

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 zeron and the zeroφeff
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 onedimensional
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 KronigPenney
delta function approach in one of our investigations. The electric
field profiles for the zeron gap soliton, zeroφeff gap soliton and
Bragg gap soliton are plotted and a comparison of their
characteristics is made. Similarly the optical bistability curves
for the onedimensional 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 onedimensional 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.

