Multiple image encryption using an aperture-modulated optical system

A multiple image cryptosystem based on different apertures in an optical set-up under a holographic arrangement is proposed. The system is a security architecture that uses different pupil aperture mask in the encoding lens to encrypt different images. Based on this approach multiple encryption is achieved by changing the pupil aperture arrangement of the optical system among exposures. In addition to the classical speckle phase mask, the geometrical parameters characterizing the apertures are introduced to increase the system security. Even when an illegal user steals the speckle phase mask, the system cannot be broken into without the correct pupil geometrical parameters. The experimental set-up is based on a volume photorefractive BSO crystal as storing device. Information retrieval is done via a phase conjugation operation. We also have to stress that the multiple storage under this scheme, is only possible with the help of the aperture mask. Simulation and experimental results are further introduced to verify the proposed method.     

Analysis of permeability for the fractal-like tree network by parallel and series models

This work investigates the hydraulic conductivity properties in the fractal-like tree networks between one point and a straight line. The expression for the effective permeability of the networks is derived based on the parallel and series models and the relationship between the effective permeability and the geometry structures of the network is analyzed. It is found the effective permeability after including tortuosity is about 20% lower than that without considering the tortuosity, and the tortuosity effect should be included in analysis of hydraulic conductivity properties in the networks; the effective permeability is very sensitive to the geometrical structures of the network. A comparison of the fractal-like tree network with the traditional parallel net indicates that the fractal-like tree network can provide much higher permeability than that of the traditional parallel net.     

微聚焦菲涅耳波带板聚焦特性研究

通过激光轰击Ti平面靶,用微聚焦菲涅尔波带板做成像器,测到了在放大倍数为66倍时X射线焦斑图像.利用Fresnel-Kirchhoff衍射积分公式数值模拟了微聚焦菲涅尔波带板的点扩展函数,模拟结果表明该微聚焦菲涅尔波带板在两倍焦距处强聚焦.改变物距和像距但保持透镜的物像距公式,也可得到类似的结果.模拟和实验表明微聚焦波带板可以应用于X射线点对点成像,实现激光等离子体X射线高空间分辨成像. 关键词： 菲涅尔波带板 Fresnel-Kirchhoff衍射 数值模拟 点扩展函数     

Geometrical frustration in 2D optical patterns

In the case of 2D optical patterns, frustration comes from the interplay between the physical constraints (light-matter interaction) and the geometrical constraints (cavity length and structure). Depending on the dynamical parameters, we are able to single out two distinct behaviors. For small diffusion and close to threshold, the system is forced to fulfill the geometrical constraints giving rise to a phase dynamics of quasicrystals. For larger diffusion, the system fragmentates into spatial domains giving rise to a competition between different patterns. By means of a geometrical argument, we show that the spatial distribution of domains is related to the symmetry imposed by the geometrical constraint and that the domain borders are disinclination defects. These defects being the nucleation centers of spatial domains, they trigger the onset of pattern competition. Received 27 December 1999 and Received in final form 29 March 2000     

AC transport and magnetic characterisation of multifilamentary Ag-BSCCO(2223) tapes with different filament arrangements

AC losses in multifilamentary tapes depend on various parameters. Among them, geometrical factors such as overall tape width and thickness as well as the precise arrangement of the filaments are expected to have an important influence. Several theoretical models describe this dependency. In order to study these geometrical effects experimentally, we prepared a series of Bi(2223)/Ag tapes with gradually changing filament arrangements and tape aspect ratio, and characterised them by AC transport and magnetic measurements. The results are compared to model predictions.     

Geometrical thermodynamics and P–V criticality of the black holes with power-law Maxwell field

We study the thermodynamical structure of Einstein black holes in the presence of power Maxwell invariant nonlinear electrodynamics for two different cases. The behavior of temperature and conditions regarding the stability of these black holes are investigated. Since the language of geometry is an effective method in general relativity, we concentrate on the geometrical thermodynamics to build a phase space for studying thermodynamical properties of these black holes. In addition, taking into account the denominator of the heat capacity, we use the proportionality between cosmological constant and thermodynamical pressure to extract the critical values for these black holes. Besides, the effects of the variation of different parameters on the thermodynamical structure of these black holes are investigated. Furthermore, some thermodynamical properties such as the volume expansion coefficient, speed of sound, and isothermal compressibility coefficient are calculated and some remarks regarding these quantities are given.     

