Abstract

Microstructured fibres which consist of a circular step index core and a liquid crystal inclusion running parallel to this core are investigated. The attenuation and electro-optic effects of light coupled into the core are measured. Coupled mode theory is used to study the interaction of core modes with the liquid crystal inclusion. The experimental and theoretical results show that these fibres can exhibit attenuation below 0.16 dB cm−1 in off-resonant wavelength regions and still have significant electro-optic effects which can lead to a polarisation extinction of 6 dB cm−1.

© 2014 Optical Society of America

1. Introduction

Microstructured fibres and especially photonic crystal fibres (PCFs) have found much attention over the last couple of years. While conventional optical fibres consist of a high index core and a low index cladding, where the light is confined inside the core by total internal reflection (TIR), the cladding of PCFs is formed by a periodic array of inclusions surrounded by glass [1] as shown in Figs. 1(a) and 1(b). The core of such fibres is formed by a defect in the array, which can take different forms. The core may be an inclusion with different optical or geometrical properties [Fig. 1(a)] than the inclusion in the array or a missing inclusion [Fig. 1(b)]. The guiding mechanism of PCFs is clearly different form conventional fibres as there is no uniform cladding surrounding the core. In general, two different types of guiding are defined: modified total internal reflection (mTIR) and photonic bandgap (PBG) guidance [1]. The former occurs if the refractive index of the core is higher than the refractive index of the inclusions, the latter if the refractive index of the core is lower than that of the inclusions.

 

Fig. 1 Schematic cross sections of microstructured fibres: (a) Hollow core PCF, (b) solid core and (c) fibre design discussed in this paper. Λdenotes the pitch in (a) and (b) and the center-center-distance in (c). dincl denotes the inclusion diameter in (a)- (c) and dcore the core diameter in (c). (d) Overview of the possible combinations of different types of PCFs and LCs and the resulting guiding principles.

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In the mTIR-approach, the PCF is modelled as a step index fibre with a circular core with its refractive index being equal to the surrounding glass. An effective refractive index for the cladding is introduced which is taken to be equal to the refractive index of the fundamental space filling mode of the infinite two dimensional array [2]. The guiding properties of the PCF can then be calculated with the standard methods for optical fibres. Accordingly, PCFs with the described guiding mechanism exhibit a high broadband transmission.

For PCFs with a low index core this approach fails. In this case, band diagrams of the period cladding are usually investigated for photonic bandgaps which can enable the guiding of light [3, 4]. Consequently, this principle is called photonic bandgap guiding. This usually leads to transmission windows as there may be wavelengths without adequate bandgaps. In the case of a solid core fibre as shown in Fig. 1(b), where the inclusions are of high index material like high index glasses or liquids, the dips in transmission can be traced back to coupling of the PCF core mode with leaky modes of the high index inclusions [4]. The leaky modes lead to photonic states in the cladding through which light can escape.

Extensive recent research on liquid crystal -filled photonic crystal fibres (LCPCFs) has enabled the development of tuneable fibre-integrated optical filters, which can be used for controlling the spectral distribution or state of polarization of the transmitted light and may be used for wavelength or polarization division multiplexing/demultiplexing concepts in optical data transmission [5]. Depending on the relative size of the refractive indices of the liquid crystal nLCand the glass nG, a broadband mTIR guiding or a frequency-selective PBG guiding mechanism may appear both in hollow core or solid core PCFs [Fig. 1(d)]. Hollow core fibres with a LC-filled core have the general disadvantage of high attenuation due to large light scattering by director fluctuations of the liquid crystal [6, 7]. The preferable solid core fibres made of standard materials (nLC>nG) show a frequency selective transmission (PBG guiding) thereby facilitating frequency selective switching, while solid core fibres comprising a liquid crystal with unusually small refractive indices or a glass with exceptionally high refractive index (nG>nLC) show large broadband transmission (mTIR guiding), which may be used for full polarization control [8].

The switching of LCPCFs, in general, is based on the change of the refractive index of the liquid crystal or the reorientation of the director inside the inclusions. This change can be caused by electric fields or change in temperature. The application of an external electric field perpendicular to the fibre axis forces the liquid crystal with positive dielectric anisotropy to orient along the electric field. This leads to strong birefringence in LCPCFs. Heating of the liquid crystal causes the ordinary and the extraordinary refractive index to approach each other due to the decreasing order parameter. The most drastic change occurs at the phase transition from the nematic to the isotropic phase. An overview of thermal or electric switching in various types of LCPCFs is given by Kitzerow in [9].

The scope of the present paper is contributing to the development of frequency selective filters with low attenuation based on liquid crystal-filled micro-structured fibres. For this purpose, a design is chosen which combines the advantages of a solid core showing a large refractive index (TIR guiding) with the opportunity of introducing addressable, frequency-selective coupling to a LC-filled inclusion [Fig. 1(c)]. This design features a single hollow inclusion running parallel to the core of a conventional step index fibre, consisting of silica cladding and a Ge-doped silica core, which can lead to significant effects if the inclusion is filled with liquids or solids. For example, the refractive index of a liquid introduced into this channel can be precisely measured [10].

In this work, we infiltrate these rather simple structured fibres with liquid crystals to achieve electrical addressability. In contrast to PCF designs [Figs. 1(a) and 1(b)], we expect a lower attenuation, because the fibre exhibits only one instead of many scattering LC inclusions. Even though these fibres appear to be very different from PCFs, they are expected to have similarities regarding the mechanism of loss and the electrooptic responses. The process of electrooptic switching should be comparable because in both cases the influence is determined by reorientation of the director inside the inclusion(s).

