Showing papers on "Plane wave published in 1974"

A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface

Abstract: A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edse formed by perfectly conducting curved ot plane surfaces is obtained. This diffraction coefficient remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. Our method is based on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray-fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresenel integrals, which ensure that the total field is continuous at shadow and reflection boundaries. The diffraction coefficients have the same form for the different types of edge illumination; only the arguments of the Fresnel integrals are different. Since diffraction is a local phenomenon, and locally the curved edge structure is wedge shaped, this result is readily extended to the curved wedge. It is interesting that even though the polarizations and the wavefront curvatures of the incident, reflected, and diffracted waves are markedly different, the total field calculated from this high-frequency solution for the curved wedge is continuous at shadow and reflection boundaries.

Shock wave study of the α ⇄ ε phase transition in iron

Abstract: Plate impact experiments producing plane waves of up to 40 GPa (400 kbar) peak stress were performed using Armco iron specimens and impactors. Highly accurate time‐resolved measurements of the resulting free‐surface velocities of the specimens were obtained with the VISAR laser interferometer instrumentation system. The free‐surface velocity profiles provide new information concerning the rate effects associated with the α → e polymorphic phase transition at 13 GPa, the material strength and release wave speeds at 10 and 40 GPa, and the stress level at which the iron reverts back to the α phase on unloading. A strong magnetic field was found to produce no measurable change in the phase‐transition stress. The accuracy of the ``factor‐of‐2'' assumption relating free‐surface velocity to particle velocity in iron was also evaluated experimentally.

Nonlinear evolution of parallel‐propagating hydromagnetic waves

Abstract: The nonlinear evolution of plane hydromagnetic fluctuations propagating along the unperturbed magnetic field direction is considered. From an expansion of the ideal magnetohydrodynamic equations and the hydromagnetic shock jump conditions, it is shown that a wave in which the magnitude of the magnetic field is nonconstant steepens into a shock and subsequently evolves toward a purely Alfvenic fluctuations of lower mean energy density. Explicit expressions are derived for the asymptotic state and for the characteristic lines which describe the evolution toward that state. A class of fluctuations which includes linearly polarized waves is shown to evolve into rotational discontinuities. The results are applied to observations of hydromagnetic fluctuations in the solar wind.

Multipole expansions and plane wave representations of the electromagnetic field

Abstract: A new and conceptually simple derivation is presented of the multipole expansion of an electromagnetic field that is generated by a localized, monochromatic charge‐current distribution. The derivation is obtained with the help of a generalized plane wave representation (known also as the angular spectrum representation) of the field. This representation contains both ordinary plane waves, and plane waves that decay exponentially in amplitude as the wave is propagated. The analysis reveals an intimate relationship between the generalized plane wave representation and the multipole expansion of the field and leads to a number of new results. In particular, new expressions are obtained for the electric and magnetic multipole moments in terms of certain components of the spatial Fourier transform of the transverse part of the current distribution. It is shown further that the electromagnetic field at all points outside a sphere that contains the charge‐current distribution is completely specified by the radiation pattern (i.e., by the field in the far zone). Explicit formulas are obtained for all the multipole moments in terms of the radiation pattern.

Interaction of Plane Waves with Vertical Cylinders

Abstract: This study deals with the interaction of linear, plane water waves with stationary groups of rigid, vertical, circular cylinders under conditions in which the inertial forces on the cylinders dominate over the drag forces. A direct matrix solution as well as multiple scattering as suggested by Twersky (1952) are used to obtain the velocity potential in the vicinity of the cylinders. The groups may consist of a number of cylinders having any geometric arrangement, may have Dirichlet, Neumann, or mixed boundary conditions, and need not have identical diameters. The study represents an extension of the single cylinder case presented by MacCamy and Fuchs in 1954. Basic scattering coefficients for 192 different arrangements of two cylinders are obtained with the aid of a Bessel coordinate transformation and a matrix inversion procedure. The resulting potential function is then applied to calculate force components in the direction of wave advance and orthogonal to it. For the cases considered the former departs as much as 65% from the force on a single cylinder and the mass coefficient is found to range from 1.19 to 3.38 - a not insignificant departure from the often used value of 2.0. Furthermore the orthogonal force may be as large as 67% of the single-cylinder force.

