Close-packed Dimers on the Line: Diffraction versus Dynamical Spectrum

The translation action of ℝ ^d on a translation bounded measure ω leads to an interesting class of dynamical systems, with a rather rich spectral theory. In general, the diffraction spectrum of ω, which is the carrier of the diffraction measure, lives on a subset of the dynamical spectrum. It is known that, under some mild assumptions, a pure point diffraction spectrum implies a pure point dynamical spectrum (the opposite implication always being true). For other systems, the diffraction spectrum can be a proper subset of the dynamical spectrum, as was pointed out for the Thue-Morse sequence (with singular continuous diffraction) by van Enter and Miȩkisz (J. Stat. Phys. 66:1147–1153, 1992). Here, we construct a random system of close-packed dimers on the line that have some underlying long-range periodic order as well, and display the same type of phenomenon for a system with absolutely continuous spectrum. An interpretation in terms of ‘atomic’ versus ‘molecular’ spectrum suggests a way to come to a more general correspondence between these two types of spectra.     

On the determination of double diffraction dissociation cross section at HERA

The excitation of the proton into undetected multiparticle states (double diffraction dissociation) is an important background to single diffractive deep-inelastic processesep→e′p′ρ ⁰,e′p′J/ψ,e′p′X at HERA. We present estimates of the admixture of the double diffraction dissociation events in all diffractive events. We find that in theJ/ψ photoproduction, electroproduction of theρ ⁰ at largeQ ² and diffraction dissociation of real and virtual photons into high mass statesX the contamination of the double diffraction dissociation can be as large as ∼30%, thus affecting substantially the experimental tests of the pomeron exchange in deep inelastic scattering at HERA. We discuss a possibility of tagging the double diffraction dissociation by neutrons observed in the forward neutron calorimeter. We present evaluations of the spectra of neutrons and efficiency of neutron tagging based on the experimental data for diffractive processes in the protonproton collisions.     

3D DuMond diagrams of multi-crystal Bragg-case synchrotron topography. I. Flat sample

The 3D representation of the DuMond diagram is used to explain the dimensional features of X-ray topographs obtained by multi-crystal configuration with a synchrotron beam. Symmetric Bragg-case reflections are considered for a flat double-crystal monochromator and a flat sample. Two ways of sample alignment are taken into account. They are referred to as σ–σ and σ–π geometries, where the diffraction plane of the sample is parallel and perpendicular, respectively, to the vertical diffraction plane of the monochromator (σ polarization). It is shown that the shape of the sample image is closely connected to the shape the diffraction domain common to monochromator and sample assumes in the 3D DuMond diagram. An experiment is reported for the less commonly used σ–π topography, showing how the lattice mismatch and its lateral homogeneity are determined in samples made by epilayer and substrate. Received: 31 July 2000 / Accepted: 25 January 2001 / Published online: 3 May 2001     

On the determination of double diffraction dissociation cross section at HERA

The excitation of the proton into undetected multiparticle states (double diffraction dissociation) is an important background to single diffractive deep-inelastic processes epMe'p'A⁰,r e'p'J/O,r e'p'X at HERA. We present estimates of the admixture of the double diffraction dissociation events in all diffractive events. We find that in the J/O photoproduction, electroproduction of the A⁰ at large Q² and diffraction dissociation of real and virtual photons into high mass states X the contamination of the double diffraction dissociation can be as large as ~30%, thus affecting substantially the experimental tests of the pomeron exchange in deep inelastic scattering at HERA. We discuss a possibility of tagging the double diffraction dissociation by neutrons observed in the forward neutron calorimeter. We present evaluations of the spectra of neutrons and efficiency of neutron tagging based on the experimental data for diffractive processes in the proton-proton collisions.     

