Arbitrary Plane Wave Research Articles

Approximations for modal coupling in scattered fields from orifices

Previous investigations have used Hankel transforms to establish the velocity potentials of the wave fields resulting from arbitrary angle plane wave impingement on a circular orifice in a rigid, thick wall. The scattered field from the orifice is examined, in particular the modal contributions to the amplitude of its velocity potential. For each m,n mode the amplitude is dependent upon the amplitude of the in-orifice waves and a driving term unique to each m,n mode. In establishing the amplitudes of the in-orifice waves, the effects of modal coupling are also considered. In this work these two components of the scattered wave amplitude are investigated on a modal basis and approximations given for coupling effects. These approximations are then used to calculate the scattered field and the results compared with conventional solutions that use full modal coupling.

Anisotropic surface relief diffraction gratings under arbitrary plane wave incidence

A modal method is used for the analysis under oblique incidence of a diffraction grating made of anisotropic material. The problem is studied viewing the structure as the cascade of junctions between periodic arrays of anisotropic slab waveguides with the same period and different heights. This diffraction problem is formulated in terms of an integral equation that enforces the continuity of the transverse magnetic field at the junction. The unknown is the transverse electric field at the junction. It is possible to use also another formulation, where the role of the two fields is exchanged. The kernels of these equations are the relevant Green's functions, which are expressed in terms of eigenfunction expansions. The determination of the modes of the various regions composed of arrays of anisotropic dielectric slabs has been carried out by the method of spectral elements, whereby the field components are represented in a polynomial basis and the original differential eigenvalue problem is converted into an algebraic one. The integral equation is solved numerically by the method of moments and each junction is characterized by its generalized scattering matrix (GSM). Finally, the diffraction efficiencies of the grating are obtained by combining the various GSM's.

Two time-derivative Lorentz material (2TDLM) formulation of a Maxwellian absorbing layer matched to a lossy medium

A two time-derivative Lorentz material (2TDLM) is introduced to define polarization and magnetization fields that lead to an absorbing layer that can be matched to a lossy dielectric medium. The 2TDLM is a generalization of the successful uniaxial polarization and magnetization time-derivative Lorentz material (TDLM) which has been introduced as an absorbing boundary condition for simulation regions dealing with lossless materials. Expressions are derived to describe the propagation of an arbitrary plane wave in this 2TDLM Maxwellian absorbing material. They are used to study the scattering from a semi-infinite 2TDLM half-space of an arbitrary plane wave incident upon it from a lossy isotropic dielectric medium. Matching conditions are derived which produce reflectionless transmission through such an interface for any angle of incidence and frequency. Numerical tests are given which demonstrate the effectiveness of the resulting 2TDLM absorbing layer.

Analysis of electromagnetic scattering by periodic strip grating on a grounded dielectric/magnetic slab for arbitrary plane wave incidence case

A new type of integral equation that is coupled with strip-electric and slot-magnetic currents is applied to the analysis of electromagnetic scattering by a periodic strip grating on a grounded dielectric/magnetic slab for an oblique incident plane wave with arbitrary polarization. In the analysis, the electric and magnetic currents are expanded into a product of a series of cosine functions and a function satisfying the edge condition. Coupled linear equations for the unknown electric and magnetic currents are obtained. From the coupled linear equations, explicit expressions for the reflection coefficients are derived by the use of a single edge-mode expansion. The validity of the method is examined by numerically calculated boundary conditions. A comparison between the calculated results from the present method and a previous method by measured ones shows that the accuracy of the method is excellent. Numerical calculations show that the method converges very rapidly with reasonable accuracy.

Scattering of a transient plane compression wave by a spherical inclusion in a Biot medium

The scattering of an arbitrary transient plane wave by a spherical inclusion in a Biot medium is modeled, by applying the single frequency, steady-state solution of Zimmerman and Stern [ 527–536 (1993)] to the discrete Fourier components of the transient signal, and assuming linear supersposition. The solution of Zimmerman and Stern is an analytical series solution. Its accuracy is mainly determined by computation errors and the convergence of the series. The incident pulse can be any combination of Biot fast and low waves. The theoretical results for certain cases are shown. They are also compared to experimental measurements. [Work supported by Naval Research Laboratory, Stennis Space Center.]

