对全入射角负折射二维光子晶体结构和电磁参量的研究

利用二维光子晶体的等频线分析原理和平面波展开方法,得到了使二维光子晶体产生全入射角负折射(All-Angle Negative Refraction,AANR)现象时,入射电磁波的频率取值范围.同时,分析了AANR频率范围随着结构参量(晶格类型、介质棒半径与晶格周期的比值)和电磁参量(介质柱介电常量、本底介电常量、入射电磁波偏振方向)变化的行为.结果表明:固定组成光子晶体的一种介质的介电常量,另一介质的介电常量只有达到一定阈值,才有可能使光子晶体出现AANR现象.在给定两种介质介电常量的条件下,存在使AANR频率范围最大化的结构参量和电磁参量.     

AANR Spaces and Absolute Retracts for Tree-Like Continua

Continua that are approximative absolute neighborhood retracts (AANR's) are characterized as absolute terminal retracts, i.e., retracts of continua in which they are embedded as terminal subcontinua. This implies that any AANR continuum has a dense arc component, and that any ANR continuum is an absolute terminal retract. It is proved that each absolute retract for any of the classes of: tree-like continua, λ-dendroids, dendroids, arc-like continua and arc-like λ-dendroids is an approximative absolute retract (so it is an AANR). Consequently, all these continua have the fixed point property, which is a new result for absolute retracts for tree-like continua. Related questions are asked.