Field Diffraction Pattern Research Articles

Diffraction of gratings with rough edges

We analyze the far field and near field diffraction pattern produced by an amplitude grating whose strips present rough edges. Due to the stochastic nature of the edges a statistical approach is performed. The grating with rough edges is not purely periodic, although it still divides the incident beam in diffracted orders. The intensity of each diffraction order is modified by the statistical properties of the irregular edges and it strongly decreases when roughness increases except for the zero-th diffraction order. This decreasing firstly affects to the higher orders. Then, it is possible to obtain an amplitude binary grating with only diffraction orders -1, 0 and +1. On the other hand, numerical simulations based on Rayleigh-Sommerfeld approach have been used for the case of near field. They show that the edges of the self-images are smoother than the edges of the grating. Finally, we fabricate gratings with rough edges and an experimental verification of the results is performed.

UV-Laser irradiation effects on silver nanostructures

The induced changes on silver nanostructures are investigated using a special experimental procedure consisting in depositing and subsequently inducing the changes directly on transmission electron microscopy grids. The nanostructures have different morphologies, from isolated spherical-like particles to quasi-percolated films. The UV laser-induced modifications were investigated using transmission electron microscopy and atomic force microscopy obtaining three-dimensional information on the nanostructures. Upon irradiation with a single laser pulse a quasi-percolated film is transformed into an assembly of silver nanoparticles. Upon further irradiation the nanoparticles grow in size. Furthermore the arrangement of these silver nanoparticles assemblies can be controlled by irradiating the nanostructured silver film through a mask. In the present work, we have used a transmission electron microscopy square grid as a diffractive device and have observed that the corresponding near field diffraction pattern is imprinted on the silver nanostructured film.

Coherent diffractive imaging and partial coherence

We formulate coherent diffractive imaging in the framework of partially spatially coherent diffraction. We find that the reconstruction can be critically dependent on the degree of coherence in the illuminating field and that even a small departure from full coherence may invalidate the conventional assumption that a mapping exists between an exit surface wave of finite support and a far field diffraction pattern. We demonstrate that the introduction of sufficient phase curvature in the illumination can overcome the adverse effects of partial coherence.

Thermally induced effects on the diffraction pattern of a dye doped nematic film

We investigate the effects produced on the diffraction pattern of a dyed nematic thin film under the action of an optical field and a low frequency AC electric field. For a homeotropically aligned mixture of the nematic E7 doped with a dichroic dye, a sequence of dynamical regimes of the far field diffraction pattern is observed. For specific values of the beam's power, frequency and amplitude of the AC field, a uniform steady rotational motion (SR) of the pattern sets in with a measured angular velocity νexp =2.58 Hz. To account for this and other observed features of the diffraction pattern an analytical model is proposed. This allows us to describe quantitatively the reorientation of the film, to calculate some specific structural features of the diffraction pattern, as well as its angular velocity. We find that the predicted angular velocity νtheor=5.7 Hz, is in quite good agreement with the measured value.

“In situ” and “Post-mortem” TEM study of the super-elastic effect in Cu–Al–Ni shape memory alloys

An analysis of the microstructure evolution during super-elastic cycling has been performed by transmission electron microscopy (TEM) in order to understand the physical mechanism responsible for the thermo-mechanical properties evolution, as well as the martensitic transformation ageing. Particularly, in this work we have studied the super-elastic effect in Cu–Al–Ni shape memory alloys by “in situ” TEM experiments. The bright field images and diffraction patterns have allowed us to determine, during the transformation, the kind of nucleated martensite variants and their relative orientations. Finally, we have analysed the super-elastic effect on the dislocation microstructure and on the transformation temperatures.

Diameter estimation of cylinders by the rigorous diffraction model

The Fraunhofer diffraction formula is commonly used for estimating the diameter of thin cylinders by far field diffractometry. However, an experimental systematic overestimation of the value of the cylinder diameter by this diffraction model and other three-dimensional models has been reported when this estimation is compared with those obtained from interferometric techniques. In this work, a rigorous electromagnetic diffraction model is analyzed to determine the cylinder diameter by using the envelope minima of the far field diffraction pattern. The results of this rigorous model are compared with those from the Fraunhofer diffraction formula. The overestimation by the Fraunhofer model is predicted theoretically, presenting a dependence on the wavelength, the polarization state of the incident wave, and the cylinder diameter. The discrepancies are shown to be due to the three-dimensional geometry.

Fabrication error model and near field beam modulation analysis for phase step diffractive gratings

The structure aberrations of color separating grating (CSG), which is caused by the fabrication process, generate great modulations to the laser beam when CSG is used in the final optical system of a high power laser system. The beam modulations may lead to severe optical damages to CSG itself and the system. In this paper, a comprehensive fabrication error model for CSG is developed to study the beam modulation characteristics in the near field. Through theoretical calculations and simulations, the near field diffraction pattern of CSG is obtained, and the relationship between beam modulations and CSG structural aberrations is presented. The results show that beam modulations are mainly caused by the stair depth error and the slope error. This study provides a convenient way to estimate the possibility of optical damages induced by CSG.

