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Showing papers on "Diffraction published in 2001"


Journal ArticleDOI
TL;DR: In this paper, a point dipole analysis predicts group velocities of energy transport that exceed 0.1c along straight arrays and shows that energy transmission and switching through chain networks such as corners and tee structures is possible at high efficiencies.
Abstract: The further integration of optical devices will require the fabrication of waveguides for electromagnetic energy below the diffraction limit of light. We investigate the possibility of using arrays of closely spaced metal nanoparticles for this purpose. Coupling between adjacent particles sets up coupled plasmon modes that give rise to coherent propagation of energy along the array. A point dipole analysis predicts group velocities of energy transport that exceed 0.1c along straight arrays and shows that energy transmission and switching through chain networks such as corners (see Figure) and tee structures is possible at high efficiencies. Radiation losses into the far field are expected to be negligible due to the near-field nature of the coupling, and resistive heating leads to transmission losses of about 6 dB/lm for gold and silver particles. We analyze macroscopic analogues operating in the microwave regime consisting of closely spaced metal rods by experiments and full field electrodynamic simulations. The guiding structures show a high confinement of the electromagnetic energy and allow for highly variable geometries and switching. Also, we have fabricated gold nanoparticle arrays using electron beam lithography and atomic force microscopy manipulation. These plasmon waveguides and switches could be the smallest devices with optical functionality.

1,650 citations


Journal ArticleDOI
TL;DR: WinPLOTR is a graphic program for the analysis of powder diffraction patterns that has been developed for a Windows 9x/2k/NT environment and can be used as a Graphic User Interface for programs defined by the user.
Abstract: WinPLOTR is a graphic program for the analysis of powder diffraction patterns. It has been developed for a Windows 9x/2k/NT environment. It takes advantage of this graphical environment to offer a powerful and user-friendly powder diffraction tool. The program is able to display and analyse many different kinds of diffraction patterns as well as calculated and observed profiles coming from the Windows/DOS version of the program FullProf. It can also be used as a Graphic User Interface (GUI) for programs defined by the user.

1,638 citations


Book ChapterDOI
TL;DR: In this paper, an isolated dark ring is created within a light beam, with an analytical description of the field, and a screw wave-front dislocation has a feature that the spatial structure of the wave front has the form of a helicoid around the dislocation axis.
Abstract: Singular optics is a branch of modern physical optics that involves a wide class of effects associated with the phase singularities in wave fields and with the topology of wave fronts. Optical singularities (optical vortices) exhibit some fundamental features absent in the "usual" fields with smooth wave fronts. Namely, optical vortices possess orbital angular momentum, topological charge for helical wave front of beams with well-defined direction of propagation. As a result, an interesting spatial evolution can be generated such as optical vortices "nucleation" and "annihilation" by pairs with participation of phase saddles, often called "optical chemistry." To study the structure of the circular edge dislocation, an isolated dark (zero-amplitude) ring is created within a light beam, with an analytical description of the field. A screw wave-front dislocation has a feature that the spatial structure of the wave front has the form of a helicoid around the dislocation axis. The chapter also describes reflection, refraction, interference and diffraction of OVs. Both frequency up- and down-conversion processes possess essential peculiarities for light beams with OVs. The chapter discusses the topology of wave fronts and vortex trajectories. Gouy phase shift in singular optics is also described in the chapter.

725 citations


Journal ArticleDOI
TL;DR: In this article, a simple and pragmatic method is suggested to determine the crystallite size distribution in the presence of strain using modified Williamson-Hall and Warren-Averbach procedures.
Abstract: Two different methods of diffraction profile analysis are presented. In the first, the breadths and the first few Fourier coefficients of diffraction profiles are analysed by modified Williamson–Hall and Warren–Averbach procedures. A simple and pragmatic method is suggested to determine the crystallite size distribution in the presence of strain. In the second, the Fourier coefficients of the measured physical profiles are fitted by Fourier coefficients of well established ab initio functions of size and strain profiles. In both procedures, strain anisotropy is rationalized by the dislocation model of the mean square strain. The procedures are applied and tested on a nanocrystalline powder of silicon nitride and a severely plastically deformed bulk copper specimen. The X-ray crystallite size distributions are compared with size distributions obtained from transmission electron microscopy (TEM) micrographs. There is good agreement between X-ray and TEM data for nanocrystalline loose powders. In bulk materials, a deeper insight into the microstructure is needed to correlate the X-ray and TEM results.

