Topology Optimization for a Dielectric Optical Cloak Based on an Exact Level Set Approach

This paper proposes a topology optimization method for a dielectric optical cloak that provides results that are perfectly free from intermediate materials, based on a level set boundary expression and the Finite Element Method. The finite element mesh is re-generated to fit the iso-surface of the level set function at every iterative step, to remove intermediate materials, so that the obtained optimal structure consists of only two materials, the dielectric material and air. First, the level set-based topology optimization is formulated and a topology optimization algorithm is proposed for the exact level set approach. Next, design requirements for the dielectric optimal cloak device are clarified and an objective functional for the design is formulated. The proposed method is then applied to a simple numerical problem to illustrate its effectiveness.