Showing papers on "Plane wave published in 1971"

The foundations of acoustics

Abstract: Preface The Symbols Historical Introduction I. Equations and Units II. Complex Notation and Symbolic Methods III. Analytic Functions: Their Integration and the Delta Function IV. Fourier Analysis V. Advanced Fourier Analysis VI. The Laplace Transform VII. Intergral Transforms and the Fourier Bessel Series VIII. Correlation Analysis IX. Wiener's Generalized Harmonic Analysis V. Transmission Factor, Filters, and Transients ("Kupfmuller’s Theory") XI. Probability Theory, Statistics, and Noise XII. Signals and Signal Processing XIII. Sound XIV. The One-Dimensional Wave Equation and Its Solutions XV. Reflection and Transmission of Plane Waves at Normal Incidence XVI. Plane Waves in Three Dimensional XVII. Sound Propagation in Ideal Channels and Tubes XVIII. Spherical Waves, Sources, and Multipoles XIX. Solution of the Wave Equation in General Spherical Coordinates XX. Problems of Practical Interest in General Spherical Coordinates XXI. The Wave Equation in Cylindrical Coordinates and Its Applications XXII. The Wave Equation in Spheroidal Coordinates and Its Solutions XXIII. The Helmholtz Huygens Integral XXIV. Huygens Principle and the Rubinowicz—Kirchhoff Theory of Diffraction XXV. The Sommerfeld Theory of Diffraction XXVI. Sound Radiation of Arrays and Membranes XXVII. The Green's Functions of the Helmholtz Equation and Their Applications XXVIII. Self and Mutual Radiation of Impedance Tables References Subject Index List of Symbols

Propagation of a Finite Optical Beam in an Inhomogeneous Medium

Abstract: The first part of this paper is devoted to extending the Huygens-Fresnel principle to a medium that exhibits a spatial (but not temporal) variation in index of refraction. Utilizing a reciprocity theorem for a monochromatic disturbance in a weakly inhomogeneous medium, it is shown that the secondary wavefront will be determined by the envelope of spherical wavelets from the primary wavefront, as in the vacuum problem, but that each wavelet is now determined by the propagation of a spherical wave in the refractive medium. In the second part, the above development is applied to the case in which the index of refraction is a random variable; a further application of the reciprocity theorem results in a formula for the mean intensity distribution from a finite aperture in terms of the complex disturbance in the aperture and the modulation transfer function (MTF) for a spherical wave in the medium. The results are applicable for an arbitrary complex disturbance in the transmitting aperture in both the Fresnel and Fraunhofer regions of the aperture. Using a Kolmogorov spectrum for the index of refraction fluctuations and a second-order expression for the MTF, the formula is used to calculate the mean intensity distribution for a plane wave diffracting from a circular aperture and to give approximate expressions for the beam spreading at various ranges.

Wave forces on a circular dock

Abstract: The scattering of surface gravity waves by a circular dock is considered in order to determine the horizontal and vertical forces and torque on the dock. An incident plane wave is expanded in Bessel functions, and for each mode the problem is formulated in terms of the potential on the cylindrical surface containing the dock and extending to the bottom. The solution is shown to have phase independent of depth and so may be obtained from an infinite set of real equations, which are solved numerically by Galerkin's method. The convergence of the solution is discussed, and some numerical results are presented.This problem has been investigated previously by Miles & Gilbert (1968) by a different method, but their work contained errors.

On the generation of long waves

Abstract: For relatively long waves generated by a piston-type wave maker, the classical linear wave-maker theory is extended to second order accuracy. Within the limits of validity of the theory, this agrees well with experimental results for the motion generated by a sinusoidally moving wave maker, and shows that secondary waves are associated with the existence of a second harmonic free wave. By giving the wave maker a motion that consists of a first and a second harmonic, it is shown that this free second harmonic wave may be eliminated, so that the generated wave is virtually of permanent form.

WKB approximation and threshold law for electron-atom ionization

Abstract: The solutions of the Hamilton-Jacobi equation and of the continuity equation for electron-atom ionization problem at zero total angular momentum are investigated in the neighbourhood of saddle points of the potential. Solutions are found which describe sets of orbits whose points of condensation coincide with the saddle points of the potential. The asymptotic behaviour of solutions corresponds to a spherically outgoing wave or to a plane wave. The energy dependence of WKB wave functions is determined and by means of a matching procedure the Wannier ionization threshold law has been confirmed. The connection between the WKB approximation and the asymptotic expansion of the zero- energy wave function has been considered.

