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We present an electrically controlled photonic bandgap fiber device obtained by infiltrating the air holes of a photonic crystal fiber (PCF) with a dual-frequency liquid crystal (LC) with pre-tilted molecules. Compared to previously demonstrated devices of this kind, the main new feature of this one is its continuous tunability due to the fact that the used LC does not exhibit reverse tilt domain defects and threshold effects. Furthermore, the dual-frequency features of the LC enables electrical control of the spectral position of the bandgaps towards both shorter and longer wavelengths in the same device. We investigate the dynamics of this device and demonstrate a birefringence controller based on this principle.
©2005 Optical Society of America
1. Introduction
Photonic crystals (PCs) have been used since their appearance to realize many devices suitable for effective control of electromagnetic radiation through proper tailoring of their periodic characteristics in one or more dimensions. Photonic crystal fibers (PCFs) belong to this category of devices, as they exhibit a microstructured refractive index profile in the fiber cross section, which allows light guidance by the so-called modified Total Internal Reflection (m-TIR) or by the photonic bandgap (PBG) effect [1,2]. Many devices have then been demonstrated, ranging from dispersion controllers to fiber lasers and non-linear devices. It has also been proposed to modify the optical properties of PCFs by filling the air holes with polymers [3], high index fluids [4] or liquid crystals (LCs) [5,6,7,8] and use the properties of these materials to obtain tunability. This was achieved taking advantage of the thermo-optic effect in the infused materials to induce index changes either using external heaters [3,4,5] or the absorption of a guided pump beam in dye-doped LCs [6]. The exploitation of the thermo-optic effect allows thermally actuated devices to be continuously tuned, except at phase transition in the LC devices, which can yield threshold-like response [5]. Electrical control of a LC filled PCF (LCPCF) has also been proposed and demonstrated [7,8]. In particular, in [7], the presence of a planar aligned nematic LC in the PCF transformed the fiber from a m-TIR to a PBG fiber type. The LCPCF was placed between two electrodes. When an electrical field was applied, the LC reoriented accordingly to the field, which induced a change in the refractive index of the LC. This device was able to operate as an optical switch, with rise and decay times of 5 and 52 ms, respectively. However, the device did not allow continuous control of the spectral position of the bandgaps because of an electric field threshold effect, the so called Frederiks transition, and reverse tilt domain defects in the LC, both of them due to the planar alignment of the LC. Figure 1 illustrates the formation of a reverse tilt domain defect in a planar aligned LC when an electric field is applied to such a LC. Due to thermal fluctuations of the direction of the optic axis (the so called director) out of the horizontal position, the director can tilt in two different directions when an electric field is applied to the LC, causing orientational defects at the border between two reverse tilt domains. Such defects cause a change in the refractive index compared to the surrounding LC which introduces loss.
In this paper we present an electrically tunable LCPCF device which does not suffer from these problems. This device is based on a dual frequency LC with pre-tilted molecules, i.e. non-planar alignment. We will show that such a LC does not suffer from reverse tilt domain defects and threshold effects thus allowing continuously tunable spectral positioning of the bandgaps. In the next section we will present a numerical investigation of the electric field distribution in a LCPCF. Then we will illustrate (section 3) the characteristics of the LC used in the experiments. In section 4 experimental results will show that the frequency dependent behavior of the chosen LC enables electrically controlled and continuous shifting of the bandgaps towards shorter and longer wavelengths depending on the frequency of the applied voltage. We will investigate the dynamics of the device and experimentally demonstrate a birefringence controller with response times in the millisecond range.
Fig. 1. Formation of a defect in a planar aligned nematic LC caused by the presence of a reverse tilt domain.
2. Numerical investigation on the electric field distribution
The fiber used in the experiment is a LMA-15, a ‘Large Mode Area’ PCF, by Crystal Fibre A/S, which is an all-silica PCF with a solid core surrounded by 5 rings of air holes arranged in a triangular lattice. The diameter L is 125 μm, the hole size d is 5 μm and the inter-hole distance Λ is 10 μm. This fiber is illustrated in Fig. 2. To analyze the strength and the distribution of the electric field in such a complex structure, numerical tools must be applied. A simulation software running in Matlab has been developed, which solves the equation ∇∙D = ε(x,y) E = 0 using an iterative finite difference technique. Here D is the dielectric displacement, E is the electric field and ε(x,y) is the dielectric permittivity profile. In the experiments described in the following, the electrodes are about 2 cm wide. In the numerical model, to reduce CPU time and memory requirements, the width of the electrodes was reduced to 1.5 times the diameter of the fiber, as shown in Fig. 2. This was enough to avoid that electrode edge effects could influence the field within the fiber. A further reduction in the model size was obtained taking advantage of the horizontal and vertical fiber symmetry. This allowed to study only one-quarter of this structure. The used mesh was of 900 × 600 points, with a grid size of 208 nm in both directions. As simulations have shown that the x-component of the field is negligible compared to the y-one, the results presented in the following will therefore refer only to the y-component.