We investigate fibres with different specifications. They vary in core diameter dcore and inclusion diameter dincl as well as core-inclusion-distance Λ. These fibres are filled with three LCs with different birefringence (cf. appendix A): MLC2103, E7 and BL036. Section 2 provides a brief overview on finite element calculations which are used to find the modes of core and inclusion waveguides in isolation. These are then used in a coupled mode approach to study the interaction of core and inclusion modes. The experimental details including attenuation measurements and quantification of the electrootpic effects are given in section 3. Section 4 shows the experimental results for different combinations of liquid crystals and fibre types and the corresponding calculations. Finally, section 5 provides a discussion on the fibre properties and a comparison to LCPCFs. A brief conclusion is given at the end.

2. Theory

Theoretical modelling of the optical properties of the liquid crystal filled fibres is done by finite element method (FEM) assisted coupled mode theory (CMT). The modes of core and inclusion are simulated separately by FEM, which yields the electromagnetic fields and the propagation constants for the different modes of the waveguides in isolation. These are further processed by CMT to calculate the coupling coefficients and the overlap integrals from which approximate normal modes and the evolution of an arbitrary input intensity can be derived.

2.1 Finite element method

All finite element simulations have been carried out by commercially available FEM software, COMSOL Multiphysics. The core waveguide is treated as an isotropic step-index profile fibre. The refractive index of the silica cladding and the Ge-doped silica core (16 mole-% of Ge) can be obtained by using the Sellmeier equations with the appropriate constants which can be found in [11] and [12], respectively. The inclusion waveguide shares the same silica cladding but its guiding core is modelled as an anisotropic liquid crystal. The inclusion can be considered as a uniaxial waveguide with its slow axis oriented along the fibre axis. This assumption is justified if the liquid crystal is anchored planar to the walls of the inclusion. The losses due to thermal fluctuations of the liquid crystal are accounted for, separately (cf. section 2.3) This approximation is justified in our case as the losses are low, which means that the imaginary part of the effective refractive index is much smaller than the real part.

The obtained guided modes for core and inclusion (electromagnetic fields and propagation constants) are further processed by coupled mode theory. Additionally, the composite waveguide is simulated, which yields the exact normal modes of the composite structure. These can be compared to the approximated normal modes of CMT.

2.2 Coupled mode theory

The coupled mode theory formulated by Hardy and Streifer [13, 14], and refined by Chuang [15, 16] is used to calculate the coupling of the glass core with the liquid crystal inclusion when light launched into the glass core. This method provides an intuitive approach and gives quantitatively very good results. In order to achieve a high coupling, the propagation constants of the modes in core and inclusion have to match. Furthermore the symmetries of the modes have to be compatible as the overlap integrals are calculated. If high coupling occurs, power is transferred from the core to the inclusion where light is attenuated due to losses in liquid crystals (see below).

2.3 Scattering by liquid crystals

Liquid crystals are strong light scatterers which pose a problem for pure LC waveguides [17] and liquid crystal filled photonic crystal fibres [7]. The scattering is caused by thermal fluctuations of the director field, which affect the refractive index. According to de Gennes, the amplitudes of the fluctuations can be derived from the equipartition theorem [6]. Based on this approach, Hu and Whinnery [17] derived an approximate formula for the attenuation due to these fluctuations which can be described by an imaginary refractive index ni:

ni=kBT8Kλne2no2no21lg(e),
where kB is the Boltzmann constant, T the temperature, K the elastic constant in one-constant approximation, λ the wavelength and no and ne are the ordinary and extra ordinary refractive indices of the LC, respectively. As the order of ni is about 105  to 104, ni is small compared to the real part of the refractive index. The imaginary part of the dielectric tensor Imε is determined by
Imε=2nrni,
where nr is the real part of the refractive index. The imaginary part of propagation constant Im β for the guided mode inside the inclusion can be approximated for low ni [18, p. 381] by the relation
Im β=2πληni,
where η is the fraction of power guided inside the inclusion.

3. Experiment

Two different types of fibres were used in the investigations; their specifications are given in Table 1. Pieces with a length of about 12 cm were cut with a fibre cleaver and filled with a solution of the surfactant glymo (1% glymo in a 50/50 mixture of water and isopropanol) by applying a pressure gradient of approximately 1 bar. Glymo induces a planar anchoring of the liquid crystal on the inclusion walls. The filled fibres were dried at 110 °C for 24 h. Three different commercially available LCs (MLC2103, E7, BL036) have been used in our studies. Their refractive indices can be found in appendix A. The coated fibres were filled with the liquid crystals by heating the LC into the isotropic state and using again a pressure gradient of 1 bar. The filled fibres were cooled down slowly to room temperature over a period of several hours. The alignment was checked by means of polarizing microscopy.

Tables Icon

Table 1. Specifications of fibres I to II: Diameters of core dcoreand inclusion dincl and center-to-center distance of core and inclusion Λ of the fibres investigated in this paper.

