We demonstrate electrically and mechanically induced long period gratings (LPGs) in a photonic crystal fiber (PCF) filled with a high-index liquid crystal. The presence of the liquid crystal changes the guiding properties of the fiber from an index guiding fiber to a photonic bandgap guiding fiber - a so called liquid crystal photonic bandgap (LCPBG) fiber. Both the strength and resonance wavelength of the gratings are highly tunable. By adjusting the amplitude of the applied electric field, the grating strength can be tuned and by changing the temperature, the resonance wavelength can be tuned as well. Numerical calculations of the higher order modes of the fiber cladding are presented, allowing the resonance wavelengths to be calculated. A high polarization dependent loss of the induced gratings is also observed.
©2007 Optical Society of America
Photonic crystal fibers (PCFs) are a special kind of optical fiber, having a microstructured cladding of air holes running along the length of the fiber. Such a fiber cladding allows an infiltration of various materials into the air holes, hereby creating highly tunable fiber devices. A demonstration of such fiber devices was first made by Eggleton et al. to create highly tunable long period and fiber Bragg gratings . If the microstructured cladding is filled with a material having a higher refractive index than silica, the fiber is no longer index guiding, but can guide light due to anti resonant reflections from the high index rods . The fiber now transmits light in a number of frequency bands where a so called bandgap exists. In these bandgaps light cannot propagate through the cladding structure and is therefore effectively confined into the core of the fiber. Such a fiber is known as a photonic bandgap (PBG) fiber and was first demonstrated by infiltrating the air holes of a PCF with a high index liquid . Highly tunable PBG fiber devices can be realized by infiltrating the holes of a PCF with a liquid crystal. These LCPBG fiber devices show a high degree of tunability. Thermally, electrically and optically tunable bandgaps have been demonstrated [4–11].
Long period gratings (LPGs) inscribed in optical fibers resonantly couple light from the core mode to copropagating higher order modes (HOMs) of the fiber. The coupling occurs at the resonance wavelength, which is the wavelength of phase match between the core mode and the HOM. The resonance wavelength λres is given by
where ΛG is the grating pitch, neff,HOM is the effective index of the core mode and n effHOM is the effective index of the HOM that is coupled to . The grating therefore results in a transfer of power from the fundamental core mode to higher order modes. This results in a loss of power at the resonance wavelength, since the HOMs usually have a much higher loss than the fundamental core mode. LPGs have a wide range of applications, among others optical filtering , gain equalization , mode conversion , temperature or strain sensors  and in biochemical sensing .
A lot of work has been made concerning the fabrication of LPGs in index guiding PCFs [18–20], but only recently, have LPGs been demonstrated in photonic bandgap (PBG) fibers [22,23]. This was realized by filling the microstructured cladding of a PCF with a high index liquid and inducing the LPG by applying a periodic pressure to the length of the fiber. It was demonstrated that narrow loss dips could be introduced in the transmission bands of the fiber and that the resonance wavelengths showed a very high degree of temperature tunability. Furthermore, electrically tunable LPGs have been realized in a single light guiding rod of liquid crystal  and in an index guiding fiber surrounded by a liquid crystal [25, 26].
In this paper we demonstrate both mechanically and electrically induced LPGs in a LCPBG fiber. Both the mechanical and the electrical gratings have a high degree of tunability, where the attenuation of the LPG is tuned by changing either the strength of the applied pressure or the electric field, and the resonance wavelengths of the grating can be tuned by temperature. For the purely electrical gratings, the advantage is that no mechanical stress is applied to the fiber, enabling the fabrication of small highly tunable fiber devices, that can easily be integrated into communication or sensor systems.