Optical vortices in the scattering field of magnetic domain holograms

Experimental investigations and theoretical-model analyses have been made of the magnetooptic diffraction of light at ferrite garnet magnetic films with a banded domain structure which includes isolated magnetic grating defects in the form of “forks” and “breaks.” An analysis of the magnetic grating structure and the light diffraction field shows that in terms of its action on laser radiation, a banded domain grating is similar to a computer-synthesized phase hologram of an isolated pure screw-wavefront dislocation. It is shown that as a result of magnetooptic diffraction at a magnetic hologram, optical vortices may be reconstructed with a helicoidal wavefront carrying the topological charge l=±1,±2. Zh. Tekh. Fiz. 68, 54–58 (December 1998)     

3D DuMond diagrams of multi-crystal Bragg-case synchrotron topography. II. Curved sample

The dimensional features of multi-crystal synchrotron X-ray topographs are explained by 3D DuMond diagrams for a flat double-crystal monochromator and a curved sample. Symmetric Bragg-case reflections are assumed for all crystals. σ–σ and σ–π geometries are considered, where the diffraction plane of the sample is parallel and perpendicular, respectively, to the vertical diffraction plane of the monochromator (σ polarization). It is shown that the shape of the sample image is closely connected to the shape of the volume shared by the diffraction domains of monochromator and sample in the 3D DuMond diagram. In particular, for the σ–π set-up, the image shape depends on the curvature value and sign. An experiment is reported for this latter crystal geometry to determine lattice mismatch, its lateral homogeneity and curvature value and sign in a sample made of epilayer and substrate. Received: 31 July 2000 / Accepted: 25 January 2001 / Published online: 26 April 2001     

Informational contenet of the high order diffraction pattern

The information content of the diffraction pattern in the region of very high orders is considered. It is shown that high order diffraction pattern represents a superresolution width indicator of the particle track in nuclear emulsion. A principally new experimental setup designed for width measurements of the wires and particle tracks is described. The first experiments performed for tungsten wire as an object are presented. It is shown that the relative error of the measurement made by this new technique is as small as 0.03% for tungsten wire of the diameter ≅26 μm. The article is published in the original.     

A QCD motivated model for soft interactions at high energies

In this paper we develop an approach to soft scattering processes at high energies which is based on two elements: the Good–Walker mechanism for low mass diffraction and multi-pomeron interactions for high mass diffraction. The principal idea, which allows us to specify the theory for pomeron interactions, is that the so called soft processes occur at rather short distances (r ² ∝1/〈p _t 〉² ∝ α′_ℙ≈0.01 GeV⁻²), where perturbative QCD is valid. The value of the pomeron slope α′_ℙ is obtained from a fit to the experimental data. Using this theoretical approach, we suggest a model that fits all soft data in the ISR-Tevatron energy range: total, elastic, single and double diffractive cross sections, as well as the t dependence of the differential elastic cross section, and the mass dependence of single diffraction. In this model we calculate the survival probability of diffractive Higgs production, and we obtain a value for this observable that is smaller than 1% at the LHC energy range.     

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 ν_exp =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 ν_theor=5.7 Hz, is in quite good agreement with the measured value.     

Magneto-optical modulation of a triple-mirror laser beam

Based on calculations and experiments, a He–Ne laser has been developed with effective intracavity magnetooptical modulation at λ = 1.15 μm. A polarization-anisotropic element — a magnetic diffraction grating made of yttrium iron garnet — is mounted in a matched passive arm of the triple-mirror cavity of the laser and serves as the modulator element. Modulation is produced using the Faraday effect, which simultaneously leads to efficient diffraction of the laser radiation on the asymmetric strip domain structure of a magnetic diffraction grating and to rotation of the E vector. The Jones matrix method is used to calculate the frequency and polarization characteristics. These, along with the modulation characteristics, were also studied experimentally. It is shown that amplitude modulation at frequencies up to 180 kHz takes place for small single-pass Faraday rotation angles (θ_F). The threshold frequency is determined by the response time of the magnetizing Helmholtz coil. The depth of modulation is 50%. For θ_F > θ_t (where θ_t is the threshold), frequency modulation takes place with a deviation of up to several megahertz. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 2, pp. 188–193, March–April, 2009.     

