Modelling of photonic band gap materials for mm-wave and optical applications

The properties of 1-, 2- and 3- dimensional periodic structures, generically known as photonic crystals, are examined using the transfer matrix technique with a view to application in the mm-wave and optical domains. Periodic structures are now well acknowledged in their ability to control the propagation of electromagnetic radiation. Through careful design of crystal lattice parameters and consideration of the materials used in fabrication, periodic materials are known to display gaps in their dispersion relation where there are no allowed modes or states: the photonic band gap, such that any impinging electromagnetic wave will be reflected regardless of its incidence angle or polarisation. Within the first half of this work several structures and approaches are examined, with the objective of finding a truly 3-dimensional photonic band gap for use as an antenna substrate. In the process, through careful investigation, many design considerations are highlighted, such that some structures are shown to be successful in achieving this goal, while other structures are shown to be inadequate. In the second half of this work the analysis moves away from the search for the complete photonic band gap by examining incomplete band gaps and the influence of various defects and alterations that may be incorporated into photonic crystal structures. These alterations or the inclusion of intentional defects are set to play a significant role in the marriage between photonic crystals and current day optoelectronic and mm-wave components