Scattering of an Arbitrary Plane Wave by an Infinite Strip Grating Loaded with a Pair of Dielectric Slabs

An accurate numerical solution for the electromagnetic scattering from an infinite strip grating is presented, where the strips are loaded with a symmetrical pair of dielectric slabs. The direction of propagation and the polarization of the incident plane wave are arbitrary. The boundary value problem is reduced to a solution of singular integral equations, which are discretized by an application of the moment method. Numerical computations are performed mainly for the purpose of designing polarization diplexers. Dependence of diplexing characteristics on grating parameters is examined in detail. Appearance of cross-polarized field at skew incidence is referred.

High-frequency backscattering from a singly curved screen

The backscattering of an arbitrary plane wave from singly curved sheets is considered. An uniform and analytical solution derived from an asymptotic evaluation of the physical optics integral is shown. The solution includes contributions from the straight edges of the screen and is valid on and near the reflection limits. That solution can be combined with the analytical result of the integral of equivalent currents of the physical theory of diffraction (PTD). A graphical comparison of these analytical calculations of the radar cross section (RCS) with other methods and experimental results is presented. >

Elastic scattering amplitude of a polarized electron in an arbitrary plane wave field

The elastic scattering amplitude of a polarized electron in an arbitrary plane wave electromagnetic field is obtained by using the method of dispersion relations. Superposition of a constant crossed field and a plane monochromatic wave of elliptic polarization is considered a particular case of giving the field. An anomalous magnetic moment is obtained for the electron in the mentioned field as are also relative contributions to the anomalous magnetic moment due to the transition into the intermediate state with and without spin turnover.

Elastic scattering amplitude of a scalar particle in a plane wave field

The elastic scattering amplitude of a scalar particle in an arbitrary plane wave electromagnetic field is obtained in the form of a double integral by the method of dispersion relations. Particular cases of giving the plane wave field are investigated. It is shown that the existence of scalar particle radiation in an arbitrary plane wave electromagnetic field results in elastic scattering, whose amplitude determines the change in particle mass in this field.

An efficient plane wave spectral analysis to predict the focal region fields of parabolic reflector antennas for small and wide angle scanning

An efficient approach is described for calculating the field distribution in the focal region of an electrically large, symmetric or offset parabolic reflector antenna with an arbitrary rim contour, when the concave reflector surface is fully illuminated by an obliquely incident arbitrary electromagnetic plane wave. The dominant contribution to the focal-region fields is found by transforming the physical-optics integral over the reflector surface into a plane-wave spectral (PWS) integral. The PWS integral is evaluated rapidly via the fast Fourier transform (FET) algorithm to furnish, in only a single computation, the field for every place in the focal plane (or any plane parallel to it) within the focal region for a given direction of the incident wave. The correction to the physical-optics field is relatively small in the focal region and may therefore be neglected. Numerical results based on this PWS approach are presented, and their accuracy is established by comparison with results based on other approaches. >

Scattering from an open spherical shell having a circular aperture and enclosing a concentric dielectric sphere

The generalized dual series solution is presented for the scattering of an arbitrary plane wave from an open spherical shell having a circular aperture and enclosing a concentric homogeneous dielectric sphere. This solution explicitly exhibits the correct edge behavior, and it can handle spheres that are electrically small or large without special considerations. A variety of cross-section results is presented for the normally incident case. It is shown that effects corresponding to the presence of the interior cavity dominate all of the scattering data. In particular, the cross sections exhibit new resonance features that are due to the cavity-backed nature of the aperture and depend on the characteristics of the interior sphere. The results demonstrate that interior information is contained in the exterior scattering data. >

Electromagnetic scattering of an arbitrary plane wave from a spherical shell with a circular aperture

The problem of the scattering of an electromagnetic plane wave with arbitrary polarization and angle of incidence from a perfectly conducting spherical shell with a circular aperture is solved with a generalized dual series approach. This canonical problem encompasses coupling to an open spherical cavity and scattering from a spherical reflector. In contrast to the closed sphere problem, the electromagnetic boundary conditions couple the TE and TM modes. A pseudodecoupling of the resultant dual series equations system into dual series problems for the TE and TM modal coefficients is accomplished by introducing terms that are proportional to the associated Legendre functions P−m0. The solutions of the TE and TM dual series problems require the further introduction of terms proportional to P−mn, where 0≤n<m. These functions effectively complete the standard spherical harmonic basis set when an aperture is present and guarantee the satisfaction of Meixner’s edge conditions. Having generated the modal coefficients, all desired electromagnetic quantities follow immediately. Numerical results for the currents induced on the open spherical shell and for the energy density of the field at its center are presented for the case of normal incidence.