665 citations


Book
01 Jan 2001
TL;DR: In this paper, the dynamical theory of diffraction of X-rays by perfect crystals is presented and the expressions for the diffracted intensity are given in both the transmission and reflection cases.
Abstract: This chapter presents the dynamical theory of the diffraction of X-rays by perfect crystals. The most important part is devoted to the case of plane waves (Section 5.1.2). The solutions of the propagation equation of plane waves in crystals are given in Section 5.1.3 using the concept of wavefields introduced by Ewald for X-rays in 1913 and by Bloch for electrons in 1928 (known in solid-state physics as Bloch waves). They are applied to the interpretation of the main properties of dynamical diffraction: anomalous transmission, standing waves and Pendellosung. The expressions for the diffracted intensity are given in both the transmission (Section 5.1.6) and the reflection (Section 5.1.7) cases. The last part (Section 5.1.8) concerns the diffraction of real and spherical waves, which is described in a qualitative way.

653 citations


Journal ArticleDOI
TL;DR: Spectral transmission from a periodic array of such slits features the same peaks with a high increase in their magnitude, confirming that a grating acts as an amplifier of those resonances.
Abstract: Interaction of TM-polarized waves with a subwavelength thick metallic slit has been analyzed. A Fabry-P\'erot-like behavior is reported. The resonance peaks, however, have very low magnitude and a systematic shift towards longer wavelengths is observed. The slit being narrow, this shift can be interpreted as the result of an aperture effect. Spectral transmission from a periodic array of such slits features the same peaks with a high increase in their magnitude, confirming that a grating acts as an amplifier of those resonances. Such a mechanism might explain the enhancement of the transmission observed in recent experiments [T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature (London) 391, 667 (1998)].

472 citations


Journal ArticleDOI
TL;DR: In this paper, a computer program was developed for the determination of microstructural parameters from diffraction profiles of materials with cubic or hexagonal crystal lattices, which were fitted by ab initio theoretical functions for size and strain broadening.
Abstract: A computer program has been developed for the determination of microstructural parameters from diffraction profiles of materials with cubic or hexagonal crystal lattices. The measured profiles or their Fourier transforms are fitted by ab initio theoretical functions for size and strain broadening. In the calculation of the theoretical functions, it is assumed that the crystallites have log-normal size distribution and that the strain is caused by dislocations. Strain and size anisotropy are taken into account by the dislocation contrast factors and the ellipticity of the crystallites. The fitting procedure provides the median and the variance of the size distribution and the ellipticity of the crystallites, and the density and arrangement of the dislocations. The efficiency of the program is illustrated by examples of severely deformed copper and ball-milled lead sulfide specimens.

396 citations


Journal ArticleDOI
TL;DR: In situ synchrotron wide-angle X-ray diffraction (WAXD) was used to monitor crystallization of isotactic polypropylene (i-PP) in the subcooled melt at 140 °C after step shear as discussed by the authors.
Abstract: In situ synchrotron wide-angle X-ray diffraction (WAXD) was used to monitor crystallization of isotactic polypropylene (i-PP) in the subcooled melt at 140 °C after step shear. The melt was subjected to a shear strain of 1430% at three different shear rates (10, 57, and 102 s-1) using a parallel-plate shear apparatus. WAXD results were used to determine the type (α- and β-crystals), orientation, and corresponding mass fractions of i-PP crystals. It was found that formation of oriented α-crystals occurred immediately after application of the shear field. Subsequently, growth of primarily unoriented β-crystals was observed. WAXD patterns clearly showed that β-crystals grew only after the formation of oriented α-crystals in the sheared i-PP melt. The contribution of β-crystals to the total crystalline phase was as high as 65−70% at high shear rates (57 and 102 s-1) and low (20%) at low shear rates (10 s-1), which was attributed to the different amount of surface area of oriented α-crystal cylindrites generate...

387 citations


Journal ArticleDOI
TL;DR: A simple, efficient, and stable method that may be applied to waveguide and grating diffraction problems is proposed and compared with the finite-difference modal method that is widely used in waveguide theory confirms the relevancy of the approach.
Abstract: Recently [Opt. Lett. 25, 1092 (2000)], two of the present authors proposed extending the domain of applicability of grating theories to aperiodic structures, especially the diffraction structures that are encountered in integrated optics. This extension was achieved by introduction of virtual periodicity and incorporation of artificial absorbers at the boundaries of the elementary cells of periodic structures. Refinements and extensions of that previous research are presented. Included is a thorough discussion of the effect of the absorber quality on the accuracy of the computational results, with highly accurate computational results being achieved with perfectly matched layer absorbers. The extensions are concerned with the diversity of diffraction waveguide problems to which the method is applied. These problems include two-dimensional classical problems such as those involving Bragg mirrors and grating couplers that may be difficult to model because of the length of the components and three-dimensional problems such as those involving integrated diffraction gratings, photonic crystal waveguides, and waveguide airbridge microcavities. Rigorous coupled-wave analysis (also called the Fourier modal method) is used to support the analysis, but we believe that the approach is applicable to other grating theories. The method is tested both against available numerical data obtained with finite-difference techniques and against experimental data. Excellent agreement is obtained. A comparison in terms of convergence speed with the finite-difference modal method that is widely used in waveguide theory confirms the relevancy of the approach. Consequently, a simple, efficient, and stable method that may also be applied to waveguide and grating diffraction problems is proposed.

