Transformation method and wave control  

作　　者：Zheng Chang Jin Hu Geng-Kai Hu 

机构地区：[1]School of Aerospace Engineering,Beijing Institute of Technology, 100081 Beijing,China [2]School of Information and Electronics, Beijing Institute of Technology,100081 Beijing,China

出　　处：《Acta Mechanica Sinica》2010年第6期889-898,共10页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(10832002);the National Basic Research Program of China(2006CB601204).

摘　　要：Transformation method provides an efficient way to control wave propagation by materials.The transformed relations for field and material during a transformation are essential to fulfill this method.We propose a systematic method to derive the transformed relations for a general physic process,the constraint conditions are obtained by considering geometrical and physical constraint during a mapping. The proposed method is applied to Navier＇s equation for elastodynamics,Helmholtz＇s equation for acoustic wave and Maxwell＇s equation for electromagnetic wave,the corresponding transformed relations are derived,which can be used in the framework of transformation method for wave control.We show that contrary to electromagnetic wave,the transformed relations are not uniquely determined for elastic wave and acoustic wave,so we have a freedom to choose them differently.Using the obtained transformed relations,we also provide some examples for device design,a concentrator for elastic wave,devices for illusion acoustic and illusion optics are conceived and validated by numerical simulations.Transformation method provides an efficient way to control wave propagation by materials.The transformed relations for field and material during a transformation are essential to fulfill this method.We propose a systematic method to derive the transformed relations for a general physic process,the constraint conditions are obtained by considering geometrical and physical constraint during a mapping. The proposed method is applied to Navier＇s equation for elastodynamics,Helmholtz＇s equation for acoustic wave and Maxwell＇s equation for electromagnetic wave,the corresponding transformed relations are derived,which can be used in the framework of transformation method for wave control.We show that contrary to electromagnetic wave,the transformed relations are not uniquely determined for elastic wave and acoustic wave,so we have a freedom to choose them differently.Using the obtained transformed relations,we also provide some examples for device design,a concentrator for elastic wave,devices for illusion acoustic and illusion optics are conceived and validated by numerical simulations.

关 键 词：Wave control Elastic wave Acoustic wave Electromagnetic wave Local affine transformation 

分 类 号：O441[理学—电磁学] TP311[理学—物理]