Theory of conducting gratings and their applications to Optics

Abstract: A method to study the diffraction of an electromagnetic plane wave by a grating,in the case where it has a finite conductivity, is described for both classical cases of polarization. The results relative to the visible and ultra-violet regions are compared to those recently obtained using an integral formalism [1],[2]. Various particular applications are given. The validity of the results is discussed.

Amplification and absorption of electromagnetic waves in overdense plasmas

Abstract: The spatial variation of the amplitude of electromagnetic radiation propagating into an inhomogeneous plasma is discussed in reference to nonlinear interaction of HCN laser radiation with plasmas and to experiments on r.f. heating of the ionosphere. Previous results on the ordinary wave and on the extraordinary wave at normal incidence are reviewed with emphasis on the physical processes affecting the amplitude behaviour. New numerical results are obtained starting from an integral representation of the solution of the wave equation for waves in a cold, inhomogeneous, magnetized plasma slab. Resonance absorption is discussed for the cases of normal incidence in the presence of a magnetic field (the Budden problem) and oblique incidence in the absence of a magnetic field.

On a variety of wave phenomena in chemical reactions

Abstract: A variety of wave phenomena are analyzed and discussed for systems in which chemical reactions and transport take place. Certain families of wave solutions of reaction‐transport equations arise owing to the weak stability of a reference state to a class of perturbations. We consider both wave induction by heterogeneities and autonomous waves and seek perturbation solutions which provide the dispersion relation and the wave vector dependence of the amplitude for one‐parameter families of waves characterized by the wave vector. For the case of an arbitrary reaction mechanism possessing a homogeneous steady state we derive, by use of bifurcation theory and frequency renormalization, small amplitude autonomous plane waves and standing and rotating waves. We find solutions corresponding to long wavelength waves, static structures, and phenomena existing only at intermediate frequencies and wavelengths. The theory is found to have a nonuniformity in convergence in the core region of pacemaker and spiral‐like so...

Reflection of thermoelastic waves at a solid half-space with thermal relaxation

Abstract: The thermal and elastic plane wave motion of small amplitude in a homogeneous, isotropic and thermally conducting solid which occupies a half-space is considered. The presence of the thermal waves effect change in the angle of emergence.

Electromagnetic fields in spatially dispersive media

Abstract: The structure of the electromagnetic field in a spatially dispersive model medium occupying a plane parallel slab is obtained, free of several customary ad hoc assumptions made in other theories. The model medium is characterized by a dielectric response function appropriate to the neighborhood of an isolated-exciton transition frequency. The exact mode expansion for the electromagnetic field in the slab is derived and it is found that, unlike in the case of an unbounded medium, a single plane wave cannot be generated in the slab. An elementary solution (a single mode) is found to consist, in general, of six plane waves (four transverse and two longitudinal ones), coupled by two linear relations. These relations are shown to be equivalent to two nonlocal boundary conditions (of the form encountered in connection with the Ewald-Oseen extinction theorem in molecular optics), which the nonlocal contribution to the induced polarization must satisfy on the faces of the slab. This result resolves a long-standing controversy about the nature of the so-called additional boundary conditions that are generally believed to be required for solving problems of interaction of an electromagnetic field with a spatially dispersive medium. The results are applied to the problem of refraction and reflection on a spatially dispersive model medium occupying a half-space and a generalization of the classic formulas of Fresnel are obtained. The behavior of the reflected and transmitted waves as functions of the angle of incidence and of the frequency are illustrated by several figures. Our results are shown to differ from those obtained by Pekar in a well-known paper. The difference is traced to the nature of the additional boundary conditions postulated by Pekar; they are found to be inconsistent with the additional boundary conditions that we derive as an exact consequence of Maxwell's theory. Comparisons with several other theories, especially with those of Sein and Birman and of Maradudin and Mills are also made.

