The vectorial angular-spectrum representation and Rayleigh–Sommerfeld diffraction formulae

The equivalence of the vectorial angular-spectrum representation and Rayleigh–Sommerfeld (RS) diffraction formulae is studied. Based on the angular-spectrum representation and the Weyl representation of a spherical wave, the vectorial RS diffraction formulae of the first and second kinds are derived in a simple way. Numercial results of diffracted divergent spherical waves are given to illustrate the application of the two vectorial RS diffraction formulae.     

Shortwave asymptotic behavior of the solution of the problem of diffraction by a convex body. III

Based on an integral representation found previously for the shortwave asymptotic behavior of the solution of the problem of diffraction by a smooth convex cylinder, the author derives asymptotic estimates for the diffraction field in the illuminated region and in a shadow region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 1, pp. 98–111, January, 1972.     

Pade form of effective rotational molecular Hamiltonians

Effective rotational molecular Hamiltonians (ERH) are constructed which differ from the traditional representation of the ERH as a power series in the total angular momentum. A Padeform of the ERH is systematically obtained and the nonuniqueness of this form is emphasized.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 8, pp. 86–90, August, 1982.Finally, the authors thank A. V. Burenin for pointing out to us the advantages of the Pade representation of the ERH in the analysis of molecular spectra.     

Grating radiation coupler with a dielectric layer: Computational relations

Computational relations are derived for radiation couplers based on a metal diffraction grating coated with a layer of dielectric material. The calculation is performed to the first approximation in the perturbation theory with respect to a small parameter and with the scattered field expanded in plane waves. The computational relations were derived under the assumption that such a representation is admissible everywhere on the surface of a grating with a shallow profile (the Rayleigh-Fano method).Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 7, pp. 74–77, July, 1989.     

REGGE Representation of Diffraction Scattering

The background integral in the Regge representation of the elastic scattering amplitude, neglected in the works of ERICSON , INOPIN , and HÖGAASEN , is calculated explicitly and found to have contributions from poles in the right and left hand γ-plane. Using a Wood-Saxon form for the scattering coefficients, this modified representation yields better oscillatory diffraction patterns.     

Application of Entangled State Representation to Deriving Normally Ordered Expansion of 1-Dimensional Coulomb Potential

Guided by Dirac’s advice that “When one has a particular problem to work out in quantum mechanics, one can minimize the labour by using a representation in which the representatives of the more important abstract quantities occurring in that problem are as simple as possible,’’ we construct the entangled state representation to derive the normally ordered expansion formula of the 1-dimensional two-body Coloumb potential. The method of integration within an ordered product of operators is also used. Further application of the new formula in some perturbation calculation is discussed.     

Spatial polarization structure of radiation formed by a retroreflector with nonmetallized faces

A polarization-wave analysis is performed for a retroreflector with nonmetallized faces, which forms a complex pattern of radiation intensity distribution due to different shifts between the strength vector components upon total internal reflection. Using the representation of the polarization-inhomogeneous field in the form of a set of Hermite-Gaussian modes, the problem of a plane wave diffraction on a retroreflector is solved and the spatial polarization structure is calculated in both the near- and far-field zones. It is shown that the considered type of retroreflectors is preferable for application in satellite ranging     

Hologram multiplexing in a highly photosensitive photopolymerizable material in a sol-gel matrix

In this paper, we present a photopolymerizable material in a sol-gel matrix suitable for recording a large number of multiplexed diffraction gratings with low total exposure energy. The matrix of this material is an inorganic porous silica glass, a material that does not shrink when radical photopolymerization is initiated. The photosensitive component is based on acrylamide, N,N′-methylenebisacrylamide, triethanolamine and yellow eosine as a photoinitiator. In the reported study, 50 holograms were angularly multiplexed with diffraction efficiencies between 0.1 and 1.9% resulting in a dynamic range of M/# = 3.9. The total exposure was 4.5 mJ/cm² and the energy used in recording each hologram was 95 μJ/cm². This indicates a very high sensitivity for this material in the range of 3.3 to 15.5 cm/mJ. Due to this good holographic performance, the material is suitable for holographic data storage applications.     

Random-Cluster Analysis of a Class of Binary Lattice Gases

We introduce a class of binary lattice gases which can be viewed as a lattice analogue of the continuum Widom–Rowlinson model, and which also is related to the beach model of Burton and Steif. This new model is shown to exhibit phase transition for large particle intensities. Stochastic monotonicity results of varying strength are derived in various parts of the parameter space. The main tool is a random-cluster representation of the model, analogous to the Fortuin–Kasteleyn representation of the Potts model.     

