Direct calculation of a three-dimensional diffracted field

We present an approach to calculating the complex amplitude of a three-dimensional (3D) diffracted light field in the paraxial approximation based on a 3D Fourier transform. Starting from the Huygens-Fresnel principle, the method is first developed for the computation of the light distribution around the focus of an apertured spherical wave. The method, with modification, is then extended to treat the 3D diffraction of an aperture with an arbitrary transmittance function.     

The mathematical simulation of a diffracted field in the target area of a mirror collimator

A mathematical model of a mirror collimator with rounded edges is developed. The problem of calculating electromagnetic field components in the target area is solved by the method of integral equations. The results of numerical computations are presented.     

Analysis of the field diffracted by a cylinder with a perforated coating

The direct and inverse problems of plane wave diffraction by a circular cylinder with a perforated coating are investigated. In the context of the direct problem, it is shown that a coated cylinder causes a more intense diffraction field than that produced by a smooth cylinder. In the context of the inverse problem, the parameters of the perforated coating are chosen so as to ensure a given level of suppression for the field diffracted by the cylinder.     

Investigation of physical processes of electron flux interaction with a diffracted field

Institute of Radiophysics and Electronics, Academy of Sciences of Ukrainian SSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 31, No. 2, pp. 190–198, February, 1988.     

The equivalence principle and an electric charge in a gravitational field

It is shown that there is no violation of the strong principle of equivalence in the case of an electric charge either falling freely or supported in a static uniform gravitational field. For a freely falling charge, the global electromagnetic field distribution at any instant is found to be the same as that of a charge which is moving uniformly with respect to an inertial frame with a velocity equal to the instantaneous velocity of the freely falling charge. In the case of a charge supported in the gravitational field, the total electromagnetic field energy, as measured by freely falling observers instantaneously at rest with respect to the charge, is shown to be equal to the Coulomb field energy of a charge permanently stationary in an inertial frame. The conclusion here, that in neither of the two cases does the charge emit electromagnetic radiation, is independent of our choice of the observer's frame of reference.     

Vectorial structure of far field of cylindrically polarized beams diffracted at a circular aperture

Based on the vector angular spectrum representation and the method of stationary phase, the analytical vectorial structure of the cylindrically polarized Laguerre-Gaussian beam diffracted at a circular aperture is derived in the far field, which provides an approach to further comprehend the vectorial properties of the apertured cylindrically polarized beams. The radially polarized, azimuthally polarized, and unapertured cases can be viewed as the special cases of our general result. The analyses show that the far-field energy flux distributions of the entire beam, the TE term, and the TM term depend on the beam order, the ratio of the waist width to the wavelength, the truncation parameter, and the angle between the electric field vector and the radial direction.     

The diffracted sound field from the transition region of an axisymmetric body in water

Understanding the physical features of the diffracted sound field on the surface of an axisymmetric body is important for predicting the self-noise of a sonar mounted on an underwater platform.The diffracted sound field from the transition region of an axisymmetric body was calculated by the geometrical theory of diffraction.The diffraction ray between the source point and the receiving point on the surface of an axisymmetric body was calculated by using the dynamic programming method.Based on the diffracted sound field,a simulation scheme for the noise correlation of the conformal array was presented.It was shown that the normalized pressure of the diffracted sound field from the transition region reduced with the increases of the frequency and the curvature of the ray.The flow noises of two models were compared and a rather optimum fore-body geometric shape was given.Furthermore,it was shown that the correlation of the flow noise in the low frequencies was stronger than that in the high frequencies.And the flow noise received by the acoustic array on the curved surface had a stronger correlation than that on the head plane at the designed center frequency,which is important for sonar system design.     

Spectral changes of diffracted polychromatic Gaussian beams in the far field

The spectral behavior of polychromatic spatially fully coherent Gaussian beams diffracted at an aperture in the far field is studied based on the propagation law of the cross-spectral density function. Detailed numerical calculation results are presented, and illustrated. It is shown that the spectral changes take place in the vicinity of zeros of the Airy pattern, and the spectral modifier depends on the truncation parameter δ and diffraction angle α. The critical diffraction angle α_c, at which the spectrum is split into two lines with equal height i.e., the spectral switch appears, varies with truncation parameter δ. The spectral switch vanishes if δ becomes large enough. A detailed comparison with the previous publications is given, showing somewhat extension made in our work.     

