General Theory Of Wave Propagation Research Articles

Super periodic potential

In this paper we introduce the concept of super periodic potential (SPP) of arbitrary order n, n∈I+, in one dimension. General theory of wave propagation through SPP of order n is presented and the reflection and transmission coefficients are derived in their closed analytical form by transfer matrix formulation. We present scattering features of super periodic rectangular potential and super periodic delta potential as special cases of SPP. It is found that the symmetric self-similarity is the special case of super periodicity. Thus by identifying a symmetric fractal potential as special cases of SPP, one can obtain the tunnelling amplitude for a particle from such fractal potential. By using the formalism of SPP we obtain the close form expression of tunnelling amplitude of a particle for general Cantor and Smith–Volterra–Cantor potentials.

General theory of wave propagation through graded interfaces between positive- and negative-refractive-index media

The introduction of metamaterials and transformation optics has brought the possibilities for manipulating electromagnetic waves to an unprecedented level, suggesting applications like super-resolution imaging, cloaking, subwavelength focusing, and field localization. The refractive index of metamaterial structures in transformation optics typically has to be spatially graded. This paper presents a full analytical method for description of the field propagation through composites with gradient refractive index. The remarkable property of this approach is that it gives explicit general expressions for the field intensity and transmission and reflection coefficients, without reference to any boundary conditions. This opens a possibility for a novel fundamental theory of a number of important electromagnetic phenomena. The method enables calculation of wave propagation parameters within structures with arbitrary losses, arbitrary spectral dispersions, and arbitrary slopes of permittivity and permeability gradients, from mild to abrupt.

Causality and the velocity of acoustic signals in bubbly liquids

Several versions of the dispersion formula governing the acoustic propagation in bubbly liquids are shown to exhibit acausal behavior. The cause of this behavior is due to the inappropriate application of a low frequency approximation in the determination of the extinction of the signal from radiative scattering. Using a corrected causal formula, several principles of wave propagation in bubbly media consistent with the general theory of wave propagation in dispersive media are demonstrated: There exist two precursors to any finite signal. Both propagate without regard to the source characteristics at velocities, frequencies, and amplitudes dependent wholly upon the characteristics of the medium supporting the wave motion. The first travels at the infinite frequency phase velocity that is coincident with the infinite frequency limit of the group velocity. That part of a propagating wave oscillating at the source frequency arrives at a time determined by the signal velocity. Analogous to the well known signal velocity of electromagnetic wave propagation in conducting media, the value of the signal velocity depends on the detailed structure of the dispersion formula in the complex frequency plane.

An approach to the theory of X-ray multilayers with graded period

A wide bandpass for multilayer mirrors can be obtained by gradually changing their period. In this paper the theory of such optical elements is developed on the basis of the general theory of wave propagation through layered medium. The results of reflectivity calculation for broadband mirrors are presented. The suggested theory is a natural step to the inverse problem – design of multilayers with the required wavelength dependence of reflectivity.

Theory Of Multilayer X-Ray Mirrors With Slowly Varying Period

Broadening of multilayer-mirror reflection band is achieved by slow variation of its period. The paper is devoted to the theory of such optical elements based on a general theory of wave propagation through a quasi-periodic medium. The calculation results are presented for the reflection coefficient of broadband mirrors in the 1 to 50 A range. A statement of the inverse problem is also considered, namely, creation of a multilayer structure possessing the prescribed reflection coefficient.

Wave propagation with mass-coupling effect in fluid-saturated porous media

This article utilizes the theory of mixtures to formulate a general theory of wave propagation with mass-coupling effect in fluid-saturated porous media. An attempt is made to discuss the physical interpretation and the thermodynamic restriction of the coefficients appearing in the equations obtained. By the comparison it is shown that Biot's classical theory and the present one are essentially consistent. Also, wave velocities in some special cases are calculated, from which it is concluded that mass-coupling and permeability of media greatly affect wave propagation behavior.

Wave propagation in nonhomogeneous multiconductor transmission systems: general theory and analysis

The paper presents a general theory of wave propagation through nonhomogeneous multiconductor systems. This theory shows that waves travelling in one direction through such a system do so independently of waves travelling in the opposite direction. The essential difference between homogeneous and nonhomogeneous systems is found to be that, in the former case, the propagation characteristics are the same in both directions, whereas in the latter case they are not. Methods for determining the forward and backward wave characteristics of a general nonhomogeous system are presented. The theory finds immediate application in the study of transient phenomena in powertransmission systems whenever nonhomogenity is involved. However, the theory is completely general, and may find useful applications in other areas.

