Showing papers on "Reflection (physics) published in 1972"

Optics in Stratified and Anisotropic Media: 4×4-Matrix Formulation

Abstract: A 4×4-matrix technique was recently introduced by Teitler and Henvis for finding propagation and reflection by stratified anisotropic media. It is more general than the 2×2-matrix technique developed by Jones and by Abeles and is applicable to problems involving media of low optical symmetry. A little later, we developed a 4×4 differential-matrix technique in order to solve the problem of reflection and transmission by cholesteric liquid crystals and other liquid crystals with continuously varying but planar ordering. Our technique is mathematically equivalent to that of Teitler and Henvis, but we used a somewhat different approach. We start with a 6×6-matrix representation of Maxwell’s equations that can include Faraday rotation and optical activity. From this, we derive expressions for 16 differential-matrix elements so that a wide variety of specific problems can be attacked without repeating a large amount of tedious algebra. The 4×4-matrix technique is particularly well suited for solving complicated reflection and transmission problems on a computer. It also serves as an illuminating alternative way to rederive closed solutions to a number of less-complicated classical problems. Teitler and Henvis described a method of solving some of these problems, briefly in their paper. We give solutions to several such problems and add a solution to the Oseen–DeVries optical model of a cholesteric liquid crystal, to illustrate the power and simplicity of the 4×4-matrix technique.

Electromagnetic fields due to dipole antennas over stratified anisotropic media.

Abstract: Solutions to the problem of radiation of dipole antennas in the presence of a stratified anisotropic media are facilitated by decomposing a general wave field into transverse magnetic (TM) and transverse electric (TE) modes. Employing the propagation matrices, wave amplitudes in any region are related to those in any other regions. The reflection coefficients, which embed all the information about the geometrical configuration and the physical constituents of the medium, are obtained in closed form. In view of the general formulation, various special cases are discussed.

Reflection‐Refraction of a Stress Wave at a Plane Boundary between Anisotropic Media

Abstract: A review is given of the pertinent equations necessary to describe the reflected and refracted waves at a plane boundary between anisotropic media and the utility of the wave surface in discussing this problem. The critical angle phenomenon in anisotropic media is discussed in terms of the energy flux vector associated with the reflected and refracted modes. The critical angle is shown to occur generally at that angle of incidence for which the energy flux vector of the reflected or refracted mode is parallel to the boundary and not when the wave vector is parallel to the boundary. The possibility of not needing a nonhomogeneous surface wave to satisfy the boundary conditions at angles of incidence greater than the critical angle is discussed for certain particular regions in some anisotropic materials.

Ionospheric propagation of oblique hydromagnetic plane waves at micropulsation frequencies

Abstract: In this paper we consider the high-latitude transmission and reflection properties of the ionosphere for oblique hydromagnetic plane waves in the Pc 1 frequency regime. Transmission and reflection coefficients for the upper and lower ionosphere are obtained for daytime and nighttime conditions. The results are compared with those obtained for a vertically incident plane wave.

Spectral resolution of breakwater reflected waves

Abstract: A means of resolving incident and reflected wave heights for a partial standing wave through the use of two fixed wave sensors is demonstrated. Field studies were conducted in which the waves incident to the permeable rubblemound breakwater located in Monterey Harbor, CA, are spectrally resolved into incident, reflected and transmitted wave components. Power-spectra and cross-spectra are calculated for various characteristic sea states. Amplitude and phase are determined for the spectral wave components compromising the partial standing wave phenomena and reflection and transmission coefficients determined. The reflection coefficients vary between 0.3 and 0.7 and the transmission coefficients between 0.1 and 0.2. The transmission and reflection coefficients are shown to be dependent on the frequency and amplitude of the incident waves and the tidal stage.

Wave propagation in a micropolar elastic half-space

Abstract: Wave propagation in an infinite micropolar elastic half space and the reflection of plane longitudinal displacement waves from a fixed flat surface of a micropolar elastic half space are investigated. Reflection laws and amplitude ratios are presented for specific cases. New propagating and reflected waves are found in addition to the classical ones.

Dielectric-waveguide discontinuities

Abstract: The discontinuity between two planar dielectric waveguides is examined on the basis of an integral-equation formulation. The aperture field is approximated by a finite set of discrete modes, characteristic of the region Z<0. Results are presented for the launching efficiency and reflection at the junction between a solid-state heterojunction laser and an optical waveguide.

A study of charge density in beryllium

Abstract: The x-ray structure amplitudes for the 27 lowest-angle Bragg reflections of beryllium metal have been measured on an absolute scale. These can be used to deduce the charge density. The measured structure amplitudes are compared with those predicted both by the free atom Hartree-Foch wave functions and by a free electron orthogonalized plane wave model. For both models the predicted value for the lowest angle reflection is close to that observed, but the structure amplitudes of subsequent reflections given by the models are significantly greater than those observed. To account for these discrepancies a model of beryllium involving 2p-like tight binding functions is proposed.