Fig. 2. Cross section of a triangular PCF filled with LC and placed between two electrodes. The most important parameters of a LC filled PCF used in the following are illustrated as well: hole size (d), inter-hole distance (Λ), diameter of the fiber (L), relative dielectric permittivity of the LC (εLC) and relative dielectric permittivity of the material surrounding the fiber (εB).
The effect of the value of the relative dielectric constant εB of the material surrounding the fiber was investigated first. The electrical field distribution across the fiber section depends on the uniformity of different dielectric materials between the electrodes. Simulations have shown that the optimal condition for uniformity occurs when the index of the external material equals a weighted average index calculated considering both fiber geometry and material characteristics. Figure 3 shows, for example, a plot of the calculated electric field within the PCF when εLC = 10.6 and εB of the insulating oil is chosen to be equal to that of the fiber cladding. The field is almost constant outside the fiber while it varies in the fiber region. To quantitatively characterize the field changes in the holes, we evaluated first the average field in each hole. Then we calculated the overall average value Eavg of these average fields in all the fiber rings. The deviation in each ring is defined as 100∙|Eextremal - Eavg| / Eavg, where Eextremal is either the minimum or the maximum value of the fields calculated in the holes of that ring. Figures 4 and 5 show, respectively, the field average values and the relevant field deviations, as a function of the dielectric constant around the fiber. The examples refer to particular dielectrics available in the laboratory (air, oil with εB = 2.5 and oil with εB = 3.91). One can see that the average electric field in the holes increases and, at the same time, its uniformity among the holes improves if an insulating oil with a relative dielectric permittivity εB = 3.91 is placed between the electrodes. Some further tests showed also that fiber orientation did not introduce significant changes in these results.
Fig. 3. Example of simulated E-field distribution normalized to V/L, field in the homogeneous structure. The PCF parameters are: d = 5 μm, A =10 μm, L = 125 μm, εLC = 10.6, εB = 3.91.
Fig. 4. Example of normalized average value of the electric field in the rings as a function of the relative dielectric permittivity of the background material. The inset shows how the rings are defined and labeled. The PCF parameters are the same of Fig. 3, but with εB varying.
Fig. 5. Maximum deviation of the electric field in each ring of holes as function of the relative permittivity of the external material.
From these results, we can conclude that the average electric field is approximately constant among the LC infiltrated holes with a maximum deviation of less than 7% when an oil with eB close to silica is placed between the electrodes. The largest deviation occurs in the outermost ring of holes, but those hole rings are less significant for the spectral properties of the LCPCF compared to the rings close to the core. The use of an external matching oil, however, requires careful device packaging, as the oil tends to spread. Though this result will then not be exploited in the experimental part of this work, anyway it should be kept in mind as it suggests that the results that we will present can be even improved.
3. Properties of the dual-frequency LC used
In this section we will describe the characteristics of the LC used to fill the fiber. The dual-frequency LC used in the experiment has tradename MDA-00-3969, fabricated by Merck, Darmstadt, Germany. It is an uniaxial birefringent material with ordinary and extraordinary refractive indices no = 1.4978 and ne = 1.7192 respectively, at λ = 589.3 nm and T=20°C.
At the frequency f = 1 kHz, the values of the relative LC permittivity along the ordinary and the extraordinary axes are εo (or ε⊥) = 7.3 and εe (or ε∥) = 10.6, respectively (technical datasheet values). Polarized microscopy observations on a 5 μm fused silica capillary tube infiltrated with MDA-00-3969 indicate that the LC is expected to align in the PCF holes in a splayed configuration with an angle at the surface of about 45 degrees. This angle changes transversally towards the center of the capillary as illustrated in Fig. 6, where the schematic drawing of the alignment is superimposed on a polarized micrograph of the LC filled capillary. The picture is taken when the angle between the capillary axis and the crossed polarizers is 0/90 degrees. The non-planar alignment of the LC molecules avoids occurrence of reverse tilt domain defects and threshold effects such as Frederiks transition. This, unfortunately, means also that it is not possible to use the simple models valid for planar aligned LC [9].
Fig. 6. Polarized micrograph of a silica capillary infiltrated with the dual-frequency LC and schematic drawing of the LC alignment in the capillary.
