Three-dimensional electromagnetic diffraction of a Gaussian beam by a perfectly conducting half-plane

Formulas are derived for the diffraction of a three-dimensional electromagnetic Gaussian beam by a perfectly conducting half-plane. The beam can be incident from any direction, and the main component of the electric field can point in any direction on the plane of the beam waist. The center of the beam waist is on the edge of the half-plane. The incident beam is constructed as a superposition of plane waves, and the total diffracted field is obtained from a superposition of the diffracted fields that are due to each plane wave. Physical constraints that limit the size and direction of the beam relative to the half-plane are described and incorporated into the theory. The scattered field in the far zone is obtained by asymptotic evaluation of the general formulas. Graphical results for the near-field as well as far-field patterns are presented and discussed.     

Phase constraint for the waves diffracted by lossless symmetrical gratings at Littrow mount

The energy conservation of grating diffraction is analyzed in a particular condition of incidence in which two incident waves reach a symmetrical grating from the two sides of the grating normal at the first-order Littrow mounting. In such a situation the incident waves generate an interference pattern with the same period as the grating. Thus in each direction of diffraction, interference occurs between two consecutive diffractive orders of the symmetrical incident waves. By applying only energy conservation and the geometrical symmetry of the grating profile to this problem it is possible to establish a general constraint for the phases and amplitudes of the diffracted orders of the same incident wave. Experimental and theoretical results are presented confirming the obtained relations.     

Wave reflection in a rotating pyroelectric half-plane

This paper describes the rotation effects on the wave reflection in a pyroelectric half-plane using an inhomogeneous wave approach. The rotation in the governing pyroelectric equation is characterized by considering the Coriolis and centrifugal accelerations. A scenario is modeled where a quasi-transverse wave is incident on the free boundary surface, resulting in reflected waves like temperature wave, quasi-transverse wave, quasi-longitudinal wave, and surface wave. Rotation’s effects on the reflection angle, velocity, attenuation, and energy coefficients of the reflected wave are presented.     

Numerical analysis of plasmon-resonance absorption in bisinusoidal metal gratings

We numerically investigate plasmon-resonance absorption of incident light energy by a bisinusoidal metal grating, i.e., one whose surface profile is sinusoidally corrugated in two orthogonal directions with a common period. Employing Yasuura's modal expansion method, we solve the problem of plane-wave diffraction by the grating and evaluate the absorption, which is observed as dips in diffraction efficiency curves. We examine the field distribution and energy flow in detail at the angles of incidence at which the absorption occurs. We show that the absorption is caused by coupling of the TM component of an evanescent order with surface plasmons. A phase-matching condition is used in the prediction of the incident angle at which the absorption occurs. This, together with the field profile in the presence of the resonance absorption, explains the mechanism of the absorption. We then illustrate interesting features of the absorption: enhancement of polarization conversion between the incident light and the reflected light and simultaneous excitation of two plasmon waves in directions that are symmetric with respect to the plane of incidence.     

Diffraction of homogeneous and inhomogeneous plane waves by a planar junction between perfectly conducting and impedance half-planes

The problem of diffraction of homogeneous and inhomogeneous plane waves at the discontinuity formed by perfectly conducting and impedance half-planes is examined by the method of modified theory of physical optics (MTPO). The MTPO integral of the reflected scattered waves by the perfectly conducting half-plane is reconstructed in order to include the effect of the diffracted wave coming from the edge of the impedance half-plane. The integrals are evaluated by a uniform asymptotic method. The results are plotted numerically and compared with the literature.     

Scattering of a Gaussian beam by an impedance half-plane

The diffraction of a Gaussian beam by an impedance half-plane is studied through the method of the modified theory of physical optics. An electric line source, which is defined in the complex space, is used to represent the Gaussian beam. The uniform evaluation of the diffraction integral is performed and the scattering patterns of the field are investigated for various numerical parameters of the incident wave.     

Scattering by a dense layer of infinite cylinders at normal incidence

The solution for scattering by a layer of densely distributed infinite cylinders is presented. The layer is irradiated by an arbitrarily polarized plane wave that propagates in the plane perpendicular to the axes of the cylinders. The theoretical formulation utilized the effective field and quasi-crystalline approximation to treat the multiple scattering interactions in the dense finite medium. Governing equations for the propagation constants and amplitudes of the effective fields are derived for TM and TE mode incident waves, from which the scattered intensity distribution and scattering cross section for arbitrary polarization are obtained. The dense medium gives rise to coherent and incoherent scattered radiation that propagates in the plane normal to the axes of the cylinders. The coherent scattered radiation includes the forward component in the direction of the incident wave and the backward component in the direction of specular reflection. The incoherent scattered intensity distribution shows a pronounced forward peak that coincides with the angle of refraction of the effective waves inside the medium. Numerical results are presented to illustrate the scattering characteristics of a dense layer of cylinders as a function of layer thickness for a given solid volume fraction.     