The geometrical optics approach for multidimensional liquid crystal cells

We present an approach based on the geometrical optics approximation (GOA) for analysis of liquid crystal cells whose director varies in more than one spatial dimension (multidimensional liquid crystal cells). The GOA is applied to calculate light transmittance and far field diffraction patterns for two- and three-dimensional nematic liquid crystal films. Important features of the GOA, such as a method of eliminating non-convergence problems that can occur during the iterative numerical solution of the equations for the amplitudes of the electromagnetic field, are described. We compare the results obtained from the GOA with those produced by the quasi-one-dimensional Jones calculus and the beam propagation method, where the latter is applicable. It was found that the refraction (or ray bending) effects, produced by the GOA, are more important than effects of diffraction and light scattering, which means that the GOA (unlike the Jones calculus) is accurate for the considered type of liquid crystal cells, whose director varies on the micron scale. The GOA is about as fast as the Jones method and is applicable for calculating optical properties of liquid crystal cells with any number of dimensions of director variations.

In situ synthesis of TiC/Fe composites by reaction casting

A new technique for reaction casting is put forward in this paper. According to the results of the temperature field and X-ray diffraction patterns, and combined with the theoretical analysis, it is proven that iron matrix composites with low volume fractions of TiC reinforcement can be produced by this technique. The process includes four steps for the reactants: added to iron matrix, dissolve and diffuse in the melt, absorb the thermal energy from the melt for reaction, and synthesize TiC in situ. The first step is the key to this approach, which is unique, novel and significantly different from the previous techniques.

Implementation of a two-telescope array as a transmitting synthesized antenna demonstrator for satellite communications

We report a preliminary experimental study on a transmitting synthesized antenna constituted by a two-lens array. We realized experimentally the shifting of the entire far field diffraction pattern over more than 100 µrad. This corresponds to a change of the global transmitting direction, by acting simultaneously on the transmitting direction of the elementary fields (tilt) and the phase difference between the elementary fields (piston). The light flux transmitted from the source is forwarded to the elementary lenses of the antenna using optical fibres. We obtain experimentally an error signal permitting servo-control of the piston of the antenna around a given functioning point.

Reducing far-field diffraction by structured apertures

We demonstrate significant reduction in the angular distribution of the far field diffraction pattern from a wavelength-sized slit when we place a narrow (sub-wavelength) strip in the middle of the slit. The higher directionality is attributed to constructive and destructive interference in the central and lateral parts of the diffracted beam, respectively. Measurements in the visible and near-IR agree well with numerical simulations.

Optical Properties of a Switchable Diffraction Grating

We have performed detailed measurements of the far field diffraction pattern of an electrically switchable liquid crystal grating. The grating, with a period of 25 microns, was formed using interdigitated aluminum electrodes with a 15 micron gap between adjacent electrodes. The homeotropically aligned liquid crystal (ZLI-4792) had a thickness of 5 microns. We measured the diffracted intensity profile of HeNe laser light (633nm) for different applied between adjacent electrodes. The amount of light diffracted into the first order relative to zeroth order is strongly dependent on the applied voltage. The locations of successive maxima and minima also shift with the applied voltage. We studied the diffraction theoretically using geometrical optics coupled with Kirchoff diffraction theory. This theoretical model is in substantial agreement with the empirical results.

Two-dimensional 45/spl deg/ surface-normal microcoupler array for guided-wave optical clock distribution

Surface-normal couplers are indispensable parts of a guided-wave optoelectronic interconnects for the coupling of optical signals into and out of the waveguides while facilitating the packaging. In this paper, integration of the 45/spl deg/ surface-normal couplers at each fanout end of the H-tree waveguide structure is described. An optical clock signal distribution system is under development using polyimide based H-tree waveguide structure. The coupler is a 45/spl deg/ slanted end surface of the polyimide waveguide. The coupler works for a wide range of wavelength. The experimentally estimated output coupling efficiency is nearly 100%. To determine the optimized size and shape of the photodetector, near and far field diffraction patterns are evaluated. Experimental results conclude that the phenomenon is dominated by the fundamental mode of the highly multimode waveguide.

Near–field diffraction by two slits in a black screen

Measurements were made with microwaves of the near–field diffraction pattern formed by two parallel slits in a highly absorbing (‘blac’) screen. The first purpose was to examine the validity of superposing the fields of the two separate slits, as would follow from the standard Kirchhoff or Rayleigh–Sommerfeld theories. An earlier paper showed that, with a conducting screen, there is a departure from exact superposition of 7%, on average, when the polarization is parallel to the slits and 25% when it is perpendicular. The new experiments, which were done at normal incidence with slit widths of 0.5λ and separation 1.5λ, show that, with a black screen, there is a departure from exact superposition of 11% when the polarization is parallel, and 15% when it is perpendicular. Each slit generates a field behind the screen, but, unlike the case of the conducting screen, the source of the field cannot be considered to be merely the slit itself; it is as if the wave field generated by each of the two slits is affected by whether the other is open or closed. The width of the maximum immediately behind a single slit depends strongly on the polarization, an observation that has implications for resolution in, for example, the making of masks using near–field optics. All scalar theories of diffraction by a black screen with translational symmetry imply that the patterns of electric field associated with two different polarizations in the incident wave are related: one is the spatial derivative of the other. The fact that this theoretical relation is obeyed by the measurements to a close approximation shows that scalar theory is applicable, as an approximation, for the imperfect ‘black’ screen used. The relation would not be obeyed for a conducting screen.