Moreover, as it has been said, the LC is dual-frequency. This means that the dielectric anisotropy ∆ε = εe-εo becomes negative at high frequencies as shown in Fig. 7, where it is shown that ∆ε = 2.98 at f = 1 kHz and ∆ε = -2.75 at f = 50 kHz.
Fig. 7. Dielectric anisotropy ∆ε as a function of the frequency of the electric field applied to the LC. The dielectric constant was measured by measuring the capacitance of a both planar and homeotropic aligned cell and calculating the dielectric constant from the capacitance.
To understand the results achieved, one must remind first that the LC molecules have a preferred direction along which they tend to lie. This direction is defined by a unit vector often named the director. When an electric field is applied to a LC it exerts a torque on the director, which, depending on the sign of the anisotropy, is rotated parallel or perpendicular to the field direction, as sketched in Fig. 8 for a single LC molecule.
Fig. 8. Depending on the sign of the dielectric permittivity, the induced polarization P gives a dielectric torque to the molecules, turning the director towards being parallel (a) or perpendicular (b) to the field direction.
In the case of the present alignment of MDA-00-3969 in the fiber holes, the voltage controlled alignment turns out to be much more complicated, as illustrated in Fig. 9, as it depends not only on the radial position but also on frequency. In particular, for what concerns the latter property, it can be observed that, when the frequency f of the applied voltage equals 1 kHz, then ∆ε > 0 and the dielectric torque tends to move the molecules along the field direction. When f = 50 kHz, then ∆ε < 0 and the molecules tend to align perpendicularly to the field direction.
Fig. 9. Reorientation of the LC when a 1 kHz voltage (a) and a 50 kHz voltage (b) are applied to the LC MDA-00-3969.
These two features (non planar alignment and dual-frequency behavior) are extremely interesting. The absence of the Frederiks transition will allow bandgap tunability at lower voltages than those observed so far. Moreover, the frequency dependent sign of the dielectric anisotropy of this LC is such that electric shifting of the bandgaps will be possible towards both longer and shorter wavelengths and the response time of the LCPCF device is expected to improve as well.
The device is fabricated by filling 8 mm section of the PCF with the dual-frequency LC described above. We experimentally observed that an uniform alignment can be achieved infiltrating the LC in nematic phase at room temperature. The LC transforms the fiber into a PBG type fiber. The LC section is then moved 2 mm into the fiber using a pressure chamber. The LCPCF is finally spliced to a PCF of the same type to allow the section of the fiber containing LC to be placed between two electrodes. The overall insertion loss of the device, including a 0.3 dB splice loss, is 13 dB at λ = 1551 nm and 6 dB at λ = 1620 nm. At the end of the filling procedure, the LCPCF is placed between the two electrodes.
4. Continuous tunability and dual-frequency control of photonic bandgaps
As mentioned in section 1, filling the air holes of an index-guiding fiber with LCs eliminates m-TIR based guidance, since the refractive index of the core becomes lower than that of the cladding and then introduces PBG type guidance. The transmission spectrum presents now minima and maxima corresponding to the PBGs of the cladding structure. Figure 10 shows the transmission spectrum of our device normalized to the spectrum of an unfilled LMA-15. The dips at 1160 nm and 1700 nm are caused by small variations in hole size which alter the behavior of the perfect structure introducing high propagation losses at some frequencies on the bandgap edge. The position of the bandgaps can be controlled by applying an electrical field to the electrodes.
Fig. 10. Transmission spectrum of the LMA-15 filled with the dual-frequency LC and coupled with a white light source.
To understand, at least qualitatively, the device behavior, the simple scalar model illustrated in [10] can be used. If the refractive index of the LC is higher than that of silica, the LC infiltrated holes can be approximated as isolated waveguides. Therefore, the minima of the transmission spectrum are basically determined by the cut-off wavelengths of a single isolated waveguide. Always according to this model, the wavelengths λm of minimum transmission in the isotropic case are simply given by:
where d is the hole diameter, n2 is the isotropic refractive index of the high-index inclusions and n1 is the refractive index of the background material (n1 ≈ 1.45 for silica). Since the transmission minima depend on n2, the position of the spectral minima can be shifted simply tuning n2. Taking advantage of the electro-optic properties of the LC, an electric field applied to the fiber forces the LC molecules to rotate and the refractive index n2 experienced by the light propagating in the LCPCF changes depending on the E-field intensity. This simple approach is valid when the material used to fill the holes is isotropic. The anisotropic case, as it is in our case, is, of course, more complicated and there may be minima of the transmission spectrum which are not directly derived from the heuristic treatment in [10]. Nevertheless, Eq. 1 can be used to intuitively understand the experimental results, in particular to know in which direction the bandgaps shift when the value and the frequency of the electric field E change. The cut-off approach have previously been used with success to predict transmission minima of planar aligned nematic LCPCFs using numerical techniques [7], but this requires a full characterization of the LC.