A theory of latitude dependent geomagnetic micropulsations: The asymptotic fields

Abstract: The asymptotic temporal behavior of hydromagnetic waves in a model of the inner magnetosphere is shown to be characterized by guided modes. The basic hydromagnetic wave equation is derived and applied to a cylindrical model of the inner magnetosphere. This model offers a good representation of the spatially dependent field line frequencies present in a dipole field. The initial value problem for the symmetric toroidal mode is solved, and its singularities are treated by Fourier superposition. Singularities also are present in the asymmetric poloidal mode wave equation and are shown to be logarithmic. Fourier superposition leads to the solutions for the electric and magnetic fields, which are asymptotic in time. The results indicate decay of the poloidal modes and domination by the toroidal modes, i.e., field line control of the propagation. At the latitude at which the maximum amplitude of a particular frequency occurs, the wave becomes linearly polarized. The asymptotic micropulsation periods depend on the characteristic field line periods and are usually longer at higher latitudes. Undamped guided waves lead to some terms, such as change density and parallel current density, that increase linearly with time. The inclusion of loss mechanisms in the wave equation, e.g., conductivity, limits the guided modes and prevents such nonphysical effects from occurring.

Analysis of Gaussian beam propagation and diffraction by inhomogeneous wave tracking

Abstract: Inhomogeneous waves behave locally like A(r) exp[ikS(r)], where A and S are spatially dependent complex amplitude and phase functions, and k is the (large) free-space wavenumber. A previously developed asymptotic theory for high-frequency propagation and scattering of such waves is here applied to the propagation and scattering of paraxial Gaussian beams. Attention is given to Gaussian beams in free space, to beams in a lens-like medium with parabolic variation of the refractive index, and to beam reflection by a cylindrical obstacle. In the latter instance, the obstacle size may be comparable to the incident beamwidth, thereby introducing substantial distortion into the reflected beam. The results obtained from the asymptotic theory are verified by comparison with rigorously derived solutions, thereby confirming the validity of the theory, which can also be applied to more general medium and obstacle configurations.

Plane wave spectrum-surface integration technique for radome analysis

Abstract: The purpose of this paper is to report an accurate boresight analysis for practical three-dimensional antenna-radome systems. The analysis of practical three-dimensional antenna-radome combinations has been impractical for antenna aperture areas greater than about 75\lambda^{2} . The principal difficulty encountered is the excessive computation time required for the large number of antenna near field calculations. The key feature of the approach taken by the authors is the use of the plane wave spectrum (PWS) formulation for calculation of the antenna near fields. The PWS formulation provides much improved efficiency over other nearfield analyses and makes this analysis possible. The method can also be applied to analyze other antenna distortion.

Index of refraction for scalar, electromagnetic, and gravitational waves in weak gravitational fields

Abstract: We consider the solutions of the scattering of scalar, electromagnetic, and gravitational waves by the gravitational field of a single particle, for the case of small wave amplitudes and weak gravitational fields. Scatterings are considered for both incident plane waves and incident spherical waves. For plane waves incident on a thin sheet of matter composed of free particles, the superimposed wave solutions give rise to a phase change arising from the coordinate dependence of the speed of light on the gravitational potential, focusing of the incident wave by the sheet, and, in some cases, a phase change due to dispersion of the wave by the matter. For gravitational waves, the index of refraction $n$ is given by $n\ensuremath{-}1=\frac{2\ensuremath{\pi}G\ensuremath{\rho}}{{\ensuremath{\omega}}^{2}}$, assuming $n\ensuremath{-}1$ is small, and for electromagnetic waves $n=1$ to the same order. The index of refraction for scalar waves depends on the form of the scalar-wave equation used. The generation of back-scattered waves is also treated. Calculations are repeated for spherical waves incident on a thin spherical shell of matter. The propagation of $\ensuremath{\delta}$-function wave packets is then treated in order to show that the solutions are consistent with causality, even though, in some cases, the group velocity exceeds the velocity of light.

