分层背景2维FDTD中斜入射平面波的引入

 对于分层介质中目标散射的时域有限差分（FDTD）计算,在分层背景中引入斜入射平面波源是一个难点。在2维Maxwell方程基础上,导出TM和TE模下含有斜入射角度的１维Maxwell方程,并用它在分层介质中连接边界上模拟斜入射平面波源,克服了分层背景时域有限差分计算斜入射平面波引入的困难。对熔石英表面覆盖薄膜的分层光学元件进行平面波斜入射时域有限差分计算结果表明,电磁波在各层内形成完好的平面波推进,验证了这种斜入射平面波添加方式的正确性。并通过对含气泡的缺陷模型的计算,来阐述这种入射波添加方式的应用。     

Surface excitation of hypersound in piezoelectric crystals by plane electromagnetic waves

The generation of hypersound at a free surface of a piezoelectric crystal by means of an incident plane electromagnetic wave is considered and the corresponding boundary problem is discussed in detail. The formula developed in this paper are quite general and can be applied to any piezoelectric crystal and any face orientation. As an important example, the excitation of sound waves at several quartz faces is treated numerically and the results are presented in diagrams showing directly the power conversion from the plane incident electromagnetic wave into the sound waves as function of the angle of incidence and of polarization directions.     

Far-field divergence of a vectorial plane wave diffracted by a circular aperture from the vectorial structure

Based on the vectorial structure of an electromagnetic wave, the analytical and concise expressions for the TE and TM terms of a vectorial plane wave diffracted by a circular aperture are derived in the far-field. The expressions of the energy flux distributions of the TE term, the TM term and the diffracted plane wave are also presented. The ratios of the power of the TE and TM terms to that of the diffracted plane wave are examined in the far-field. In addition, the far-field divergence angles of the TE term, the TM term and the diffracted plane wave, which are related to the energy flux distribution, are investigated. The different energy flux distributions of the TE and TM terms result in the discrepancy of their divergence angles. The influences of the linearly polarized angle and the radius of the circular aperture on the far-field divergence angles of the TE term, the TM term and the diffracted plane wave are discussed in detail. This research may promote the recognition of the optical propagation through a circular aperture.vspace1mm     

Transformation of a monochromatic plane wane by the pulse-periodic time modulation of an infinite medium

An exact solution to the problem of the transformation of a monochromatic plane wave by a finite train of equally spaced rectangular pulses of permittivity and conductivity of an infinite medium is considered. The permittivity pulse train is shifted relative to the conductivity pulse train by an arbitrary time. The problem is studied analytically in terms of the second-order Volterra integral equation describing the electromagnetic wave transformation in a medium with time-dependent parameters. The equation is solved using the resolvent technique. Expressions for the amplitude of the transformed electric field component for any time instant at any spatial point are derived and analyzed.     

Diffraction of a plane electromagnetic wave by a slot in a conducting screen with a transverse dielectric layer

The problem of diffraction of a plane electromagnetic wave by a slot in a planar perfectly conducting arbitrary thick screen with an infinite planar dielectric layer passing through the slot transversely to the screen is solved rigorously. In each of the field existence domains (two domains on either side of the screen and the interior of the slot), the solution is represented as an expansion in piecewise harmonic or exponential modes that allow for reflection and refraction at the boundaries of the dielectric layer. It is found that a set of functions describing such modes is complete enough to construct a solution satisfying all boundary conditions of the diffraction problem. The procedures of solution construction for the case at hand and for the same diffraction structure without the dielectric layer are compared.     

Maxwell stress distributions in chiral sculptured thin films due to obliquely incident plane waves

When a circularly polarized plane wave is obliquely incident on a chiral sculptured thin film (STF), the Maxwell stress dyadic exhibits a decreasing periodic variation across the thickness of the film. Normal and tangential surface tractions exist on the two faces of the chiral STF, as well as a net normal pressure across the film. These stresses are affected by the incidence angle of light, and are maximized when (i) the incident plane wave and the chiral STF are co-handed, (ii) the wavelength falls within a regime called the Bragg regime, (iii) the ratio of film thickness to the structural period of the chiral STF reaches a saturation value, and (iv) the deviation from normal incidence is small.     