380 citations


Journal ArticleDOI
TL;DR: The successful phasing of an oversampled hard x-ray diffraction pattern measured from a single nanocrystal of gold is reported, and this has recently been demonstrated.
Abstract: Inverse problems arise frequently in physics: The magnitude of the Fourier transform of some function is measurable, but not its phase. The "phase problem" in crystallography arises because the number of discrete measurements (Bragg peak intensities) is only half the number of unknowns (electron density points in space). Sayre first proposed that oversampling of diffraction data should allow a solution, and this has recently been demonstrated. Here we report the successful phasing of an oversampled hard x-ray diffraction pattern measured from a single nanocrystal of gold.

378 citations


Journal ArticleDOI
08 Nov 2001-Nature
TL;DR: It is shown that a large number of pinholes distributed appropriately over the Fresnel zones make it possible to focus soft X-rays to spot sizes smaller than the diameter of the smallest pinhole.
Abstract: Fresnel zone plates consisting of alternating transmissive and opaque circular rings can be used to focus X-rays1. The spatial resolution that can be achieved with these devices is of the order of the width of the outermost zone and is therefore limited by the smallest structure (20–40 nm) that can be fabricated by lithography today2. Here we show that a large number of pinholes distributed appropriately over the Fresnel zones make it possible to focus soft X-rays to spot sizes smaller than the diameter of the smallest pinhole. In addition, higher orders of diffraction and secondary maxima can be suppressed by several orders of magnitude. In combination with the next generation of synchrotron light sources (free-electron lasers) these ‘photon sieves’ offer new opportunities for high-resolution X-ray microscopy and spectroscopy in physical and life sciences.

Journal ArticleDOI
TL;DR: Comparison with high-resolution confocal images exhibits a resolution much beyond the diffraction barrier, particles that are only 65-nm apart are resolved with focused light.
Abstract: We report on the generation of various hole-centered beams in the focal region of a lens and investigate their effectiveness to break the diffraction barrier in fluorescence microscopy by stimulated emission. Patterning of the phase of the stimulating beam across the entrance pupil of the objective lens produces point-spread-functions with twofold, fourfold, and circular symmetry, which narrow down the focal spot to 65--100 nm. Comparison with high-resolution confocal images exhibits a resolution much beyond the diffraction barrier. Particles that are only 65-nm apart are resolved with focused light.

Journal ArticleDOI
01 Nov 2001-Nature
TL;DR: A near-field probe with atomic-scale resolution—a single calcium ion in a radio-frequency trap—that causes minimal perturbation of the optical field and is an ideal system for performing cavity quantum electrodynamics experiments with a single particle.
Abstract: In near-field imaging, resolution beyond the diffraction limit of optical microscopy is obtained by scanning the sampling region with a probe of subwavelength size. In recent experiments, single molecules were used as nanoscopic probes to attain a resolution of a few tens of nanometres. Positional control of the molecular probe was typically achieved by embedding it in a crystal attached to a substrate on a translation stage. However, the presence of the host crystal inevitably led to a disturbance of the light field that was to be measured. Here we report a near-field probe with atomic-scale resolution a single calcium ion in a radio-frequency trap that causes minimal perturbation of the optical field. We measure the three-dimensional spatial structure of an optical field with a spatial resolution as high as 60 nm (determined by the residual thermal motion of the trapped ion), and scan the modes of a low-loss optical cavity over a range of up to 100 m. The precise positioning we achieve implies a deterministic control of the coupling between ion and field. At the same time, the field and the internal states of the ion are not affected by the trapping potential. Our set-up is therefore an ideal system for performing cavity quantum electrodynamics experiments with a single particle.

Journal ArticleDOI
TL;DR: In this article, a qualitative relationship between peak intensities of the X-ray diffraction patterns and the degrees of nanotube alignments was established, which provides a simple way to characterize the alignment degree of as-grown large-area CNTs.