Acoustic reflection from the boundary of anisotropic thermoviscoelastic solid with fluid

Vertical slownesses of waves at a boundary of an anisotropic thermoviscoelastic medium are calculated as roots of a polynomial equation of degree eight. Out of the corresponding eight waves, the four, which travel towards the boundary are identified as upgoing waves. Remaining four waves travel away from the boundary and are termed as downgoing waves. Reflection and refraction of plane harmonic acoustic waves are studied at a plane boundary between anisotropic thermoviscoelastic solid and a non-viscous fluid. At this fluid-solid interface, an incident acoustic wave through the fluid reflects back as an attenuated acoustic wave and refracts as four attenuating waves into the anisotropic base. Slowness vectors of all the waves in two media differ only in vertical components. Complex values of vertical slowness define inhomogeneous refracted waves with a fixed direction of attenuation, i.e. perpendicular to the interface. Energy partition is calculated at the interface to find energy shares of reflected and refracted waves. A part of incident energy dissipates due to interaction among the attenuated refracted waves. Numerical examples are considered to study the variations in energy shares with the direction of incident wave. For each incidence, the conservation of incident energy is verified in the presence of interaction energy. Energy partition at the interface seems to be changing very slightly with the azimuthal variations of the incident direction. Effects of anisotropy, elastic relaxation and thermal parameters on the variations in energy partition are discussed. The acoustic wave reflected from isothermal interface is much significant for incidence around some critical directions, which are analogous to the critical angles in a non-dissipative medium. The changes in thermal relaxation times and uniform temperature of the thermoviscoelastic medium do not show any significant effect on the reflected energy.     

Ultrafast Kikuchi diffraction: nanoscale stress-strain dynamics of wave-guiding structures

Complex structural dynamics at the nanoscale requires sufficiently small probes to be visualized. In conventional imaging using electron microscopy, the dimension of the probe is large enough to cause averaging over the structures present. However, by converging ultrafast electron bunches, it is possible to select a single nanoscale structure and study the dynamics, either in the image or using electron diffraction. Moreover, the span of incident wave vectors in a convergent beam enables sensitivity levels and information contents beyond those of parallel-beam illumination with a single wave vector Bragg diffraction. Here, we report the observation of propagating strain waves using ultrafast Kikuchi diffraction from nanoscale volumes within a wedge-shaped silicon single crystal. It is found that the heterogeneity of the strain in the lateral direction is only 100 nm. The transient elastic wave gives rise to a coherent oscillation with a period of 30 ps and with an envelope that has a width of 140 ps. The origin of this elastic deformation is theoretically examined using finite element analysis; it is identified as propagating shear waves. The wedge-shaped structure, unlike parallel-plate structure, is the key behind the traveling nature of the waves as its angle permits "transverse" propagation; the parallel-plate structure only exhibits the "longitudinal" motion. The studies reported suggest extension to a range of applications for nanostructures of different shapes and for exploring their ultrafast eigen-modes of stress-strain profiles.     

Dynamics response of complex defects near bimaterials interface by incident out-plane waves

Dynamics response of an elliptical cavity and a crack (on different sides) near bimaterials interface under incident out-plane waves is studied by applying the methods of complex variables and Green’s function. Firstly, based on “conjunction,” the analytical model is divided along the horizontal interface into an elastic half-plane possessing an elliptical cavity and a full elastic half-plane containing a crack. Using complex variables, the scattering displacement field of the half-plane containing an elliptical cavity under incident out-plane waves is then derived. According to the method of Green’s function, the corresponding Green’s functions of two half-planes impacted by an out-plane source load are further deduced. Combined with “crack division,” a crack at the full elastic the half-plane is created, and thus, expressions of displacement and stress are derived while the cavity coexists with the crack. Undetermined antiplane forces are loaded on the horizontal surfaces for conjunction of two sections and then solved by a series of Fredholm integral equations on account of continuity conditions of the interface. Finally, this paper focuses on the discussion of the influence law of different parameters on the dynamics response of complex defects near bimaterials interface by comprehensive numerical results.     

