Applications And Effective Medium Theory Of Checkboard Structure Systems

Effective medium theory(EMT)can achieve similar functions of the overall system by defining material averages with effective parameters,which is a powerful tool to design the complex material parameters and solve various electromagnetic problems.There are two famous theories of traditional effective medium approaches,i.e.,the Maxwell-Garnett theory(MGT)and the Bruggeman effective medium theory(BEMT),which are both based on material characteristics of each component in the mixtures.Depending on material characteristics of each component in the mixtures,as well as the relative concentration of the inclusions and the difference in the manufacturing structure,the effective medium exhibits different electromagnetic properties.This thesis mainly studies the effective medium theory of checkboard structures in square and rectangular lattices,and applying them to transformation optical(TO)devices.From the introduction of the effective medium theory to the derivation and application of the effective medium formula in two checkboard structures,we combined the analysis and data fitting to give a new idea to realize the TO devices.Main work and arrangement of this thesis are as follows:(1)For the two-dimensional checkboard structures,we analyzed the effective medium parameters of the square and rectangular checkboard structures from the analysis and numerical fitting.For the square checkboard structures,its isotropic effective medium formula could be accurately obtained;For the rectangular checkboard structures,when the wavelength is much larger than the structural dimensions,we give the formula of the anisotropic equivalent medium parameters by extracting the effective refractive index from the dispersion band slope of the checkboard structures fitting its anisotropic effective medium formula in a large number of structure parameters.Finally,by comparing the field distributions of the incident waves passing through the checkboard structures and the effective medium,we verified the validity of the effective medium formula within a certain range.(2)By applying the effective medium formula of the checkboard structures to the TO devices,we used the checkboard structures to design a series of TO devices,including concentrators,rotators,and wave shifters,stretchers and compressors.Most of these TO devices have very complex structures and electromagnetic parameters,and we can use different checkboard structures to realize the material parameters of TO devices by reasonable structural designs.Thus,this work provides a new and alternative idea to design and realize the TO devices.