In order to characterise the optical properties of the fibre, the attenuation and the electrooptic effect on the transmission were measured. Both measurements were performed using the setup depicted in Fig. 2. Light from a Xe-arc lamp travels through a grating monochromator and is then coupled into a single mode fibre (SMF) by a microscope objective (20x, NA = 0.17). The SMF is spliced to the sample fibre by use of UV-curable adhesive Norland Optical Adhesive NOA61. The outgoing light passes through a polariser and is detected by a photomultiplier in case of visible light and a GaInAs photo diode in the case of infrared (IR) radiation, respectively. The attenuation a in dB cm−1 has been determined by cut-back technique according to

a=10lg(I0 Is)1s ,
where I0 is the intensity at the shortest fibre length and Is the intensity after a fibre length of s. For electrooptic measurements, the fibres were sandwiched between two indium tin oxide (ITO) coated glasses [Fig. 2(b)]. The fibre was adjusted by hand in such way, that the axis connecting the center of core and inclusion lies parallel to the ITO plates within a few degrees. Voltages up to 1000 V were applied with a frequency of 1 kHz for quasi-static behaviour. To quantify the effects of electrooptical switching for a specific polarisation, a relative power per unit length (short: relative power) in dB cm−1
relative power= 10lg(PV=0V PV)1L 
is introduced, where PV=0V is the optical power measured for the off-state and PV the optical power with an applied voltage; L denotes the fibre length. Analogue to this, the polarization extinction per unit length (short: extinction) is defined by
extinction= 10lg(Ix Iy)1L 
In order to ensure that there is no influence of the splicing on the attenuation and the electrooptic measurements, both experiments were performed with the same fibre and same splice.

 

Fig. 2 (a) Schematics of the setup for measuring the attenuation and the electro-optic properties. (b) Image of the cell for electro-optic measurements. For further explanation see text.

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This has been realised by sandwiching only a part of the fibre (3 to 4 cm) between two indium tin oxide (ITO) coated glass substrates close to the cold splice, leaving 8 to 9 cm for performing attenuation measurements. After completing the attenuation measurement, the electrooptic measurement could be performed on the residual fibre which was completely sandwiched.

4. Results

As mentioned before, two types of fibres were investigated in this work. The specifications of the fibres lead to certain restrictions for the wavelength region these fibres can be used for. On the one hand, fibres of type I are viable only for the visible range as the core is about 1 µm which leads to poor confinement in the IR range. On the other hand, fibres of type II are restricted to the IR range as the modes are almost completely confined to the core in the visible range, leaving almost no possibility for interactions due to evanescent coupling. Consequently, the investigation is focussed on the visible range for fibres of type I and on the infrared range for fibres of type II.

4.1 Fibre I, liquid crystal MLC2103

The simplest case is given by fibre I filled with MLC2103. The low core diameter along with the small inclusion diameter and the low ordinary refractive index of the LC leads to both waveguides being single mode waveguides in isolation. Furthermore, the small core size restricts the waveguide to the visible wavelength range.

Figure 3(a) shows the measured attenuation spectrum (red line, □) which can be roughly divided in three different regions 1, 2 and 3, which are marked green. In region 1, the measured attenuation is low (about 0.1 dB cm−1). A maximum of attenuation of 1.3 dB cm−1 can be found at 610 nm in region 2. Finally, region 3 exhibits an attenuation of about 0.5 dB cm−1. The calculated attenuation [Fig. 3(a), black line, ∎] exhibits the same behaviour even though the width of the peak in region 2 is narrower.

 

Fig. 3 (a) Experimentally determined attenuation spectrum (red solid line, □) and the predicted attenuation by CMT (black line, ∎) of fibre I filled with MLC2103. The blue lines correspond to the effective refractive indices of core (▼) and inclusion (▲) HE11 modes calculated with FEM. (b) The three patterns show the calculated square of the transverse electric fields of the normal modes labelled in (a) (marked with green dashed lines). The Ge-doped core is on the left and the liquid crystal inclusion on the right side in each image.

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This behaviour can be understood by investigating the effective refractive indices neff of the modes of the isolated waveguides [Fig. 3(a), blue lines, ▼ ▲]. Region 1 is characterised by a distinct difference between the effective indices of core and inclusion. Therefore, light coupled into the core is efficiently guided with low attenuation. The crossing of the core and the inclusion effective index in region 2 coincides with the wavelength of highest attenuation. Here, the power transfer from the core to the inclusion is most efficient. The residual attenuation in region 3 is caused by the same effect because the effective refractive indices are still close even though they do not cross or touch. The increase in the calculated attenuation towards longer wavelengths is a result of the spreading of modal field which leads to a higher modal overlap.

The intensity patters of the normal modes are displayed in Fig. 3(b) for three different wavelengths in the regions 1, 2 and 3. In region 1, the corresponding normal mode almost exclusively consists of the core mode. At the maximum of attenuation 2 the normal mode has heavy contributions of both, the core and the inclusion waveguide modes. Finally, at 3, the normal mode is dominated by the core waveguide but still there are some contributions of the inclusion waveguide. It should be pointed out that there are no polarisation dependent effects observed because both waveguides only support the HE11 mode which is rotationally symmetric and twofold degenerate with orthogonal (almost linear) polarisations, therefore only modes of the same polarisation couple.

In contrast, the electrooptic experiments exhibit a significant difference for the two output polarisations [Fig. 4]. For the polarisation coinciding with the direction of the applied electric field, an increase in the relative power at about 600 nm is apparent while the orthogonal polarisation exhibits almost no change. This can be explained qualitatively as the applied voltage aligns the director along the field (y-axis). Consequently, the interaction of y-polarised light with the LC is described mostly by the extraordinary refractive index. This leads to a strong change of the waveguiding properties of the inclusion. In contrast, the x-polarised light is still mainly influenced by the ordinary refractive index of the LC. This is a very simple picture as there are effects on the x-polarisation as can be seen for wavelengths higher than 750 nm. The director field is not uniformly aligned along the electric field over the whole inclusion cross section because the liquid crystal is still aligned partially parallel to the walls due to the strong anchoring.

