| Photonic crystals can enhance the performance of various microwave and photonic devices when incorporated as part of the device's design. In this thesis, numerical techniques for the simulation of electromagnetic devices incorporating photonic crystals are developed. In addition, this work also offers optimization techniques for speeding up the proposed simulation techniques.; In summary, the transmission line matrix method is presented as an efficient simulation technique for the analysis of electromagnetic band-gap structures. The work describes important aspects for the computation of the dispersion relation of photonic crystals. It also proposes two methods for reducing the computational effort involved in the simulations. One method is based on a real-valued implementation of the periodicity condition, and the other one is based on the use of a multi-grid mesh. Depending on the physical geometry of the crystal, computational savings of over 50% can be easily achieved. The advantages and limitations of these methods are described. The suitability of the transmission line matrix method to handle photonic crystals with more general material properties such as frequency dependent metals and semiconductors is also demonstrated.; Finally, the mesh conditions that produce the least numerical dispersion error in complex meshes are investigated. Specifically, we analyze in detail how geometrical factors influence node dispersion and obtain guidelines for use with general meshing tools. To conclude, the accuracy and efficiency of various complex meshes are evaluated by analyzing real-world problems and novel applications of electromagnetic band-gap structures. |