Microstructural characterization of polymer blends

AbstractMicroscopy techniques for direct visualization of phases in polymer blends are reviewed. Light microscopy is suitable for immiscible blends and contrast techniques include polarized light, phase contrast, differential interference contrast, and fluorescence. Each technique has an application for a particular polymer system. Scanning electron microscopy is used for study of surface morphology and contrast can be enhanced by electron beam damage or by chemical etching. Cutting often provides sufficient contrast, but surface preparation by fracture or by solvent extraction must be used with caution. Surface carbon replica is a good alternative that provides better resolution and contrast. A new technique of selective swelling will be discussed. Transmission electron microscopy has very good resolution and can thus be used for the study of very fine dispersion in miscible blends. Contrast can be enhanced electronically or by staining of pre‐irradiated samples. It will be shown that the latter, together with mass loss measurements, can provide some new and unique information on the polymer blend system. Crystallographic studies are limited by the beam damage. It is nevertheless possible with some specialized techniques (STEM and microdiffraction) to obtain several dark field images and diffraction patterns from one area of highly beam sensitive polymers.

Effects of binary phase plates on the far field diffraction pattern of an out of phase coupled linear array of waveguide lasers

In this paper we study the use of a binary phase plate for transforming the double-lobed far-field diffraction pattern of an array oscillating on the out-of-phase mode into a single-lobed pattern. We analyse, versus the filling factor of the array and the distance between the array and the phase filter, the amount of the emitted energy contained in the main lobe. We then compare, in terms of the power concentrated in the central lobe, various configurations of a linear array phase-coupled by the Talbot effect.

Optical Frederiks Transition: Bulk Director Reoriententation Measurement From Diffraction Pattern and T.I.R Investigations

Abstract Three different results on optically distorded nematic films are presented. They have been derived from T.I.R. experiments and graphical discussion on the observed far field diffraction pattern. First, the optically induced director reorientation profile (radial dependence) in a nematic film can be much more larger than the pump beam profile. Second, a maximum reorientation tilt angle as large as 80 degrees can be obtained and third, the same sample can be focusing, diffracting and defocusing depending on the pump power. The later is a pure thermal effect and occurs as the boundary conditions are very weak.

Use of the moire effect to improve diameter measurements with charge coupled imagers

An optoelectronic setup has been developed for in-situ measurements of thin glass cylinder diameters. The principle of the method is based on the in-line far field diffraction pattern analysis. The photometric signal is recorded with a 2-D CCD array sensor. The running time is reduced (0.25 s) using the Newton method to solve the inverse problem of the diffraction. It is worth noting that the 2-D analysis of an 1-D diffraction pattern provides several spatial sampling lines at a given time. Thus, the signal to noise ratio (SNR) is improved with an average along the cylinder axis. Other filtering techniques and interpolation algorithms can be applied. After this signal processing, a moire pattern is observed. This pattern is strongly dependent on the object angular position and the distance between the object and the detector. Then, it provides additional information which can be used to validate the recording cycle.

Electron diffraction through an aperture in a potential wall

We study the diffraction of a two-dimensional Gaussian wavepacket through a rectangular aperture in a finite potential wall (one slit experiment). For wavepacket with incident wavevector k 0 satisfying the diffraction condition, k 0 = 2 π/ w, w being the slit width, the near field (Fresnel-like) diffraction pattern behind the slit can be clearly seen for small time duration (<0.2ps). At later time steps, the diffracted beam is fragmented into lobes (perpendicular to the direction of incidence of the wavepacket) as a result of the multiple reflections of the wavepacket inside the slit (assumed to be of finite thickness). At later time, no far-field Fraunhoffer diffraction pattern is observed in our numerical simulations.

Electron spectroscopic imaging (ESI) on multiphase polymer materials

In transmission electron microscopy the natural contrast of polymers is very low. Thus the contrast has to be enhanced by staining with heavy metals. The resolution is limited by the size of the staining particles and by the fact that electrons with different energy are focused in different image planes due to the chromatic aberration of the magnetic lenses. The integration of an electron energy loss spectrometer into the optical coloumn of a transmission electron microscope offers the possibility to use monoenergetic electrons and to select electrons with a certain energy for imaging. Thus contrast and resolution are enhanced. By imaging only electrons with an element specific energy loss the element distribution in the sample can be obtained. In addition, elastic bright field images and diffraction patterns yield excellent resolution. Some applications of the method on multicomponent polymer materials are discussed.Bulk polymer samples were prepared by ultramicrotoming at room temperature or well below the glass transition temperature. Very thin films for the direct observation of the structure in semicrystalline polymers were obtained by melt-spinning. Specimens were examined with a ZEISS CEM 902 operated at 80 kV.