Field generated by an anisotropic conducting plane in a half-space with chiral properties

This article inaugurates theoretical studies on a new class of composite structures that are a combination of anisotropically conducting surfaces and media possessing chiral properties. To test the mathematics, we solved the simplest model of the problem in which an in-phase electric current filament excites a plane formed by a layer of straight conductors at the interface of two isotropic media, one of which is chiral. The solution is given as a Fourier integral. As shown by analysis, one retarded wave of a discrete spectrum and three waves of a continuous spectrum are excited in the given structure. The first one exists only because of the anisotropically conducting plane and does not exist without it, while the latter three are associated with plane waves of corresponding homogeneous media, magnetodielectric and chiral.V. D. Kuznetsov Siberian Physicotechnical Institute, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 34–38, September, 1994.     

Wave functions of a nucleon in a plane electromagnetic wave

An exact solution is derived for Dirac's equation for a nucleon moving in the field of a plane electromagnetic wave in a given coordinate system.I am indebted to S.V. Izmailov and R. Yu. Volkovyskii for discussions.     

The wave flow effect on a plane boundary between vacuum and an optical medium with a quasi-zero refractive index

A boundary problem in which a plane electromagnetic wave is reflected and refracted at a plane boundary of a semi-infinite optical medium with a quasi-zero refractive index has been solved. Such a medium has a random refractive index taking values in an interval from zero to some finite value less than unity. It means that the concept of a sharp interface between two media loses its meaning, the boundary of the medium becomes inhomogeneous, and laws of reflection and refraction of light become non-Fresnelian. Formulas for non-Fresnelian amplitudes of reflection and refraction have been derived. It is shown that a surface wave arises near the boundary of a medium with a quasi-zero refractive index. The wave propagates both on the inside and outside of the boundary.     

Nonlinear interaction of plane ultrasonic waves with an interface between rough surfaces in contact

A theoretical investigation of the nonlinear interaction between an acoustic plane wave and an interface formed by two rough, nonconforming surfaces in partial contact is presented. The macroscopic elastic properties of such a nonlinear interface are derived from micromechanical models accounting for the elastic interaction that is characteristic of spherical bodies in contact. These results are used to formulate set of boundary conditions for the acoustic field, which are to be enforced at the imperfect interface. The scattering problem is solved for plane wave incidence by using a simple perturbation approach and the harmonic balance method. Sample results are presented for arbitrary wave polarization and angle of incidence. The relative magnitude of the nonlinear signals and their potential use toward the nondestructive evaluation of imperfect interfaces are assessed. In particular, attention is drawn to the enhanced nonlinear response of an interface insonified by a shear vertical wave in the neighborhood of the longitudinal critical angle. The motivation for this investigation is provided by the need to develop nondestructive methods to detect and localize small, partially closed cracks in metals with coarse microstructures.     

Application of the wavenumber jump condition to the normal and oblique interaction of a plane acoustic wave and a plane shock

A kinematic approach is considered whereby the wavenumber jump conditions in conjunction with the appropriate dispersion relations is applied to the investigation of the normal and oblique interaction of a plane acoustic wave with a plane shock wave. For the normal interaction of an acoustic wave with a stationary plane shock a logarithmic shift in the wave spectra is obtained. For the normal interaction with a moving shock front it is shown that for shock Mach numbers above a critical value, the frequency of the transmitted wave becomes negative. This results in the fact that the crests of the transmitted signal arrive at a fixed observer in a reverse order to their generation. Finally, the oblique interaction of an acoustic wave with a stationary shock is considered. The “Snell's Law” for the transmitted wave is derived and two special angles of incidence are identified. The first is a no-refraction angle: i.e., the transmitted wave angle is the same as the incident wave angle. The second is a critical angle such that for incident angles greater than this critical angle there is no transmitted wave. A necessary and sufficient condition for the existence of a transmitted wave is derived in terms of the speed of sound and Mach number of the fluid and the frequency and tangential wavenumber component of the incident wave.The dynamics aspects of the interaction concerning the determination of the frequency independent transmission coefficients and shock displacements are determined for the simple case of the normal interaction with a moving shock as an illustration.     

Dynamics of a charged particle in a progressive plane wave

The dynamics of a charged particle in a relativistic strong electromagnetic plane wave propagating in a medium is studied. The problem is shown to be integrable when the wave propagates in vacuum. When it propagates in plasma, and when the full plasma response is considered, an exhaustive numerical work allows us to conclude that the problem is not integrable.     