Journal ArticleDOI
TL;DR: In this paper, a procedure for Rietveld quantitative amorphous content analysis (RQACA) is outlined, in which the effects of systematic errors in the powder patterns are studied.
Abstract: A procedure for Rietveld quantitative amorphous content analysis (RQACA) is outlined, in which the effects of systematic errors in the powder patterns are studied. The method derives the amorphous content from the small overestimation of an internal crystalline standard in a Rietveld refinement of an appropriate mixture. Of several standards studied, Al2O3 gave the best results. The statistical analysis of standard mixtures with a known amount of amorphous content indicated that this is a precise and accurate tool. It enables the measurement of the amorphous content with an accuracy close to 1%. Sample preparation and Rietveld analysis need to be optimized in order to minimize the systematic errors. The analysis of samples with phases displaying strong preferred orientation effects gives very high errors in the amorphous content. Samples with different absorption coefficients have also been studied in order to evaluate the importance of microabsorption. This plays an important role but it can be adequately corrected if the absorption coefficients of the standard and the sample are not very different. RQACA has been applied to tricalcium silicate, C3S, which is the main component of Portland cement. The average amorphous content of C3S, after microabsorption correction using two standards of higher and lower absorption coefficients, was found to be 19%.

Journal ArticleDOI
TL;DR: In this paper, a commercial 2205 duplex stainless steel with three different solution treatments (at 1020, 1080 and 1200°C for 3 min) followed by continuous cooling at four respective cooling rates (1, 0.5,0.25 and 0.1°C s −1 ) has been investigated by means of optical metallography, transmission electron microscopy, electron probe microanalysis, X-ray diffraction and differential thermal analysis.
Abstract: A commercial 2205 duplex stainless steel with three different solution treatments (at 1020, 1080 and 1200°C for 3 min) followed by continuous cooling at four respective cooling rates (1, 0.5, 0.25 and 0.1°C s −1 ) has been investigated by means of optical metallography, transmission electron microscopy, electron probe microanalysis, X-ray diffraction and differential thermal analysis. It is found that the lower solution treatment temperature with the lower cooling rate significantly enhanced the σ phase transformation. The σ precipitate could be detected when the specimens were solution-treated at 1020 and 1080°C and cooled at the rate of 0.25°C s −1 ; substantial amounts of σ phase formed when the specimens were cooled at 0.1°C s −1 . The precipitation of σ phase was considerably retarded as the solution temperature increased from 1080 to 1200°C. The precipitation behaviors of σ phase and M 23 C 6 carbide were characterized by transmission electron microscopy. The results indicated that the Cr- and Mo-rich σ phase preferentially nucleated at the pre-formed M 23 C 6 carbide particles, which were located at δ / γ interface or within δ ferrite grain. The selected area diffraction patterns displayed the complicated crystallography of σ phase, and revealed the orientation relationships between the interfacial σ precipitate and adjacent matrix phases.

Book
30 Nov 2001
TL;DR: In this paper, basic acoustic equations for a homogeneous atmosphere are presented. But they do not consider the effect of irregular terrain on the dynamics of the atmosphere. And they only consider a single point source, not a set of points.
Abstract: Preface. 1. Introduction. 2. Unbounded homogeneous atmosphere. 3. Homogeneous atmosphere above a ground surface. 4. Atmospheric refraction. 5. Atmospheric turbulence. 6. Irregular terrain. 7. Noise barriers. A. Basic acoustic equations for a homogeneous atmosphere. B. Free field of a point source. C. Acoustic impedance. D. Reflection of sound waves. E. Basic acoustic equations for a layered refracting atmosphere. F. Generalized Fast Field Program (FFP). G. Parabolic Equation (PE) method. H. Green's Function Parabolic Equation (GFPE) method. I. Atmospheric turbulence. J. Atmospheric turbulence in the PE method. K. Analytical model for a non-refracting turbulent atmosphere. L. Ray model including caustic diffraction fields. M. Computational methods for irregular terrain. N. Wind and temperature profiles in the atmosphere. O. Sound propagation over a screen. P. The method of stationary phase. References. List of symbols. Index.