Propagation of waves along an impedance boundary

Abstract: A theoretical analysis of the scalar wave field due to a point source above a plane impedance boundary is presented. A surface wave is found to be an essential component of the total wave field. It is shown that, as a result of ducting of energy by the surface wave, the amplitude of the total wave near the boundary can be greater than it would be if the boundary were perfectly reflecting. Asymptotic results, valid near the boundary, are obtained both for the case of finite impedance (the soft-boundary case) and for the limiting case in which the impedance becomes infinite (the hard-boundary case). In the latter, the wave amplitude in the farfield decreases essentially inversely as the horizontal propagation distance; in the former (if the surface-wave term is neglected), it decreases inversely as the square of the horizontal propagation distance.

Application of complex ray tracing to scattering problems

Abstract: Representations and geometric constructions associated with complex points, complex lines, and complex rays are introduced. They are applied to the problem of scattering of an evanescent plane wave by a conducting circular cylinder. This problem has an exact solution, which provides a check of the validity of complex ray tracing and suggests more general applications. An important role is played by the transformation that maps the point of reflection, on the complex extension of the scattering surface, onto the trace in real space of the complex reflected ray. For the particular problem considered, the phase and amplitude of the reflected field are computed and the "phase paths" and "phase fronts" are constructed. The reflected field and phase paths obtained in this manner are not to be taken in their entirety because some reflection points are not "illuminated" by the incident wave, and because the reflector may be only part of the cylinder. Tentative selection and truncation rules are used which yield good agreement with the exact solution over some regions. The disagreement, where it occurs, comes-as it does for real rays-from neglecting the diffracted field such as the creeping waves around smooth surfaces and, in the case of truncation, the edge waves from the discontinuity. Some consideration is given to scattering by an arbitrary smooth conductor. Some problems peculiar to the use of complex rays are stated.

Nonlinear Capillary Waves on the Surface of Liquid Column

Abstract: Weakly nonlinear capillary waves on a liquid column of circular cross-section are investigated on the basis of the derivative expansion method It is found that the complex amplitude of a quasi-monochro-matic travelling wave can be described by a nonlinear Schrodinger equation in a frame of reference moving with the group velocity The known property of this equation reveals that wave trains of constant amplitude are modulationally unstable, which suggests a new possibility of the break-up of column On the other hand, the complex amplitude of a quasi-monochromatic standing wave near the cut-off is governed by another type of nonlinear Schrodinger equation in which the role of the time and that of the space are interchanged This equation makes it possible to estimate the nonlinear effect on the cut-off wave-number

Proper dynamics of a rigid point particle

Abstract: A spinor formulation of the classical Lorentz force is given which describes the precession of an electron's spin as well as its velocity. Solutions are worked out applicable to an electron in a uniform field, a plane wave, and a Coulomb field.

Self-focusing of very powerful laser beams II

Abstract: In a recent paper the author proposed a self-focusing theory based on linear stability analysis of the quasi-optical equation [1]. Strictly, the theory applies only to a plane wave of infinite aperture. In this paper the theory is extended to beams of finite aperture, which may be initially convergent or divergent.

Anisotropic relaxation times for impurity scattering on the Fermi surface

Abstract: A theoretical calculation is described for the anisotropic relaxation time due to impurity scattering on the Fermi surface of simple metals. The calculation is based on a multiple plane wave scattering formalism using pseudopotentials and phase shifts. The pseudowavefunctions and the Fermi surface are obtained from a four orthogonalised plane wave calculation while the scattering pseudopotentials are taken from form factors which are locally rescreened and corrected for lattice distortion around impurities. Detailed results are presented for impurity in Al. Calculated Dingle temperatures are in reasonable agreement with experimental results. A phase shift model is introduced which allows the Dingle temperature to be expressed in terms of impurity phase shifts and pseudowavefunction amplitudes. These amplitudes have been calculated for several orbits on the Fermi surfaces of Al, In and Pb. The influence of impurities on the low field Hall effect is also discussed.

