1. Introduction

Specialty fibers, waveguides, microcavity and microfludic channels with light guiding cores made of electro-optics materials or nonlinear optical materials have been studied in various contexts [1–18]. In particular, optical fibers made by infiltrating liquid crystals in capillaries or holey (photonic-crystals) fibers have been demonstrated [5–18]. Various ordered phases of liquid crystals such as cholesterics, nematics, smectic and ferroelectrics have been used, but nematic liquid crystals (NLC) are by far the most popular one because of their extraordinarily large birefringence, electro-optical and nonlinear optical responses. In general, there are two difficulties and limitations associated with using nematic liquid crystals in their ordered phases, namely, uniform alignment of the liquid crystal axis on the boundary surfaces and scattering loss. Although alignment of the director axis in the hard-to-reach inner surfaces of these pores/voids can be mediated by photo-alignment materials [17], and scattering/absorption loss can be reduced by employing smaller confinement geometry and/or going to longer-wavelength region [18], the highly birefringent nature of the nematic liquid crystal core still makes it very difficult to avoid depolarization and other polarization sensitive degrading effects.

In this paper, we report the use of Blue Phase Liquid Crystals (BPLC) as fiber waveguiding cores that are optically isotropic, polarization insensitive and relatively low-loss. BPLC’s [19–22] are cholesteric liquid crystals in which the director axes are self-assembled in double twisted helix to form 3D regular lattices of disclinations (defects); c.f. Fig. 1(a) . Typical lattice spacing is on the order of several hundred nanometers, and thus BPLC’s exhibit selective Bragg reflections (photonic bandgaps) of light in the visible spectrum, even as bulk BPLC’s are optically isotropic. Because of the tightly-wound director axis arrangement in BPLC, the scattering loss associated with director axis fluctuations is largely reduced and allows good transmission through long (several mm’s) interaction length. The small remnant scattering loss in bulk BPLC is due mainly to the discontinuous grain boundaries among the self-assembled crystal platelets [23]. They are therefore a natural candidate for fabricating optical fiber with 3-D photonic crystal properties. Just as their chiral nematic LC counterparts [24–26], BPLC possess large (ac or optical) Kerr constants and nonlinearity [27–30], and therefore will enable various electro-optical, nonlinear or all-optical modulation/switching possibilities.

 

Fig. 1 (a) Double helix arrangement of the BPLC director axis and the crystal lattice structures corresponding to the BPI and BPII phases; (b) Upper: schematic depiction (not to scale) of the capillary array with BPLC filled pores; lower: Microscope photograph of one end face of the BPLC fiber array illuminated by obliquely incident white light showing green reflections from the fiber ends; ambient temperature is 25 °C (BPI phase).

Download Full Size | PDF

2. Fiber array fabrication and characterization

The capillary arrays were procured from a commercial source [Collimated Holes Inc. CA]; these capillary array are usually in circular platelet forms with dimensions: areal diameter of 1cm −2.5 cm; pore diameter ranges from 10 microns to 30 microns, and respective thicknesses (which define the fiber lengths) of 2 mm to 5 mm. The BPLC mixture used for infiltrating the capillaries is the one reported in previous studies [22,30]. It consists of three ingredients: E48 (32%), 5CB (32%) and S811 (36%)] and exhibits Blue-Phase II below ~30 °C and Blue Phase I below ~28°C, and the highly scattering focal conic cholesteric phase below 24 °C. The mixture is first heated to well over its clearing point to engender filling the capillaries by osmosis action. The entrance and exit planes of the fiber array are optically flat glass windows. The capillary array is made of silica of index ~1.54, whereas the BPLC refractive index is >1.55 for the temperature range in which the studies are conducted. Accordingly, the BPLC filled capillary acts as a multi- mode optical fiber waveguide.

