Manipulations Of The Band Diagrams Of Photonic Crystals And The Control Of Microwave Propagation

Photonic crystals(PCs), optical structures with periodic material distributions, have been proved to be a useful platform to control the flow of electromagnetic waves. In our work, we introduce the ways to manipulate the band diagrams of photonic crystal to realize peculiar propagation properties of microwave.In chapter 1, we first introduce photonic crystal. A lot of interesting properties were realized and demonstrated by PC, including waveguide, negative refraction et al. Band diagrams and band gaps are the important properties of PC. We can manipulate the band diagrams to control the propagation of microwave. The iso-frequency is an effective method to understand wave propagation properties. Our microwave PC structures are fabricated and microwave experiment procedures are also introduced.In chapter 2, three different methods to create deterministic interface states in twodimensional PC system are introduced. Different to previously proposed methods to use surface decorations or photonic heterostructures, our interface states are deterministic that we can design the existence of them from the bulk band properties and the surface impedance of the bulk PC. The condition of the interface state formation of two two-dimensional PCs is that the summation of surface impedance of two PCs to construct the interface is zero. A rigorous relationship between the surface impedance of PC and its bulk geometric Zak phases is established. Our results hold for any PCs with inversion symmetry. Our results provide new insights into the relationship between surface scattering properties, the bulk band properties, and the formation of interface states. The interface states are experimentally realized and characterized by our microwave experiments. A multiband waveguide using PC with deterministic interface states is also proposed.In chapter 3, the topological transition of iso-frequency contour in PC is studied. By breaking the rotation symmetry of photonic crystals, extra degree of freedom is introduced to the system and fruitful physics can be observed. The iso-frequency contour, originally to be circular in isotropic medium, will become elliptical, hyperbolic and linear-cross. Tunable beam splitting can be realized using the linear crossing iso-frequency contour we designed whose splitting angle can be controlled by the local geometry. We can also map our PC to anisotropic zero index medium and good consistence can be found between our simulations and microwave experiments. By locally rotating PC blocks, we realized omni-directional cloaking of a more than ten times wavelength objects.Even though our experiments are carried at microwave frequencies, we only adopt dielectric materials with reasonable permittivity. Thus, with the development of nanoscience and microstructure, similar PC structures can be fabricated working at higher frequencies and might lead to some optical applications.Finally, conclusions of our work are presented in chapter 5, as well as the brief discussion about the further work.