Induced Fields and Heating Within a Cranial Structure Irradiated by an Electromagnetic Plane Wave

Abstract: The induced fields and the static heating patterns within a multilayered spherical model that approximates the primate cranial structure irradiated by plane waves in the microwave spectrum are calculated. The relation of the model to the biological structure and the sensitivity of the results to the uncertainties in the dimensions and electrical properties of biological material are investigated. A method of solution for both the scattered and the interior fields for a sphere with an arbitrary number of electrically different concentric layers is developed in a form readily amenable to machine computation. It is shown that the semi-infinite slab model is inappropriate for calculating the microwave radiation dosage for the human head and similar structures.

Temporal-Frequency Spectra for a Spherical Wave Propagating through Atmospheric Turbulence

Abstract: Tatarski has found the frequency spectra for the amplitude, phase, and phase-difference fluctuations of an infinite plane wave propagating through turbulence. Many practical optical beams, used in atmospheric studies, closely resemble point sources, for which the spherical-wave theory is more applicable. The same spectra, calculated for spherical waves, reveal contributions at higher frequencies for amplitude scintillations, nearly identical phase results, and a phase-difference spectrum with no nulls, in contrast with the plane-wave results. Comparison with recent data is shown.

Transmission of electromagnetic waves into time-varying media

Abstract: Expressions are obtained for the electromagnetic fields transmitted into the time-varying medium when a plane wave is incident upon either a dielectric or dispersive half-space. Solutions are obtained for the case when the medium is changed in a stepwise fashion, and also for the case when the medium varies slowly and continuously.

Diffraction of Electromagnetic Waves by a Conducting Screen Perforated Periodically with Holes

Abstract: The reflection and transmission of a plane wave incident on a thin perfectly conducting screen perforated periodically with circular holes are considered. The spacings between holes may be comparable to or less than the wavelength. The metal screen is assumed to be either backed by a flat dielectric sheet, or sandwiched between two or more dielectric sheets that are used to match the susceptsnce of the screen. The techniques of transmission line analysis and the method of moments are employed to obtain a solution for this general class of boundary-value problems. Numerical results for several cases of interest in both X and Ku bands were obtained and shown to be in good agreement with experimental measurements.

Plane Waves in Linear Viscoelastic Media

Abstract: Summary A class of plane inhomogeneous waves which propagate in linear viscoelastic media is considered. A theoretical description of the physical properties and energy associated with these waves is given. Attention is restricted to harmonic P- and SV-waves.

On the motion and radiation of charged particles in strong electromagnetic waves. I - Motion in plane and spherical waves

Abstract: Charge particle motion and radiation in strong plane and spherical electromagnetic waves with nonthermal astrophysical applications

On the scattering of aerodynamic noise

Abstract: According to the Lighthill acoustic analogy, the sound induced by a region of turbulence is the same as that due to an equivalent distribution of quadrupole sources within the fluid. It is known that the presence of scattering bodies situated near such multipoles can convert some of their intense near field energy into the form of sound waves whose amplitude is far greater than that of the incident field. Calculations are here presented to determine the extent of this conversion, for hard and soft bodies of various shapes, making use of the reciprocal theorem to recast the problem into one of finding the field, near the obstacle, induced by an incident plane wave. If the obstacle is small compared with a wavelength, then its presence is equivalent to an additional dipole (or source) whose greater efficiency as a sound radiator implies that the familiar intensity law I ∝ U8, for far field intensity I against typical turbulence velocity U for an unbounded flow, is replaced by I ∝ U6 (or I ∝ U4) for a hard (or soft) body. For the situation where the scatterer is large compared with wavelength, the prototype problem of a wedge of exterior angle (p/q)π is shown to yield an intensity law I ∝ U4+2q/p for both hard and soft surfaces. This result is shown to hold for the more general ‘wedge-like’ surfaces, whose dimensions are large scale and whose edges may be smoothed out on a small scale, compared with wavelength. The method used involves the matching of an incompressible flow, on the fine scales typical of the edge geometry, to an outer flow determined by the large scale features of the surface. Favourable comparisons are made with previous results pertaining to the two-dimensional semi-infinite duct and to the half-plate of finite thickness.