Mitigation of Diffraction Fringe in Quasi-Far Field Pattern Using an Edge-Shaped Plate

A new concept is developed for improving the laser intensity distribution in quasi-far field using geometrical optics of a continuous phase (so-called edge-shaped plate). The diffraction fringe on a quasi-far field beam pattern of a well collimated He-Ne laser beam 5 cm in diameter is mitigated by the insertion of an edge-shaped plate with a super-Gaussian (n=40) surface profile. A diffraction code using Fresnel-Kirchhoff diffraction integration was developed to calculate diffraction patterns of aspherical optical elements. The measured beam profile is in good agreement with the calculated beam pattern.     

A setup to study aero-acoustics for finite length ducts with time-varying shape

Elastic ducts with time-varying geometry are a recurrent issue in many engineering and physiological flow or sound production problems. In this study, we present and characterize a setup to study aero-acoustic phenomena through a deformable duct with time-varying geometry. The setup is designed in such a way that experimental control parameters relate directly to input parameters of a quasi-analytical geometrical model (Van Hirtum, 2015). We focus on low Mach number and moderate Reynolds number applications pertinent to physiological problems for which geometrical model input parameters can be related to well defined physiological quantities. Therefore, data gathered using the presented setup allow to study underlying physical phenomena and in addition favor comparison with high performance computational simulations as well as with analytical models for which a limited number of physiological meaningful input parameters are essential. Typical measurements illustrate the impact of geometrical control parameters on the acoustic pressure field in absence and in presence of flow, respectively.     

Special features of the diffraction of light on optical Fibonacci gratings

Diffraction gratings designed on the basis of the geometrical properties of 1D quasicrystalline structures are considered. It is shown that the diffraction peak position is highly stable against small perturbations of the grating profile when the periodic pattern of the alternating elements comprising the profile remains unchanged. The fractal character of the diffraction patterns is also preserved during perturbations, with the fractal geometry obeying the principle of the Golden ratio.     

Shifting curves based on the detector integration effect for x-ray phase contrast imaging

In theory, we find that the actual function of the analyzer grating in the Talbot–Lau interferometer is segmenting the self-images of the phase grating and choosing integral areas, which make sure that each period of self-images in one detector pixel contributes the same signal to the detector. Furthermore, in the case of the lack of an analyzer grating, the shifting curves are still existent in theory as long as the number of fringes is non-integral in a detector pixel, which is a sufficient condition for creating shifting curve. The sufficient condition is available for not only the Talbot–Lau interferometer and the inverse geometry of Talbot–Lau interferometer, but also the x-ray phase contrast imaging system based on geometrical optics. In practical applications, we propose a method to improve the performances of the existing systems by employing the sufficient condition. This method can shorten the system length, is applicable to large period gratings, and can use the detectors with large pixels and large field of view. In addition, the experimental arrangement can be simplified due to the lack of an analyzer grating. In order to improve detection sensitivity and resolution, we also give an optimal fringe period.We believe that the theory and method proposed here is a step forward for x-ray phase contrast imaging.     

带有相位拓朴数的环形相位板调控高斯光束的梯度力

 用基于德拜近似条件的矢量衍射理论研究了带有相位拓朴数的环形相位板调控高斯光束的光梯度力分布,改变相位板环形区的相对半径或当相位板的相位以一定拓扑数呈现拓扑变化时,可以调节光学系统焦点区域的光梯度力分布,形成各种非常有规则的几何形状的光陷阱,如当拓朴数分别取3,4,5,6时,可形成三角形、四边形、五边形和六边形光陷阱。此种相位板可用来构建可调的光镊系统,且通过调节相位板的各区域半径和拓扑数可以得到所希望的光陷阱。     