 

Fig. 4 Plot of the relative power for fibre I filled with MLC2103 for the x- (blue line, □) and the y-polarisation (orange line, ○) with an applied voltage of 500 V at 1 kHz. The inset in the upper left corner shows a schematic of the electrooptic cell with labelled axes and the direction of the applied electric field E.

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4.2. Fibre I, liquid crystal BL036

The use of a LC with higher refractive indices no and ne leads to the appearance of multiple modes in the inclusion which can couple with the fundamental core mode. In case of fibre I filled with BL036, this leads to coupling with the degenerate HE31 modes at about 510 nm and with the degenerate HE12 modes at 580 nm, respectively. The attenuation spectra are depicted in Fig. 5(a). As these higher order modes are no longer linear polarised and the intensity is not radial symmetric, they may couple differently with the degenerate HE11 modes of the core. Of the two degenerate HE31 modes, one couples to the x-polarised HE11 core mode and is therefore called HE31,x. However, this does not imply this mode is polarised along the x-axis. Analogous, the other HE31 mode couples to the y-polarised HE11 core mode and will be referred to as HE31,y. The coupling between the HE11,x and HE31,x is almost identical to the coupling of HE11,y and HE31,y.

 

Fig. 5 (a) The upper graph shows the effective refractive indices of the HE11 core mode (black) and the inclusion modes HE31 (magenta) and HE21 (green) for fibre I filled with BL036. The attenuation (solid) is plotted in the middle for the y-polarisation and at the bottom for the x-polarisation. The dashed curves in the latter two plots correspond to the attenuation determined by coupled mode theory. (b) The mode intensity patterns of the HE31 and HE21 modes at 500 nm, both are twofold degenerate. The arrows indicate the direction of the transversal electric field.

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However, this is drastically different for the HE21 inclusion modes. Again, each one of the degenerate HE21 only couples to one of the core modes. But the coupling of the y-polarised core mode with the HE21,y inclusion mode is very weak. This is clear from the normal mode patterns [Fig. 5(b)] as the intensity in direction of the core is low.

This is also confirmed by the electro-optic measurements shown in Fig. 6. For both polarisations, there is an increase in the relative optical power at 510 nm, which corresponds to the vanishing of the HE31,x and HE31,y modes. For the x-polarisation, an additional strong increase at 580 nm is observed which matches the position of the former HE12,x mode. It should be pointed out, that the disappearance of the modes coupling to the x-polarisation occurs due to the fact that these modes are influenced by the x- and the y-component of the refractive index of the liquid crystal. However, for both polarisations a decrease in intensity is measured for wavelengths higher than 600 nm. The y-polarised light is more strongly attenuated than the x-polarised which is emphasized by the polarisation extinction [Fig. 6 blue curve, ∎]; an extinction of over 4 dB cm−1 can be observed in the wavelength range from 650 to 750 nm. A possible explanation of this effect would be the appearance of new modes due to reorientation of the director inside the inclusion. These modes would be mainly y-polarised as the effective refractive index would be much larger than in the x-direction. In the extreme case of complete orientation of the director along the y-axis this can easily be confirmed by simulations.

 

Fig. 6 Plot of the relative power for fibre I filled with BL036 for the x- (green, ▲) and the y- polarisation (red, ▼) with an applied voltage of 500 V at 1 kHz. The blue curve (∎) shows the polarisation extinction at 500V.

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The electrooptic responses are shown in Fig. 7 for different voltages up to 500 V at 590 nm for x-polarised light. The switching times τon andτoff are determined by the time needed for a change in intensity from 10 to 90%. The fastest τon is reached at 500 V with τon=2.0ms which is of the same order for liquid crystal-filled photonic crystal fibres reported in the literature [19]. For the switching-off time values of about τ=3.5±0.2ms are achieved which is faster than reported for LCPCFs [19, 20] due to the small inclusion diameter [21].

 

Fig. 7 Switching behaviour (left on, right off) at 590 nm with different applied voltages at 1 kHz: 200 V (black), 300 V (red), 400 V (green), 500 V (blue). Switching on/off occurs at t=0. The experiment has been performed with x-polarized light.

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4.3. Fibre II, liquid crystals E7 & BL036

The larger core diameter of fibre II leads to better confinement of modes in the infrared. Unfortunately, the modes in the visible wavelength range are also better confined prohibiting efficient coupling. Consequently, these fibres show low attenuation (<0.1 dB cm1) but marginal electrooptic effects in the visible spectral range. Furthermore, if these fibres are filled with liquid crystal MLC2103, they show almost no effects, neither in regards to attenuation nor for electrooptic experiments, which makes them unfit for our studies.

While fibres filled with E7 and BL036 also exhibit marginal attenuation in the visible and near infrared, the spectra of the relative power shown in Fig. 8 show very distinct electrooptic effects. As is apparent from this figure, the characteristics are quite similar for both liquid crystals. This is a consequence of the refractive indices which are very much alike (cf. appendix A). Electrical addressing leads to a significant decrease in intensity over the broad range of 1100 nm to 1350 nm with up to 8 dB cm−1 change in transmission for the y-polarisation. The x-polarisation also shows a decrease in this range but with 2 dB cm−1 not quite as significant. It is the same effect already explained above for fibre I and leads to a polarisation extinction [Fig. 8, blue curve] of up to 6 dB cm−1 for fibre II filled with BL036.

