Study On Edge Modes And Fano Resonances In Metamateirals

With the development of metamaterial,more and more novel phenomena have been discovered in electromagnetic systems.The thesis focus on edge modes and Fano resonances in metamaterials.For the study on edge modes,our contributions are listed as follows:First,by introducing the concept of surface wave,we define the surface impedance.The TM surface wave will produce inductive surface impedance while TE surface wave will produce capacitive surface impedance.After introducing the edge mode between inductive metasurface and capacitive metasurface discovered by Sievenpiper's group,we apply the SommerfeldMaliuzhinets transform to solve the edge mode analytically.By comparing with the simulation results,we verify the correctness of our theory.Second,we introduce the concept of topology of a band after introducing the band theory.We can figure out the Chern number by three different methods: Berry curvature integration,kp pertubation theory,and hopping model.We discover the similarity among these methods.Simulation results of the edge modes in structures with different Chern numbers on the two sides are given.Also,we focus on the edge modes exist in structures with the same topology.By comparing with the edge modes caused by Zak phase and glide symmetry,we show the novelty of our edge modes found on antiphase boundary since it can support one-way propagation wave.By tuning the offset of the anti-phase boundary and optimizing the source,we provide comprehensive analysis of the structure.For the study of Fano resonance,we mainly focus on the Fano resonaces found in high permittivity materials.We apply Mie theory to analyze the scattering fields of spheres and core-shell particles.By rewriting the scattering coefficients in the form of Fano formula,we proof the existence of Fano resonances in these structures.Temporal coupled-mode theory is used to analyze the scattering field of a rounded-corner triangle.We find that the scattering field can be viewed as the superposition of scattering field of PEC and sharp resonances.At last,we use band theory to analyze the Fano resonances in periodic structures.We find the Fano resonances in periodic structures is the superposition of Bloch waves and Mie scattering waves.The Bloch waves as sharp resonances determine the positions of Fano resonances.