Journal ArticleDOI
TL;DR: In this article, the structure and composition of CO2 hydrate were determined from single-crystal X-ray diffraction data at 173 K for a crystal grown over heavy water and liquid CO2.
Abstract: The structure and composition of CO2 hydrate were determined from single-crystal X-ray diffraction data at 173 K for a crystal grown over heavy water and liquid CO2. Superior diffraction data allowed the derivation of a structural model of unprecedented quality for the hydrate, giving the location of the disordered CO2 molecules in the two cages. In the large cage, the guests are shown to be off-center, with a bimodal distribution of out-of-plane orientations for the long axis of the molecule (173 K). Also, the absolute cage occupancies were determined from the structural model, thus allowing a reliable and direct evaluation of the hydrate composition for this crystal, CO2·6.20(15) D2O. The temperature dependence of the lattice parameters for the single crystal was measured between 123 and 223 K and found to be in good agreement with recent neutron powder diffraction results, and data from all sources were fit to a single polynomial function. The hydrate composition and density are discussed in terms of t...

Proceedings ArticleDOI
01 Aug 2001
TL;DR: A efficient way for computing the acoustical effect of diffraction paths using the UTD for deriving secondary diffracted rays and associated diffraction coefficients is proposed and a real-time auralization system demonstrating that diffraction dramatically improves the quality of spatialized sound in virtual environments is demonstrated.
Abstract: Realistic modeling of reverberant sound in 3D virtual worlds provides users with important cues for localizing sound sources and understanding spatial properties of the environment. Unfortunately, current geometric acoustic modeling systems do not accurately simulate reverberant sound. Instead, they model only direct transmission and specular reflection, while diffraction is either ignored or modeled through statistical approximation. However, diffraction is important for correct interpretation of acoustic environments, especially when the direct path between sound source and receiver is occluded.The Uniform Theory of Diffraction (UTD) extends geometrical acoustics with diffraction phenomena: illuminated edges become secondary sources of diffracted rays that in turn may propagate through the environment. In this paper, we propose an efficient way for computing the acoustical effect of diffraction paths using the UTD for deriving secondary diffracted rays and associated diffraction coefficients. Our main contributions are: 1) a beam tracing method for enumerating sequences of diffracting edges efficiently and without aliasing in densely occluded polyhedral environments; 2) a practical approximation to the simulated sound field in which diffraction is considered only in shadow regions; and 3) a real-time auralization system demonstrating that diffraction dramatically improves the quality of spatialized sound in virtual environments.

Journal ArticleDOI
TL;DR: In this article, numerical calculations on the field distribution in the focus of an optical system with high numerical aperture are presented, where diffraction integrals based on the Debye approximation are derived and evaluated for a radially polarized input field with a doughnut-shaped intensity distribution.
Abstract: We present numerical calculations on the field distribution in the focus of an optical system with high numerical aperture. The diffraction integrals which are based on the Debye approximation are derived and evaluated for a radially polarized input field with a doughnut-shaped intensity distribution. It is shown that this mode focusses down to a spot size significantly smaller as compared to the case of linear polarization. An experimental setup to measure the three-dimensional intensity distribution in the focal region is presented, which is based on the knife-edge method and on tomographic reconstruction.

Journal ArticleDOI
TL;DR: In this paper, different features of diffraction peak profiles such as broadening, asymmetric peak shape, peak shifts and anisotropic broadening provide a variety of microstructural parameters by modelling crystallite size and strain.
Abstract: X-ray diffraction peak profile analysis has become a powerful tool during the last two decades for the characterisation of microstructure either in the bulk or in loose powder materials. The evaluation and modelling procedures have developed together with the experimental techniques. It will be shown that the different features of diffraction peak profiles such as (i) broadening, (ii) asymmetric peak shape, (iii) peak shifts and (iv) anisotropic broadening provide a variety of microstructural parameters by modelling crystallite size and strain. Modelling strain by assuming dislocations will be more extensive. Two different procedures will be considered: (1) evaluation by using characteristic parameters of individual peak profiles, especially the FWHM, the integral breadths and the Fourier coefficients and (2) multiple whole profile fitting (MWPF) procedure using ab initio size and strain functions scaled by the contrast factors of dislocations. The two procedures will be discussed and illustrated by different case studies.

Journal ArticleDOI
TL;DR: In this paper, the beam tracing technique is used to describe the propagation and absorption of Gaussian wave beams with frequencies in the electron-cyclotron frequency range in a fusion plasma.

Journal ArticleDOI
TL;DR: For the first time, self-focusing and self-defocusing have been achieved for the same medium, structure, and wavelength in arrays of waveguides.
Abstract: We show that two regimes of diffraction exist in arrays of waveguides, depending upon the input conditions. At higher powers, normal diffraction leads to self-focusing and to the formation of bright solitons through the nonlinear Kerr effect. By slightly changing the input conditions, light experiences anomalous diffraction and is nonlinearly defocused. For the first time, self-focusing and self-defocusing have been achieved for the same medium, structure, and wavelength.