Natural-mode representation of transient scattering from rotationally symmetric bodies

Abstract: A procedure for calculating the natural frequencies and the current distribution of the natural modes of a perfectly conducting body of revolution is presented. The analysis is based on the magnetic-field integral equation simplified to account for rotational symmetry. A technique is developed for the numerical evaluation of the natural frequencies and modes of a perfectly conducting rotationally symmetric body. The technique is used in a numerical sample calculation of natural frequencies and modes of a prolate spheroid. The general method of treating transient electromagnetic scattering problems developed previously is specialized to perfectly conducting bodies of revolution. In particular, scattering of a step-function plane wave from a prolate spheroid is treated numerically. The time response of the induced surface current is constructed from the natural modes in the same way as in network theory. The convergence of the solution, as the number of modes is increased, is also considered.

Almost all about waves

Abstract: Among his peers, John R. Pierce is properly appreciated as a creator of complex engineering realities from the most basic of scientific insights. To those of more modest technical attainment, he can be directly valued as a teacher with a talent for making his concerns understandable to those willing to commit their interest and attention. In this book, he once again brings a diffuse and difficult subject within reach of nonspecialized readers. The book presents waves in all their manifestations and realizations, a subject that perfectly joins basic science and everyday reality. And it does so with what, nowadays, might be regarded as a modicum of mathematics, venturing just across the line of partial differential equations, which is where the wave equation is at home and emerges to be seen fully revealed.Pierce considers waves in the most general light as one of the great unifying concepts of physics. This approach will allow the reader to comprehend an almost unlimited array of specific phenomena: "Modern physics is full of waves," Pierce writes, "the earthquake waves which seismologists study; the waves and ripples on oceans, lakes, and ponds; the waves of sound which travel through the air; the mechanical waves in stretched strings and in the quartz crystals that are used to control the frequency of radio transmitters; the electromagnetic waves that constitute light, and that are radiated by radio transmitters and received by radio receivers; and finally, the waves of what?--probability, perhaps--which are used in quantum mechanics to predict the behavior of electrons, atoms, and complex substances."The emphasis is on behavior common to all these and other waves: what happens when waves interact with one another in waveguides and traveling-wave tubes; the behavior of waves in moving media; the directional patterns of complex sources; transmission between directive antennas; waves from bodies moving faster than the speed of waves in the medium and waves carried along by bodies moving more slowly than waves in the medium and the nature of plane and nearly plane waves. Among the concepts covered are phase velocity and group velocity, vector and complex representation, energy and momentum, coupled modes and coupling between modes, polarization, diffraction, and radiation.

Lectures on the scattering of light

Abstract: The exact (Mie) theory for the scattering of a plane wave by a dielectric sphere is presented. Since this infinite series solution is computationally impractical for large spheres, another formulation is given in terms of an integral equation valid for a bounded, but otherwise general array of scatterers. This equation is applied to the scattering by a single sphere, and several methods are suggested for approximating the scattering cross section in closed form. A tensor scattering matrix is introduced, in terms of which some general scattering theorems are derived. The application of the formalism to multiple scattering is briefly considered.

Radiation fields of GaAs-(AlGa)As injection lasers

Abstract: Theoretical radiation patterns from a multilayer model of a dielectric waveguide are fitted to single mode experimental profiles of three symmetrical double-heterojunction cavities to test the adequacy of the model and study the effect of the dielectric parameters on the beam pattern. The radiation from the normal TE modes is approximated by plane waves, while for the TM modes it is given by boundary value solutions of the Maxwell equations. The adequacy of the theory is shown by the faithfulness of the fit out to large beam angles and low intensities, and the agreement of the adjusted cavity parameters to the experimental values. Small changes in either the cavity thickness or the dielectric constant of the internal n-type region have similar first order effects on the angular position of the minima in the profile as well as in the amplitude of the sidelobes. Depths of the minima decrease with departures of the structure from planarity. Pattern distortion from mode coupling at the interfaces and facets is not observed.

Integral equation solution and RCS computation of a thin rectangular plate

Abstract: In this work, a new integral equation is employed to calculate the current distribution on a rectangular plate which is illuminated by a plane wave. Numerical results are also obtained for the radar cross section (RCS) of the plate for different angles of incidence and different dimensions of the plate. These results are compared with other RCS computations using geometrical theory of diffraction, physical optics, and variational methods.