Design method for quasi-isotropic transformation materials based on inverse Laplace's equation with sliding boundaries

摘要

The deformation method of transformation optics has been demonstrated to be auseful tool, especially in designing arbitrary and nonsingular transformationmaterials. Recently, there are emerging demands for isotropic materialparameters, arising from the broadband requirement of the designed devices. Inthis work, the deformation method is further developed to designquasi-isotropic/isotropic transformation materials. The variational functionalof the inverse Laplace's equation is investigated and found to involve thesmooth and quasi-conformal nature of coordinate transformation. Together withthe sliding boundary conditions, the inverse Laplace's equation can be utilizedto give transformations which are conformal or quasi-conformal, depending onfunctionalities of interest. Examples of designing an arbitrary carpet cloakand a waveguide with arbitrary cross sections are given to validate theproposed idea. Compared with other quasi-conformal methods based on gridgeneration tools, the proposed method unifies the design and validation oftransformation devices, and thus is much convenient.