Numerical investigations of two-dimensional photonic crystal optical properties, design and analysis of photonic crystal based structures

Two-dimensional (2D) photonic crystals (PhCs) operating in the near-infrared wavelengths are promising candidates for novel integrated optics applications. In this work the optical properties of the Bloch modes in 2D photonic crystals have been investigated theoretically using different numerical methods. The plane wave expansion (PWE) method have been formulated in a general form for arbitrary 2D photonic crystal and applied for detailed analysis of the properties of the Bloch modes. The k space based and the frequency based PWE methods have been derived and used, which allowed us to analyze both propagating and evanescent modes. The guided mode expansion method has been used to take into account three-dimensional distribution of the electromagnetic field in the planar photonic crystals and improve the accuracy of the analysis. A new method of calculation of the sensitivity of the photonic crystal optical properties to small variations of the photonic crystal parameters has been developed. This method is based on the perturbation theory and allows fast and accurate estimation of the optical properties corrections as a result of a change the parameters of the photonic crystal. The developed methods have been used for design and analysis of different photonic crystal based structures, such as cavities, waveguides, coupled-cavity waveguides and polarization beam splitter. The developed methods proved to be efficient and accurate tools for modelling two-dimensional photonic crystal properties and design of photonic crystal based devices.