Optical properties of cubic blue phase liquid crystal in photonic microstructures.

In this work, optical properties of a cubic blue phase liquid crystal (BPLC) in photonic microstructures were investigated. The experiments were carried out in microcapillaries with different inner diameters and in a photonic crystal fiber (PCF). For the first time, white-light beam propagation through a BPLC (BP II) in a microcapillary with a 60-µm inner diameter at a distance of 26 mm was demonstrated. Furthermore, it was conclusively shown that the cylindrical geometry and the size of its inner diameter influence BP domains orientation, which can lead to a uniform texture of the BPLC with a dominant Bragg wavelength. This study also proves that a BPLC-filled PCF provides very attractive tunable properties. It was presented that by applying an external electric field, a control of the transmitted light intensity for particular wavelengths can be achieved, depending on the input polarization. Moreover, a range of the wavelengths corresponding to low transmission appeared to be tunable, whereas for x- and y-polarized light, respectively, both narrowing (from 16 nm to 9 nm) as well widening (from 13 nm to 22 nm) of the bandgaps were observed. Finally, the obtained experimental results were found qualitatively consistent.

Interplay between tie strength and neighbourhood topology in complex networks.

Granovetter's weak ties theory is a very important sociological theory according to which a correlation between edge weight and the network's topology should exist. More specifically, the neighbourhood overlap of two nodes connected by an edge should be positively correlated with edge weight (tie strength). However, some real social networks exhibit a negative correlation-the most prominent example is the scientific collaboration network, for which overlap decreases with edge weight. It has been demonstrated that the aforementioned inconsistency with Granovetter's theory can be alleviated in the scientific collaboration network through the use of asymmetric measures. In this paper, we explain that while asymmetric measures are often necessary to describe complex networks and to confirm Granovetter's theory, their interpretation is not simple, and there are pitfalls that one must be wary of. The definitions of asymmetric weights and overlaps introduce structural correlations that must be filtered out. We show that correlation profiles can be used to overcome this problem. Using this technique, not only do we confirm Granovetter's theory in various real and artificial social networks, but we also show that Granovetter-like weight-topology correlations are present in other complex networks (e.g. metabolic and neural networks). Our results suggest that Granovetter's theory is a sociological manifestation of more general principles governing various types of complex networks.

Periodic liquid crystalline waveguiding microstructures.

Different methods allowing for creating optical waveguides with liquid-crystal (LC) cores, in which molecules form periodic patterns with precisely controlled periods, are reported. The first one is based on reversible photoalignment with high-resolution selective illumination and allows to control the period of LC molecules inside silica microcapillaries. The second method employs microstructures formed in PDMS, allowing to obtain both: LC-core waveguides and a set of specially designed periodic microelectrodes used for the periodic reorientation of molecules. Using both methods, we successfully controlled the period of the patterned alignment in the range from about 500 µm and scaled it down to as small as 20 µm. We performed experimental studies on waveguiding phenomenon in such structures, in view to obtain transmission spectra typical to optical fiber gratings. Since the results achieved in experimental conditions differed from those expected, the additional numerical simulations were performed to explain the observed effects. Finally, we obtained the waveguiding in a blue phase LC, characterized by naturally created three-dimensional periodicity with periods smaller than one micrometer. In such a structure, we were able to observe first-order bandgap, and moreover, we were able to tune it thermally in nearly the whole visible spectral range.

Achiral Nanoparticle-Enhanced Chiral Twist and Thermal Stability of Blue Phase Liquid Crystals.

Blue phase liquid crystals (BPLCs) are chiral mesophases with 3D order, which makes them a promising template for doping nanoparticles (NPs), yielding tunable nanomaterials attractive for microlasers and numerous microsensor applications. However, doping NPs to BPLCs causes BP lattice extension, which translates to elongation of operating wavelengths of light reflection. Here, it is demonstrated that small (2.4 nm diameter) achiral gold (Au) NPs decorated with designed LC-like ligands can enhance the chiral twist of BPLCs (i.e., reduce cell size of the single BP unit up to ∼14% and ∼7% for BPI and BPII, respectively), translating to a blue-shift of Bragg reflection. Doping NPs also significantly increases the thermal stability of BPs from 5.5 °C (for undoped BPLC) up to 22.8 °C (for doped BPLC). In line with our expectations, both effects are saturated, and their magnitude depends on the concentration of investigated nanodopants as well the BP phase type. Our research highlights the critical role of functionalization of Au NPs on the phase sequence of BPLCs. We show that inappropriate selection of surface ligands can destabilize BPs. Our BPLC and Au NPs are photochemically stable and exhibit great miscibility, preventing NP aggregation in the BPLC matrix over the long term. We believe that our findings will improve the fabrication of advanced nanomaterials into 3D periodic soft photonic structures.

Self-Organized, One-Dimensional Periodic Structures in a Gold Nanoparticle-Doped Nematic Liquid Crystal Composite.

Composite structures exhibiting a periodic arrangement of building blocks can be found in natural systems at different length scales. Recreating such systems in artificial composites using the principles of self-assembly has been a great challenge, especially for 1D microscale systems. Here, we present a purposely designed composite material consisting of gold nanoparticles and a nematic liquid crystal matrix that has the ability to self-create a periodic structure in the form of a one-dimensional photonic lattice through a phase separation process occurring in a confined space. Our strategy is based on the use of a thermoswitchable medium that reversibly and quickly responds to both heating and cooling. We find that the period of the structure is strongly related to the size of the confining space. We believe that our findings will allow us to not only better understand the phase separation process in multicomponent soft/colloid mixtures with useful optical properties but also improve our understanding of the precise assembly of advanced materials into one-dimensional periodic systems, with prospective applications in future photonic technologies.