Ray acoustic analysis of plane‐wave coupling into large open waveguides: Circular geometry

Sound penetration into large enclosures can be modeled approximately by ray methods. When these enclosures are elongated so as to admit simulation by a waveguide, the interplay between rays and guided modes becomes important. To clarify the relevant phenomenology, we examine the prototype problem of a rigid semi‐infinite baffled or unbaffled circular waveguide. Using the methodology of the geometrical theory of diffraction (GTD) and its modification to account for a guiding environment [L. B. Felsen and H. Y. Yee, J. Acoust. Soc. Am. 44, 1028–1039 (1968)], the interior field for arbitrary plane wave incidence is constructed by edge diffracted‐multiple reflected ray tracing, by modal expansion, and by physical optics (PO) applied to the aperture field. Stationary phase evaluation of the PO modal excitation coefficients establishes the connection with GTD, especially the mechanism of coupling from GTD into the modal fields. By reciprocity, the radiation problem can be handled in a similar way. Some conclusions are drawn for guides with noncircular cross section. [Work supported by ONR.]Sound penetration into large enclosures can be modeled approximately by ray methods. When these enclosures are elongated so as to admit simulation by a waveguide, the interplay between rays and guided modes becomes important. To clarify the relevant phenomenology, we examine the prototype problem of a rigid semi‐infinite baffled or unbaffled circular waveguide. Using the methodology of the geometrical theory of diffraction (GTD) and its modification to account for a guiding environment [L. B. Felsen and H. Y. Yee, J. Acoust. Soc. Am. 44, 1028–1039 (1968)], the interior field for arbitrary plane wave incidence is constructed by edge diffracted‐multiple reflected ray tracing, by modal expansion, and by physical optics (PO) applied to the aperture field. Stationary phase evaluation of the PO modal excitation coefficients establishes the connection with GTD, especially the mechanism of coupling from GTD into the modal fields. By reciprocity, the radiation problem can be handled in a similar way. Some conclusi...

Fluid and solid motion in the neighborhood of a fluid‐filled borehole due to the passage of a low‐frequency elastic plane wave

The exact problem of the interaction of an arbitrary plane wave in a homogeneous elastic medium with a fluid‐filled circularly cylindrical borehole is formulated to analyze three‐axis, full‐waveform borehole seismic data. The plane elastic wave (which may be incident upon the borehole from any direction) is partially scattered around the hole and an acoustic field is induced in the borehole fluid. Since seismic wavelengths tend to be much larger than diameters of boreholes, the exact solution may be expanded in powers of Ω (a small number), the incident wavenumber times the borehole radius. In the limit as Ω→0, the scattered field in the elastic medium is of O(Ω); in this limit the borehole crosssection is undistorted and moves with the velocity of the incident wave as if no borehole were present. Neglecting terms proportional to [Formula: see text] or higher leaves three kinds of θ‐dependent terms, where θ is the azimuthal angle about the borehole axis measured with respect to the wavenumber vector of the incident wave. Terms independent of θ (n = 0) give radial motion for incident P- or SV-waves, or rotational motion for incident SH-waves, and fall off as inverse distance from the borehole axis, i.e., 1/r. Terms proportional to cos θ for incident P- or SV-waves or sin θ for incident SH-waves (n = 1) give axial motion that falls off as 1/r. Terms proportional to sin 2θ or cos 2θ (n = 2) give motion in the plane perpendicular to the borehole axis, part of which falls off as 1/r and part as [Formula: see text]. At the borehole wall, the n = 2 terms express the deformation of the borehole cross‐section into an ellipse whose major and minor axes interchange as the wave passes. In the limit as Ω→0, the fluid velocity is constant over the borehole cross‐section. In the plane perpendicular to the borehole axis the fluid is constrained to move with the solid. However, in the axial direction the fluid velocity differs from that of the borehole wall for incident P- or SV-waves (for incident SH-waves the axial fluid and solid velocities both vanish as Ω→0). The ratio of axial fluid velocity to axial solid velocity at the borehole wall, for given elastic medium and acoustic fluid properties, is a function of both the wave type and the angle between the incident wavenumber vector and the borehole axis. Further, for incident P-waves, the axial fluid and solid velocities are in‐phase while for incident SV-waves, they are 180 degrees out‐of‐phase. Thus, as a plane wave passes a given level in a fluidfilled borehole, the plane‐wave type and (for P- or SV-waves) its angle of propagation relative to the borehole axis are theoretically obtainable by measuring fluid and solid axial velocities at that level.