Optical Properties of Cholesteric Liquid Crystals

A general theory of wave propagation in helical structures is developed. It is shown that this problem is quite similar to the well-known wave propagation in solid crystal lattices. If energy dissipation is neglected there are shown to exist frequency bands for wave propagation without attenuation separated by frequency bands where waves are damped out and cannot propagate. Formally, the waves have the form of Bloch waves ${e}^{i\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}.\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}}u(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$, having the character of plane waves modulated by a function $u(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ which is periodic with the structure. Based on this theory, for reflection of light by homogeneously ordered cholesteric liquid crystals the following results are obtained: For incident light parallel to the helical axis there exists only one band of selective reflection. For obliquely incident light, however, an infinite series of higher-order reflection bands occur. Each reflection band is split into two branches. The angular dependence of the reflection bands and the sequence of the higher-order reflections on the wavelength scale bear a certain analogy to Bragg reflection.

Propagation of Plane Waves in Biaxially Anisotropic Layered Media*

This paper is concerned with the general theory of wave propagation in layered biaxially anisotropic media. Details are presented for the calculation of the induced waves that are due to an arbitrarily polarized and obliquely incident wave impinging on a three-layer structure. The total numbers of partial waves with their respective phase velocities, direction of phase propagation, and polarization are determined by the use of the Fresnel equation and Snell’s law applied to each layer. The vector amplitudes of the partial waves are found by proper matching of the field components at the interfaces. The expressions thus found are shown to reduce to known results for a uniaxial three-layer structure. An extension of this theory to an arbitrary number of layers is also presented.

Theoretical explanation of the solar limb effect

The general theory of relativity predicts a wavelength shift of the lines in the solar spectrum with respect to corresponding terrestrial lines by an amount of 2.12 × 10 −6. However, it is an established fact that at the extreme solar limb (at radial distances greater than about 95 per cent of the radius of the disk) the Fraunhofer lines exhibit a red-shift substantially exceeding the shift required by the relativity theory (the phenomenon will be referred to as limb effect). On the basis of the general theory of wave propagation in inhomogeneous moving media it is shown that the extreme red-shift values observed at the solar limb are produced by radial currents in the solar atmosphere due to an effect different from the familiar one which is responsible for the wavelength shifts observed at the inner parts of the solar disk.

Wave propagation in random media

This paper discusses a general theory of wave propagation through a random medium whose random inhomogeneities are confined to small deviations from the mean. The theory is initially worked out in detail for the propagation of transverse waves along an infinite stretched string whose density is a random function of position. The manner in which the mean wave profile is modified by scattering from the density inhomogeneities is discussed in great detail, with particular emphasis on physical interpretation. The general theory of wave propagation in arbitrary dispersive or non-dispersive media is then discussed, and it is shown how the theory may be extended to wave propagation problems involving scattering from rough boundaries.

Dependence of Image Quality on Horizontal Range in a Turbulent Atmosphere

The dependence of the complex optical transfer function of an image-forming system on range through the atmosphere has been investigated experimentally. The simple case of a horizontal line of sight over flat terrain has been studied and empirical equations have been obtained which relate the transfer function to range and to the atmospheric temperature structure function. These equations agree with a general theory of wave propagation in a turbulent medium and are therefore applicable to a wide range of situations, provided that the distribution of the temperature structure function along the line of sight can be obtained. The experimental results also furnish evidence that the Kolmogorov expression for the temperature structure function (“the two-thirds law”) is applicable to scale sizes of about a centimeter or so.

Contributions to the Theory of Waves in Non-linear Dispersive Systems

This paper makes contributions to the general theory of wave propagation in conservative systems under conditions when the proportional change in amplitude or wavenumber over a distance of one wavelength is very small. For linear systems, such propagation is governed by the well-known theory of group velocity; there is “frequency dispersion”, in the sense that energy in components of different frequency is propagated at different group velocities. For non-linear systems without frequency dispersion, e.g. acoustic systems, a different, but also well-known, modification of the waveform occurs. It may be called “amplitude dispersion”, in that different values of an amplitude variable like the pressure are propagated at different speeds.

On the Existence of Uller's Waves*

Abstract A re귡mination of a general theory of wave propagation proposed by Uller is carried out. The conclusion is reached that his hypothesis has not been placed on a firm physical foundation and cannot be considered valid in interpreting seismic data.