Passive and Lossless Conformal Huygens’ Metasurfaces for Arbitrary Wave Transformation

We discuss a general framework for designing irregularly shaped passive and lossless conformal Huygens’ metasurfaces (HMS), derived from the theory of transformation optics. Through a conformal coordinate transformation, the physical space in which the HMS resides is mapped to a computational space, in which the surface geometry is significantly simpler. The mapping preserves the boundary conditions governing the field transformations, meaning any previously developed design methods for flat HMSs remain valid. Importantly, it also facilitates the identification of completely passive and lossless surface designs, which are usually sought-after for their ease of implementation.