Showing papers on "Plane wave published in 1968"

A statistical theory of mobile-radio reception

Abstract: The statistical characteristics of the fields and signals in the reception of radio frequencies by a moving vehicle are deduced from a scattering propagation model. The model assumes that the field incident on the receiver antenna is composed of randomly phased azimuthal plane waves of arbitrary azimuth angles. Amplitude and phase distributions and spatial correlations of fields and signals are deduced, and a simple direct relationship is established between the signal amplitude spectrum and the product of the incident plane waves' angular distribution and the azimuthal antenna gain. The coherence of two mobile-radio signals of different frequencies is shown to depend on the statistical distribution of the relative time delays in the arrival of the component waves, and the coherent bandwidth is shown to be the inverse of the spread in time delays. Wherever possible theoretical predictions are compared with the experimental results. There is sufficient agreement to indicate the validity of the approach. Agreement improves if allowance is made for the nonstationary character of mobile-radio signals.

Synthesis of a Layered Medium from its Acoustic Transmission Response

Abstract: A direct (noniterative) method is presented to determine an acoustic layered medium from the seismogram due to a time-limited plane wave incident from the lower halfspace. It is shown that one side of the autocorrelation of the seismogram due to an impulsive source at depth is the seismogram due to an impulsive source on the surface. This transforms the problem to the acoustic reflections problem as solved by Kunetz. Both the deep source time function and the layering can be determined from a surface seismogram.

Scattering of Electromagnetic Waves From a Tilted Slightly Rough Surface

Abstract: The interaction of a plane wave and a slightly rough surface tilted away from a reference plane is investigated Expressions for the scattered fields are obtained to second order for a perfectly conducting and a dielectric surface In the limiting case of no tilt the fields agree with those of Rice When the normal to the surface is rotated about the intersection between the incidence plane and the reference plane, the treatment yields important polarization effects and gives explicitly as a function of the tilt which irregularities on the surface contribute to the scattered power Numerical results are obtained to investigate the relative magnitudes of the terms contributing to the cross sections

Anomalous skin effect for specular electron scattering and optical experiments at non-normal angles of incidence.

Abstract: The anomalous skin effect for specular electron scattering at the metal surface is studied, permitting the impinging plane wave to have an arbitrary angle of incidence. It is shown that the expressions for the surface impedance for a non-normal angle of incidence obtained by Reuter and Sondheimer as a generalization from their work at normal incidence are correct for $S$ polarization but incorrect for $P$ polarization. The correct surface impedance for $P$ polarization leads to an additional absorption peak in the frequency range ${10}^{\ensuremath{-}2}{\ensuremath{\omega}}_{p}\stackrel{\ensuremath{\sim}}{l}\ensuremath{\omega}\stackrel{\ensuremath{\sim}}{l}{\ensuremath{\omega}}_{p}$, where ${\ensuremath{\omega}}_{p}$ is the free-electron plasma frequency. This additional absorption, particularly pronounced for long electron lifetimes, is investigated in detail. One important conclusion drawn from this work is that, in general, optical experiments performed at non-normal angles of incidence cannot be analyzed in terms of a single complex frequency-dependent dielectric function. In the frequency range of the additional $P$ absorption, two such dielectric functions are needed, one function for describing $P$ polarization and a different function for describing $S$ polarization.

Theory of Gyrotropic Birefringence

Abstract: A theoretical treatment of the optical effect known as gyrotropic or nonreciprocal birefringence is presented By suitably renormalizing the electric dipole moment tensor, it is shown, for the case of lossless media, that 10 of the 18 independent quantities in the gyrotropic-birefringence tensor have their origin in electric quadrupole effects The other eight are shown to be related to the magnetoelectric effect The general results are applied to the materials ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$ and MnTi${\mathrm{O}}_{3}$ The propagation of a plane wave along one of the crystalline axes of ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$ is then considered It is shown that the gyrotropic birefringence exhibits itself as a rotation of the principal optic axes, together with a change in the velocity of propagation of the wave in the medium Next, the modified boundary conditions corresponding to the renormalized field vectors are given, and the case of a plane wave normally incident on a gyrotropically birefringent medium is discussed It is noted that the field relations at a boundary will be modified even when the quadrupole contribution vanishes and the magnetoelectric tensor is isotropic, a case in which there is no gyrotropic birefringence in the medium itself Foinally, a quantum-mechanical calculation of the gyrotropic-birefringence tensor at 0\ifmmode^\circ\else\textdegree\fi{}K is given The expression obtained is applied to the case of ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$, and the electric quadrupole and magnetoelectric contributions are separated It is roughly estimated that, at optical frequencies, the electric-quadrupole-induced rotation of the principal optic axes of ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$ is of the order of ${10}^{\ensuremath{-}6}$ rad, and the magnetoelectric-induced shift is two orders of magnitude less