Propagation of thickness-twist waves in an inhomogeneous piezoelectric plate with an imperfectly bonded interface

The propagation of thickness-twist waves in an inhomogeneous piezoelectric plate with an imperfectly bonded interface is investigated. Based on the spring-type relation, the imperfectly bonded interface is dealt with, and the exact solution is obtained from the equations of the linear theory of piezoelectricity. The amplitude ratio between the incident wave and the reflected wave, the displacement component and the stress component are all obtained and plotted. Both theoretical analysis and numerical examples show that the effect of the mechanical imperfection on the wave propagation is more evident than that of the electrical imperfection. When the incident wave frequency and the mechanical imperfect parameter meet some particular relation, no reflected waves can appear in the piezoelectric plate. The results are of fundamental importance to the design of resonators and other devices when imperfect joints are considered.     

Diffraction of horizontal shear waves by a moving interface crack

Summary An analysis of the diffraction of horizontally polarized shear waves by a finite crack moving on a bimaterial interface is carried out. Fourier transform method is used to reduce the mixed boundary value problem to the solutions of two pairs of dual integral equations. These equations are further reduced to a pair of Fredholm integral equations of the second kind. The dynamic stress intensity factors are obtained for several values of wave number, incident angle, crack velocity, and material constants.With 7 Figures     

Reflection and refraction of an arbitrary electromagnetic wave at a plane interface separating an isotropic and a biaxial medium.

Exact solutions are obtained for the reflected and transmitted fields resulting when an arbitrary electromagnetic field is incident on a plane interface separating an isotropic medium and a biaxially anisotropic medium in which one of the principal axes is along the interface normal. From our exact solutions for the reflected fields resulting when a plane TE or TM wave is incident on the plane interface, it can be inferred that the reflected field contains both a TE and a TM component. This gives a change in polarization that can be utilized to determine the properties of the biaxial medium. The time-harmonic solution for the reflected field is in the form of two quadruple integrals, one of which is a superposition of plane waves polarized perpendicular to the plane of incidence and the other a superposition of plane waves polarized parallel to the plane of incidence. The time-harmonic solution for the transmitted field is also in the form of two quadruple integrals. Each of these is a superposition of extraordinary plane waves with displacement vectors that are perpendicular to the direction of phase propagation.     

Analysis of diffracted fields with the extended theory of the boundary diffraction wave for impedance surfaces

Uniform diffracted fields from impedance surfaces are investigated by the extended theory of boundary diffraction wave (ETBDW). The new vector potential of the ETBDW is constructed by considering the pseudoimpedance boundary condition. The method is applied to the diffraction problem from an impedance half-plane. It is shown that the total fields from an impedance half-plane reduce to the case of a perfectly electric or magnetic conducting and opaque half-plane for special values of surface impedance. The total and diffracted fields are compared numerically with the exact solution for the impedance half-plane and modified theory of physical optics (MTPO) solution for an impedance wedge. The numerical results show that the field expressions are in very good agreement with the exact and MTPO solutions.     

Intensity and Phase in Fresnel Diffraction by a Plane Screen Consisting of Parallel Strips

Using the Huygens-Fresnel principle the expressions for the intensity and the phase in Fresnel diffraction phenomena have been derived. The cases of spherical, cylindrical and plane scalar waves incident upon the plane diffraction screen have been investigated. The diffraction screen may consist of any number of parallel strips of different transmissivities and different phase shifts, the width of the individual strips being large compared with the wave-length. As special cases of the general formulae, the intensity and phase distributions in the diffraction patterns for the following forms of the diffraction screen have been calculated: opaque and partially transparent half-plane, slit, strip and double slit. By means of the derived expressions, the validity of Babinet's principle for Fresnel diffraction phenomena of this type has been verified.     

Diffraction of evanescent plane waves by a resistive half-plane

Diffraction of evanescent plane waves by a resistive half-plane is examined. The scattering integrals are constructed with the modified theory of physical optics. These integrals are evaluated uniformly by using an unusual method. The scattered fields of evanescent waves are obtained by giving the angle of incidence a complex value. The diffracted waves are plotted numerically for different parameters of the incident field.     

Obliquely incident surface waves in shallow water of slowly varying depth

Summary The propagation properties of obliquely incident, weakly nonlinear surface waves in shallow water of slowly varying depth are studied analytically. The depth changes slowly in a direction that makes a constant angle with the propagation direction of the incident wave, initially travelling in a region of uniform depth. In the adjacent inhomogeneous region, the depth variations occur on a scale shorter than that on which the wave evolves. It is shown that the problem then reduces to an evolution equation with constant coefficients. Since weak three-dimensional effects are also taken into account, this equation is related to the KP equation. The effect of oblique incidence on mass transfer is studied in detail. In addition, it is shown that the conditions for fission of an incident solitary wave differ from the case of normal incidence. An erratum to this article is available at .