Computational Abstraction

Representation and abstraction are two of the fundamental concepts of computer science. Together they enable “high-level” programming: without abstraction programming would be tied to machine code; without a machine representation, it would be a pure mathematical exercise. Representation begins with an abstract structure and seeks to find a more concrete one. Abstraction does the reverse: it starts with concrete structures and abstracts away. While formal accounts of representation are easy to find, abstraction is a different matter. In this paper, we provide an analysis of data abstraction based upon some contemporary work in the philosophy of mathematics. The paper contains a mathematical account of how Frege’s approach to abstraction may be interpreted, modified, extended and imported into type theory. We argue that representation and abstraction, while mathematical siblings, are philosophically quite different. A case of special interest concerns the abstract/physical interface which houses both the physical representation of abstract structures and the abstraction of physical systems.     

The Bohm-Aharonov effect: A seven-dimensional structural group

We realize a nonfaithful representation of a seven-dimensional Lie algebra, the extension of which to its universal enveloping algebra contains most of the observables of the scattering Aharonov-Bohm effect, as essentially self-adjoint operators: the scattering Hamiltonian, the total and kinetic angular momenta, the positions and the kinetic momenta. By restriction, we obtain the model introduced in Lett. Math. Phys. 1 (1976), 155–163.     

阻抗劈绕射对破碎波后向散射特性的影响

海浪的破碎区会导致海面电磁散射特性发生很大改变,导致海尖峰现象的产生.本文结合阻抗劈结构模型分析了劈绕射对破碎波后向散射特性的影响.首先利用基尔霍夫近似求解破碎波的物理光学场;基于Maliuzhinets方法,从波动方程及精确阻抗边界条件出发,由谱函数的积分形式得到阻抗劈的一致性绕射系数,结合物理光学绕射系数导出阻抗劈等效边缘电磁流;利用边缘绕射场修正物理光学场,得到考虑劈绕射效应的破碎波散射总场.数值结果表明,阻抗劈的绕射场在Keller锥内出现HH极化大于VV极化的现象,因此计入绕射场的影响会使得破碎波生长到临近坍塌阶段时,小擦地角逆风观测出现总场的后向散射截面HH极化大于VV极化的现象,说明劈绕射是造成海尖峰现象产生的原因之一.     

Use of edge-wave representation in numerical solution of problems of diffraction by bodies of complex shape with impedance boundary conditions

A representation of the surface-current density for impedance bodies of large electrical dimensions with edges is obtained. The representation considerably reduces calculations and increases accuracy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 7, pp. 806–810, July, 1991.     

Total electronic energy of a noble metal ordered alloy in the pseudopotential method

Application of the pseudopotential method to noble metal ordered alloys is considered in this paper. Expressions are obtained for the Fourier components of the crystal potential and for the total electronic energy of the alloy. The pseudopotential matrix elements are factorized, and the possibility of transforming to a pair interaction representation is shown. Expressions are obtained for the pair potential of indirect interionic interactions in a noble metal binary ordered alloy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 21–28, August, 1973.     

Invariance of interval and length in the theory of relativity

Two representations are discussed: the standard representation regarding the contraction of a moving body, and a locational representation regarding its elongation. It is shown that the first representation is not relativistically invariant, but the second is and is unique, being consistent with the invariance of interval under a Lorentz transformation.Joint Institute of Nuclear Research. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 125–128, February, 1995.     

Photodiffraction in InGaAs/InGaAsP multiple quantum wells enclosed in a microcavity

We report new results on the diffraction properties of photoinduced gratings in InGaAs/InGaAsP MQW structures. The original feature of this device is that the QWs are enclosed in an asymmetric Fabry–Perot microcavity in order to increase the diffraction efficiency. We observe oscillations in the diffraction efficiency due to resonant effects in the microcavity. The experimental spectra are compared with theory. Diffraction efficiency at 1.55 μm attains a maximum value of 2.7% at a write beam fluence of 260 μ J cm⁻², and then decreases at higher fluences. We explain this phenomenon by an absorption saturation at high excitation.     

Geometrical interpretation of spinors

Geometrical properties of elements of the unique representation of the Clifford algebra of quadratic form (+, –, –, –) are investigated. A connection between horospheres on the positive Lobatschevsky space of timelike directions and spinors is established.Partly supported by the Polish Government under the Research Program MR I.7.     

On the propagation of pulses

The diffraction of a plane or cylindrical electromagnetic or acoustic pulse by a perfectly reflecting wedge is investigated. The method applied is based upon the representation of a function by aLaplace transform and upon the solution of the corresponding time harmonic problem. Other problems will be considered in a forthcoming paper.     

A role of second-order derivatives of amplitudes in X-ray beam dynamical diffraction equations

Dynamical diffraction equations for X-ray beams are considered with retaining the second-order derivatives of amplitudes in the direction perpendicular to the diffraction plane. For the dynamical diffraction problem, the retarded Green function is determined in case of a perfect crystal. Amplitudes of transmitted and diffracted waves in the crystal are represented as convolution over the crystal surface with use of determined Green function. Such representation can be used for solving diffraction problems in Laue and Bragg geometries in perfect crystals with both plane and not plane entrance and exit surfaces.