 

Fig. 8 Plot of the relative optical power per unit length (green, ▲: y- polarisation, red, ▼: x-polarisation) and the polarisation extinction (blue, ∎) for fibre II filled with E7 (left) and BL036 (right) with an applied voltage of 500 V.

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The switching behaviour of fibres of type II filled with E7 is shown in Fig. 9 for different voltages at 1310 nm. The switching times are higher (τon=(5±1) ms, τoff=(6.8±0.5) ms) than for fibre I as would be expected due to the higher inclusion diameter [21].

 

Fig. 9 Switching behaviour of fibre II filled with E7 (left on, right off) at 1310 nm with different applied voltages at 1 kHz: 200 V (black), 300 V (red), 400 V (green), 500 V (blue). Switching on/off occurs at τ = 0. The experiment has been performed with y-polarized light.

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5. Discussion

Basically, the transmission of the discussed fibres is determined by the Ge-doped core and the silica cladding, i. e., a high transmission is expected, similar to conventional step index fibres. However, regions of high attenuation occur if the propagation constants of core and inclusion modes match, which leads to a power transfer of light coupled into the glass core to the inclusion waveguide where the light is scattered. Even though this mechanism is not equivalent to the loss of confinement in band gap fibres, both originate from interactions with the modes of the high index inclusion(s). In the case of PBG guiding the modes involved are leaky modes and not guided modes, though. The electrooptic switching speed is equal to or faster than comparable LCPCFs due to the small inclusion diameter.

The described design has several additional advantages. The guiding mechanism originates from total internal reflection which solely depends on the geometric and material properties of the core and the cladding. Consequently, these properties can be chosen independently of the design of the inclusion. This, however, is not true for PCFs because the guiding properties strongly depend on the pitch and the inclusion diameter due to the photonic band gap guiding [1]. This independence gives more degrees of freedom for designing fibres analogue to those presented in this paper. They can be adjusted to exhibit multiple (anti-)crossings of core and inclusions modes or none at all, depending on the intended application. Furthermore, the switching times are mainly determined by the inclusion diameter, as stated above. Finally, additional inclusions could be included to enhance optical effects. The resulting effects may correspond to selective filling of PCFs, where more elaborate techniques have to be applied [22].

6. Conclusion

We have shown that a liquid crystal inclusion running parallel to a conventional glass core of a step index optical fibre has a distinct effect on the transmission through the core and is electrically tuneable. The observed behaviour is a result of coupling of core and inclusion modes which can be treated by coupled mode theory. The two different fibres investigated here, one for the visible and one for the infrared region, show significant polarisation extinction of up to 6 dB cm−1 in broad wavelength regions. The attenuation of these fibres (0.16dBcm1) is clearly lower than frequency selective liquid crystal filled photonic crystal fibres (1dBcm1 [7],) and it is comparable to TIR guiding LCPCFs (0.19dBcm1 [8],). The switching times presented here with τon+toff<6 ms (fibre I/BL036) and τon+toff<12 ms (fibre II/E7) are faster than the switching speed observed in LCPCFs [7].

Appendix A. Liquid crystal properties

The refractive indices of the liquid crystals E7, BL036 and MLC2103 were measured with a Jelly type refractometer in a wavelength range of 450 to 750 nm. Extrapolation to the NIR was done by using a Cauchy fit of the form ne,o(λ)=ne,o0+Ae,oλ2+Be,oλ4.  The results for the coefficients for the ordinary and extraordinary refractive index are given in Table 2.

Tables Icon

Table 2. Coefficients for Cauchy fit of the refractive indices for the employed liquid crystals.

Acknowledgments

The authors are grateful to the German Research Foundation (GRK 1464) for support and would like to thank Philipp Russell and Markus Schmidt from the Max Planck Institute in Erlangen for providing the microstructured optical fibres.

References and links

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19. A. Lorenz, R. Schuhmann, and H. S. Kitzerow, “Switchable waveguiding in two liquid-crystal-filled photonic crystal fibers,” Appl. Opt. 49(20), 3846–3853 (2010). [CrossRef]   [PubMed]  

20. 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]  

