The Properties And Applications Of The Impedance Match In Photonic Crystals

In recent years,photonic crystals(PhCs)as a new kind of promising artificial micro-structural materials,have attracted much attention in the fields of electromagnetism,optics and material science.Ph Cs are composed of different materials with periodic arrangement,whose size are close to the wavelength.EM waves,when propagating in PhCs,would be modulated to be photonic band gaps due to Bragg's effect.As bandgap materials,PhCs play vital roles in light confinement and optical manipulation,such as waveguides,fibers,high-Q nanocavities and lasers,omnidirectional reflectors and etc.People have focused on the methods and properties of controlling PhCs' band gaps for a long time but rarely done the deep researches on PhCs' impedance.In this paper,we will discuss the effect of impedance match,structures and applications of PhCs.The main results are as follows:1.Definition of PhCs impedance and impedance match theoryWe discuss the methods of definitions of PhCs' impedance and furtherly derived the PhCs impedance match equations.For extremely low-frequency light,the impedance can be calculated by PhC's effective permittivity and effective permeability under quasistatic conditions.As for low frequency light,there exist several types of impedance definitions under a single-mode approximation.This dissertation discusses the impedance of one dimensional and two dimensional PhCs,and we propose a new kind of nonlocal effective medium theory to optimize PhCs' impedance to make it match with the impedance of the background(e.g.air).Furtherly,we first introduce the concept of ultratransparency to clarify the properties of impedance match intuitively.2.The properties of the impedance match in 1D PhCsWe study the effect and demonstrate the properties of the impedance match in 1D dielectric PhCs.We noticed that,for the symmetrically structured 1D PhCs,the elliptical EFCs near X point of Brillouin zone in the second band satisfy the wide-angle and broadband impedance match conditions.Therefore,the PhCs show the properties of broadband,wide-angle,polarization-insensitive transparency(transmittance is much higher than the materials themselves).In the following simulations,we demonstrate that these properties originate from impedance match of the PhCs.3.The properties of the impedance match in 2D PhCsWe design the structure and analysis the effect of the impedance match in 2D dielectric PhCs.The unit cell of 2D transparent PhCs are symmetrically structured as well,and the EFCs that satisfy the impedance match conditions appear near the boundary of Brillouin zone in the third band.What's more,by designing the micro-structure of the PhCs,we achieve the properties of omnidirectional transparency(-89°,89°)and the transmittance is more than 99% due to the perfect impedance match effect.Furtherly,with PhCs' nonlocal effective medium theory,we analyze the PhCs' effective parameters and the impedance.Most importantly,we proved the impedance match effect of PhCs by experiments at the microwave frequency regime.4.The applications of transparent PhCs in transformation optics(TO)We first demonstrate the equivalence between the 1D transparent PhC and the TO materials(formed by stretching/compressing air).The results show that,at the working frequency,the only difference between these two kinds of material lies in the shift of Ph C's EFC in(38)(34)direction,which won't affect the refractive behavior but will introduce a new freedom of phase modulating instead,breaking the limit of the design for TO devices with local media.Based on this property,we have made the cylindrical concentrator utilizing 1D transparent PhCs,and achieved the illusion of wave scattering and source positional illusion as well.