Time-varying Medium Research Articles

Signal processing in a nonperiodically time-varying magnetoelastic medium

Wave propagation in a nonperiodically time-varying medium provides a means for realizing in simple physical structures a variety of signal-processing operations, such as frequency translation and coding, variable delay recall, gating, time-scale stretching or shrinking, and time reversal. The use of low-velocity modes, such as acoustic, spin, or magnetoelastic waves in solids, reduces the length of the propagation structure required to less than an inch. A general review is given of the principles of wave propagation in a spatially uniform medium with nonperiodic time variation. Both abrupt and gradual time variations are discussed. Illustrations are given for the cases of spin-wave and magnetoelastic-wave propagation and signal processing operations in these media are explained. Consideration is given to the problem of spin-wave propagation in a time-and space-varying magnetic field of the form encountered in experiments; and it is shown that a simple separated variable solution exists. For the more difficult problem of magnetoelastic propagation with both space and time variations, an approximate space-time ray theory is described. Experimental results for pulsed-field processing of spin and magnetoelastic waves are given and related to the theory.

Energy-transport velocity of electromagnetic waves in isotropic nondispersive media

Recent letters have discussed the velocity of energy transport for a propagating electromagnetic wave in a homogeneous, time-invariant medium. This letter, as an extension, treats the same subject for an unbounded inhomogeneous time-varying medium, using similar mathematical steps.

Partially coherent processing by optical means

When the coherence time of a signal propagated through a time-varying medium is less than the signal duration, detection methods using conventional coherent correlation processes are not appropriate. Instead, mixed integration techniques can be used, with the coherent integration interval matched to the signal coherence time. A mixed integration can be simulated quite easily in an optical correlator by controlling the degree of coherence of the illumination at the first aperture. A partially coherent optical correlator produces an output light intensity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I(x_{0}) = \int \int \gamma\(x, x')s(x - x_{0})r(x)s(x' - x_{0})r(x')dxdx'</tex> where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\gamma (x, x')</tex> is the coherence factor and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s(x)</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r(x)</tex> are the received signal and reference. This equation is derived for a partially coherent optical correlator, and the range of output correlation intensities, which are directly related to processing gain, is determined as a function of the coherence width inherent in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\gamma(x, x')</tex> .

THE NONLINEAR INTERACTION OF AN ELECTROMAGNETIC WAVE WITH A TIME-DEPENDENT PLASMA MEDIUM

A one-dimensional, inhomogeneous model is used to describe the nonlinear interaction of a radio-frequency plane wave with a time-varying plasma medium. A monochromatic plane wave is normally incident upon an electron density profile where the electron density gradients are shallow compared to a wavelength. Changes in electron temperature and electron density are induced which continually alter the pattern of electromagnetic energy deposition into the medium. The electron energy relaxation time is much longer than the period of the electromagnetic wave, so that the electron temperature does not follow the rapid variations in the impressed field. A nonlinear constitutive relationship is derived relating the macroscopic current density to the impressed electric vector, assuming that the wave field is almost monochromatic in the medium. The time-dependent response of the plasma medium may be found by numerically solving the energy-balance equations and the continuity equation for the electron gas. The spread in frequency of the electromagnetic wave field due to the time-varying electrical conductivity may be computed by employing the WKB approximation as a solution to the wave equation for a time-varying medium. Graphs are presented which represent the time-dependent response of the electron temperature and electron density as a function of the incident r-f. field amplitude.

Sommerfeld-Runge Law in Three and Four Dimensions

The Sommerfeld-Runge law, a law of geometric optics expressing that the propagation vector is irrotational, is useful for general deductions and for computations of geometric-optical wave fields, for which it proves without supplementary notions sufficient under a wide range of conditions. Application to inhomogeneous anisotropic media, though not necessitating recourse to the concept of rays, yields the equation of ray paths. Absorption and lateral intensity variation of waves are accounted for by introducing complex propagation vectors.A four-dimensional generalization of the law is applicable to modulated waves and time-varying media. The four-dimensional considerations, to which it leads, deal with group propagation (in time-constant and time-varying media), with isotropy in space-time (relating to the law $uv={c}^{2}$), and with refraction and reflection at discontinuities in time and at moving boundaries. A brief discussion of focusing and diffraction in the scope of four-dimensional geometric optics is also given.

Information Theory Aspects of Propagation through Time-Varying Media

The channel capacity of a communications system which utilizes wave propagation through a time-varying medium such as the ionosphere or troposphere is evaluated in terms of the statistical properties of the medium and of the noise. The signal fading in such a system reduces the capacity. Rayleigh fading is found to give rise to an equivalent signal to noise ratio of 1.72, while shallow fading of the Gaussian type augments the noise in the channel by a fraction of the signal power proportional to the fading depth. An optimum manner of band width subdivision is shown to exist when selective fading is present. Information theory concepts are broadened to include the possibility of multiple reception at spaced receiving sites, and the consequent increase in theoretical channel capacity is computed as a function of the number of such sites and the signal statistics. The method of maximum liklihood is utilized to obtain optimum combinatorial laws for the multiple signals. The commonly employed maximum signal selection diversity system is shown to perform as well as the optimum system in the presence of Rayleigh fading, for a small number of receiving sites.