Topology optimization based inverse synthesis of spectral 3D metamaterials

Official URL: http://dx.doi.org/10.1109/USNC-URSI.2014.6955465

Recent studies on artificial materials and metamaterials 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 formal synthesis schemes. Existing “conventional” metamaterials are based on analytical or experimental studies, i.e. a formal design approach to predict the exact spatial combination of material constituents from scratch does not exist. In this paper, we develop a versatile approach to design the microstructure of 3D 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. Towards that goal, earlier developed synthesis framework [Y. El-Kahlout and G. Kiziltas, PIER, 115, 343–380, 2011] that is capable of realizing predefined material constitutive parameters via designing the microstructure of artificial electromagnetic substrates will be updated to incorporate spectral dispersion and three dimensionality. The goal is to develop a formal design framework suitable for realizing the ‘unconventional’ microstructure of 3D metamaterials that are inherently spectrally dispersive. The current design framework is suitable for designing the periodic microstructure of desired anisotropic artificial magneto-dielectrics from available isotropic material phases by integrating Finite Elements (FE) based analysis tool (using COMSOL MULTIPHYSICS-PDE Coefficient Module) with optimization tools. Homogenizing Maxwell's Equations (MEQ) in or- er to estimate the effective spectral material parameters of the composite made of a periodic microstructure is the initial task of the framework. The FE analysis tool is used to evaluate intermediate fields at the ‘micro-scale’ level of the periodic unit cell that is integrated with the homogenized MEQ's in order to calculate the ‘macro-scale’ effective constitutive parameters of the overall bulk periodic structure that is spectral in nature. Consequently, the proposed framework based on the solution of homogenized MEQ's via the micro-macro approach allows topology design capabilities of microstructures with desired frequency dependent material properties in three dimensions. This capability is demonstrated on a comparison with known spectral behaviors of metamaterials in literature including hyperbolic media. Then, the developed material model is employed to solve a two step inverse design problem. First, metamaterials with desired novel reflection/transmission response will be designed to determine their ‘effective’ spectral material properties via optimization schemes. Next step will be to synthesize the microstructure of the effective material property obtained earlier. Initial design results show that the creation of a new class of 3D artificial material to custom design is indeed possible pointing towards the possibility to synthesize alternative metamaterial microstructures with low loss from ‘scratch’ overcoming the loss issue known of existing metamaterials. If successful when combined with advanced manufacturing schemes such as self-assembly, direct printing and novel sintering schemes, these capabilities will allow the automatic generation of totally novel yet unthinkable material designs that will lead to a new paradigm in electromagnetic material design.