2. Mechanically induced long period gratings in LCPBG fibers
The fiber used in the experiment is a silica large mode area (LMA-10) fiber from Crystal Fibre A/S.The diameter of the holes is 3.45 μm, the inter hole distance is 7.15 μm and the diameter of the core is approximately 10 μm. Figure 1(a) shows a scanning electron microscope (SEM) image of the fiber end facet. The unfilled fiber is an index guiding fiber, i.e. guides light by the principle of modified total internal reflection. When the air holes of the fiber are infiltrated with a liquid crystal having a refractive index higher than that of silica, a high index region is created around the core and the fiber becomes a photonic bandgap guiding fiber.
In this experiment, the liquid crystal used is E7 from Merck, which has a wavelength dependent ordinary and extraordinary refractive index of n 0=1.52 and ne=1.75, respectively, at 589.3 nm. The electrical permittivity at 1 kHz is ϵ⊥=5.2ϵ0 along the ordinary axis and ϵ∥ =19.3ϵ0 along the extraordinary axis. All values are at 20°C.
Mechanical LPGs are realized in the LCPBG fiber using a brass block with 26 periodically cut V-grooves. The spacing between the grooves or the grating pitch is ΛG=800 μm. Figure 1(b) shows a schematic illustration of the LCPBG fiber placed underneath this grating. The transmission of the fiber device is measured using white light from a Tungsten-Halogen light source as seen in fig. 1(c). Light from the source is guided to the fiber by a LMA fiber and coupled into the LCPBG fiber by aligning the two fibers on an xyz-stage. The transmission is then measured by an optical spectrum analyzer, and normalized to that of an unfilled fiber. Figure 2 shows the transmission of the LCPBG fiber when an increasing pressure is applied to the grating. The blue curve shows the transmission of the fiber when no pressure is applied. For an increasing pressure applied to the LCPBG fiber, loss dips appear in the bandgap centered around 1500 nm, as illustrated with the green and red curve. A loss dip also appears at the short wavelength edge of the bandgap centered around 1000 nm. This loss dip is not observed when using a mechanical grating with a pitch less than ΛG =800 μm and is therefore attributed to a grating resonance. The other bandgaps show no loss dips, but are instead slightly attenuated. The fiber coating is not removed where the pressure is applied.
The transmission spectra of the LCPBG fiber can be determined by calculating the effective indices of the modes in the liquid crystal filled rods. Between the cut off wavelengths of these modes a core guided mode can exist. This is simulated in fig. 2(b) where the blue lines show the effective indices of the rod modes and the black line is the core guided mode. The simulated wavelength bands, where a core guided mode exists, fits well with the experimentally measured transmission. The small transmission band measured at 1200 nm is due to an anisotropic splitting of the LP21 band, that is split up into two sub-bands containing the HE11 and the HE31 modes.
3. Electrically induced long period gratings in LCPBG fibers
Within the holes of the PCF, the liquid crystal is planar aligned with its director along the fiber axis . An electric field applied to the liquid crystals inside the fiber, results in a dielectric torque that aligns the liquid crystal molecules parallel to the electric field [5, 6]. By using a comb electrode, a periodically varying electric field can be induced in the fiber. This results in a periodic index variation along the length of the fiber, since the liquid crystals will align parallel to the applied field. This principle is shown in fig. 3. In the figure, the alignment of the liquid crystals inside a single capillary tube, placed underneath a comb electrode can be seen. In (a) the field is off and the liquid crystals have a planar alignment. In (b) the electric field is turned on and the liquid crystals between the electrodes will realign, such that they are parallel to the applied electric field, thereby creating a periodic variation in the refractive index in the length of the fiber.
The comb electrode used in this work, is the brass block with periodically cut V-grooves seen in fig. 1(a). The electrical signal is generated by a signal generator, that is amplified using a high voltage amplifier. The DC component of the electrical signal is removed using a high-pass filter and the signal is monitored on an oscilloscope. Figure 4 shows the transmission bandgap around 1500 nm, when a voltage is applied to the grating. The temperature is fixed at 25°C and no pressure is applied to the grating. The voltage threshold where changes appear in the spectrum is at VRMS=30 V. This is the voltage where the liquid crystals start to reorient. Two distinct peaks are visible at a voltage of VRMS=43.8 V. One at 1565 nm and one at 1480 nm. When the voltage is increased to VRMS=68.9 V two more dips appear, one at 1515 nm and a small one at 1440 nm. The spectral positions of the loss dips are in good agreement with the observed transmission of the mechanically induced gratings. The resonance wavelengths are the same within the tolerances of the fiber dimensions. A slight shift in resonance wavelength is observed for the electrically induced gratings, when the field strength is increased. We believe this is due to a slight change in effective index of the cladding modes, which will move the resonance wavelengths slightly.