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References

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  1. P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006).
    [Crossref]
  2. Z. Zhu and T. G. Brown, “Analysis of the space filling modes of photonic crystal fibers,” Opt. Express 8(10), 547–554 (2001).
    [Crossref] [PubMed]
  3. J. Pottage, D. Bird, T. Hedley, J. Knight, T. Birks, P. Russell, and P. Roberts, “Robust photonic band gaps for hollow core guidance in PCF made from high index glass,” Opt. Express 11(22), 2854–2861 (2003).
    [Crossref] [PubMed]
  4. T. A. Birks, G. J. Pearce, and D. M. Bird, “Approximate band structure calculation for photonic band gap fibres,” Opt. Express 14(20), 9483–9490 (2006).
    [Crossref] [PubMed]
  5. D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, and R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab Chip 12(19), 3598–3610 (2012).
    [Crossref] [PubMed]
  6. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, 1993).
  7. A. Lorenz, R. Schuhmann, and H. S. Kitzerow, “Infiltrated photonic crystal fiber: experiments and liquid crystal scattering model,” Opt. Express 18(4), 3519–3530 (2010).
    [Crossref] [PubMed]
  8. S. Ertman, T. R. Woliński, D. Pysz, R. Buczynski, E. Nowinowski-Kruszelnicki, and R. Dabrowski, “Low-loss propagation and continuously tunable birefringence in high-index photonic crystal fibers filled with nematic liquid crystals,” Opt. Express 17(21), 19298–19310 (2009).
    [Crossref] [PubMed]
  9. H.-S. Kitzerow, “Photonic micro-and nanostructures, metamaterials,” in Handbook of Liquid Crystals, J. W. Goodby, P. J. Collings, T. Kato, C. Tschierske, H. Gleeson, and P. Raynes, eds. (Wiley-VCH, 2014), Chap. 7.
  10. H. W. Lee, M. A. Schmidt, P. Uebel, H. Tyagi, N. Y. Joly, M. Scharrer, and P. S. Russell, “Optofluidic refractive-index sensor in step-index fiber with parallel hollow micro-channel,” Opt. Express 19(9), 8200–8207 (2011).
    [Crossref] [PubMed]
  11. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55(10), 1205–1209 (1965).
    [Crossref]
  12. O. Butov, K. Golant, A. Tomashuk, M. van Stralen, and A. Breuls, “Refractive index dispersion of doped silica for fiber optics,” Opt. Commun. 213(4-6), 301–308 (2002).
    [Crossref]
  13. A. Hardy and W. Streifer, “Coupled modes of multiwaveguide systems and phased arrays,” J. Lightwave Technol. 4(1), 90–99 (1986).
    [Crossref]
  14. A. Hardy and W. Streifer, “Coupled mode solutions of multiwaveguide systems,” IEEE J. Quantum Electron. 22(4), 528–534 (1986).
    [Crossref]
  15. S.-L. Chuang, “A coupled mode formulation by reciprocity and a variational principle,” J. Lightwave Technol. 5(1), 5–15 (1987).
    [Crossref]
  16. S.-L. Chuang, “A coupled-mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation,” J. Lightwave Technol. 5(1), 174–183 (1987).
    [Crossref]
  17. C. Hu and J. R. Whinnery, “Losses of a nematic liquid-crystal optical waveguide,” J. Opt. Soc. Am. 64(11), 1424–1432 (1974).
    [Crossref]
  18. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).
  19. A. Lorenz, R. Schuhmann, and H. S. Kitzerow, “Switchable waveguiding in two liquid-crystal-filled photonic crystal fibers,” Appl. Opt. 49(20), 3846–3853 (2010).
    [Crossref] [PubMed]
  20. 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]
  21. E. Jakeman and E. Raynes, “Electro-optic response times in liquid crystals,” Phys. Lett. A 39(1), 69–70 (1972).
    [Crossref]
  22. S.-M. Kuo, Y.-W. Huang, S.-M. Yeh, W.-H. Cheng, and C.-H. Lin, “Liquid crystal modified photonic crystal fiber (LC-PCF) fabricated with an un-cured SU-8 photoresist sealing technique for electrical flux measurement,” Opt. Express 19(19), 18372–18379 (2011).
    [Crossref] [PubMed]

2012 (1)

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, and R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab Chip 12(19), 3598–3610 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (2)

2009 (1)

2006 (2)

2005 (1)

2003 (1)

2002 (1)

O. Butov, K. Golant, A. Tomashuk, M. van Stralen, and A. Breuls, “Refractive index dispersion of doped silica for fiber optics,” Opt. Commun. 213(4-6), 301–308 (2002).
[Crossref]

2001 (1)

1987 (2)

S.-L. Chuang, “A coupled mode formulation by reciprocity and a variational principle,” J. Lightwave Technol. 5(1), 5–15 (1987).
[Crossref]

S.-L. Chuang, “A coupled-mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation,” J. Lightwave Technol. 5(1), 174–183 (1987).
[Crossref]

1986 (2)

A. Hardy and W. Streifer, “Coupled modes of multiwaveguide systems and phased arrays,” J. Lightwave Technol. 4(1), 90–99 (1986).
[Crossref]

A. Hardy and W. Streifer, “Coupled mode solutions of multiwaveguide systems,” IEEE J. Quantum Electron. 22(4), 528–534 (1986).
[Crossref]

1974 (1)

1972 (1)

E. Jakeman and E. Raynes, “Electro-optic response times in liquid crystals,” Phys. Lett. A 39(1), 69–70 (1972).
[Crossref]

1965 (1)

Alkeskjold, T.

Anawati, A.

Asquini, R.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, and R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab Chip 12(19), 3598–3610 (2012).
[Crossref] [PubMed]

Bassi, P.

Beccherelli, R.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, and R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab Chip 12(19), 3598–3610 (2012).
[Crossref] [PubMed]

Bird, D.

Bird, D. M.

Birks, T.

Birks, T. A.

Bjarklev, A.

Breuls, A.

O. Butov, K. Golant, A. Tomashuk, M. van Stralen, and A. Breuls, “Refractive index dispersion of doped silica for fiber optics,” Opt. Commun. 213(4-6), 301–308 (2002).
[Crossref]

Brown, T. G.

Buczynski, R.

Butov, O.

O. Butov, K. Golant, A. Tomashuk, M. van Stralen, and A. Breuls, “Refractive index dispersion of doped silica for fiber optics,” Opt. Commun. 213(4-6), 301–308 (2002).
[Crossref]

Cheng, W.-H.

