Analytical Investigations of Nonlinear Waves in Semiconductor Superlattlee Plasmas.

Abstract

This project was started on 1/11/95. In this project we analyticallly investigate the wave propagation in semiconductor layered structures (or so called superlattices). Our first problem was on parametric instabilities of nonlinear waves in a sinusoidal periodic piezoelectric semiconductor structure. Various techniques are used to model a periodic structure/medium. In this problem we use a periodically modulated medium (sinusoidal), which is considered to be ana ogous with the well known Kronig-Penney Model. This work was presented at the 5th National Symposium on Frontiers in Physics, (Dec, 1995) at Q.A.U. Islamabad After completing the above work we undertook a problem related with solitons. In this work we investigated the propagation of helicon solitons in a semiconductor supcrlattice plasma, The nonlinear evolution equations governing the propagation of these solitons is the set of Zakharov equations (which are a more generalized form of the nonlinear Schrodinger Equation, which relates the nonlinear analog of the Bloch wave number with different parameters. We have numerically investigated the dependence of the nonlinear Bloch wave number on the propagation frequency and have established a propagation band and gap structure for the helicon soliton in a semiconductor superlattice plasma In semiconductor plasma physics transverse circularly polarized wav s, which propagate parallel to the ambient magnetic field in is known as the Helicon wave, but in gaseous plasmas the same wave is often referred to as the whistler wave. We also completed a problem which describe the possible electron heating in the solar wind via the dissipation of obliquely propagating whistler waves. This work has been accepted in the Bulletin of Pure and Applied Sciences and it would appear in Vol.18 D 1999.

Finally we tackled a problem regarding density-wave propagation in a high- temperature superconducting medium, consisting of a finite number of layers. An

electromagnetic wave interacts with superconducting electrons to set up charge- density gradients within the superconduting electron plasma. We use the London

equations and a two fluid approach in order to investigate the wave behavior in the layered structure, by deriving a dispersion relation. It is shown that the electromagnetic wave dissipates in t e layered superconducting m dium. We numerically investigate the depet dence of the complex Bloch-wave number on the propagation frequency using the standard boundary conditions. Expressions of reflectivity and transmissivity are derived tor a periodic layered structure consisting

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of a finite number of superconducting layers, these quantities are investigated numerically and their dependence on background parameters di cussed.