Pawel S. Jung

Power-induced evolution and increased dimensionality of nonlinear modes in reorientational soft matter

We demonstrate the evolution of higher order one-dimensional guided modes into two-dimensional solitary waves in a reorientational medium. The observations, carried out at two different wavelengths in chiral nematic liquid crystals, are in good agreement with a simple nonlocal nonlinear model.

Quasi two-dimensional astigmatic solitons in soft chiral metastructures.

We investigate a non-homogeneous layered structure encompassing dual spatial dispersion: continuous diffraction in one transverse dimension and discrete diffraction in the orthogonal one. Such dual diffraction can be balanced out by one and the same nonlinear response, giving rise to light self-confinement into astigmatic spatial solitons: self-focusing can compensate for the spreading of a bell-shaped beam, leading to quasi-2D solitary wavepackets which result from 1D transverse self-localization combined with a discrete soliton. We demonstrate such intensity-dependent beam trapping in chiral soft matter, exhibiting one-dimensional discrete diffraction along the helical axis and one-dimensional continuous diffraction in the orthogonal plane. In nematic liquid crystals with suitable birefringence and chiral arrangement, the reorientational nonlinearity is shown to support bell-shaped solitary waves with simple astigmatism dependent on the medium birefringence as well as on the dual diffraction of the input wavepacket. The observations are in agreement with a nonlinear nonlocal model for the all-optical response.

Stable vortex soliton in nonlocal media with orientational nonlinearity

We report on the first experimental observation of stable vortex solitons in nematic liquid crystals with nonlocal nonlinear reorientational response. We show how these nonlinear vortex beams can be formed and confined in extraordinary optical waves by employing the cell with no lateral boundary conditions and the application of an external magnetic field that effectively controls the molecular direction and propagation of the self-trapped beams. We also find that these vortex solitons can be generated in certain ranges of the input beam power.

Supermode spatial optical solitons in liquid crystals with competing nonlinearities

We study numerically the formation of spatial optical solitons in nematic liquid crystals with competing nonlocal nonlinearities. We demonstrate that at a sufficiently high input power the interplay between focusing and thermally induced defocusing may lead to the formation of two-peak fundamental spatial solitons. These solitons have a constant spatial phase and hence represent supermodes of the self-induced extended waveguide structure. We show that these two-peak solitons are stable in propagation and exhibit an adiabatic transition to a single-peak state under weak absorption.

Discrete light propagation in photonic liquid crystal fibers

In this paper, the results of theoretical analyses and experimental tests related to the light propagation in the photonic crystal fiber (PCF) infiltrated with liquid crystal (LC) are presented. While refractive index of the inclusion is higher than that of silica glass, analyzed photonic structure can be considered as a matrix of mutually parallel waveguide channels. This connotes discrete light propagation to be observed in the photonic liquid crystal fiber (PLCF), with the output beam profile strongly dependent on geometrical and optical properties of both the beam and the fiber. Moreover, when the optical nonlinearity is taken into account, spatial light localization and/or delocalization can be obtained with the final scenario implied by the amount of optical power and the molecular orientation of LC. In special cases discrete spatial soliton can be obtained, paving thus the way for all-optical switching to be developed n PLCFs.

Evanescent field boundary conditions for modelling of light propagation

Abstract In this work, we introduce a straightforward and original approach for evanescent field boundary conditions (EBCs), which can be, in principle, applied in both Beam Propagation Method (BPM) and Finite Difference Time Domain Method (FDTD) numerical simulations. Importantly, suggested method may serve as an efficient alternative to typically applied ones, such as transparent boundary conditions (TBCs), absorbing boundary conditions (ABCs) or perfectly matched layer (PML) boundary conditions, giving comparable or even better results in terms of smaller reflections and of shorter computation time. Definition of proposed evanescent function, a way of its practical implementation, as well as an influence of its parameters on the light beam propagation in the free-space and in exemplary photonic structures are described in detail. In addition, results of EBCs application are compared with those achieved for Dirichlet, TBC and PML boundary conditions used in analogous arrangement of the physical systems.

Semi-analytical approach to supermode spatial solitons formation in nematic liquid crystals

We study light propagation in nematic liquid crystals in the context of spatial optical solitons formation. We propose a simple analytical model with multiplicative nonlinearity, which represents (qualitatively) the liquid crystal response by comprising the competition between focusing (reorientational) and defocusing (thermal) nonlocal nonlinearities. We show that at sufficiently high input power the interplay between both nonlinearities leads to the formations of two-peak solitons, which represent supermodes of the self-induced extended waveguide structure. We explain the beam splitting mechanism, discuss threshold effects and conclude that similar phenomena might be present in other media with competing nonlocal nonlinearities.

Tunability of discrete diffraction in photonic liquid crystal fibres

In this paper theoretical and experimental results regarding discrete light propagation in photonic liquid crystal fibres (PLCFs) are presented. Particular interest is focused on tunability of the beam guidance obtained due to the variation in either external temperature or optical power (with assumption of thermal nonlinearity taking place in liquid crystals). Highly tunable (discrete) diffraction and thermal self-(de)focusing are studied and tested in experimental conditions. Specifically, spatial light localization and/or delocalization due to the change in tuning parameters are demonstrated, with possibility of discrete spatial (gap) soliton propagation in particular conditions. Results of numerical simulations (performed for the Gaussian beams of different widths and wavelengths) have been compared to those from experimental tests performed in the PLCFs of interest. Owning to the limit of experimental means, direct qualitative comparison was not quite accessible. Nevertheless, a qualitative agreement between theoretical and experimental data (obtained in analogous conditions) has been achieved, suggesting a compact and widely-accessible platform for the study of tunable linear (and nonlinear) discrete light propagation in two-dimensional systems. Proposed photonic structures are of a great potential for all-optical beam shaping and switching.

All-optical control of discrete light propagation in photonic liquid crystal fibers

Summary form only given. Over the last decade, photonic liquid crystal fibers, PLCFs [which are formed of photonic crystal fibers (PCFs) infiltrated with liquid crystals (LCs)] are subjected to intense scientific investigations. Unique characteristics of the host structures and guest materials translate into the special properties of PLCFs. In fact, LCs used as inclusions allows the optical parameters of PLCFs to be dynamically adjusted by external fields and factors (e.g. by electric and magnetic fields, temperature, strain and pressure) [1] and/or by light beams themselves (i.e. when nonlinear effects are considered in LCs) [2].In this work, the results of theoretical studies and experimental tests on the light propagation in PLCFs are presented. While refractive index of typical LC is higher than that of silica glass, analyzed photonic structure can be considered as a matrix of mutually parallel waveguide channels. This connotes discrete light propagation [3] to be observed in PLCFs, with the output beam profile strongly dependent on geometrical and optical properties of both the beam (i.e. its wavelength and size) and the fiber (i.e. its periodicity and index contrast). Importantly, discrete light propagation in PLCFs can be tuned dynamically - not only by external fields and factors but also, what is particularly important in the context of this communication, by varying optical power of the signal optical beam. As it is shown by numerical simulations, when optical nonlinearity is considered, spatial light localization and/or delocalization can be obtained with the final scenario dependent on the optical power level and the molecular orientation and reorientation of LC (see Fig. 1b-c). Under particular conditions, discrete spatial soliton can be obtained, paving thus the way for all-optical switching to be obtained in PLCFs. Experimental data, acquired with use of the signal beam from Ti:Sapphire laser, also confirm a powerdependence of the beam profile at the output facet of PLCF. A weak collinear probe at the different wavelength was also applied to monitor how the single waveguide channel is decoupled from the rest of the matrix.

The influence of smoke on the THz imaging

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