Pakistan Research Repository 







Title
of Thesis 

ANALYTICAL INVESTIGATIONS OF NONLINEAR WAVES IN SEMICONDUCTOR SUPERLATTICE PLASMAS 

Author(s) 

Rashid Ali 

Institute/University/Department
Details 

University of the Punjab, Lahore /Center Of Excellence In Solid State Physics 

Session 

2000 

Subject 

Physics 

Number
of Pages 

112 



Keywords
(Extracted from title, table of contents and abstract of thesis) 

Nonlinear Waves, Semiconductor Superlattice Plasmas, Helicon Envelope Solitons, 



Abstract 

In the present work we have investigated nonliner wave propagation through semiconductor superlattice plasmas; we have considered different types of layered superlattices or media through which the waves propagate. First of all we consider the propagation of helicon envelope solitons through layered semiconductor superlattice plasma. The nonliner evolution, equation governing the propagation of these envelope solution is the set of Zakharov equations, which are a more generalized form of the Nonliner Scrodinger Equation (NLS). We derive the set of equations, which have a known evelope soliton solution. We use the KroningPenney model along with the relevant boundary conditions to investigate propagation of helicon solitons in the layered medium. These boundary conditions are useful for connecting the envelops soliton fields across the layers. We obtain a nonlinear dispersion relation which relates the nonlinear analogue of the Bloch wave number with different parameters. We numerically investigate the dependence of the nonlinear Bloch wave number on the propagation frequency we see that a propagation band and gap structure for the helicon envelope soliton solution in a layered semiconductor plasma. Owing to the recent experimental importance of device fabrication (e.g. amplifiers etc), superconductivity is a subject of investigation for a number of reason. In the second problem we investigate the propagation of density waves in a hightemperature superconducting medium consisting of a finite number of layers. An electromagnetic wave interacts with superconducting electrons to set up chargedensity gradients within the superconducting electron plasma. We use the London equations and the two fluid approaches to derive a linear dispersion relations, for the propagation of the density waves within each layer. Once again the KronigPenney model is used to model the layered medium and a dispersion relation governing the properties of the chargedensity wave in the layered medium. The electromagnetic wave dissipates in the layered superconducting medium. We numerically investigate the dependence of the complex Blochwave number on the propagation frequency using the standard boundary conditions. Reflectivity and transmissivity have been discussed for periodic layered structure consisting of a finite number of superconducting layers, we numerically discussed these quantities and their dependence background parameters have been discussed. In the third problem we take the same set of equations and investigate the propagation of nonlinear charge density waves in a superconducting layered structure. It is seen that the nonlinear Schrodinger (NLS) equation governs the propagation in the superconducting plasmas. We investigate the modulational instability of the NLS equation. Subsequently we use boundary conditions of the standard KronigPenney model to derive a nonlinear dispersion relation relating the Bloch wave vector to the propagation frequency. This nonlinear dispersion is also numerically investigated. In the last problem, we investigate the propagation of nonlinear coupled electromagnetic waves in a composite medium having properties of ferromagnetic and semiconductor materials. We derive nonlinear evolution equation using reductive perturbation method for which we obtain soliton solution. We also investigate the limiting cases and find that our results reduce to the previously investigated. 



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