Computational studies of one and two-dimensional photonic microstructures
This work is concerned with the study of photonic crystals and other topical photonic microstructures, whose optical properties are investigated by solving the Maxwell equations using appropriate theoretical and computational schemes, which are described. The work focuses on the photonic band gap, the existence of which is crucial for most applications of photonic crystals. Disorder in photonic crystals has been studied. The photonic eigenmodes of an ensemble of a type of disordered one-dimensional photonic crystal are investigated statistically for three different models of disorder and a certain type of disordered two-dimensional photonic crystal has also been studied. It is seen that the disorder introduces photonic modes into the band gap, and the properties of disorder-induced modes localised on random micro cavities are discussed for both one and two-dimensional photonic crystals. It is apparent, however, that there is a certain level of disorder below which the probability of finding disorder-induced photonic modes with eigenfrequencies in the centre of the photonic band gap is negligible, and this produces a threshold-like behaviour as a function of the disorder parameter in the transmission properties of the photonic crystals. Novel designs for two-dimensional photonic crystals based on the deep etching of a Bragg reflector and on a unit cell with local quasicrystalline order are considered. Both are found to possess wide complete photonic band gaps for one polarisation of light over a wide range of geometrical parameters, and the parameters of the structures are investigated in order to optimise the properties of the photonic band gap. An approach using a simple analytical theory has been developed for the design of multi layered optical band pass filters based on coupled microcavity layers embedded in an one- dimensional photonic crystal and the parameters of the optimal structure are presented. A formalism based on non-local dielectric response theory and a Green function technique has been developed to describe the interaction of a quantum well exciton with an evanescent optical mode of a planar waveguide, and the dispersion relations of waveguide polantons in a planar dielectric waveguide with an embedded quantum well have been calculated.