-crystal photonic bandgap fiber," Appl. Opt. 45, 2261-2264 (2006). [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. H. Matthias, A. Lorenz, and H.-S. Kitzerow, "Tuneable photonic crystals obtained by liquid crystal infiltration," Phys. Status Solidi A 11, 3754-3767 (2007).
  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. H. K. Bücher, R. T. Klingbiel, and J. P. VanMeter: "Frequency-addressed liquid crystal field effect," Appl. Phys. Lett. 25, 186-188 (1974). [CrossRef]
  10. M. Schadt, "Low-Frequency Dielectric Relaxations in Nematics and Dual-Frequency Addressing of Field Effects," Mol. Cryst. Liq. Cryst. 89, 77-92 (1982). [CrossRef]
  11. N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. M. de Sterke, "Resonances in microstructured optical waveguides," Opt. Express 11, 1243-1251 (2003). [CrossRef] [PubMed]
  12. T. P. White, R. C. McPhedran, C. M. de Sterke, N. M. Litchinitser, and B. J. Eggelton, "Resonance and Scattering in microstructured optical fibers," Opt. Lett. 27, 1977-1979 (2002). [CrossRef]
  13. H. Bartelt, J. Kirchhof, J. Kobelke, K. Schuster, A. Schwuchow, K. Mörl, U. Röpke, J. Leppert, H. Lehmann, S. Smolka, M. Barth, O. Benson, T. Taccheo, and C. D’Andrea: "Preparation and application of functionalized photonic crystal fibres," Phys. Status Solidi A 204, 3805-3821 (2007). [CrossRef]
  14. G. P. Crawford, J. A. Mitcheltree, E. P. Boyko, W. Fritz, S. Zumer, and J. W. Doane, "K33/K11 determination in nematic liquid crystals: An optical birefringence technique," Appl. Phys. Lett. 60, 3226-3228 (1992). [CrossRef]
  15. S. Kralj and S. Žumer, "The stability diagram of a nematic liquid crystal confined to a cylindrical cavity," Liq. Cryst. 15, 521-527 (1993). [CrossRef]

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