Optical Guided Wave Mode Conversion by an Acoustic Surface Wave

Abstract: The experimental observation of efficient (55%) mode conversion of thin‐film optical guided waves by a collinear interaction with a surface acoustic wave is reported. The effects of waveguide dispersion and finite geometry are discussed.

Scattering by dielectric-loaded screen

Abstract: A numerical solution for the problem of scattering of a plane wave by a dielectric sheet with an imbedded periodic array of conducting strips is presented. The primary motivation for introducing the strips is to reinforce the mechanical hardness of the sheet in certain radome applications. The study shows that with proper design the additional strips can also improve the electric transmission through the composite structure.

Electron States in Ferromagnetic Iron. I. Band Properties

Abstract: A new band-structure calculation is reported for the ferromagnetic state of iron, in which the exchange interaction is given particularly careful treatment. A variational procedure was used with the wave functions expanded in terms of tight-binding functions and orthogonalized plane waves. Hybridization and spin polarization of the wave functions were allowed. Correlation corrections were incorporated. The energy bands are somewhat wider than those previously published; comparison is made with photoemission and optical reflection and x-ray emission data. The calculation leads self-consistently to the observed magnetic moment. The roles of intra-atomic exchange and itinerancy in the origin of iron's ferromagnetism are discussed.

The reflexion of internal/inertial waves from bumpy surfaces

Abstract: When internal and/or inertial waves reflect from a smooth surface which is not plane, there is in general some energy flux which is ‘back-reflected’ in the opposite direction to that of the incident energy flux (in addition to that ‘transmitted’ in the direction of the reflected rays), provided only that the incident wavelength is sufficiently large in comparison with the length scales of the reflecting surface. The reflected wave motion due to an incident plane wave is governed by a Fredholm integral equation whose kernel depends on the form of the reflecting surface. Some specific examples are discussed, and the special case of the ‘linearized boundary’ is considered in detail. For an incoming plane wave incident on a sinusoidally varying surface of sufficiently small amplitude, in addition to the main reflected wave two new waves are generated whose wave-numbers are the sum and difference respectively of those of the surface perturbations and the incident wave. If the incident wave-number is the smaller, the difference wave is back-reflected.

Semidispersive wave systems

Abstract: The statistical initial-value problem for a class of weakly coupled waves whose linear dispersion relation is ω ∞ ± | k | is examined. It is found that in two and higher dimensions a natural asymptotic closure is possible. The redistribution of energy is achieved by means of two mechanisms; the first by a resonance between collinear wave vectors; the second by a local transfer between adjacent rays. The entropy functional is ∫ log n ( k ) d k and corresponds to particles obeying Bose–Einstein statistics.

Diffraction characteristics of a slit in a thick conducting screen

Abstract: The diffraction of a plane electromagnetic wave by a slit in a conducting screen of finite thickness is investigated using the Wiener-Hopf and generalized matrix techniques. For purposes of the analysis, the diffraction by two identical semi-infinite parallel-plate waveguides forming a tandem slit configuration is treated first in order to determine the interaction between the open ends of the waveguides. This interaction term is then utilized in solving for the thick slit geometry which is obtained by filling the parallel-plate regions with a dielectric whose relative permittivity is allowed to approach infinity. Although the integral equations occurring in the tandem slit configuration are similar to those given by Jones for the parallel-strip case, they are solved here by a somewhat different method. In contrast to the limitation on the strip-strip separation imposed by Jones, our solution is not restricted to the special case of large separation between the two slits. For an E -polarized incident plane wave, the far field diffracted by each edge of the thick slit is viewed in ray-optical terms as that due to a thin edge centered at the middle of the thick edge modified by a multiplication factor. The thick edge-edge interaction term, on the other hand, is also modified such that each thick edge is viewed by the other as a combination of a line source as well as a line dipole which vanishes when the thickness approaches zero. It is shown that for ratios of screen thickness to slit width below \approx0.5 , the beamwidth is larger than that of the thin slit, while for larger ratios the beamwidth is smaller. Typical diffraction patterns, which are in good agreement with experiment, are presented to illustrate this phenomenon.