In our experiments, a 1 kHz sine wave signal is applied first to the electrodes and polarized light in the range 1520 -1620 nm is launched in the LCPCF device. In this case ∆ε > 0 and then n2(Eon) > n2(Eoff) causing a positive shift ∆λm. The voltage is increased until a small shift in the bandgaps is observed. When the applied voltage reaches about 19 Vrms a shift of 0.3 nm is measured, as shown in Fig. 11(a). Continuous tunability of the bandgaps is observed by further increasing the applied voltage: some of the measured values are reported in Fig. 11(c), on the right part of the x-axis. Moreover, at 70 Vrms and 200 Vrms shifts of 10 nm and 40 nm are also measured. These values, however, are not reported in Fig. 11(c) as the vertical scale would change too much making the data at low voltage, which are interesting here, unreadable. These results can be explained by observing that the MDA-00-3969 molecules are tilted with respect to the fiber axis. In this LC alignment there is no Frederiks transition threshold and the LC director rotates for values of the electric field below the Fredericks threshold of a planar oriented LC, improving the tuning characteristics of this device.
The frequency dependent behavior of the LC enables shifting of the bandgaps also towards shorter wavelengths. Applying an electric field at a frequency f = 50 kHz, the shift ∆λm is negative. In this case, in fact, ∆ε < 0 making n2(Eon) < n2(Eoff). This is shown in Fig. 11(b). Values of the shifts are also reported as a function of the applied voltage in Fig. 11(c) in the left part of the x-axis to allow direct comparison with results at f = 1 kHz.
A last comment on this figure concerns the differences in the shapes of the band edges of Fig. 11(a) and Fig. 11(b), which should not exist at 0 Vrms. These differences can be explained in terms of different temperatures present in the laboratory when the two different measurements have been performed. To avoid this kind of undesirable effects, the device should then be temperature stabilized.
Measurements about the polarization properties of the device have also been performed. Close to the center of the bandgap no polarization sensitivity of the transmission level is observed, while polarization sensitivity is observed on the edge of the bandgap. Using a polarized tunable laser we have measured the polarization sensitivity on the bandgap edge from 1520 nm to 1620 nm and have observed a small shift (5-6 nm) of the bandgap edge depending on the polarization of the laser.
All these measurements have been done using a tunable laser source ANDO AQ4321D.
Fig. 11. (a) Positive shift (towards longer wavelengths) of the bandgaps when a 1 kHz E-field is applied to the LCPCF. (b) Negative shift (towards shorter wavelengths) of the bandgaps at 50 kHz. (c) Functional dependence of the shift on voltage for 1 kHz (right part of the x-axis) and 50 kHz (left part of the x-axis).
5. Dynamics
The dynamic properties of the device are investigated as a function of the applied voltage by coupling polarized light at 1551 nm wavelength into the LCPCF. The chosen wavelength is located on the short-wavelength edge of the bandgap. The light can be amplitude modulated by shifting the bandgap towards shorter and longer wavelengths. Light polarization is adjusted for maximum transmission and the insertion loss at this wavelength is 13 dB. An oscilloscope displays the transmitted light detected by a photodiode. A 1 kHz sine wave is amplitude modulated with a 50% duty cycle 10 Hz square wave signal and applied to the electrodes. When the E-field is off, there is high transmission at 1551 nm. When the E-field is on, the bandgap shifts towards longer wavelengths and low transmission is detected at 1551 nm. Therefore, the light at 1551 nm is amplitude-modulated by a 10 Hz square wave, as shown in Fig. 12.
Fig. 12. Photodiode voltage when a 1 kHz sine wave with a 96 Vrms voltage and amplitude modulated by a 10 Hz square signal is applied to the electrodes.
The rise and decay time τON and τOFF are measured from 10% to 90% amplitude modulation, and shown in Fig. 13 as function of the applied voltage. As one can see, the response time is limited by the decay time when the E-field is removed from the device and the LC molecules relax back to equilibrium. We expect that the decay time can be reduced and be comparable with the rise time by using a frequency modulation scheme, which switches between a 1 kHz and a 50 kHz signal, whereby a dielectric torque would assist the LC molecules back into equilibrium – effectively reducing the decay time.
