Filip A. Sala

Modeling of molecular reorientation and beam propagation in chiral and non-chiral nematic liquid crystals

The exact molecular reorientation model for nematic liquid crystals taking into account all diagonal Frank elastic constants and using two angles to describe director orientation is presented. Solutions and simplified equations are shown for the most common planar and chiral configurations. Gaussian beam propagation simulated using fully vectorial Beam Propagation Method in nonlinear case is also provided. Detailed comparison between exact solutions and single Frank constant approximation is made. However, no significant differences between these two models were found neither in beam propagation nor in polarization distribution, some difficulties may occur in choosing single Frank constant especially when it comes to quantitative results. Presented results correspond to a propagation of a beam of the Gaussian or topologically similar shapes.

Chiral and nonchiral nematic liquid-crystal reorientation induced by inhomogeneous electric fields

We present exact equations and numerical solutions for molecular reorientation in chiral and nonchiral nematic liquid crystals induced by the inhomogeneous field of a shape corresponding to the Gaussian light beam. We show the importance of the individual terms for different light polarization and intensity. We also present examples of simplified equations for particular cases.

Numerical simulation of beam propagation in a layer filled with chiral nematic liquid crystals

The paper presents the way that colour can serve solving the problem of calibration points indexing in a camera geometrical calibration process. We propose a technique in which indexes of calibration points in a black-and-white chessboard are represented as sets of colour regions in the neighbourhood of calibration points. We provide some general rules for designing a colour calibration chessboard and provide a method of calibration image analysis. We show that this approach leads to obtaining better results than in the case of widely used methods employing information about already indexed points to compute indexes. We also report constraints concerning the technique. Nowadays we are witnessing an increasing need for camera geometrical calibration systems. They are vital for such applications as 3D modelling, 3D reconstruction, assembly control systems, etc. Wherever possible, calibration objects placed in the scene are used in a camera geometrical calibration process. This approach significantly increases accuracy of calibration results and makes the calibration data extraction process easier and universal. There are many geometrical camera calibration techniques for a known calibration scene [1]. A great number of them use as an input calibration points which are localised and indexed in the scene. In this paper we propose the technique of calibration points indexing which uses a colour chessboard. The presented technique was developed by solving problems we encountered during experiments with our earlier methods of camera calibration scene analysis [2]-[3]. In particular, the proposed technique increases the number of indexed points points in case of local lack of calibration points detection. At the beginning of the paper we present a way of designing a chessboard pattern. Then we describe a calibration point indexing method, and finally we show experimental results. A black-and-white chessboard is widely used in order to obtain sub-pixel accuracy of calibration points localisation [1]. Calibration points are defined as corners of chessboard squares. Assuming the availability of rough localisation of these points, the points can be indexed. Noting that differences in distances between neighbouring points in calibration scene images differ slightly, one of the local searching methods can be employed (e.g. [2]). Methods of this type search for a calibration point to be indexed, using a window of a certain size. The position of the window is determined by a vector representing the distance between two previously indexed points in the same row or column. However, experiments show that this approach has its disadvantages, as described below. * E-mail: A.Nowakowski@ire.pw.edu.pl Firstly, there is a danger of omitting some points during indexing in case of local lack of calibration points detection in a neighbourhood (e.g. caused by the presence of non-homogeneous light in the calibration scene). A particularly unfavourable situation is when the local lack of detection effects in the appearance of separated regions of detected calibration points. It is worth saying that such situations are likely to happen for calibration points situated near image borders. Such points are very important for the analysis of optical nonlinearities, and a lack of them can significantly influence the accuracy of distortion modelling. Secondly, such methods may give wrong results in the case of optical distortion with strong nonlinearities when getting information about the neighbouring index is not an easy task. Beside this, the methods are very sensitive to a single false localisation of a calibration point. Such a single false localisation can even result in false indexing of a big set of calibration points. To avoid the above-mentioned problems, we propose using a black-and-white chessboard which contains the coded index of a calibration point in the form of colour squares situated in the nearest neighbourhood of each point. The index of a certain calibration point is determined by colours of four nearest neighbouring squares (Fig.1). An order of squares in such foursome is important. Because the size of a colour square is determined only by the possibility of correct colour detection, the size of a colour square can be smaller than the size of a black or white square. The larger size of a black or white square is determined by the requirements of the exact localisation step which follows the indexing of calibration points [3]. In this step, edge information is extracted from a blackand-white chessboard. This edge information needs larger Artur Nowakowski, Wladyslaw Skarbek Institute of Radioelectronics, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warszawa, A.Nowakowski@ire.pw.edu.pl Received February 10, 2009; accepted March 27, 2009; published March 31, 2009 http://www.photonics.pl/PLP

