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

Recently, there are emerging demands for isotropic material parameters, arising from the broadband requirement of the functional devices. Since inverse Laplace's equation with sliding boundary condition will determine a quasi-conformai mapping, and a quasi-conformal mapping will minimize the transformation material anisotropy, so in this work, the inverse Laplace's equation with sliding boundary condition is proposed for quasi-isotropic transformation material design. Examples of quasi-isotropic arbitrary carpet cloak and waveguide with arbitrary cross sections are provided to validate the proposed method. The proposed method is very simple compared with other quasi-conformal methods based on grid generation tools.