Journal ArticleDOI
TL;DR: In this article, the spatial resolution for infrared microspectroscopy was investigated to determine the practical limits imposed by diffraction or optical aberrations, and the results were obtained using high brightness synchrotron radiation, which serves as a diffraction-limited infrared point source for the microscope.
Abstract: The spatial resolution for infrared microspectroscopy is investigated to determine the practical limits imposed by diffraction or optical aberrations. Quantitative results are obtained using high brightness synchrotron radiation, which serves as a diffraction-limited infrared “point source” for the microscope. The measured resolving power is in good agreement with diffraction theory, including a ∼ 30% improvement for a confocal optical arrangement. The diffraction calculation also shows how the confocal setup leads to better image contrast. The full width at half maximum of the instrument’s resolution pattern is approximately λ/2 for this arrangement. One achieves this diffraction limit when the instrument’s apertures define a region having dimensions equal to the wavelength of interest. While commercial microspectrometers are well corrected for optical aberrations (allowing diffraction-limited results), the standard substrates used for supporting specimens introduce chromatic aberrations. An analysis of ...

Patent
21 Sep 2001
TL;DR: In this article, a rigorous model is used to calculate intensity or ellipsometric signatures of the diffracting structure of a semiconductor wafer, which is then matched with the signatures in the database to determine the grating shape parameters of the structure.
Abstract: Before the diffraction from a diffracting structure on a semiconductor wafer is measured, where necessary, the film thickness and index of refraction of the films underneath the structure are first measured using spectroscopic reflectometry or spectroscopic ellipsometry. A rigorous model is then used to calculate intensity or ellipsometric signatures of the diffracting structure. The diffracting structure is then measured using a spectroscopic scatterometer using polarized and broadband radiation to obtain an intensity or ellipsometric signature of the diffracting structure. Such signature is then matched with the signatures in the database to determine the grating shape parameters of the structure.

Journal ArticleDOI
TL;DR: It is shown that remarkable spectral changes take place in the neighborhood of phase singularities near the focus of a converging, spatially fully coherent polychromatic wave diffracted at an aperture.
Abstract: It is shown that remarkable spectral changes take place in the neighborhood of phase singularities near the focus of a converging, spatially fully coherent polychromatic wave diffracted at an aperture. In particular, when the spectrum of the wave in the aperture consists of a single line with a narrow Gaussian profile, the spectrum near a phase singularity (i.e., near points of zero intensity of some particular spectral component) changes drastically along a closed loop around the singularity. The spectrum is redshifted at some points, blueshifted at others, and is split into two lines elsewhere.

Journal ArticleDOI
13 Sep 2001-Nature
TL;DR: The diffraction of free electrons from a standing light wave is reported—a realization of the Kapitza–Dirac effect as originally proposed.
Abstract: In their famous 1927 experiment, Davisson and Germer observed the diffraction of electrons by a periodic material structure, so showing that electrons can behave like waves. Shortly afterwards, Kapitza and Dirac predicted that electrons should also be diffracted by a standing light wave. This Kapitza-Dirac effect is analogous to the diffraction of light by a grating, but with the roles of the wave and matter reversed. The electron and the light grating interact extremely weakly, via the 'ponderomotive potential', so attempts to measure the Kapitza-Dirac effect had to wait for the development of the laser. The idea that the underlying interaction with light is resonantly enhanced for electrons in an atom led to the observation that atoms could be diffracted by a standing wave of light. Deflection of electrons by high-intensity laser light, which is also a consequence of the Kapitza-Dirac effect, has also been demonstrated. But the coherent interference that characterizes wave diffraction has not hitherto been observed. Here we report the diffraction of free electrons from a standing light wave-a realization of the Kapitza-Dirac effect as originally proposed.

Journal ArticleDOI
TL;DR: The proposed approach is quite general and can be used for any given crystallite shape and different distribution functions; moreover, the Fourier transform formalism allows the introduction in the line-profile expression of other contributions to line broadening in a relatively easy and straightforward way.
Abstract: Diffraction patterns for polydisperse systems of crystalline grains of cubic materials were calculated considering some common grain shapes: sphere, cube, tetrahedron and octahedron Analytical expressions for the Fourier transforms and corresponding column-length distributions were calculated for the various crystal shapes considering two representative examples of size-distribution functions: lognormal and Poisson Results are illustrated by means of pattern simulations for a fcc material Line-broadening anisotropy owing to the different crystal shapes is discussed The proposed approach is quite general and can be used for any given crystallite shape and different distribution functions; moreover, the Fourier transform formalism allows the introduction in the line-profile expression of other contributions to line broadening in a relatively easy and straightforward way