Curved optical solitons subject to transverse acceleration in reorientational soft matter

We demonstrate that optical spatial solitons with non-rectilinear trajectories can be made to propagate in a uniaxial dielectric with a transversely modulated orientation of the optic axis. Exploiting the reorientational nonlinearity of nematic liquid crystals and imposing a linear variation of the background alignment of the molecular director, we observe solitons whose trajectories have either a monotonic or a non-monotonic curvature in the observation plane of propagation, depending on either the synergistic or counteracting roles of wavefront distortion and birefringent walk-off, respectively. The observed effect is well modelled in the weakly nonlinear regime using momentum conservation of the self-collimated beams in the presence of the spatial nonlocality of the medium response. Since reorientational solitons can act as passive waveguides for other weak optical signals, these results introduce a wealth of possibilities for all-optical signal routing and light-induced photonic interconnects.

NEMATICONS PROPERTIES AND STABILITY IN CHIRAL NEMATIC LIQUID CRYSTAL

We report on the experimental and numerical results of the nonlinear light beam propagation in planar samples of chiral nematic liquid crystals, for both high- and low-birefringence chiral nematic liquid crystals. We investigate the properties and stability of obtained nematicons. We found that reorientational spatial solitons require larger excitation powers in low-birefringence chiral nematics than in high-birefringence but remain more stable and self-focused.

Spatial routing with light-induced waveguides in uniaxial nematic liquid crystals

In reorientational soft-matter with uniaxial character, such as nematic liquid crystals (NLCs), self-confined beams into spatial optical solitons are graded-index waveguides subject to birefringent walkoff. We investigate a router to be realized in a planar cell with an inhomogeneous distribution of the optic axis. Based on the input beam position, the proposed demultiplexer can direct the soliton and the copolarized guided-wave signal(s) to various output ports, enhancing the transverse separation of the exit channels and therefore minimizing crosstalk. Both the soliton and the signal(s) maintain their phasefronts normal to launch and exit wavevectors, allowing for excellent coupling into output channels/fibers at the device exit.

Design of false color palettes for grayscale reproduction

Design of false color palette is quite easy but some effort has to be done to achieve good dynamic range, contrast and overall appearance of the palette. Such palettes, for instance, are commonly used in scientific papers for presenting the data. However, to lower the cost of the paper most scientists decide to let the data to be printed in grayscale. The same applies to e-book readers based on e-ink where most of them are still grayscale. For majority of false color palettes reproducing them in grayscale results in ambiguous mapping of the colors and may be misleading for the reader. In this article design of false color palettes suitable for grayscale reproduction is described. Due to the monotonic change of luminance of these palettes grayscale representation is very similar to the data directly presented with a grayscale palette. Some suggestions and examples how to design such palettes are provided.

Discrete Diffractions and Nematicons in Chiral Nematic Liquid Crystals

In the following paper we present numerical results of light propagation in a cell filled with low birefringent chiral nematic liquid crystals with a small pitch. Due to the periodicity of a structure typical diffraction is substituted with the discrete diffraction similar to the coupling in waveguide array. For particular anisotropy and appropriate pitch diffraction can be controlled by power. Discussion about the shape and the direction of the launched beam is also provided.

Application of planar waveguides with gradient index profile to determine parameters of thin active layers used in waveguide sensors

The presence of thin cover layer on planar waveguide influences its propagation characteristics. A generalized m-line spectroscopy method enables the evaluation of the parameters (the refractive index, n and the thickness, t) of the subguiding layers deposited on a planar waveguide. In this paper algorithm for determination of the parameters of the thin layer (deposited on waveguide with previously evaluated index profile by m-line method) has been presented.

Optical steering of mutual capacitance in a nematic liquid crystal cell

In this study, a variable capacitor made of a nematic liquid crystal cell is proposed and analyzed theoretically. The mutual capacitance is steered with an optical beam of a Gaussian shape launched into the cell. The optical field changes the orientation of the molecules and affects the capacitance. By using Frank–Oseen elastic theory, the molecular reorientation is simulated. The influence of various parameters on capacitance, such as beam width, anchoring condition, externally applied voltage, beam power, and launching position, is presented. For instance, the maximum tuning range is achieved for wide beams and the molecules initially aligned close to the propagation axis. It is also proved that launching position, especially for narrow beams, has limited influence on capacitance. The proposed component can be used, for instance, in optical power meters, as feedback in laser or light-emitting diode systems or just as a variable capacitor in optoelectronic circuits. One of the advantages of this device is that the beam passes through the element, so steering of the capacitance or measuring the parameters of the beam can be realized in-system, without splitting the beam. Moreover, due to the low thickness of the liquid crystal layer, the attenuation is very low.