Ray Theory of Reflection from the Open End of a Waveguide

Abstract: Ray methods have been widely used to calculate high frequency scattering by objects in an unbounded medium, but they have not been used much for waveguide problems. To show that they can be used for waveguides, we treat by ray methods reflection from an open-ended parallel plane waveguide propagating several modes. The incident mode is decomposed into two plane waves whose scattering by the edges at the termination produces the reflected field. The singly diffracted cylindrical wave originating at each. edge, which is known from the asymptotic theory of diffraction by a single wedge, is represented by means of diffracted rays. Then the stem of the fields on the multiply reflected rays is converted into modal form. This yields formulas for the reflection coefficients in the various modes due to single diffraction. In addition double and multiple diffraction are also taken into account, yielding improved formulas for the reflection coefficients. The results of extensive numerical calculations for $TE$ and $...

Conditions for the Validity of the Angular Spectrum of Plane Waves

Abstract: The representation of the electromagnetic field as an angular spectrum of plane waves is becoming increasingly popular in the treatment of certain problems in physical optics. In this paper the equivalence of the angular-spectrum representation and of one of Rayleigh’s integral transforms is demonstrated. Making use of conditions under which the Rayleigh integral formula exists as the unique solution to a certain class of boundary-value problems, conditions under which the angular-spectrum representation is valid are discussed.

Charged‐Particle Motion in Large‐Amplitude Electromagnetic Fields

Abstract: The relativistic motion of a charged particle in large amplitude, inhomogeneous electromagnetic fields is studied for several situations. This study involved the numerical integration of the equations of motion including the relativistic mass correction and the nonlinear rf v×B force term. The cases studied include particle motion in linearly and circularly polarized, homogeneous plane waves with a homogeneous steady magnetic field parallel to the direction of propagation; particle motion in linearly and circularly polarized TE‐11 modes in waveguides of circular cross section immersed in a uniform steady axial magnetic field; and particle motion in cavity resonators of circular cross section (TE‐111 mode) immersed in a nonuniform steady axial magnetic field. This study is concerned with the maximum energy gains possible in the above situations with field amplitudes appropriate to high‐power microwave experiments. To verify the features of the particle motion as predicted in the numerical study, and to investigate effects which could not be easily included in the analysis, such as space charge from the electron beams, beam‐induced cavity fields, and ionization of residual gas in a cavity resonator, certain experiments were performed. These involved the injection of 1–100‐mA electron beams at 100–1000 V on the axis of circular cross‐section cavity resonators (10 GHz and 1.0 GHz) immersed in a steady axial magnetic field. With pulsed operation, an energy increase of 460 keV was obtained for a drive power of 46 kW at an over‐all efficiency of acceleration of approximately 10%. Higher‐efficiency pulsed operation and continuous operation at lower power levels were also investigated experimentally.

New Theoretical Expressions for Predicting Shielding Effectiveness for the Plane Shield Case

Abstract: The problem of the electromagnetic shielding effectiveness of a thin, plane metal sheet of infinite extent on the electromagnetic field generated by a circular loop field source with uniform current I is solved by application of the quasi-near and near field approximations to the exact integral expressions. The results are shown to be in close agreement with experimental data as well as numerical integration results. Also, they are similar to the results obtained from the plane wave shielding theory of Schelkunoff.

Wave propagation and boundary instability in erodible-bed channels

Abstract: Wave propagation in one-dimensional erodible-bed channels is discussed by using the shallow-water approximation for the fluid and a continuity equation for the bed. In addition to gravity waves, a third wave, which gives the velocity of propagation of a bed disturbance, is found. An appropriate dimensional analysis yields the quasi-steady approximation for the complete shallow-water equations.The well-known linear stability analysis of free-surface flows is extended to include the erodibility of the bed. The critical Froude number Fc above which the free-surface of the fluid may become unstable is obtained. It is shown that erodibility increases the stability of the free surface, in qualitative agreement with previous experiments if qb > qs, qb and qs being respectively the contact-bed discharge and suspended-material discharge. The stability theory is also used to discuss coupled beds and surface waves. From it, five different configurations have been obtained: a sinusoidal wave pattern moving downstream, a transition zone and antidunes moving upstream, moving downstream and stationary. These bed forms are in agreement with experimental results; hence shallow-water theory seems to give a reasonable explanation of the boundary instability.It is shown that the quasi-steady approximation and Kennedy's (1963) stability analysis will be in agreement if (kh)2 [Lt ] 1, where k is the wave number, and h is the depth of the water. When the phase shift δ is introduced in the quasi-steady approximation, the five bed patterns derived from the full equations are found again.

