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Title of Thesis

Nonlinear Wave Propagation in Photonic Band Gap Materials

Author(s)

Munazza Zulfiqar Ali

Institute/University/Department Details
Centre for Solid State Physics / University of The Punjab, Lahore
Session
2008
Subject
Physics
Number of Pages
177
Keywords (Extracted from title, table of contents and abstract of thesis)
Nonlinear, Wave, Propagation, Photonic, Band, Gap, Materials, artificial, periodic, structures, metamaterials

Abstract
This research work is concerned with the nonlinear wave propagation in photonic band gap (PBG) materials. Photonic band gap materials are artificial periodic structures that exhibit bands and gaps for the propagation of light in certain frequency ranges depending on the periodicity of the structure. Nonlinear PBG materials can be defined as the periodic structures that have the ability to control light with light and produce a structural enhancement of nonlinear effects. The optical properties of such materials can show dramatic changes with the changing intensity of light. An interesting manifestation of nonlinear effects in these structures is the formation of gap solitons and the associated phenomenon of optical bistability. Promising applications for such phenomena include optical switches, logic gates, transistors etc.
Recent theoretical and experimental studies have suggested the possibility of creating artificial metamaterials that can possess a negative real part of magnetic permeability and/or a negative real part of electric permeability and are known as double and single negative metamaterials (DNG, SNG). The main focus of the present study is to explore the new features of the nonlinear wave propagation due to the inclusion of double negative and single negative metamaterials in PBG structures. The conventional PBG structures are characterized by Bragg gaps whereas in PBG structures containing DNG and SNG meta materials, mechanisms other than Bragg reflections can produce gaps such as the zero-n and the zero-φeff gaps. The real advantage of these new gaps is the fact that these are relatively insensitive to the incident angle and disorders in the structures.
In the present work we have considered only one-dimensional structures. The transfer matrix approach and the characteristic matrix approaches are mainly used to study the wave propagation through these structures. We have also applied the Kronig-Penney delta function approach in one of our investigations. The electric field profiles for the zero-n gap soliton, zero-φeff gap soliton and Bragg gap soliton are plotted and a comparison of their characteristics is made. Similarly the optical bistability curves for the one-dimensional structure containing alternate DNG and regular materials and containing SNG materials are also plotted. We have considered normal as well as oblique incidence. The properties of an angular gap in one-dimensional structures containing SNG layers are investigated. We have also investigated some defect structures. The properties of the resulting localized mode are studied. The results of the investigations are summarized at the end.

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S. No. Chapter Title of the Chapters Page Size (KB)
1 0 CONTENTS

 

iv
24 KB
2

1

INTRODUCTION

1.1 Photonic band gap materials

1.2 Nonlinear wave propagation

1.3 Thesis layout

1
114 KB
3 2 DOUBLE AND SINGLE NEGATIVE METAMATERIALS

2.1 Introduction

2.2 Origin of negative permittivity and negative permeability

2.3 Metamaterials

2.4 Some properties of DNG materials
2.5 The zero-n gap
2.6 The zero-φeff gap

21
82 KB
4 3 THE MATHEMATICAL FORMALISM

3.1 Introduction

3.2 The Kronig-Penney delta function model
3.3 The characteristic matrix approach
3.4 The nonlinear transfer matrix approach

36
63 KB
5 4 NONLINEAR WAVE PROPAGATION IN ONE-DIMENSIONAL PHOTONIC BAND GAP MATERIALS CONTAINING RIGHT-HANDED AND LEFT-HANDED LAYERS

4.1 Introduction

4.2 The zero-n gap soliton

4.3 The global transmission diagrams

4.4 Conclusions

46
389 KB
6 5 WAVE PROPAGATION IN ONE-DIMENSIONAL PHOTONIC BAND GAP MATERIALS CONTAINING SINGLE NEGATIVE MATERIALS

5.1 Introduction

5.2 The mathematical formalism

5.3 The zero-φeff gap soliton

5.4 The angular gap

5.5 Conclusions

73
162 KB
7 6 DEFECT MODES IN ONE-DIMENSIONAL PHOTONIC BAND GAP STRUCTURES

6.1 Introduction

6.2 Defect modes within the zero-n and the zero-φeff gaps
6.3 Nonlinear localization due to a left-handed layer within a zero-φeff gap

6.4 Conclusions

100
85 KB
8 7 CONCLUSIONS AND PERSPECTIVES 114
33 KB
9 8 REFERENCES & APPENDICES

119


1,704 KB