Chuang, S.-L.

S.-L. Chuang, “A coupled mode formulation by reciprocity and a variational principle,” J. Lightwave Technol. 5(1), 5–15 (1987).
[Crossref]

S.-L. Chuang, “A coupled-mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation,” J. Lightwave Technol. 5(1), 174–183 (1987).
[Crossref]

d’Alessandro, A.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, and R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab Chip 12(19), 3598–3610 (2012).
[Crossref] [PubMed]

Dabrowski, R.

Ertman, S.

Golant, K.

O. Butov, K. Golant, A. Tomashuk, M. van Stralen, and A. Breuls, “Refractive index dispersion of doped silica for fiber optics,” Opt. Commun. 213(4-6), 301–308 (2002).
[Crossref]

Hardy, A.

A. Hardy and W. Streifer, “Coupled modes of multiwaveguide systems and phased arrays,” J. Lightwave Technol. 4(1), 90–99 (1986).
[Crossref]

A. Hardy and W. Streifer, “Coupled mode solutions of multiwaveguide systems,” IEEE J. Quantum Electron. 22(4), 528–534 (1986).
[Crossref]

Hedley, T.

Hermann, D.

Hu, C.

Huang, Y.-W.

Jakeman, E.

E. Jakeman and E. Raynes, “Electro-optic response times in liquid crystals,” Phys. Lett. A 39(1), 69–70 (1972).
[Crossref]

Joly, N. Y.

Kitzerow, H. S.

Knight, J.

Kriezis, E. E.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, and R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab Chip 12(19), 3598–3610 (2012).
[Crossref] [PubMed]

Kuo, S.-M.

Lee, H. W.

Lin, C.-H.

Lorenz, A.

Malitson, I. H.

Nielsen, M.

Nowinowski-Kruszelnicki, E.

Pearce, G. J.

Pottage, J.

Pysz, D.

Raynes, E.

E. Jakeman and E. Raynes, “Electro-optic response times in liquid crystals,” Phys. Lett. A 39(1), 69–70 (1972).
[Crossref]

Riishede, J.

Roberts, P.

Russell, P.

Russell, P. S.

Russell, P. St. J.

Scharrer, M.

Schmidt, M. A.

Schuhmann, R.

Scolari, L.

Streifer, W.

A. Hardy and W. Streifer, “Coupled mode solutions of multiwaveguide systems,” IEEE J. Quantum Electron. 22(4), 528–534 (1986).
[Crossref]

A. Hardy and W. Streifer, “Coupled modes of multiwaveguide systems and phased arrays,” J. Lightwave Technol. 4(1), 90–99 (1986).
[Crossref]

Tomashuk, A.

O. Butov, K. Golant, A. Tomashuk, M. van Stralen, and A. Breuls, “Refractive index dispersion of doped silica for fiber optics,” Opt. Commun. 213(4-6), 301–308 (2002).
[Crossref]

Tyagi, H.

Uebel, P.

van Stralen, M.

O. Butov, K. Golant, A. Tomashuk, M. van Stralen, and A. Breuls, “Refractive index dispersion of doped silica for fiber optics,” Opt. Commun. 213(4-6), 301–308 (2002).
[Crossref]

Whinnery, J. R.

Wolinski, T. R.

Yeh, S.-M.

Zhu, Z.

Zografopoulos, D. C.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, and R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab Chip 12(19), 3598–3610 (2012).
[Crossref] [PubMed]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

A. Hardy and W. Streifer, “Coupled mode solutions of multiwaveguide systems,” IEEE J. Quantum Electron. 22(4), 528–534 (1986).
[Crossref]

J. Lightwave Technol. (4)

S.-L. Chuang, “A coupled mode formulation by reciprocity and a variational principle,” J. Lightwave Technol. 5(1), 5–15 (1987).
[Crossref]

S.-L. Chuang, “A coupled-mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation,” J. Lightwave Technol. 5(1), 174–183 (1987).
[Crossref]

A. Hardy and W. Streifer, “Coupled modes of multiwaveguide systems and phased arrays,” J. Lightwave Technol. 4(1), 90–99 (1986).
[Crossref]

P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006).
[Crossref]

J. Opt. Soc. Am. (2)

Lab Chip (1)

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, and R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab Chip 12(19), 3598–3610 (2012).
[Crossref] [PubMed]

Opt. Commun. (1)

O. Butov, K. Golant, A. Tomashuk, M. van Stralen, and A. Breuls, “Refractive index dispersion of doped silica for fiber optics,” Opt. Commun. 213(4-6), 301–308 (2002).
[Crossref]

Opt. Express (8)

H. W. Lee, M. A. Schmidt, P. Uebel, H. Tyagi, N. Y. Joly, M. Scharrer, and P. S. Russell, “Optofluidic refractive-index sensor in step-index fiber with parallel hollow micro-channel,” Opt. Express 19(9), 8200–8207 (2011).
[Crossref] [PubMed]

A. Lorenz, R. Schuhmann, and H. S. Kitzerow, “Infiltrated photonic crystal fiber: experiments and liquid crystal scattering model,” Opt. Express 18(4), 3519–3530 (2010).
[Crossref] [PubMed]

S. Ertman, T. R. Woliński, D. Pysz, R. Buczynski, E. Nowinowski-Kruszelnicki, and R. Dabrowski, “Low-loss propagation and continuously tunable birefringence in high-index photonic crystal fibers filled with nematic liquid crystals,” Opt. Express 17(21), 19298–19310 (2009).
[Crossref] [PubMed]