There is no memory effect of the gratings, i.e. when the voltage is turned off the grating dips completely disappear. Although the dynamics of the grating device where not measured, it is believed that these are the same as described by Haakestad et al.  for a plain electrode. In the experiment the coating of the fiber placed between the electrodes is removed and the voltage is applied at 1 kHz.
4. Simulation of long period grating resonances
We employ a commercial finite element code (Comsol MultiphysicsTM ) for the calculation of the resonance wavelengths. The code uses an adaptive mesh algorithm for generating the mesh. The mesh consists of 94.500 quadratical Lagrange elements. The fiber is simulated by the full cross section shown in fig. 1(a) without the polymer coating, and metallic boundary conditions are used at the outer boundary of the fiber. We believe that the use of metallic boundary conditions is acceptable in this case since the field decays rapidly outside the fiber, due to the large index difference between air and silica. In our simulations we solve for the propagation constants, β, for the modes of the fiber at a fixed frequency, ω, which enables us to include material dispersion in a consistent manner. For the refractive indices of the materials we use a Sellmeier expression for the silica and a Cauchy equation for the LC in the holes. The Cauchy equations are 
Figure 5 shows the transverse mode profile of the fundamental core mode of the fiber and the profiles of the HOMs that, we believe, the core mode couples to. The HOMs are modes of the microstructured cladding and are LP11 and LP12 type modes. The found LP1x modes can be divided into the TE0x, TM0x and HE2x like modes, all having slightly different effective indices.
Using equation 1 the resonance wavelength of the fundamental core mode and the HOMs can be calculated. The calculation shows that a slight shift of 60 nm towards longer wavelengths is observed for the numerically calculated spectral positions of the loss dips. We ascribe this to the fact that the simulations are made for a perfect uniform cladding structure, without taking small structural variations of the fiber into account, and because of uncertainties in the value of the refractive index of the liquid crystal. The refractive index of the liquid crystal is measured at visible wavelengths and then extrapolated using Cauchy equations to infrared wavelengths. Furthermore, the refractive indices are measured in a planar cell, in which the liquid crystal molecular ordering might be slightly different from the ordering in a capillary tube with an inner diameter of a few micron, due to a stronger surface anchoring in surface coated planar cells. Figure 4 shows the experimentally measured transmission together with the simulated phase matching curves shifted 60 nm in order to match the measurements. The figure shows that even though the simulations have a phase match shift towards longer wavelengths, the relative position of the simulated phase match coincides with the measured positions of the spectral dips.
5. Temperature tuning of long period grating resonances
By tuning the temperature of the liquid crystals inside the fiber, the refractive index changes and, therefore, the position of the loss peaks can be tuned. This temperature tuning can be seen in fig 6(a), where the spectral position of the loss dip with the highest loss at a temperature of 25°C, 40°C and 58°C are shown. The loss peaks move towards shorter wavelengths when the temperature is changed from 25°C to 40°C, and towards longer wavelengths from 40°C to 59°C. The spectral position of the loss dip as a function of temperature is shown in fig. 6(b). The figure shows that a very high degree of tuning can be achieved. In the temperature interval from 55°C to 59°C the resonance wavelength is tuned 11 nm/°C. The shift in the resonance wavelength can be explained by the change in the ordinary and extraordinary refractive indices as a function of temperature. These are shown in the inset of fig. 6(b). The shift of the resonances is mainly determined by the ordinary refractive index, since the electric field is mostly in this direction. Below 40 degrees, the gradient of the ordinary index is almost zero, while the extraordinary index decreases as a function of the increase of temperature. Above 40 degrees, the ordinary index starts to increase and, since the resonance wavelength is mostly affected by this, the resonances start to shift towards longer wavelengths. When the temperature approaches the clearing temperature of E7 the ordinary index increases rapidly and results in the large degree of tuning observed in fig. 6(b).