Diffraction of a plane wave from a wedge in a chiral medium

In a rigorous electrodynamic formulation, we have investigated diffraction of a plane wave in a chiral medium from a wedge with ideally conducting faces. The boundary-value problem is reduced to a system of functional equations which are transformed to Fredholm integral equations and singular integral equations. We have carried out an asymptotic analysis of the diffraction fields. The scattered field contains plane waves reflected by the faces and cylindrical waves due to the edges, having two opposite types of circular polarization, and also two refraction waves whose polarization corresponds to polarization of the slower characteristic wave in the chiral medium.This paper is dedicated to the memory of Professor M. S. Bobrovnikov.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 108–116, October, 1993.     

High-frequency plane wave diffraction by an ideal strip at oblique incidence: Parabolic equation approach

The problem of diffraction of a high-frequency plane wave by a strip with ideal boundary conditions is considered for the case of oblique incidence. The study is based on the parabolic approximation, which is used to construct an expression for the directional pattern in terms of single quadratures. A similar result is obtained using the embedding formula. It is shown that the derived expression approximates the classical Michaeli result. A proof of the optical theorem for the parabolic problem is presented.     

Diffraction of plane electromagnetic waves by a wedge with perfect mixed anisotropic conductivity sides in a chiral medium

The Sommerfeld–Malyuzhinets integral method is used to solve the problem of the diffraction of plane circlepolarized electromagnetic waves normally incident on the edge of a wedge with the sides possessing perfect mixed anisotropic conductivity, which is immersed in an isotropic chiral medium.     

Diffraction of plane Beltrami waves by a wedge with nonidentical sides showing mixed anisotropic conduction immersed in a chiral medium

The Sommerfeld–Malyuzhinets integral method is applied to solve the problem of diffraction of plane electromagnetic Beltrami waves normally incident on an edge of a wedge with the sides showing ideal mixed anisotropic conduction, the wedge being in an isotropic chiral medium. The anisotropy directions of the sides are mutually orthogonal.     

平面波照射下无限大导体板上周期孔阵屏蔽效能的解析研究

本文针对平面电磁波对无限大导体平板上周期孔阵的透射问题,首先用Bethe小孔理论将孔阵表示成偶极子阵列,然后用平均化处理得到均匀的等效磁化/极化强度,进而引入等效面源导出透射电磁波表达式,最终给出了孔阵对平面电磁波屏蔽效能的解析公式.该公式分别针对横电和横磁两种极化方式,将屏蔽效能表示成孔阵周期面积、孔的极化系数、波长和入射角的简单函数,其计算结果与全波仿真结果一致性好.结果表明,透射场强的幅值与孔极化系数和波频率成正比,与周期面积成反比;在横电极化方式,波频率和周期面积不变的情况下,透射场强的幅值与入射角的余弦值成正比,入射角越大屏蔽效能越高;在横磁极化方式下,透射场强幅值与入射角的关系相对复杂,但在入射角较小时与入射角的余弦值近似成反比,总体上入射角越大屏蔽效果越低.     

Transmission of a Transient electromagnetic plane wave through a grating of circular cylinders

An analysis of the transmission of a transient electromagnetic plane wave through a grating formed by an infinite array of circular cylinders is presented. Emphasis is placed on the transient shielding characteristics of the grating for various cylinder spacings and angles of incidence. The transient results are obtained by first obtaining analytical experssions for the fields in the frequency domain and then performing a numerical inverse Fourier transformation. Some physical interpretations of the shielding effectiveness of the grating are given.     

Magneto-optical transverse Kerr effect in a film-substrate system

The problem of electromagnetic reflection at an oblique angle of incidence in a system consisting of an isotropic ambient, a magnetic film and a thick magnetic substrate is studied. The magnetizations in both the film and substrate are assumed normal to the plane of incidence (transverse geometry). The results are expressed in terms of the reflection matrix. The solution includes the conditions for guided wave propagation in the system. As a special case of the general formulae the reflection matrix in a system consisting of a uniaxial film and a uniaxial substrate optical axes of which are oriented normal to the plane of incidence are obtained.     

Diffraction of a plane electromagnetic wave by a cylindrical wedge with a rounded apex

We reduce the rigorously formulated problem of diffraction of a plane electromagnetic wave by a perfectly conducting cylindrical wedge with a rounded apex to solving the system of linear algebraic equations of the second kind for unknown coefficients of the Fourier expansions of the diffracted-field components. The expansion coefficients are determined analytically in the long-wavelength approximation. The results of calculations of the diffracted field in the far zone are presented with a given accuracy in the case of an E-polarized wave. It is shown that the rounding of the apex of a cylindrical wedge leads to an increase in the backscattering coefficient of the structure in the long-wavelength range. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 5, pp. 447–451, May 2008