Propagation of electromagnetic waves in a plasma with a sheared magnetic field

Abstract: The propagation of an extraordinary wave in a toroidal plasma is investigated taking into account small shear. It is shown that an ordinary component can be generated at the upper hybrid frequency. The amplitude of the ordinary wave is proportional to the spatial derivative of θ = Bθ/B0, where B0 is the main magnetic field and Bθ the poloidal component. The result is of a form suggesting a diagnostic scheme for measuring the local value of dθ/dr. A numerical application is given for the case of a T-3 Tokamak.

New technique for beam steering with fixed parabolic reflectors

Abstract: A technique is described which offers the potential of achieving wide-angle beam steering with fixed parabolic reflectors. The technique involves a primary-feed device with an aperture field distribution which can be adapted to match the distorted field distributions resulting from a parabolic reflector when an off-axis plane wave is incident. To provide an adaptation without deterioration of the system signal/noise ratio, which requires only a movement of the primary feed along a given locus and an adjustment of noninteracting phase shifters, the primary feed carries out a spatial Fourier transformation of the intercepted fields. The technique has been implemented in an experimental X band antenna and beam steering of ±15 beamwidths achieved with negligible distortion of the directional pattern and less than 0.5 dB loss in gain.

High frequency electromagnetic field in plasma with negative dielectric constant

Abstract: A nonlinear mechanism is considered for the penetration of a transverse electromagnetic field into plasma with E=1- omega 02 >Ti. It is shown that the modulated finite amplitude electromagnetic wave produces plasma density fluctuations which form an electro-acoustic wave and transmits the electromagnetic field into the plasma with a velocity of the order of that ion sound. A theory describing the formation and evolution of the electroacoustic waves is developed.

Continuous Mode Spectrum of a Circular Dielectric Rod

Abstract: The continuous modes for a circular dielectric rod are derived. These modes are identified with the fields due to the scattering of a plane wave at oblique incidence from a dielectric rod, thus providing insight into their behavior. This identification suggests that the modes be classified as incident transverse magnetic (ITM) modes when the incident plane-wave portion of H/sub z/ is zero and as incident transverse electric (ITE) modes when the incident plane-wave portion of E/sub z/ is zero. The transition region from discrete to continuous modes is analyzed in detail. Very simple approximate modes are derived for use in optical waveguide studies.

A high energy approximation : I. Proton-hydrogen charge transfer

Abstract: The proton-hydrogen ground state charge transfer process is studied in a first order approximation in which the proton-proton interaction is treated as belonging to the unperturbed part of the problem. This results in the appearance of a Coulomb wave rather than a plane wave in the final state of the T matrix. The result is a cross section which lies between the Brinkmann-Kramers and Jackson-Schiff results, with the high energy limit of 0.810 sigma BK.

Calculation of Second‐Harmonic Generation in a Piston Beam

Abstract: We discuss the nonlinear generation of a second‐harmonic component in the first‐harmonic beam from a circular plane piston, radiating into a fluid. First‐order perturbation theory is used; higher harmonics, absorption, and depletion of each harmonic are ignored, although a partial correction for the last two effects is applied later. The ratio of piston diameter to first‐harmonic acoustic wavelength is assumed to be about 30 or greater. In particular, the axial behavior of the second harmonic, which has marked structure, is found to agree well with experimental results in water. Also, the average value of the second‐harmonic field is calculated over a circle coaxial with the source, parallel to it, and of the same size. This average differs considerably from the result of an oversimplification that treats the first‐harmonic beam as cylindrically collimated plane waves. When compared with measurements in water, the average agrees well at a source pressure of 3 atm but progressively less well at 5 and at 6 ...

Perturbation Analysis for Reflection From Two‐Dimensional Periodic Sea Waves

Abstract: Reflection of a vertically polarized electromagnetic plane wave from a periodic rough surface is considered. The surface is characterized locally by a boundary impedance. By using a perturbation analysis, we obtained expressions for the spectral components of the reflected waves. It is shown that the results at grazing incidence lead to an effective surface impedance that is consistent with an earlier analysis by Rice (1950) for a perfectly conducting sinusoidal surface.

Scattering of Sound by Sound

Abstract: The debate about scattering of interaction‐frequency components when two sound waves interact at a non‐zero angle has not been resolved because no positive evidence of such scattering outside the interaction volume has been put forward. In this contribution, an attempt is made to review the situation in view of the available experimental evidence relating to interaction between a plane wave and a “collimated” pump wave.