Ali, Rashid (2000) *ANALYTICAL INVESTIGATIONS OF NONLINEAR WAVES IN SEMICONDUCTOR SUPERLATTICE PLASMAS.* PhD thesis, University of the Punjab, Lahore.

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## Abstract

In the present work we have investigated non-liner 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 non-liner evolution, equation governing the propagation of these envelope solution is the set of Zakharov equations, which are a more generalized form of the Non-liner Scrodinger Equation (NLS). We derive the set of equations, which have a known evelope soliton solution. We use the Kroning-Penney 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 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 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 Kronig-Penney model is used to model the layered medium and a dispersion relation governing the properties of the charge-density wave in the layered medium. The electromagnetic wave dissipates in the layered superconducting medium. We numerically investigate the dependence of the complex Bloch-wave 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 Kronig-Penney 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.

Item Type: | Thesis (PhD) |
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Uncontrolled Keywords: | Nonlinear Waves, Semiconductor Superlattice Plasmas, Helicon Envelope Solitons, |

Subjects: | Physical Sciences (f) > Physics(f1) |

ID Code: | 345 |

Deposited By: | Mr Ghulam Murtaza |

Deposited On: | 27 Jun 2006 |

Last Modified: | 04 Oct 2007 21:00 |

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