Figure 1(b) shows a microscope-photograph of the exit face of the BPLC fiber array with oblique illumination by a white light source when the ambient temperature is around 25 °C, i.e. BPI phase, clearly showing color (mostly green) reflections from the fiber ends. As the temperature is varied, these reflections change from a bluish-color at a temperature just below the clearing point (BPI), to green at lower temperature (BPII), mimicking the reflections from bulk cells [30].

The optical properties of the fiber array depend critically on the refractive index of the BPLC core. Using an interferometer set up, c.f. Fig. 2 (top), we have measured the temperature dependence of the hitherto unreported refractive index for this particular BPLC mixture. As shown in Fig. 2 (bottom), the refractive index increases monotonically as the temperature is lowered from the isotropic liquid phase. The typical value for the extraordinary refractive index n_e of the mixture constituents [e.g. 5CB or E48] is ~1.69 whereas the ordinary index n_o is ~1.50. Therefore the average index of the optically isotropic BPLC cell is estimated to be n_av = ([(n_e² + 2n_o²)/3])^1/2 ~1.56. This is close to the experimental measured values [1.555 at 37°C and 1.564 at 25°C]. The magnitude of the thermal index gradients in the Blue phase (I or II) are generally higher than the isotropic phase; we have dn/dT = −0.00090 °C⁻¹ (BPI); dn/dT = −0.00123 °C⁻¹ (BPII); and dn/dT = −0.00051 °C⁻¹ (isotropic liquid phase). These observations are consistent with our general understanding of the temperature dependence of n_e and n_o [31,32] in nematics. In general, both n_e and n_o are functions of the density ρ and the order parameter S. In the isotropic liquid phase, when S = 0, dn_av/dT is negative due to the contribution from dρ/dT which is negative in sign. Below the clearing point T_C when the mixture is in the Blue-phases, dn_e/dT is negative while dn_o/dT is positive. Owing to the much larger magnitude of dn_e/dT compared to dn_o/dT, the effective refractive index gradient is negative. The magnitudes of the index gradients (due mainly to dS/dT with smaller dρ/dT contribution) in the ordered BP phases are larger than the above-T_c isotropic liquid phase value (due mainly to dρ/dT).

 

Fig. 2 (top) Interferometer set-up for measuring the temperature dependent refractive index gradient of BPLC cell. Index changes of the bulk cell give rise to moving fringe pattern detected by the slit-detector. (bottom) Temperature dependence of the refractive index of a 1-mm thick BPLC cell measured at the He-Ne laser wavelength λ = 6328 nm. Photos depict the reflected colors of the BPLC cell in the respective phases

Download Full Size | PDF

As a result of these temperature dependencies, the photonic bandgaps associated with the lattice structures corresponding to the BPII and BPI phases also vary considerably. We have measured the transmission spectrum of the BPLC cored fiber by exploiting the ultra-wide spectral band (400 nm – 1200 nm) of a white light continuum laser [WhiteLase-Sc Model]; c.f. insert in Fig. 3 ; the small divergence of the laser allows easier focusing/coupling into a single fiber within the array. Figure 3(a)-(b) show representative transmission spectra with the fiber array maintained at temperatures corresponding to the BPII and BPI phases. They clearly exhibit strong reflection bands associated with the photonic bandgaps in the visible (400 nm – 600 nm) region, similar to their bulk BPLC counterpart [30]. In BPII phase, the transmission minimum shows an extinction of ~-20 dBm whereas in the BPI phase, the transmission dips even further to ~-35 dBm with a widening towards the long wavelength region.

 

Fig. 3 (a) Experimental set-up used for measuring the transmission spectrum of a BPLC fiber with white light continuum laser. (b) Transmission spectrum of a single BPLC cored fiber at 29 °C - BPII phase; (c) Transmission spectrum at 25 °C – BPI phase.

