Electromagnetic complementary media with arbitrary geometries and non-conformal boundaries

A generalized folded transformation procedure is presented for the space with arbitrary shapes. General expressions for the constitute parameters of complementary media are deduced, which can be readily applied to design complementary media based transformation optics devices (CMTOD) with arbitrary shapes. It's no longer limited to the situation when the inner and outer boundaries of the CMTOD are conformal or similar shapes, and can be available for the non-conformal situations. Three kinds of CMTOD are designed and studied, which involves a super-lens, an external cloak that hides object outside the cloaking shell, and an illusion optics device that transforms one object to another. Full-wave simulations are carried out to validate the proposed approach. The generalization introduced here makes a step forward for the flexible design of CMTOD with arbitrary geometries.