Two Dimensional Photonic Crystal Modes and Resonances in Three-dimensional Structures

We present three-dimensional analysis of two-dimensional guided resonances in photonic crystalslab structures. This analysis leads to a new understanding of the complex spectral properties of such systems. Specifically, we calculate the dispersion diagrams, the modal patterns, and transmission and reflection spectra of these resonances. From these calculations, a key observation emerges involving the presence of two temporal pathways for transmission and eflection processes. Using this insight, we introduce a general physical model that explains the essential features of complex spectral properties. Finally, we show that the quality factors of these resonances are strongly influenced by the symmetry of the modes, and the strength ofthe index modulation.