Inverse Synthesis of Electromagnetic Mate- Rials Using Homogenization Based Topology Optimization

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 Received 16 August 2010, Accepted 7 April 2011, Scheduled 8 April 2011 Corresponding author: Gullu Kiziltas ([email protected]). † Also with Sabanci University, Orhanli 34956, Tuzla, Istanbul, Turkey. 344 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.