Reflection of Surface Waves on a Dielectric Image Line with Application to "Guided RADAR"

Abstract: The dielectric image line is treated as an example of a line that can support a surface-wave mode, and reflections from metallic obstacles on the line are considered. This problem finds its application in an obstacle detection scheme for guided ground transportation where the metallic obstacle may represent a preceding vehicle. An integral equation for the currents on the obstacle is solved by the moment method and the surface-wave reflection coefficient is obtained.

Modal matching applied to a discontinuity in a planar surface waveguide

Abstract: A modal-matching method is used to evaluate the transmission and reflection coefficients at a junction between two planar surface waveguides. Results are obtained for parameters which represent the junction between a solid-state laser and a planar optical waveguide. Favourable comparison is made with results obtained from an integral-equation method.

Reflection of short pulses in linear optics

Abstract: Two methods of calculating the reflected wave generated by a short optical pulse falling on a linear dielectric medium are given. As examples the cases of an input sech pulse modulating a resonant carrier wave and an input delta function are calculated. At atomic densities greater than about 1018 atoms cm-3 an appreciable amount of the energy of the sech pulse is reflected. It is suggested that any nonlinear theory which ignores reflection may break down at these densities.

Reflection of Phonons at an Interface between a Solid and Liquid Helium

Abstract: The reflection coefficient of phonons at a boundary between several dielectric crystals and liquid helium has been measured by the heat-pulse technique. The reflection coefficient is found to be smaller for transverse phonons than for longitudinal.

Seismic Wave Scattering by Obstacles on Interfaces

Abstract: Summary A unified treatment of the scattering of seismic waves by small obstacles is presented. The method is based on an integral equation formulation and the use of first-order perturbation theory. This approach is used to consider elastic wave scattering by interface irregularities and obstacles at the interface of two elastic media, whose elastic properties are different from those of the bounding media. The results obtained by this method are shown to reduce to those of previous authors when applied to their more specialized problems. It is well known that in regions of irregular topography much noise is present in both reflection and refraction seismic records; this is attributed to scattering by surface and sub-surface topography and inclusions with elastic properties which differ from those of the surrounding matrix. Also much of the signal-related noise at seismic recording stations appears to be due to scattering by obstacles at or below the surface in the vicinity of the station. Gilbert & Knopoff (1960) considered the scattering produced by a surface irregularity on a uniform half space. Their treatment was subsequently extended by Hudson (1967) to deal with a three-dimensional surface obstacle whose elastic properties differ from those of the half space. This method is suitable for small obstacles whose bounding surfaces have only small slopes. Recently Aki & Larner (1970) and Slavin & Wolf (1970) have considered larger interface irregularities by constructing solutions in which the boundary condition mismatch is minimized by a least squares technique. In this paper we will consider only the first order perturbations for small obstacles, andpresentaunified treatment of the scattering of elastic wavesby interface irregularities and obstacles at the interface of two elastic media, whose elastic properties differ from those of the bounding media. The method is based on an integral equation approach and has the advantage that it is an extension of the normal methods for layered media. The results obtained reduce to those of Gilbert & Knopoff and of Hudson when applied to their more specialized problems. 2. Basic equations for an irregular interface We consider isotropic media, and for simplicity only two-dimensional problems where all stresses and displacements are independent of the coordinate y. A harmonic time dependence of the form exp (- iwt) will be assumed throughout, though it will not be explicitly represented. Away from the neighbourhood of irregular interfaces we shall consider media

Diffraction by a Flanged Parallel‐Plate Waveguide

Abstract: Radiation from a flanged parallel-plate waveguide is studied analytically using the Weber-Schafheitlin discontinuity integral when the waveguide is excited by TE-mode waves, TM-mode waves, or an electromagnetic line source Electromagnetic fields are represented by the discontinuity integral in the exterior space, and in the waveguide region they are expanded by normal modes of the waveguide Imposing the boundary conditions in the aperture gives a set of simultaneous equations for the expansion coefficients Once the solutions of these equations are determined, quantities of interest, such as reflection coefficients, modal coefficients of higher-order modes excited at the aperture, and radiation patterns, are readily obtained without knowing the field distribution in the aperture Numerical calculations for the radiation patterns, reflection coefficients, and modal coefficients of higher order modes are carried out, and a part of the results is compared with the asymptotic solution by Lee [1970] The effect of truncation in solving the equations numerically is also studied, and this method is found to exhibit rapid numerical convergence

Structure of Ion Acoustic Solitons and Shock Waves in a Two‐Component Plasma

Abstract: Time-independent solitary waves and shocks are investigated in a two-component plasma using a fluid model and kinetic theory It is found that very small concentrations of a light ion can drastically alter the structure, changing the potential maximum by an order of magnitude For a fixed Mach number, a critical density ratio of light to heavy ions is found at which the potential maximum changes discontinuously from a value large enough to reflect the light ions to one which allows them to traverse the shock front and enter the downstream flow The downstream oscillatory structure normally seen in a shock is completely quenched by dissipation due to light ion reflection at concentrations of 3-8% He in an Ar plasma for typical electron to ion temperature ratios and Mach number values