X‐ray Pendellösung fringes in Darwin reflection

Abstract: Oscillations have been observed in the tails of the Darwin curve from thin specimens of silicon. Dynamical theory predicts such oscillations (Pendellosung) for plane wave incident conditions in which two wave points on the same branch of the dispersion surface interfere and produce beating in the diffracted intensity. The usual Pendellosung is observed in transmission in which beating occurs between wavefields on different branches of the dispersion surface related by spherical rather than plane wave conditions. The present experiment uses an asymmetrically cut first crystal to increase the effective width of the incident wave and therefore approach the plane wave condition. Quantitative fringe measurements versus thickness are in fair agreement with theory. The intensity and contrast of the fringes are in poor agreement with theory. Several of the more important factors which reduce the contrast are discussed. With a relatively simple assumption, the observed and expected intensity dislocations can be brought into good agreement.

Etude théorique de la propagation des rayons X dans un cristal parfait ou légèrement déformé

Abstract: Takagi's theory is used to calculate the propagation of X-rays in perfect and nearly perfect crystals. In the general case, the equations have to be solved on a computer. The principle of the calculation is given. It has been applied to the case where an incident plane wave is collimated by a slit. The separation of wavefields is observed, each presenting a fine structure shown to be due to the diffraction by the slit. The same calculation is extended to a crystal submitted to a thermal gradient.The propagation and the intensities of wavefields are in good agreement with the predictions of Penning and Polder.

Scattering of a beam wave by a spherical object

Abstract: The theoretical analysis of the scattering of a beam wave by a small spherical object, which exists at the neighborhood of the beam waist on the propagation axis, is treated. In this analysis, the property of a spherical object is generalized so as to have an r -dependent dielectric constant. Through numerical calculations for the case of the conducting sphere, the difference between the scattering of a beam wave and that of a plane wave are discussed.

Resonant absorption of electromagnetic waves in a non-uniformly magnetized plasma

Abstract: The propagation and collisionless absorption of electromagnetic waves propagating in non-uniformly magnetized plasmas with regions of cyclotron resonance are computed. The particle dynamics associated with motion in a non-uniform magnetic field near cyclotron resonance is considered explicitly. Above a critical plasma density complete wave absorption is predicted. At high plasma densities particles with high velocities along the field lines are heated preferentially whereas at lower densities the slower particles gain more energy per particle from the wave. At high densities the wave is attenuated by the high energy tail of the velocity distribution; this dissipation is shown to be consistent with the uniform field results of Stix. The lack of heating observed in Princeton ioncyclotron wave absorption experiments is resolved by considering the wave launching efficiency.

Theories of Elastic Continua and Crystal Lattice Theories

Abstract: This paper is concerned with the relations between discrete and continuum theories of the elastic behavior of perfect crystals. The point of view adopted is that the validity of any extension of the classical theory of elasticity, intended to accommodate effects of the atomic structure of crystalline solids, can be tested by comparison with an appropriate lattice theory. The particular test to be applied is how well and to how short wave lengths the dispersion relation for plane waves, deduced from the continuum theory, reproduces that for the lattice.

Propagation of acoustic waves through a system undergoing phase transformations

Abstract: The propagation of a sound wave through a system in which phase transformations are possible is examined. Dispersion and attenuation of the wave are found if the wave frequency is comparable to the reaction rate. Sharp changes in the phase velocity and relative energy loss per cycle are expected when phase boundaries are crossed. The attenuation due to a phase transformation can be sufficiently large to contribute to seismic losses in the mantle.

Refraction of Water Waves

Abstract: An investigation is presented of the propagation of three-dimensional, harmonic waves of small amplitude through water of constant depth or gradually varying depth. Within the framework of linear theory for potential flow, the results are exact for propagation over horizontal bottoms, e.g., diffraction, and approximate for propagation over sloping bottoms, e.g., refraction combined with diffraction. An expression is given for the velocity potential of three-dimensional waves, harmonic in time. The velocity potential must fulfill the classical hydrodynamical conditions. An analysis of the resulting relationships shows that the magnitudes of phase speed and energy flux are affected by amplitude variations. The time-averaged energy flux is directed along wave rays, regardless of amplitude gradients along the wave crests. The expressions for phase speed and energy flux do not involve wave rays; they provide the basis of a computational scheme in which the wave characteristics are computed in grid points which have a predetermined location. Such method may be an alternative for existing methods which utilize wave rays.

