Three-dimensional Scaling Transformation Optics(3-D STO) And Its Application In The Design Of Electromagnetic Devices

The theoretical basis of transformation optics(TO)is the form-invariance of Maxwell's equations under coordinate transformations,which means TO provides a way to alter the field distribution by changing variables in Maxwell's equations.This article introduces the research background of transformation optics and the current research situations and obtained achievements,and then introduces some methods of coordinate transformation and spatial transformation,which focuses on conformal transformation optics(CTO)and quasi-conformal transformation optics(QCTO)in spatial transformation.In fact,due to the form-invariance of Maxwell's equations,the spatial coordinate transformation gives the appropriate permittivity and permeability tensors.Therefore,from macroscopic to microscopic,light is controllable at any scale.Based on TO,in the past ten years,researchers have explored many novel complex electromagnetic devices.The main research contents of this artical are as follows:First,a new strategy to implement the 3-D transformation optics,i.e.three-dimensional scaling transformation optics(3-D STO),which only requires the operation of scaling transformation,is proposed in this article.This method divides the virtual and physical spaces into small regions with similar spatial angles and maps each of them through a radial scaling map.Since the proposed method only requires applying positive scaling operators to the relative permittivity and permeability of the material,all the elements of the transformed Jacobian matrix are positive.The material parameters will be positive as long as they are positive in virtual spaces.Second,based on the proposed 3-D STO,four kinds of new electromagnetic devices are designed:a three-dimensional collimating lens,a new structure of radome,a converging lens to improve the directivity of broadband OAM beams,and arbitrary-way multi-modal OAM generator.The effectiveness and practicability of 3-D STO are verified.Compared with the existing methods for designing 3-D TO devices,this method not only inherits the advantage of CTO that can obtain isotropic transformed media,but also greatly reduces the complexity of the transformation.Moreover,the permittivity obtained by this method is a stepwise function.Therefore,in these designs,we can ensure that the material in each segment is uniform by simple segmentation,and provide a simple and feasible manufacturing method.