On the theory of polarization radiation in media with sharp boundaries

Polarization radiation generated when a point charge moves uniformly along a straight line in vacuum in the vicinity of media with a finite permittivity ɛ(ω) = ɛ′ + iɛ″ and sharp boundaries is considered. A method is developed in which polarization radiation is represented as the field of the current induced in the substance by the field of the moving charge. The solution to the problem of radiation induced when a charge moves along the axis of a cylindrical vacuum channel in a thin screen with a finite radius and a finite permittivity is obtained. Depending on the parameters of the problem, this solution describes various types of radiation (Cherenkov, transition, and diffraction radiation). In particular, when the channel radius tends to zero and the outer radius of the screen tends to infinity, the expression derived for the emitted energy coincides with the known solution for transition radiation in a plate. In another particular case of ideal conductivity (ɛ″ → ∞), the relevant formula coincides with the known results for diffraction radiation from a circular aperture in an infinitely thin screen. The solution is obtained to the problem of radiation generated when the charge flies near a thin rectangular screen with a finite permittivity. This solution describes the diffraction and Cherenkov mechanisms of radiation and takes into account possible multiple re-reflections of radiation in the screen. The solution to the problem of radiation generated when a particles flies near a thin grating consisting of a finite number of strips having a rectangular cross section and a finite permittivity and separated by vacuum gaps (Smith-Purcell radiation) is also obtained. In the special case of ideal conductivity, the expression derived for the emitted energy coincides with the known result in the model of surface currents.     

Fabrication and stitching of embedded multi-layer micro-gratings in fused silica glass by fs laser pulses

Fabrication and stitching of internal 2D, 1D and multi-layer micro-gratings in fused silica glass using amplified Ti:sapphire femtosecond laser were reported. These gratings have the pitch of 4 μm and the size of 400 μm×400 μm. For a two-layer 1D micro-grating where a second-layer grating was overwritten on a first-layer grating at the exact X,Y position and the different Z depth, the diffraction efficiency can reach more than 25% due to the grating thickness increase. If a second-layer grating was stitched with a first-layer by the shift of 2 μm in the X direction and at the different Z depth, the diffraction angle was doubled but the diffraction efficiency was about 9%. The last result has the potential application for fabricating high-density micro-/nano-structures beyond the diffraction limit through 3D stitching. PACS 42.79.Dj; 42.40.Lx; 42.62.Cf     

Cubic superspace symmetry and inflation rules in metastable MgAl alloy

The diffraction properties of a quenched Al-Mg alloy which has been recently termed as a “cubic quasicrystal” are quantitatively reanalyzed. It is shown that the phase can be interpreted within the superspace formalism as an ordinary incommensurately modulated structure. The cubic six-dimensional superspace group that describes its symmetry properties has been determined. The additional inflation symmetry features exhibited by the diffraction diagram can be summed up by its invariance for the inflation factor , but this property has its origin in the specific value of the modulus of the modulation wave vectors, which is composition dependent. Other particular values of this modulus can give rise to similar scaling properties. Further experiments are required to ellucidate if the mentioned inflation symmetry is a fortuitous situation in a composition dependent wave vector, or has indeed the physical significance which would allow to describe the system as a “cubic quasicrystal”. Received: 25 June 1998 / Received in final form and Accepted: 23 September 1998     

Babinet’s principle in scalar theory of diffraction

In this work, we present an original proof of Babinet’s principle within the framework of the scalar theory of diffraction. The proof is derived in the case of the Fraunhofer diffraction, directly from the Fresnel-Kirchhoff formula, using properties of Fourier analysis and integral calculus, without considering Babinet’s principle itself for scalar waves. From the same proof, we also mathematically verify that, in the case of Fresnel diffraction, Babinet’s principle is fulfilled but in its more general scalar version.     

The diffraction cone for exclusive vector meson production in deep inelastic scattering

We develop the color dipole gBFKL phenomenology of a diffraction cone for photo-and electroproduction γ*N−VN of heavy vector mesons (charmonium & bottomonium) at HERA and in fixed target experiments. We predict a substantial shrinkage of the diffraction cone from the CERN/FNAL to the HERA range of c.m.s. energy W. The Q ²-controlled sensitivity to the color dipole size (scanning phenomenon) is shown to lead to a decrease of the diffraction slope with Q ² (which is supported by the available experimental data). We predict an approximate flavor independence of the diffraction slope in the scaling variable Q ²+m _V ² . For diffractive production of the radially excited 2S states (Ψ′, γ′), a counterintuitive inequality of diffraction slopes B(2S)≲B(1S) is predicted, which defies the common wisdom that diffraction slopes are larger for reactions with larger size particles. Zh. éksp. Teor. Fiz. 113, 1930–1962 (June 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Ultrasound diffraction of light beams in gyrotropic crystals