The Description of Polarization in Classical Physics

Abstract: An alternate derivation of the Stokes polarization parameters is presented; the parameters are obtained from the elliptic equation of polarization rather than the plane wave equations. As a result of deriving the parameters in this manner, the relationship between the polarization ellipse and the Stokes parameters is clarified. The Stokes parameters for various states of polarized light are briefly reviewed. The remainder of this article is then devoted to obtaining the Stokes parameters for a number of important physical phenomena such as the classical Zeeman effect, synchrotron radiation, Thomson scattering, reflection of electromagnetic waves by dielectric surfaces, and wave propagation in a plasma.

An Exact Solution for the Scattering of Electromagnetic Waves from Conductors of Arbitrary Shape. I. Case of Cylindrical Symmetry

Abstract: The problem of the scattering of an electromagnetic plane wave, incident along the axis of symmetry on a cylindrically symmetric, though otherwise arbitrarily shaped conductor, is solved exactly by means of a perturbation-expansion technique developed for this purpose The solution obtained is an exact analytical solution, equally valid in the near and far zones, as well as over the entire frequency range, including the resonance region The general solution is obtained, and several special cases are treated in detail The term-by-term agreement of the perturbation-series solution with the known exact solution is demonstrated analytically for the case of a sphere The form of the solution is particularly well suited for methodical numerical evaluation by machine calculation

Electromagnetic Scattering by a Moving Conducting Sphere

Abstract: A relativistically correct expression for the far zone electromagnetic field scattered by a perfectly conducting sphere, moving with constant velocity, through an incident plane wave is developed. It is seen that if the scattered field is expressed in a special "retarded" coordinate system, a result that is more tractible, allowing physical interpretation, is obtained. When the field is expressed in this way, the expected first-order effects are manifest, yet the higher order effects are also present. This solution may be directly applied to the finite bodies with more complicated shapes than the sphere. For the case of the sphere it is found that the form of the scattered field allows the calculation of the scattering cross section, the total scattering cross section, and the rate of exchange of electromagnetic and mechanical energies. The Special Theory of Relativity gives a rigorous means of discussing a situation involving electromagnetic scattering by a uniformly moving body, For such a situation, in free space, the theory specifies how one may restate the problem so that it is viewed with respect to an observer moving with the body. From this viewpoint the problem appears that of scattering by a stationary body. This implies that there exists a straightforward means of obtaining the field scattered by a uniformly moving body in free space, providing only that its stationary scattering properties are known. Historically, the first situation attacked by this method was that of reflection by a moving infinite mirror (Sommerfeld, 1964b; Pauli, 1958). Scattering by a moving dielectric half space also has been discussed by Tai (1965), Yeh (1965), and by Pyati (1966). Their work has been extended to a moving uniaxially anisotropic half space by Lee and Lo (1967). Recently, Lee and Mittra (1967) have considered the case of scattering by a moving conducting cylinder. It is seen that as the geometry of the scattering body becomes more complex, the original symmetry of the stationary solution is lost in the transformation between the moving systems, resulting in an expression that is awkward, yielding little physical meaning. In this paper a coordinate system is chosen to express the far field scattered by a moving finite body, a sphere, giving a solution that is relativistically correct and at the same time allows physical interpretation. Although a sphere is considered here, the method may be used to express the far field scattered by other moving finite objects or the radiation field from a finite, moving electro­ magnetic source.

Diffusion Analysis for the Propagation of Mutual Coherence

Abstract: A new method of evaluating the mutual-coherence function for propagation in a randomly inhomogeneous medium like the atmosphere is presented. The new method, which is highly physical, as distinct from a mathematical approach, does not involve the treatment of any differential equations. Instead, the treatment is based on decomposition of a randomly distorted wavefront into a set of plane waves with random amplitudes. These plane waves constitute orthogonal modes. Propagation in a random medium is treated as the physical process of diffusion of amplitude (or energy) between the modes, and a short-path-propagator function for this diffusion is developed. From the short-path-propagator function, a long-path-propagator function is easily obtained, and from this the mutual-coherence function is computed. Starting from the known short-path mutual-coherence function, which is known to be accurate, the mutual-coherence function for long paths is obtained. The results are in agreement with previous results, all of whose derivations have recently been subject to criticism. Because this derivation is not a mathematical exercise, it should not be subject to any of these or similar criticisms, which were primarily questions of mathematical rigor.