Download Full Size | PDF

3. Imaging and nonlinear transmission

Nonlinear optical fiber arrays can function as image transmitting faceplate with large field of view as well as efficient passive optical limiting device [33]. Figure 4 shows the experimental set up used in our feasibility study. A fiber array [core diameter: 10 μm; fiber length: 3 mm] is placed in the focal plane of a 1x telescope and distant objects are viewed through it and photographed. Since each of the fiber defines an image pixel, the resolution is dependent on the fiber core diameter and the cladding thickness; the smaller is the core + cladding dimension, the better is the resolution. Furthermore, the index difference between the BPLC core and the silica cladding in conjunction with the core diameter defines the numerical aperture and therefore the field of view [1,5,33]. As such, the fiber arrays with core diameter of 10-μm provide reasonably good-quality imaging capability; c.f. photo-inserts (a) and (b) in Fig. 4; with a cladding thickness of ~5 μm, the fiber array is capable of a resolution limit of ~60 lines/mm. The enlarged view of the transmitted image in Fig. 4(b) shows that in the isotropic phase, the fiber array exhibits good transmission for all colors. In the Blue Phases, and as the temperature is lowered further, the transmission in the blue and green regions become poorer, while fairly good transmission can still be maintained for red and yellow colors, consistent with the temperature dependent bandgaps discussed earlier.

 

Fig. 4 (a) Experimental set up where a fiber array is inserted in the image plane inside a 1x telescope. Photograph at bottom shows the image of color bars on white paper viewed through the telescope. (b) Enlarged view of the transmitted image where individual image pixel defined by a single fiber of the fiber array is clearly visible. Upper image is obtained above the clearing temperature showing good transmission for all colors in the isotropic phase. Lower image is obtained at the temperature corresponding to BPII phase with poor transmission in the blue-green spectrum, while good transmission in the yellow and red region is still maintained.

Download Full Size | PDF

Another possible application of BPLC core fiber array in a 1x telescope is nonlinear transmission leading to passive optical limiting action [33]. As a feasibility demonstration of optical limiting action, and ease in focusing the laser into a single fiber, the experiment is conducted with a larger core diameter (30 μm) and thicker (5 mm) BPLC fiber array. The same broadband (400 nm to1200 nm) cw white light continuum laser is used to study its power dependent transmission through a BPLC fiber within the array. The laser system emits a continuous pulse train of ~100 ps pulses at 80 MHz with a maximum total output power of over 2.5 Watt; this equates to maximum individual pulse energy of ~30 nJ and intensity of ~30 MW/cm² in the 30 μm diameter fiber core. Although BPLC are transparent in the visible-near infrared region, finite linear absorption around the short wavelength regime (below 400 nm) of the high power laser could give rise to substantial thermal heating of the BPLC, as we will see presently. At high intensity level, it is likely that nonlinear multi-photon absorptions leading to further heating could also take place, since most of the organic constituent molecules of BPLC are known to have significant two- and multi-photon absorption coefficients [34,35].

In propagation through the fiber core, these absorption induced heating effects give rise to a decrease in the core index, which in turns reduces the core-guiding modes as some of the higher order modes evolve into lossy cladding modes [5]. Furthermore, self-defocusing at the input region will also diminish coupling into the fiber core. These intensity dependent effects will all act in concert to reduce the guided transmission as the input laser intensity is increased; c.f. Fig. 5 . The fiber would thus function as an optical limiter if the cladding around the core is opaque such as those used in [33], or an aperture is placed on the exit end to monitor only the fiber core transmission.

 

Fig. 5 Schematic depiction of some nonlinear optical absorption and scattering processes that cause nonlinear transmission of the laser through the fiber core.

Download Full Size | PDF

Figure 6 shows some exemplary nonlinear transmission results obtained with the BPLC fiber array for two distinct cases. In case (i) the array is maintained above the clearing point (T_1 = 35°C), and shows an initial transmission value of ~16%; the low transmission value is due mainly to un-optimized input coupling of the continuum laser into the fiber, as well as reflection losses from multiple uncoated glass surfaces enclosing the fiber array. As a result of defocusing and guiding-cladding modes change, the transmission progressively decreases with increasing laser power, and eventually reaches an almost vanishing value (<0.01Watt) at an input power of 2.4 Watt. The accompanying photos show how a weak laser is completely coupled into a single fiber core, whereas a high power laser is scattered into cladding modes and thus emerges from many fibers.

