Topology-optimized carpet cloaks based on a level-set boundary expression.

The concept of topology-optimized carpet cloaks is presented using level-set boundary expressions. Specifically, these carpet cloaks are designed with the idea of minimizing the value of an objective functional, which is here defined as the integrated intensity of the difference between the electric field reflected by a flat plane and that controlled by the carpet cloak. Made of dielectric material, our cloaks are designed to imitate reflections from a flat plane, and with some cloaks, the value of the objective functional falls below 0.12% of that for a bare bump on a flat plane. These optimal carpet cloaks spontaneously satisfy the time-reversal symmetry of the scattered field during the optimization process. The profiles associated with optimal configurations are controlled by adjusting a regularization parameter. With this approach, a variety of configurations with different structural characteristics can be obtained.