Statistical properties of one-dimensional inversion for the wave field diffracted by a two-dimensional phase screen

We study theoretically the statistical properties of one-dimensional wave-field inversions. We show that the real and imaginary parts of the logarithm of the normalized coherence function are the invariants of the inverted field if the field is measured on the statistical symmetry axis. Using these invariants, one can easily reconstruct two-point statistical moments of the phase distribution on the screen. We derive equations for the reconstruction of phase-distribution moments in the general case. Numerical simulations show that these equations can be solved by an iterative technique. The convergence range of the iteration method with variation in the parameters is studied. A. M. Obukhov Institute for Physics of the Atmosphere of the Russian Academy of Sciences, Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 3, pp. 234–242, March., 2000.     

环形光束锥形衍射出射光场偏振特性及光场调控

环形光束的锥形衍射效应对于微粒的操控具有重要的应用价值.本文建立了环状高斯光束的锥形衍射模型,并基于Berry理论给出了线偏振态下环形光束锥形衍射出射光场的计算公式.理论仿真了环状光锥形衍射出射光场的偏振特性,得出环光锥形衍射出射光场的内、外亮环具有相互正交的偏振分布特性.搭建了线偏振态下环状高斯光锥形衍射的实验系统,实验验证了出射光场的偏振特性.针对环形光束锥形衍射出射光场具备的偏振特性,设计了一种组合偏振片,理论和实验研究了该组合偏振片对环光锥形衍射出射光场的调控.结果表明,随着组合偏振片方位角的变化,锥形衍射出射光场的内、外环强度发生周期性的变化.     

被圆相位片衍射的空心高斯光束的远场矢量结构特征

基于麦克斯韦方程组解的矢量角谱表述与稳相法,在仅有远场近似的条件下,得到了被圆相位片衍射的空心高斯光束远场能流密度分布的解析表达式.结果表明,光束的总能流可以表示为自由项与附加项之和,其中附加项是相位片对能流分布的影响;总能流、自由项能流、附加项能流又可以分别表示为各自的TE项和TM项之和.利用所导出的公式,描绘了空心高斯光束的总能流、自由项能流、附加项能流及其各自的TE项与TM项能流的横截面分布图.讨论了截断参数与附加相移对纵向总能流分布的影响.     

The pauli principle for a quantum theory on T with magnetic field

We discuss the reducible representation of n particles on a torus with magnetic field, where the gauge automorphisms are unitarily implementable. This representation is of type II_∞, if B is not integer. We show that there is a natural splitting into I_∞ ⊗ II₁ such that the Pauli exclusion principle acts only in the first factor. Under this condition we estimate the ground state energy for several particles and show that in the thermodynamic limit we obtain the correct result.     

Plane-wave analysis of the near field of light diffracted by ultrasound.

Although the phenomenon of light diffraction by ultrasound has been studied very extensively during the last 40 years, almost all investigations were concentrated on the individual far field (Fraunhofer) diffraction orders. In the present paper, the basic theory is developed for studying the near field (Fresnel region) of light diffracted by an arbitrary plane ultrasonic wave and the fundamental periodicity properties are stated. The general plane-wave theory of Raman-Nath has been taken as a starting point. From the analysis, the near field of the diffracted light is seen to be highly sensitive to variations of the ultrasonic amplitude and this feature provides a useful technique for observing weak ultrasonic waves. In particular, for the specific case of Raman-Nath-type diffraction, a procedure is presented allowing the reconstruction of the time waveform of the ultrasonic wave from the diffracted light intensity signal.     

Boundary of a boundary principle and geometric structure of field theories

We formulate the boundary of a boundary principle, review its applications in electrodynamics, Yang-Mills theory, and general relativity and translate its basic ideas into geometric language. In each of these three theories the density of the source lets itself be constructed-we discover-out of the curvature associated with the field as a Cartan-like moment of this curvature.     

High-frequency asymptotics of wave field diffracted by plane angular sector. I

The problem of plane-wave diffraction by an angular sector is examined. It is assumed that the wave process is described by the Helmholtz equation and that the Dirichlet or Neumann boundary conditions are satisfied on the sector. An exact solution of the problem is constructed in the form of a Sommerfeld integral, which is convenient for study of the problem in a high-frequency approximation.     

Anomalous spectral behaviour of diffracted chirped Gaussian pulses in the near field

By using the Fourier transform method, analytical expressions for the axial power spectrum and near-field intensity in the spacetime domain of chirped Gaussian pulses diffracted at an aperture are derived, which permit us to study changes in spectral and temporal profiles of the chirped Gaussian pulses both analytically and numerically. Detailed numerical results and physical analysis show that spectral anomalies take place in the neighbourhood of certain critical distances, and the shifting of maximum and splitting of temporal intensity profiles appear. In particular, for ultrashort chirped pulses, there exists also spectral switch. Besides the truncation parameter, the chirp parameter and pulse duration affect the behaviour of spectral switches.