The features of the Bragg diffraction of Gaussian light beams at ultrasound waves in gyrotropic crystals were investigated. The dependence of the diffraction efficiency on the intensity of an ultrasound beam, the cross-section radius of a light beam, and their divergence ratio was found. An asymptotic expression for the transverse distribution of a diffracted beam was derived. The crystal gyrotropy has been found to affect significantly the change in the amplitude profile of the diffracted light at ultrasound frequencies of f ∼ 10²–10³ MHz. The maximum diffraction efficiency in the gyrotropic medium is shown to be reached at a certain ratio between the divergences, ultrasound intensity, and specific gyration of the crystal. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 3, pp. 370–374, May–June, 2000.     

New Prospects for de Broglie Interferometry

We consider various effects that are encountered in matter wave interference experiments with massive nanoparticles. The text-book example of far-field interference at a grating is compared with diffraction into the dark field behind an opaque aperture, commonly designated as Poisson’s spot or the spot of Arago. Our estimates indicate that both phenomena may still be observed in a mass range exceeding present-day experiments by at least two orders of magnitude. They both require, however, the development of sufficiently cold, intense and coherent cluster beams. While the observation of Poisson’s spot offers the advantage of non-dispersiveness and a simple distinction between classical and quantum fringes in the absence of particle wall interactions, van der Waals forces may severely limit the distinguishability between genuine quantum wave diffraction and classically explicable spots already for moderately polarizable objects and diffraction elements as thin as 100 nm.     

Modelling the structure and ionic conduction of amorphous (AgI)x(AgPO3)1−x with the RMC method

For the first time neutron diffraction, X-ray diffraction and EXAFS data have been combined simultaneously using the RMC method to model the fast-ion conducting glass, (AgI)_x(AgPO₃)_1−x. This material is of considerable technological and scientific interest due to its high ionic conductivity at ambient temperature. We present some details of the RMC technique and highlight some of the structural information obtained from our models. The origin of the “first sharp diffraction peak” in the neutron diffraction data is explained, about which there has been considerable speculation. Diffusion pathways for ionic conduction are observed. A simple analysis of available free volume shows that a percolation transition in the ionic conductivity occurs between x=0.2 and 0.3, in agreement with a prediction based on conductivity measurements. This study highlights the considerable power that these developments of the RMC method have for the structural modelling of complex amorphous materials. Paper presented at the 1st Euroconference on Solid State Ionics in Zajkynthos, Greece, 11–18 Sept. 1994     

Novel spatial solitons in light-induced photonic bandgap structures

The study of wave propagation in periodic systems is at the frontiers of physics, from fluids to condensed matter physics, and from photonic crystals to Bose-Einstein condensates. In optics, a typical example of periodic system is a closely-spaced waveguide array, in which collective behavior of wave propagation exhibits many intriguing phenomena that have no counterpart in homogeneous media. Even in a linear waveguide array, the diffraction property of a light beam changes due to evanescent coupling between nearby waveguide sites, leading to normal and anomalous discrete diffraction. In a nonlinear waveguide array, a balance between diffraction and self-action gives rise to novel localized states such as spatial “discrete solitons” in the semi-infinite (or total-internal-reflection) gap or spatial “gap solitons” in the Bragg reflection gaps. Recently, in a series of experiments, we have “fabricated” closely-spaced waveguide arrays (photonic lattices) by optical induction. Such photonic structures have attracted great interest due to their novel physics, link to photonic crystals, as well as potential applications in optical switching and navigation. In this review article, we present a brief overview on our experimental demonstrations of a number of novel spatial soliton phenomena in light-induced photonic bandgap structures, including self-trapping of fundamental discrete solitons and more sophisticated lattice gap solitons. Much of our work has direct impact on the study of similar discrete phenomena in systems beyond optics, including sound waves, water waves, and matter waves (Bose-Einstein condensates) propagating in periodic potentials.