Physical design of periodic structures: From photonic crystals to phononic crystals

On-demand structure design is the key challenge confronted by the artificial structures. In this thesis we investigate on designing periodic complex media for photonics and phononics structures. The objective of the research is to explore the unit-cell design and optimization of photonic/phononic materials in two-dimensions for a broad range of applications. We explore the general features that give rise to band gaps and unusual diffraction for classical waves. Particularly, we address the analytical structure design method to control classical wave propagation in periodic systems. The findings enable progress in engineering of photons and phonons in both fundamental and applied aspects.