Using another liquid crystal, a linear tuning over a broad temperature interval can be achieved. Such a tuning is shown in fig. 7(a), when a mechanical grating with a pitch of ΛG = 800 μm is induced in a LMA-10 fiber filled with MDA-00-3969. This liquid crystal has an ordinary and extraordinary refractive index of no=1.498 and ne=1.719, respectively, at a wavelength of 589.3 nm and a temperature of 20°C . Figure 7(b) shows the spectral position of the resonance wavelength as a function of temperature, and a linear tuning of -2.4 nm/°C is observed. As for E7, the shift can be explained by the refractive indices of the liquid crystal shown in the inset of fig. 7(b). As can be seen in the figure the ordinary index of this liquid crystal is almost constant, whereas the extraordinary index decreases linearly. This results in the linear tuning of the resonance wavelength.
Unfortunately, it was not possible to realize electrically tunable gratings in this fiber. We simply did not observe any grating dips when an electric field was applied to the electrical grating. We believe this is due to a strong alignment anchoring of this liquid crystal inside the capillary, which did not allow a reorientation of the liquid crystals.
6. Polarization dependence of long period grating resonances
The polarization dependence of the induced LPG in the E7 filled fiber is investigated using linearly polarized light from a tunable laser source. The wavelength of the laser is tuned to the wavelength of the loss dip induced by the LPG, and by tuning the polarization of the input light with a polarization controller, the polarizations that give the lowest and the highest transmission loss of the dip are found. The wavelength is then tuned from 1520 nm to 1620 nm and the transmission is measured with an optical spectrum analyzer. Figure 8 shows the setup.
The polarization dependence of both the electrically and the mechanically induced gratings is shown in fig. 9(a) and (b), respectively. Both the electrical and mechanical gratings show a high dependence on the polarization of the light that is launched into the grating. For the electrically tunable gratings at an applied voltage of VRMS = 68.9 V, there is a difference of the maximum attenuation of the loss dip between the two polarizations of 12.5 dB. The reason for this is that light polarized in the same direction as the applied electric field will experience a higher perturbation of the refractive index, due to the fact that the liquid crystal is oriented in this direction.
The result is a stronger coupling to the cladding mode and, therefore, a higher transmission loss for this polarization. The spectral position of the loss dip is also shifted slightly for the two polarizations. This is because the applied electric field induces a slight birefringence in the fiber, giving rise to a slight shift in the resonance wavelength for the two polarizations. The mechanically induced gratings also show a high degree of polarization dependence. For the pressure applied in fig. 9(b) a difference between the maximum attenuation of the two loss dips of 5.0 dB is observed. The resonance wavelength for the mechanically induced gratings is also slightly shifted for the two polarizations. This is again due to the grating inducing a birefringence in the fiber.
We have demonstrated electrically and mechanically induced LPGs in a LCPBG fiber device. The strength of the gratings can be tuned for the mechanical gratings by changing the pressure exerted onto the grating, and for the electrical gratings by changing the strength of the applied electric field. The resonance wavelengths can be tuned by temperature, and a very high degree of tuning up to 11 nm/°C is demonstrated. A linear tuning of -2.4 nm/°C over a broad temperature interval from 30°C to 80°C is also demonstrated. Using numerical simulations we show that the relative position of the loss peaks can be determined within 4% accuracy, but that a more accurate measure of the refractive index of the liquid crystal and fiber structure is required, in order to perform more accurate simulations concerning the position of the loss peaks. Furthermore, the polarization dependence of the induced gratings is investigated and a strong polarization dependence is observed.
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