Wave reflection and transmission for pile arrays

Abstract: A group of piles in a specific geometric pattern may represent a part of a foundation supported by multiple pilings or a porous sea wall or other type of porous coastal structure. "Wave characteristics" of such a structure will include not only the wave transmission but also wave reflection characteristics. Most of the experiments in the past on pile groups were mainly concerned with wave transmission characteristics as a function of wave height and period. The main purpose of these previous studies was to evaluate the absorption characteristics of pile groups, and wave reflections were generally not measured, or evaluated. Variables in this study included wave characteristics such as wave height and length and three types of symmetric pile arrays, two providing clear spacing in the direction of the wave between pile rows and one with a staggered arrangement. The results presented in dimensionless form show the effect of pile geometry and wave steepness on the coefficient of reflection and transmissibility.

Exact Solution of the Equations of Molecular Optics for Refraction and Reflection of an Electromagnetic Wave on a Semi-Infinite Dielectric*

Abstract: The exact solution of the basic equations of molecular optics is obtained for the problem of refraction and reflection of any given monochromatic electromagnetic wave (not necessarily a plane one) that is incident on a linear, homogeneous, isotropic, nonmagnetic dielectric filling a half-space. Our analysis provides a new derivation of the laws of refraction and reflection and of Fresnel formulas and throws some light on the role played by the Ewald–Oseen extinction theorem in solving the molecular-optics equations. The methods developed in this paper may be employed in determining solutions of the molecular-optics equations for other problems that involve the interaction of electromagnetic radiation and bulk matter.

The propagation of water waves over sediment pockets

Abstract: Wave diffraction due to a rectangular domain of finite depth and width containing two fluids of constant but different densities connected to two channels of constant but different depths is considered. The implied scattering problem is modeled subject to the usual assumptions of linearized waterwave theory. The analysis is restricted to monochromatic plane progressive surface waves normally incident on the inhomogeneous domain. This results in a linear two-dimensional boundary-value problem for the velocity-potential. The scattering problem is formulated in terms of complementary variational integrals of Schwinger's type; symmetry relations between the complex amplitudes of the scattered potential are developed; and numerical calculations for the complex reflection and transmission coefficients are presented for a range of the physical variables. The analysis shows that sediment pockets can exhibit resonant behavior due to the combined effects of density stratification and pocket geometry. This offers a plausible explanation for offshore pipeline migration during storms.

Harmonic Generation of Shallow Water Waves Over Topography

Abstract: We investigate the reflection and nonlinear interaction between the first and second harmonics of a two-dimensional Boussinesq wavetrain. Effects of topography are included, the depth departing from a constant in a finite region. It is found that topography can speed up or retard energy transfer between first and second harmonics. The reflection coefficient in the present context is significantly different from the one obtained by using linear theory. This is partly due to partitioning of energy between harmonics.

Sensitivity of Radio Frequency Measurements in the Presence of Oscillator Noise

Abstract: The inherent sensitivity of an rf measuring system and the effect of the system transmission characteristics on the detectability of the rf source noise are examined. The results are applied to resonant reflection and transmission systems and to a nonresonant transmission system. The conventional reflection cavity paramagnetic resonance system is discussed in detail, and the conclusion is that this configuration will be source noise limited at power levels above 1 mW. Unconventional configurations, such as a dual mode induction cavity or a dual cavity transmission system, would have to be used to achieve higher sensitivity.

Plasma distribution function near the loss cone of a mirror machine

Abstract: The particle distribution in phase space near the loss cone of a stable mirror machine is determined by an asymptotic analysis based on the smallness of λ, the ratio of transit time between mirrors to mean collision time. Away from the loss cone, the solution is obtained by averaging over a bounce motion. Near the loss Cone, i.e., within a distance scaling as λ1/2, the governing equations are converted into a Wiener-Hopf equation along a boundary line in phase space whose solution yields the desired distribution. It is found that the ratio of plasma density in the mirror throat to central density scales as λ3/4 while the ratio of external density to central density scales as λ. For typical reactor conditions, these ratios correspond to densities of 1011 cm−3 and 108, respectively. Since the distance over which this drop occurs scales as λ1/2 times the local magnetic scale length, it is necessary to re-examine the reflection of unstable plasma waves in the neighbourhood of the mirrors.

Reflection and transmission for a porous structure

Abstract: Effects of characteristics of incident waves and of the thickenss of structure on wave reflection by and transmission through a porous structure were studied. Use of an idealized porous structure which is a lattice composed of circular cylinders was made. The relative thickness of structure B/L was found to have appreciable effects on reflected and transmitted wave energies. The reflection coefficient Kr reaches to a maximum of it for B/L of about 0.2 to 0.25, then decreases as B/L increases, and remains approximately uniform for B/L larger than about 0.6. The transmission coefficient Kt, however, decreases nearly exponentially as B/L increases. Measurement of wave height within structure revealed a Dattern of standing waves having a loop at the front face and a node at the rear face of it. That relates to the trend of Kr. Analytical approaches to predict the transmitted wave height, and wave heights before and within porous structures are found to be useful.