Z. Zhu and T. G. Brown, “Analysis of the space filling modes of photonic crystal fibers,” Opt. Express 8(10), 547–554 (2001).
[Crossref] [PubMed]

J. Pottage, D. Bird, T. Hedley, J. Knight, T. Birks, P. Russell, and P. Roberts, “Robust photonic band gaps for hollow core guidance in PCF made from high index glass,” Opt. Express 11(22), 2854–2861 (2003).
[Crossref] [PubMed]

T. A. Birks, G. J. Pearce, and D. M. Bird, “Approximate band structure calculation for photonic band gap fibres,” Opt. Express 14(20), 9483–9490 (2006).
[Crossref] [PubMed]

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]

S.-M. Kuo, Y.-W. Huang, S.-M. Yeh, W.-H. Cheng, and C.-H. Lin, “Liquid crystal modified photonic crystal fiber (LC-PCF) fabricated with an un-cured SU-8 photoresist sealing technique for electrical flux measurement,” Opt. Express 19(19), 18372–18379 (2011).
[Crossref] [PubMed]

Phys. Lett. A (1)

E. Jakeman and E. Raynes, “Electro-optic response times in liquid crystals,” Phys. Lett. A 39(1), 69–70 (1972).
[Crossref]

Other (3)

H.-S. Kitzerow, “Photonic micro-and nanostructures, metamaterials,” in Handbook of Liquid Crystals, J. W. Goodby, P. J. Collings, T. Kato, C. Tschierske, H. Gleeson, and P. Raynes, eds. (Wiley-VCH, 2014), Chap. 7.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, 1993).

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

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Figures (9)

Fig. 1
Fig. 1 Schematic cross sections of microstructured fibres: (a) Hollow core PCF, (b) solid core and (c) fibre design discussed in this paper. Λ denotes the pitch in (a) and (b) and the center-center-distance in (c). d incl denotes the inclusion diameter in (a)- (c) and d core the core diameter in (c). (d) Overview of the possible combinations of different types of PCFs and LCs and the resulting guiding principles.
Fig. 2
Fig. 2 (a) Schematics of the setup for measuring the attenuation and the electro-optic properties. (b) Image of the cell for electro-optic measurements. For further explanation see text.
Fig. 3
Fig. 3 (a) Experimentally determined attenuation spectrum (red solid line, □) and the predicted attenuation by CMT (black line, ∎) of fibre I filled with MLC2103. The blue lines correspond to the effective refractive indices of core (▼) and inclusion (▲) HE11 modes calculated with FEM. (b) The three patterns show the calculated square of the transverse electric fields of the normal modes labelled in (a) (marked with green dashed lines). The Ge-doped core is on the left and the liquid crystal inclusion on the right side in each image.
Fig. 4
Fig. 4 Plot of the relative power for fibre I filled with MLC2103 for the x- (blue line, □) and the y-polarisation (orange line, ○) with an applied voltage of 500 V at 1 kHz. The inset in the upper left corner shows a schematic of the electrooptic cell with labelled axes and the direction of the applied electric field E.
Fig. 5
Fig. 5 (a) The upper graph shows the effective refractive indices of the HE11 core mode (black) and the inclusion modes HE31 (magenta) and HE21 (green) for fibre I filled with BL036. The attenuation (solid) is plotted in the middle for the y-polarisation and at the bottom for the x-polarisation. The dashed curves in the latter two plots correspond to the attenuation determined by coupled mode theory. (b) The mode intensity patterns of the HE31 and HE21 modes at 500 nm, both are twofold degenerate. The arrows indicate the direction of the transversal electric field.
Fig. 6
Fig. 6 Plot of the relative power for fibre I filled with BL036 for the x- (green, ▲) and the y- polarisation (red, ▼) with an applied voltage of 500 V at 1 kHz. The blue curve (∎) shows the polarisation extinction at 500V.
Fig. 7
Fig. 7 Switching behaviour (left on, right off) at 590 nm with different applied voltages at 1 kHz: 200 V (black), 300 V (red), 400 V (green), 500 V (blue). Switching on/off occurs at t=0 . The experiment has been performed with x-polarized light.
Fig. 8
Fig. 8 Plot of the relative optical power per unit length (green, ▲: y- polarisation, red, ▼: x-polarisation) and the polarisation extinction (blue, ∎) for fibre II filled with E7 (left) and BL036 (right) with an applied voltage of 500 V.
Fig. 9
Fig. 9 Switching behaviour of fibre II filled with E7 (left on, right off) at 1310 nm with different applied voltages at 1 kHz: 200 V (black), 300 V (red), 400 V (green), 500 V (blue). Switching on/off occurs at τ = 0 . The experiment has been performed with y-polarized light.

Tables (2)

Tables Icon

Table 1 Specifications of fibres I to II: Diameters of core d core and inclusion d incl and center-to-center distance of core and inclusion Λ of the fibres investigated in this paper.

Tables Icon

Table 2 Coefficients for Cauchy fit of the refractive indices for the employed liquid crystals.

Equations (6)

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

n i = k B T 8Kλ n e 2 n o 2 n o 2 1 lg(e) ,
Imε=2 n r n i ,
Im β= 2π λ η n i ,
a=10lg( I 0   I s ) 1 s  ,
relative power= 10lg( P V=0V   P V ) 1 L  
extinction= 10lg( I x   I y ) 1 L  

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