?-Meson decay in an arbitrary plane wave electromagnetic field

In this work we study the leptonic-decay processes of a π-meson in a field that is a superposition of a crossed field and the field of a plane electromagnetic wave. Expressions for the decay probability are obtained that take into account a non-zero neutrino mass. The dependence of the probabilities on the spin of the created lepton is investigated. The values of the parameters of the external field are indicated for which it is possible to isolate the decay process depending on the neutrino mass, which may be of interest for the solution of the problem of the existence of the neutrino mass.

A solution for TM‐mode plane waves incident on a two‐dimensional inhomogeneity

Quantitative interpretation of magnetotelluric (MT) surveys depends at present on the availability of an efficient forward modeling algorithm. To date, two major numerical techniques have been used to obtain the scattered fields from buried inhomogeneities in plane‐wave fields: methods solving the governing differential equation which generally uses a finite‐element or finite‐difference approach, and methods which solve an integral‐equation formulation of the problem. For two‐dimensional (2-D) inhomogeneities a solution for incident fields with the electric field parallel to the strike of the inhomogeneity (TE mode solution) was developed by Hohmann (1971) using the integral‐equation approach. For a perfect conductor an integral formulation, for surface scattering currents, for the TM mode (magnetic field parallel to the strike of the inhomogeneity) was developed by Parry (1969). General 2-D solutions in the presence of an arbitrary mode plane wave (mixed TE-TM) were obtained by Ryu (1970), Swift (1971), and Rijo (1977) using either a finite‐element or finite‐difference technique.

Reflection from a periodically perforated plane using a subsectional current approximation

The scattering from a zero thickness plane having finite sheet resistance and perforated periodically with apertures is calculated for arbitrary plane wave illumination. The surface current density within the unit cell is approximated by a finite number of current elements having rooftop spatial dependence. The transverse electric field is expressed in terms of the current, and the electric field boundary condition is satisfied in an integral sense over the conductor, generating a finite dimension matrix equation whose solution is the current density. Since the conductor shape is defined through the locations of subsectional current elements, arbitrary shaped apertures can be handled. The reflection coefficient and current distribution are calculated for square apertures in both perfectly conducting and resistive sheets, and for cross-shaped apertures. Finite resistivity is shown to cause the magnitude of the transverse magnetic (TM) reflection coefficient to decrease more rapidly and its phase to decrease less rapidly, as the angle of incidence approaches glancing. Through detailed plots of the current density, the current crowding around the apertures is made clearly evident.

EM scattering from bodies of revolution with attached wires

The scattering of an arbitrary plane wave by a body of revolution with multiple attached wires is calculated by the method of moments (MM). Predicted and measured results are presented for sphere/wire, cylinder/wire, and spherical end-capped cylinder/wire-loop geometries for resonant region body sizes.

Surface Current and Charge Density Induced on Aircraft

The usefulness of the geometrical theory of diffraction (GTD) in computing the surface current and charge density induced on aircraft is illustrated. This is a high-frequency solution for an arbitrary incident plane wave and fuselage observation points. A pattem is presented for an arbitrary incident plane wave as well as a series of frequency and time domain plots for roil plane incidence. A 3-dimensional pattem is presented for plane wave incidence (as a function of incidence angle) as well as examples of roll plane results in both the frequency and time domain.

Surface current and charge density induced on aircraft

The usefulness of the geometrical theory of diffraction (GTD) in computing the surface current and charge density induced on aircraft is illustrated. This is a high-frequency solution for an arbitrary incident plane wave and fuselage observation points. A pattern is presented for an arbitrary incident plane wave as well as a series of frequency and time domain plots for roll plane incidence. A 3-dimensional pattern is presented for plane wave incidence (as a function of incidence angle) as well as examples of roll plane results in both the frequency and time domain.