Topology optimized design of carpet cloaks based on a level set approach

This paper presents topology optimized designs of carpet cloaks made of dielectrics modeled by a level set boundary expression. The objective functional, evaluating the performance of the carpet cloaks, is defined as the integrated intensity of the difference between electric field reflected by the flat plane and that controlled by a carpet cloak covering a bump. The dielectric structures of carpet cloak are designed to minimize the objective functional value and, in some cases, the value reach 0.34% of that when a bare bump exists. Dielectric structures of carpet cloaks are expressed by level set functions given on grid points. The function becomes positive in dielectrics, negative in air and zero on air-dielectric interfaces and express air-dielectric interfaces explicitly.