Inverse Synthesis of Electromagnetic Materials Using Homogenization Based Topology Optimization

Abstract

Abstract-Recent studies on artificial materials demonstrate that substantial improvements in electromagnetic response can be attained by combining different materials subject to desired metrics. However, the perfect material combination is unique and extremely difficult to determine without automated synthesis schemes. In this paper, we develop a versatile approach to design the microstructure of periodic materials with prescribed dielectric and magnetic material tensors. The proposed framework is based on a robust material model and generalized inverse synthesis tool relying on topology optimization. The former is derived using homogenization theory and asymptotic expansion applied to Maxwell equations and can characterize the effects of anisotropy and loss of materials with periodic unit cells of arbitrary geometries and multi-phases much smaller than the wavelength. Resulting Partial Differential Equation (PDE) is solved numerically using Finite Element Analysis (FEA) and is validated with results in literature. The material model proves to be fast and numerically stable even with complex inclusions. The topology optimization problem is applied for the first time towards designing the unit cell topology of periodic electromagnetic materials from scratch with desired dielectric and magnetic tensors using offthe-shelf materials, i.e., readily available constituents obtained from El-Kahlout and Kiziltas isotropic ceramic powders. The proposed framework's capability is demonstrated with five design examples. Design with anisotropic permittivity is also fabricated. Results show that the framework is capable of designing, in an automated fashion, non-intuitive material compositions from scratch with desired electromagnetic properties.

Inverse design of EBG waveguides through scattering matrices

“…Obviously, because of the huge number of involved parameters and the corresponding high number of trials, this is a far-from effective way to proceed. More rigorous design approaches are those based on inverse design, such as the inverse homogenization problems [10,11] which are mainly devoted to synthesizing effective electromagnetic properties of unit cells. Unfortunately, the arising dielectric profiles exhibit a complex distribution which is difficult to fabricate [10], so that fabrication-oriented tools are needed.…”

“…More rigorous design approaches are those based on inverse design, such as the inverse homogenization problems [10,11] which are mainly devoted to synthesizing effective electromagnetic properties of unit cells. Unfortunately, the arising dielectric profiles exhibit a complex distribution which is difficult to fabricate [10], so that fabrication-oriented tools are needed. In this respect, topology optimization [12] based design tools have been widely adopted during the years.…”

Inverse Design of Dielectric Materials by Topology Optimization

“…However, meta-heuristic approaches such as GAs, Particle Swarm Optimization (PSO), and Simulated Annealing (SA) are generally not suitable for topology optimization since the number of design variables is usually so large that the optimization becomes too computationally costly [18]. Hence in [12] design resolution was limited to extremely coarse discretizations. In this work, a gradientbased topology optimization method is used to find the distribution of dielectric material for the unit cell of a periodic microstructure, where densities are updated based on the sensitivities.…”

“…Topology optimization methods have been applied to a variety of problems such as electromagnetic problems (e.g., [2][3][4][5]), fluid dynamics problem (e.g., [6]), phononics [7] and others. Topology optimization has also been successfully applied to various microstructure design problems aiming to develop materials that have extreme properties such as a negative thermal expansion coefficient [8], a negative Poisson's ratio [9], and materials with a prescribed value of a constitutive tensor such as Young's modulus [10], magnetic permeability [11], a dielectric constant [12], and so on. These problems are called inverse homogenization problems [10].…”

“…In a previous study on the microstructure design of dielectric materials [12], a genetic algorithm (GA) was used in the optimization method. However, meta-heuristic approaches such as GAs, Particle Swarm Optimization (PSO), and Simulated Annealing (SA) are generally not suitable for topology optimization since the number of design variables is usually so large that the optimization becomes too computationally costly [18].…”