The faster response times of this device compared to those presented in [7], is mainly caused by a lower dielectric permittivity of MDA-00-3969 yielding a higher field strength across the LC during reorientation. Moreover, since the LC molecules in MDA-00-3969 are tilted, they start to reorient at electric field strengths below the value required for a planar oriented LC.
6. Continuously tunable birefringence controller
A feature which can be usefully exploited comes from the fact that the LC is anisotropic and the LCPCF, thereby, becomes anisotropic when an E-field is applied. The guided modes then loose their degeneracy and experience a different phase delay when propagating through the LCPCF. This gives the possibility of having electrically controlled birefringence, which can be used to realize electrically driven polarization controllers. Birefringence control has also been demonstrated in [11] using temperature tuning of the refractive index of a polymer partially infiltrated in some of the air holes of a ‘grapefruit’ fiber.
To demonstrate birefringence control, a polarized laser source at 1600 nm is connected to the LCPCF through a polarization analyzer, as shown in the setup of Fig. 14. The polarization of the laser is adjusted such that approximately equal optical power is launched into the two orthogonal states of the LCPCF device. There is no PDL at the chosen wavelength as it is close to the center of the bandgap. The insertion loss of the device at 1600 nm is 6.5 dB. The polarization analyzer launches the light in the LCPCF and resolves the output light into the Stokes parameters plotted on the Poincaré sphere. Each point on the sphere represents an unique polarization state. The north and the south poles represent circularly polarized light. Points on the equator correspond to linear polarizations. Other points on the sphere represent elliptical polarization. When an electric field is applied to the LCPCF, the LC reorients depending on the applied voltage. The two orthogonal polarized guided modes experience different refractive indices compared to the case in which the field is off and this introduces a phase shift between them. Any phase shift between the orthogonal polarizations corresponds to a change of the representing point on the Poincaré sphere. The phase shift is related to the change in birefringence by the following formula:
where ∆n’ and ∆n is the birefringence with and without an applied electric field, respectively, and L is the length of the PCF section in which the LC is infiltrated. Therefore, the change in birefringence caused by the application of a voltage can be determined from the observed phase shift.
Voltages of 18 Vrms, 35 Vrms, 55 Vrms and 82 Vrms at 1 kHz are applied to the LCPCF device. The rotation of the state of polarization on the Poincaré sphere is shown in Fig. 15, while the corresponding induced birefringence is shown in Fig. 16. As it can be observed, a birefringence of 3 × 10-5 can be induced applying a voltage of 82 Vrms, which corresponds to a phase shift of approximately λ/6 at 1600 nm. To obtain full polarization control, a phase shift corresponding to λ/2 must be obtained. This requires an increase in controllable birefringence by a factor 3.
We believe that the birefringence control can be improved using a PCF with a smaller structure, for example a LMA-8 (d = 2.744 μm, Λ = 5.6 μm, 7 rings). In smaller structures, the optical field has a higher overlap with the LC and, therefore, allows an higher degree of tunable birefringence.
Fig. 15. Phase shift on the Poincaré sphere when (a) 18 Vrms, (b) 35 Vrms, (c) 55 Vrms, (d) 82 Vrms are applied to the LCPCF device.
7. Conclusion
We have proposed an electrically tunable LCPCF that allows continuous control of the spectral position of the bandgaps. The most significant property of this device is its electrically controlled continuous tunability, which is achieved by filling the air holes of the PCF with a dual frequency LC. This kind of LC allows shifting of the bandgaps towards both longer and shorter wavelengths. The properties of this device have allow to demonstrate a birefringence controller. The dynamic response characterization has also shown the possible use of this device as a low speed electro-optical modulator with rise and decay times better than previously demonstrated ones. Further improvements can be obtained by controlling the device using a frequency modulation scheme instead of an amplitude modulation scheme. Concerning the birefringence control, a higher degree of tunable birefringence can be achieved if a PCF with a smaller structure is used. Theoretical calculations show also that these results are expected to improve if the LCPCF is inserted in an index matching oil that increase the uniformity of the structure on which the electric field is applied.
The limit in modulation speed of these devices make them unsuitable for high bit rate TLC transmission systems. Nevertheless, there are many other applications operating at low bit rates where all-fiber and in-line devices could be highly desirable also to reduce costs. Electrically tuned LCPCF devices such as polarization controllers, tunable attenuators, low bit rate electro-optical modulators and, combined with grating technology, tunable optical filters can in fact be useful in applications such as sensors or other niche applications. Moreover, one can also foresee computer controlled versions of these devices which could be attractive for laboratory applications allowing set up automation or operation stabilization using feed back controls.
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