Geometry in transition: a model of emergent geometry

We study a three matrix model with global SO(3) symmetry containing at most quartic powers of the matrices. We find an exotic line of discontinuous transitions with a jump in the entropy, characteristic of a 1st order transition, yet with divergent critical fluctuations and a divergent specific heat with critical exponent alpha=1/2. The low temperature phase is a geometrical one with gauge fields fluctuating on a round sphere. As the temperature increased the sphere evaporates in a transition to a pure matrix phase with no background geometrical structure. Both the geometry and gauge fields are determined dynamically. It is not difficult to invent higher dimensional models with essentially similar phenomenology. The model presents an appealing picture of a geometrical phase emerging as the system cools and suggests a scenario for the emergence of geometry in the early Universe.     

Analysis and prediction of single laser tracks geometrical characteristics in coaxial laser cladding process

Direct Laser Fabrication is a promising new manufacturing technology coming from laser cladding process. From a coaxial nozzle, powder is fed through a laser beam on a substrate. The powder melting and solidification processes lead to the fabrication of a part layer by layer. In this work 316L stainless steel powder is used to form laser tracks on a low carbon steel substrate. The layer geometry is an important process characteristic to control the final part of fabrication. This paper presents analytical relationships between the laser tracks geometrical characteristics (width, height, area, penetration depth) and the processing parameters (laser power P, scanning speed V and powder mass flow Q_m). Three values of each processing parameters are fixed and so 27 different experiments have been made and analyzed. The validity of these results is discussed studying the correlation coefficient R, the graphical analysis of the residuals and the uncertainty evaluations. Two kinds of models are studied to predict the form and the geometrical characteristics of the single laser tracks cross sections. The first one is an analytical model in which the distribution of the powder in the feed jet is supposed to govern the laser clad geometry. Three distributions are proposed: Gaussian, uniform and polynomial. In the second model the general form of the clad cross section is supposed to be a disk due to the surface tension forces. Analytical relationships are established between the radius and the center of the disk in one hand and the process parameters in the other hand. This way we show that we can reproduce the laser track geometry in all the area experimentally explored.     

Strain mapping of semiconductor specimens with nm-scale resolution in a transmission electron microscope

The last few years have seen a great deal of progress in the development of transmission electron microscopy based techniques for strain mapping. New techniques have appeared such as dark field electron holography and nanobeam diffraction and better known ones such as geometrical phase analysis have been improved by using aberration corrected ultra-stable modern electron microscopes. In this paper we apply dark field electron holography, the geometrical phase analysis of high angle annular dark field scanning transmission electron microscopy images, nanobeam diffraction and precession diffraction, all performed at the state-of-the-art to five different types of semiconductor samples. These include a simple calibration structure comprising 10-nm-thick SiGe layers to benchmark the techniques. A SiGe recessed source and drain device has been examined in order to test their capabilities on 2D structures. Devices that have been strained using a nitride stressor have been examined to test the sensitivity of the different techniques when applied to systems containing low values of deformation. To test the techniques on modern semiconductors, an electrically tested device grown on a SOI wafer has been examined. Finally a GaN/AlN superlattice was tested in order to assess the different methods of measuring deformation on specimens that do not have a perfect crystalline structure. The different deformation mapping techniques have been compared to one another and the strengths and weaknesses of each are discussed.     

Correlation of electron self-energy with geometric structure in low-energy electron diffraction

In low-energy electron diffraction (LEED) studies of surface geometries where the energy dependence of the intensities is analyzed, the in-plane lattice parameter of the surface is usually set to a value determined by x-ray diffraction for the bulk crystal. In cases where it is not known, for instance in films that are incommensurate with the substrate, it is desirable to fit the in-plane lattice parameters in the same analysis as the perpendicular interlayer spacings. We show that this is not possible in a conventional LEED I(E) analysis because the inner potential, which is typically treated as an adjustable parameter, is correlated with the geometrical structure. Therefore, without having prior knowledge of the inner potential, it is not possible to determine the complete surface structure simply from LEED I(E) spectra, and the in-plane lattice parameter must be determined independently before the I(E) analysis is performed. This can be accomplished by establishing a more precise experimental geometry. Further, it is shown that the convention of omitting the energy dependency of the real part of the inner potential means geometrical LEED results cannot be trusted beyond a precision of approximately 0.01 ?.     

