Inhomogeneous Isotropic Medium Research Articles

Wave Propagation in Stratified Absorbing or Amplifying Media*

Solutions are found to the wave equations that describe the steady-state propagation of electromagnetic radiation through an isotropic inhomogeneous medium capable of an irreversible exchange of energy with the radiation field. These solutions are obtained for media in which the inhomogeneity consists of a slow variation of the relevant material parameters along one particular direction in space. The mechanism by means of which energy is dissipated in matter may involve the conductivity of the medium, or by magneticor electric-dipole allowed transitions in the medium.

Rays and Waves in an Arbitrarily Moving Medium

A graphical method is given relating the ray, ray speed, wave normal, and wave speed at a point in an arbitrarily moving inhomogeneous isotropic medium. A distinction is made between “advancing” and “receding” wavelets. At a supersonic point, there are in any given permissible direction two rays, a fast and a slow one, and the angle between ray and velocity may not exceed the Mach angle. This paper explains the ambiguities mentioned in the preceding one.

Theory of the refraction of electromagnetic waves in a two-dimensional inhomogeneous isotropic medium

Theory of the refraction of electromagnetic waves in a two-dimensional inhomogeneous isotropic medium

Intergranular temperature relaxation in an inhomogeneous isotropic medium

Intergranular temperature relaxation in an inhomogeneous isotropic medium

Reflection of VLF radio waves from an inhomogeneous ionosphere. Part III. Exponential model with hyperbolic transition

This is a continuation of two earlier papers on the subject of reflection of waves from inhomogeneous isotropic media. In this particular paper an exponential conductivity profile is perturbed in such a manner that the conductivity is increased for all heights above a certain level. A hyperbolic tangent transition is employed in order to avoid discontinuities in the conductivity versus height profile.

A note on the expansion coefficient of geometrical optics

Abstract : The expansion coefficient of geometrical optics is a measure of the cross section os, New York U., N. Y. A NOTE ON THE EXPANSION COEFFICIENT OF GEOMETRICAL OPTICS, by Morris Kline. 1961, 12p. (Research rept. no. EM-166) (Contract AF 19(604)5238) Unclassified report DESCRIPTORS: *Optics, *Electromagnetic theory, *Differential geometry, Light, Electron optics, Series, Geometry. The expansion coefficient of geometrical optics is a measure of the cross section of a tube of rays and has the physical significance of measuring the intensity of the light propagating along the tube. Strictly, it is a point concept and measures the intensity along an individual ray. This paper presents a convenient expression for the expansion coefficient. The mathematics involved is merely an application of known differential geometry but the expression derived seems to be new and is apparently unknown to workers in electromagnetic theory. The new feature of this paper is that the formula given for the variation of the expansion coefficient holds in inhomogeneous isotropic media and reduces immediately to the widely known expression for the expansion coefficient in homogeneous media, which involves the Gauss curvature of the wave front. (Author)

Geometrical theory of sound propagation in the atmosphere

This paper deals with the geometry of sound waves and rays propagated in a moving inhomogeneous medium with particular reference to the atmosphere. The theory developed is, essentially, a generalization of that in geometrical optics for the propagation of light in an inhomogeneous isotropic medium to' the case where the medium is in motion. Differential equations defining the wavefront and rays of a sound propagation in an inhomogeneous moving medium are derived, and then transformed by expressing the unit normal of the wavefront in terms of certain trace velocities. With the equations in this form, an integral is immediately obtainable for sound propagated in the atmosphere by assuming that the velocity of sound and wind-velocity vector are functions of height only. From this solution the law of refraction, the condition for total reflection of a sound ray, and the equations for the wave-front at any time are found. By way of example, the theory is applied to a simple velocity of sound v. height relation, and expressions are obtained for the range and time at which the abnormal sound propagation from a ground-level source returns to earth. Numerical results calculated from these formulae are found to be in accord with observations that have been made on this phenomenon.

Three-Dimensional Photoelasticity

The classical Sommerfeld-Runge method for deriving the laws of geometric optics in isotropic inhomogeneous media from Maxwell's equations is applied to problems in ``weakly'' anisotropic and inhomogeneous media. This leads to a generalized Hamilton-Jacobi partial differential equation for the phases of the two waves (eikonals) which can propagate with finite velocity in such a medium. If one restricts oneself to a limited class of stress distributions, one derives a very powerful method of solving axially and spherically symmetric problems which would be very difficult to treat by the direct solution of the classical equations of elasticity. The Maxwell-Neumann law is derived in variational form so that, in principle, one can estimate in any given case the error involved in the conventional assumption that the paths are straight lines instead of the actual Fermat paths. The last section treats the so-called general problem of photoelasticity in which the principal stress directions in the plane of the wave front rotate arbitrarily as the latter propagates through the medium. Again the Sommerfeld-Runge method gives one a solution which claims that if the rate of rotation is small in a wavelength one can ignore the contributions of the rotation to the integrated phase. An experiment is proposed to check this claim.