 

Fig. 6 Plots of the core transmission data as a function of the input laser power for fiber array maintained at various ambient temperatures: (i) T_1 = 35°C (above the clearing points) and (ii) T_2 = 24°C (below the BPI phase). Attached photos (top to bottom) are taken of the exit end of the fiber array in isotropic phase, showing initial transmission through a single fiber at low power, and increasingly more transmission through the neighboring fibers at high input laser power.

Download Full Size | PDF

In case (ii), the fiber is at room temperature (24°C), which is below the BPI phase, and there is practically no transmission due to the highly scattering focal conic structure in this phase. Upon further increase in the laser power, some finite transmission begins to appear. At an input power of 0.5Watt, the fiber is evidently heated through the isotropic phase, and a well formed beam emerges from the exit end. Above this input power level, the transmission is observed to decrease in a manner closely resembling the isotropic case. The slight difference between the transmission (normalized to the input power) in the blue phase and that in the isotropic phase is probably due to the fact that in the former case, some input laser power is needed (absorbed) to maintain the fiber above the clearing point as opposed to the latter which is maintained at the isotropic phase by external means.

We have carried out a separate experiment to further illustrate the absorption-heating induced (negative) thermal index mechanism by the white light continuum laser. In this study using the same experimental set up, c.f. Fig. 7 , the fiber array is replaced by a 1-mm thick planar bulk BPLC cell maintained at various temperatures corresponding to the isotropic, BPII, BPI and focal conic phase. The far-field exit beam profiles are monitored as the input laser power is increased. In all phases, very strong self-defocusing effects are observed. As shown in the photos in Fig. 7, the exit laser beam profile acquires an increasing larger dark central portion; the overall beam divergence is also dramatically enlarged. For the particular case where the BPLC cell is at room temperature, i.e. just below the BPI phase when the sample is highly scattering, there is practically no transmission at low input power. However, when the input power is raised to ~0.5 Watt, one can observe with the naked eye that the spot under illumination becomes clear and the laser is almost fully transmitted with a dark-ended central region; at higher input power, these central darkening and beam divergence become more pronounced, similar to those depicted in Fig. 7.

 

Fig. 7 Schematic depiction of self-defocusing action on the cw white light continuum laser with a bulk planar BPLC cell at room temperature (focal conic phase). Attached photos shows the input and exit beam profiles at two laser powers when strong defocusing effects are evident. Similar results are obtained for isotropic phase and BPI and BPII phase.

Download Full Size | PDF

4. Conclusion

In conclusion, we have reported the fabrication of Blue-phase liquid crystal cored fiber arrays that possess photonic-crystal like properties. These arrays allow good-quality image transmission as well as optical limiting actions. The refractive index of the core BPLC material and its temperature gradients in various phases have been measured and utilized to demonstrate the feasibility of optically induced core-cladding switching and optical limiting action with a cw white light continuum laser. With optimization such as the introduction of absorbing azo-dyes or other nano-particles, much lower threshold and faster responses can be expected of such thermal/density/order parameter mediated transmission switching operations, as demonstrated in previous studies [24–26,36,37]. These dynamical studies are currently being pursued, with the objective of determining parameter set for optimal performance in the image transmission and optical limiting action. Compared to using aligned nematic liquid crystals as the nonlinear guiding core materials, BPLC’s optical isotropy and polarization-independent nonlinear optical responses are clearly an advantage, in addition to the fact that there is no need for surface treatment or alignment agent during the fabrication process. The BPLC used in the present study also possesses large ac-field Kerr constant, and therefore, with the suitable introduction of electrodes into the fiber array or other nano-structures, we envision the possibilities of realizing a wide range of device configurations for electro-optical modulation, switching and tunable filter applications.