Time‐Harmonic Fields in Source‐Free Bianisotropic Media

Abstract: A bianisotropic medium is defined as one in which the field vectors D and H depend on both E and B, but may not be parallel to either. A moving medium appears bianisotropic to the laboratory observer, even if it is isotropic in its rest frame. It is shown that, for time‐harmonic fields, a bianisotropic medium can be viewed as one which is electrically and magnetically anisotropic with properly defined dyadic operators. In particular, a moving medium can be characterized by a permittivity tensor and a permeability tensor for plane‐wave propagation. This characterization simplifies the solution of electromagnetic problems in moving media. As illustrated, the dispersion relations in a moving uniaxially anisotropic medium are obtained, and the problem of a plane wave normally incident upon a moving uniaxial medium is solved.

Ray‐Theory Analysis of Magnetoelastic Delay Lines

Abstract: Magnetoelastic wave propagation at microwave frequencies in single‐crystal yttrium iron garnet, of various nonellipsoidal geometries, has been intensively investigated experimentally in recent years in connection with delay‐line applications. However, two important features, namely the detailed nature of the energy paths and the magnetic excitation mechanisms, have received scant attention. This paper examines these features from the viewpoint of geometrical ray theory. Attention is first directed to two basic phenomena: magnetoelastic wave anisotropy, which gives rise to deflection of the group velocity from the phase velocity vector, and refraction, which arises from the inhomogeneous internal magnetic field. Consideration is then given to justifiable approximations for the wave behavior and magnetic field, and guidelines which enable a specification of the launching surface to be made. Ray plots are presented for the axially magnetized rod, which is found to be strongly focusing, and for the complement...

Crystal symmetries of plane-wave-like functions. I. The symmorphic space groups

Abstract: A set of tables of coefficients for forming linear combinations of plane waves, both without and with spin, symmetrized with respect to all the necessary sub-groups of all 73 symmorphic space groups, is presented here. A symmetry analysis of all the Brillouin zone symmetry points of these 73 space groups is also included and serves as an index to the coefficient tables. A discussion of the method of calculation is included as well as a review of the theory which underlies the desirability of symmetrized functions, and the theory of the projection operator, by which these coefficients were calculated. Section 4, a guide to the use of the tables, may be read independently of the rest.

The `muffin-tin' approximation in the calculation of electronic band structure

Abstract: Several standard techniques for the calculation of electronic band structures in solids seem to require the crystal potential to be of `muffin-tin' form, but an elementary calculation shows that contributions from variations of the potential in the interstitial region may easily be included in the secular determinants of the augmented plane wave and Korringa-Kohn-Rostoker-Ziman methods. The corrections in the Korringa-Kohn-Rostoker formalism are more complex. A numerical example for germanium shows that these terms can be significant.

Scattering from hollow conducting cylinders

Abstract: The paper deals with reradiation from the interior of cylindrical conducting structures of finite length and arbitrary termination. Expressions are developed for far fields at points in the principal plane. For rectangular cross-sections this plane is one containing a broad side of the structure, whereas for circular cross-sections it is a plane containing the longitudinal axis of the structure. Incident plane waves having the propagation vector parallel to the principal plane and polarised either vertically or horizontally with respect to the principal plane are considered. The method of solution involves use of normal-mode techniques in conjunction with the Stratton-Chu integral. Comparisons of computer-calculated theoretical data and measured data were made for illumination of rectangular and circular structures. The theoretical and experimental data, which were for zero bistatic angle and short-circuit terminations of the structures, show remarkably good agreement. For aspect angles of less than about 60°, the return from the interior is dominant, while for larger aspect angles the return from the outer surface masks the interior return. The theory is also valid for nonzero bistatic angles.

Ray Method for Sound‐Wave Reflection in an Open‐Ended Circular Pipe

Abstract: Modal reflection and coupling coefficients are calculated for a semi‐infinite flanged and unflanged hard‐wall circular tube excited by one of the propagating modes. The calculation is performed by a ray method wherein the incident mode is decomposed into local plane waves impinging on the rim. Consequent diffraction effects establish the reflected waves and are represented equivalently in terms of radiation from a nonisotropic ring source having a radiation pattern determined by the local scattering properties of the rim. The rays emitted by the nonisotropic ring source and reflected repeatedly from the tube wall are summed into modal form, the quality of the resulting asymptotic mode series being improved by comparison with the exact solution for an isotropic ring source. Reflection and coupling coefficients are provided by the modal amplitudes in this representation and are determined for primary diffraction due to the incident mode only and also for multiple diffraction due to interaction across the mouth of the tube. Comparison with exact computations for the thin‐walled tube shows that the multiple interaction ray‐acoustical calculation is capable of high accuracy not only at high frequencies but even in the dominant mode regime. Data are also presented for flanged terminations for which no exact solution is available.