Inverse design of dielectric materials by topology optimization

Abstract—The capabilities and operation of electromagnetic devices can be dramatically enhanced if artificial materials that provide certain prescribed properties can be designed and fabricated. This paper presents a systematic methodology for the design of dielectric materials with prescribed electric permittivity. A gradient-based topology optimization method is used to find the distribution of dielectric material for the unit cell of a periodic microstructure composed of one or two dielectric materials. The optimization problem is formulated as a problem to minimize the square of the difference between the effective permittivity and a prescribed value. The optimization algorithm uses the adjoint variable method (AVM) for the sensitivity analysis and the finite element method (FEM) for solving the equilibrium and adjoint equations, respectively. A Heaviside projection filter is used to obtain clear optimized configurations. Several design problems show that clear optimized unit cell configurations that provide the prescribed electric permittivity can be obtained for all the presented cases. These include the design of isotropic material, anisotropic material, anisotropic material with a non-zero off-diagonal terms, and anisotropic material with loss. The results show that the optimized values are in agreement with theoretical bounds, confirming that our method yields appropriate and useful solutions

Level Set-Based Topology Optimization for the Design of an Electromagnetic Cloak With Ferrite Material

This paper presents a structural optimization method for the design of an electromagnetic cloak made of ferrite material. Ferrite materials exhibit a frequency-dependent degree of permeability, due to a magnetic resonance phenomenon that can be altered by changing the magnitude of an externally applied dc magnetic field. Thus, such ferrite cloaks have the potential to provide novel functions, such as on-off operation in response to on-off application of an external magnetic field. The optimization problems are formulated to minimize the norm of the scattering field from a cylindrical obstacle. A level set-based topology optimization method incorporating a fictitious interface energy is used to find optimized configurations of the ferrite material. The numerical results demonstrate that the optimization successfully found an appropriate ferrite configuration that functions as an electromagnetic cloak