Theoretical studies of one-dimensional and two-dimensional photonic structures

This thesis is concerned with the theoretical study of one-dimensional and two-dimensional photonic structures. Plane-wave calculation methods have been employed to model one-dimensional waveguides and two-dimensional photonic crystals. The one-dimensional structures considered are slab waveguide interferometer devices. A transfer matrix method is described which has been implemented in a biosensor technique know as dual polarisation interferometry. The method presented is used for the characterisation of thin biological films. A similar slab waveguide device is described for the wavelength locking of diode lasers and a novel athermal solution to the problem is proposed. The study of two-dimensional photonic crystals employed a standard bandstructure method and also proposed new approaches to complex photonic bandstructures which are not believed to be available elsewhere. An interface matching calculation is described which employs complex photonic bandstructures and is believed to be the first use of the method described for photonic structures. The theoredcal methods are applied to consider the super- prism effect in square and hexagonal lattice photonic crystals. Optimum superprism structures are arrived at for both lattices. Reflection results from the optimum hexagonal structure are also considered, combined with coupling efficiency to the superprism mode. As a result of the work on photonic crystals new theoretical approaches have been described and implemented to assist with their establishment as calculation tools for two- dimensional photonic crystal structures.