Characterization of micro-lenses based on single interferogram analysis using Hilbert transformation

Measurement of the shape, surface quality, and optical performance of micro-lenses, as well as, the uniformity of the parameters across the wafer is an important issue. In this paper we describe a reflection/transmission microscopic interferometer for characterization of micro-lens array. A Hilbert transform (HT) based method is applied to enhance the fringe contrast and to recover the phase from a single fringe pattern with closed fringes. The reflection mode of operation reveals the geometrical properties of the array whereas transmission mode of operation provides information regarding the focal properties of the micro-lenses. Experimental results on a square-packed fused silica micro-lens array are presented.     

Structural aspects of solid-state amorphization in Eu<Subscript>2</Subscript>(MoO<Subscript>4</Subscript>)<Subscript>3</Subscript> single crystals

X-ray diffraction studies of Eu₂(MoO₄)₃ single crystals were performed, which demonstrate that, in contrast to polycrystalline samples, these crystals do not exhibit amorphous-like diffraction patterns during the reverse transition from the high-pressure phase into the initial β phase; rather, the diffracted intensity in their diffraction patterns decreases significantly to the background. Such a diffraction pattern can be explained under the assumption that a single crystal is divided into small (nanoscopic) regions inside which the lattice parameters of the high-pressure phase and the initial β phase change continuously. The simultaneous recovery of the single-crystal state of the β phase from this intermediate state in all nanoscopic regions as the annealing temperature increases indicates that nanocrystals in this state are structurally correlated with each other. This result suggests that the halo-type diffraction patterns of polycrystalline samples reflect an intermediate state between the high-pressure phase and the β phase in every initial crystallite (as in the single crystals) rather than being caused by an amorphous structure of the sample. In this case, the total diffraction pattern of differently oriented crystallites gives an amorphous-like diffraction pattern reflecting the contributions from numerous various crystallographic planes involved in diffraction.     

Geometrical theory of energy launching and pulse distortion in dielectric optical waveguides

In this paper the geometrical theory of pulse distortion and energy launching into multimode optical fibres is generalized when skew rays are taken into account. To this purpose, within the geometrical theory of skew rays, we firstly obtained a new expression for the numerical aperture. From this expression we derived an extensive analysis of the energy launched and the pulse response of a multimode optical fibre. A better launching efficiency and a different pulse form at the output of the fibre together with a larger broadening are obtained in comparison with the results derived from theories only for meridional rays. The theory is also applied to sources having planar geometry (such as LED) and linear geometry (such as semiconductor lasers), and the response to some rectangular-shaped pulses is investigated. Finally some considerations concerning scattering effects are described.     

Designing Ultra-High-Birefringent Photonic Crystal Fibers with Circular Air Holes in the Cladding

Abstract

This article reports a new air-silica photonic crystal fiber structure of high birefringence (~10^?2). The birefringence is due to large axial anisotropy introduced in the fiber geometry by a preferred arrangement of circular air holes of different sizes in the cladding structure along orthogonal directions. A series study of birefringence and cut-off properties of the fiber that leads to optimization of geometrical parameters toward maximized birefringence achievable in the single-mode regime through this micro-structure is provided. Also, other inherently related modal properties of the fiber and the stack design toward preform realization are investigated. The findings should be useful in realizing high-performance high-birefringence fiber.     

Ultrafast optical switching by use of fully phase-matched cascaded second-order nonlinearities in a polarization-gate geometry

We show that cascaded second-order nonlinear-optical processes can occur in a convenient polarization-gate beam geometry. Our arrangement uses type II phase matching, and both individual second-order processes (upconversion and downconversion) are simultaneously phase matched. This geometry can be applied to efficient ultrafast optical switching. With a beta-barium borate crystal and lightly focused 250-fs, 7.3-microJ pulses, we achieve a switching efficiency of 15% and an on-off ratio of 3 x 10(4) on a pulse-length-limited time scale.