Journal ArticleDOI
TL;DR: In this paper, the relative change of d values and the broadening of diffraction peaks have been investigated for three cubic substances, CeO2, the high-pressure rocksalt phase of ZnO, and Au.
Abstract: The hydrostaticity of a helium-pressure medium has been evaluated with powder x-ray diffraction techniques up to 77 GPa at room temperature. The relative change of d values and the broadening of diffraction peaks have been investigated for three cubic substances, CeO2, the high-pressure rocksalt phase of ZnO, and Au. I observed no evidence of nonhydrostaticity of the helium-pressure medium to at least 50 GPa. The powder x-ray diffraction method has been compared with the ruby fluorescence method in order to get a better understanding of nonhydrostatic stress conditions.

Book
01 Jan 2001
TL;DR: In this article, the authors presented a detailed analysis of the effect of the Evanescent Field on the propagation of light through an Aperture and Dipolar Radiation in the Vicinity of a Surface.
Abstract: I. The Evanescent Field.- 1. Total Internal Reflection.- 1.1 The Electromagnetic Field at Total Internal Reflection.- 1.1.1 Snell's Law.- 1.1.2 Analysis of Total Internal Reflection on the Basis of Maxwell's Equations.- 1.1.3 Components of the Electric Field in the Second Medium in the z = 0 Plane.- 1.2 Flux of the Poynting Vector Associated with the Evanescent Field.- 1.3 Shifts of the Beams at Total Internal Reflection.- 1.4 Frustrated Total Internal Reflection.- 1.5 Resonant Tunneling Effect.- 1.6 Conclusion.- 2. Diffraction from an Aperture and Dipolar Radiation.- 2.1 Analysis of the Propagation of Light Through an Aperture.- 2.2 Diffraction of Light from a Circular Aperture.- 2.2.1 Diffraction from an Aperture in an Infinitely Thin Plane.- 2.2.2 Diffraction from a Circular Aperture in a Thick Screen.- 2.3 Coupling Between Several Apertures.- 2.4 Dipolar Emission.- 2.4.1 Expression of the Dipolar Field.- 2.4.2 Energy Emitted by a Dipole.- 2.5 Dipolar Emission in the Vicinity of a Surface.- 2.6 Conclusion.- 3. The Evanescent Field in Guided Optics.- 3.1 The Evanescent Field in Planar Optics.- 3.1.1 Analysis of Planar Waveguides.- 3.1.2 Production of Step-Index Planar Waveguides.- 3.2 Confined Waveguides.- 3.3 Optical Fibers.- 3.3.1 Ray-Optical Analysis of the Propagation in Optical Fibers.- 3.3.2 Modes of Step-Index Fibers.- 3.3.3 Modes of Inner-Cladding Fibers.- 3.3.4 Modes of Annular-Core Fibers.- 3.3.5 Modes of Graded-Index Fibers.- 3.3.6 Modes of Polarization-Preserving Fibers.- 3.4 Whispering-Gallery Modes.- 3.5 Band-Gap Photonics Waveguides.- 3.6 Conclusion.- Conclusion of Part I.- II. Delocalized Interaction with the Evanescent Field.- 4. Evanescent-Field Optical-Fiber Couplers.- 4.1 Types of Couplers.- 4.2 Fabrication Techniques of Evanescent-Field Fiber-Optic Couplers.- 4.2.1 Twist-Etched Fiber Couplers.- 4.2.2 Mechanically Polished Fiber Couplers.- 4.2.3 Fused-Tapered Fiber Couplers.- 4.2.4 Comparison Between the Different Types of Couplers.- 4.3 Analysis of the Coupling.- 4.3.1 Coupled Power Between Two Parallel Uniform Fibers.- 4.3.2 Step-Index Fibers.- 4.3.3 Inner-Cladding Fibers.- 4.3.4 Variable-Diameter Couplers.- 4.4 Spectral Filters and Spectral Multiplexers.- 4.5 Polarization Splitters.- 4.6 Production of Modal Filters.- 4.7 Devices Produced from Evanescent-Field Couplers.- 4.7.1 Optical-Fiber Gyroscope.- 4.7.2 Fiber Lasers.- 4.8 Conclusion.- 5. Integrated-Optical Evanescent-Field Couplers.- 5.1 Description of Integrated-Optical Couplers.- 5.2 Analysis of the Coupling Between Two Waveguides.- 5.3 Active Couplers.- 5.4 Coupling from a Fiber to a Planar Waveguide.- 5.5 Integration of a Waveguide and a Photodiode.- 5.6 Conclusion.