|M.Sc Thesis||Department of Electrical Engineering|
|Supervisor:||Prof. Leviatan Yehuda|
A photonic bandgap is a range of frequencies, for which the propagation of light through a region of spatially periodic dielectric constant is inhibited. In photonic-crystal fibers this range is utilized to guide light; a photonic-crystal cladding confines light to a core, which may be either solid or hollow. Many applications in science and technology are envisioned for these new waveguides. Their analysis, however, is in general more involved than the analysis of standard optical fibers, and requires efficient numerical modeling schemes. The aim of this work is to present such a scheme based on a source-model technique.
The formulation will be given for a general cylindrical waveguide, made of a piecewise homogeneous dielectric. This geometry is adequate for the description of a variety of photonic-crystal fibers that have been suggested in the literature.
The advantages and limitations of the technique will be dwelt upon, and a few examples of its application will be presented. These include solid and hollow-core photonic-crystal fibers, which have a photonic-crystal cladding, consisting of a triangular lattice of circular air veins running parallel to the propagation axis. Results for photonic-crystal fibers with elliptical veins, which exhibit strong birefringence, will be also be shown. Strictly-bound modes, which have received little attention in the literature, as well as the more widely analyzed leaky modes, will be considered. For the leaky modes, calculation of the confinement losses is of interest, and will be effected by a rigorous method and by a perturbational one.