- 6. Evanescent-Field Waveguide Sensors.- 6.1 General Points on Sensors.- 6.2 Fiber-Optic Sensors.- 6.2.1 Monitoring of a Chemical Reaction by Fluorescence Detection.- 6.3 Integrated-Optical Sensors.- 6.3.1 Analysis of the Sensitivity of Integrated-Optical Sensors.- 6.3.2 Creating the Sensing Region.- 6.3.3 Evanescent-Field Interferometric Sensors.- 6.3.4 Amplification of the Evanescent Field by a Multilayered System and Applications to Biosensors.- 6.4 Conclusion.- 7. Internal-Reflection Spectroscopy.- 7.1 Effect of Index Variations on Total Internal Reflection.- 7.1.1 Effective Thickness.- 7.1.2 Measurement of the Dielectric Constants in an Arbitrary Medium.- 7.2 Spectroscopy Devices Based on Total Internal Reflection.- 7.2.1 Description of Different Systems Generating Total Internal Reflection.- 7.2.2 Description of Internal-Reflection Spectroscopes.- 7.2.3 Quality of the Reflective Element.- 7.2.4 Constraints in the Preparation of the Samples.- 7.3 Atom Spectroscopy in the Vicinity of Interfaces.- 7.4 Conclusion.- 8. Evanescent-Wave Atom Optics.- 8.1 Atomic Interferences.- 8.2 Reflection of Atoms.- 8.3 Deflection of Atoms.- 8.3.1 Deflection Based on the Use of Evanescent Waves Generated at Total Internal Reflection.- 8.3.2 Deflection Based on the Use of the Evanescent Field of Whispering-Gallery Modes of a Sphere.- 8.4 Atom Guiding.- 8.5 Conclusion.- 9. Dark-Field Microscopy and Photon Tunneling Microscopy.- 9.1 Dark-Field Microscopy.- 9.1.1 Basic Principles.- 9.1.2 Description of the Dark-Field Microscope.- 9.1.3 Comparison between Dark-Field and Bright-Field Images.- 9.1.4 Dark-Field Microscopy and Fluorescence.- 9.2 Photon Tunneling Microscopy.- 9.3 Conclusion.- Conclusion of Part II.- III. Localized Interaction with the Evanescent Field.- 10. Scanning Tunneling Optical Microscopy.- 10.1 Fundamental Principles of the Scanning Tunneling Optical Microscope.- 10.2 Detection of the Near-Field in the Vicinity of a Plane Surface.- 10.3 Early Results in Scanning Tunneling Microscopy.- 10.4 Near-Field Study of Homogeneous Samples.- 10.4.1 Effects of the Polarization and Orientation of the Source.- 10.4.2 Effect of the Distance Between the Probe and the Surface.- 10.4.3 Effect of the Coherence of the Source.- 10.4.4 Effect of the Wavelength.- 10.4.5 Effect of the Probe.- 10.5 Near-Field Study of Non-Homogeneous Samples.- 10.6 Near-Field Study of Optical Waveguides.- 10.6.1 Observation of the Index Variations of a Waveguide.- 10.6.2 Detection of the Evanescent Field of Guided Modes.- 10.6.3 Near-Field Analysis of the Structure of Guided Modes.- 10.7 Local Near-Field Spectroscopies.- 10.8 Photon Scanning Tunneling Microscopy and Fluorescence.- 10.9 Near-Field Study of Surface Plasmons.- 10.10 Conclusion.- 11. Micro-Aperture Microscopy.- 11.1 Fundamental Principles of the Scanning Near-Field Optical Microscope.- 11.2 The Breaking of the Rayleigh Limit on Resolution for Microwave and Optical Frequencies.- 11.3 Description of the Scanning Near-Field Optical Microscope.- 11.4 Effects of the Physical Parameters on the Formation of the Images.- 11.4.1 Effect of the Polarization.- 11.4.2 Effect of the Wavelength.- 11.4.3 Effect of the Coherence of the Source.- 11.4.4 Effect of the Distance Between the Probe and the Surface.- 11.5 Local Fluorescence Detection.- 11.6 Near-Field Optics and Photolithography.- 11.7 Conclusion.- 12. Apertureless Microscopies.- 12.1 Near-Field Optical Microscope Based on the Local Perturbation of a Diffraction Spot.- 12.2 Scanning Interferometric Apertureless Microscope.- 12.3 Tetrahedral Probe Microscope.- 12.4 Local Probe Microscope Derived from the PSTM.- 12.5 Radiation Pressure Scanning Microscope.- 12.6 Conclusion.- Conclusion of Part III.- References.