Inverse Design of Dielectric Materials by Topology Optimization

Abstract

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.

A topology optimization method based on the level set method for the design of negative permeability dielectric metamaterials

“…Zhou et al [25] proposed an inverse homogenization method for the design of metamaterials, where both permittivity and permeability are simultaneously maximized. El-Kahlout and Kiziltas [47], and Otomori et al [48] introduced inverse homogenization methods for the design of dielectric materials that demonstrate a desirable prescribed effective permittivity value, using an asymptotic expansion-based homogenization method and Genetic Algorithms (GAs) [47], and an energy-based homogenization method and density-based topology optimization [48], respectively. GAs have also been used to find optimized layouts of a metallic inclusion in the metamaterial unit cell for a negative permeability design problem [49], and for different multi-objective problems [50,51] in which the refractive index and impedance were simultaneously designed [50], and the bandwidth of the negative refractive index was maximized and the dissipation minimized [51].…”

Inverse design of EBG waveguides through scattering matrices

“…In fact, by starting from a basic structure, inverse design procedures are exploited to modify (part of) the lattice for an improving of the VSWR (i.e., saying it in other words, for avoiding waves coming back along the defect). A similar problem has been dealt with in [13][14][15][16][17]. In particular, we apply the I-SMM to improve guiding performance of straight and bent EBG waveguides.…”

“…As the name suggest, this kind of techniques aims at modifying the topology of the device at hand, that is, the geometrical and e.m. characteristics of the object being designed, in such a way some assigned specifications are satisfied. Developed design tools based on topology optimization [13][14][15][16][17] or the like [18,19] are able to realize binary devices wherein just two materials (one of which is usually air) are involved. Other types of design tools based on group theory [9] and the emerging concept of deep neural network [20] have been also proposed.…”

Topology Optimisation of Wideband Coaxial-to-Waveguide Transitions

“…For design problem within electromagnetics, the development has been much slower. The layout design of dielectric materials using topology optimisation can be carried out with a similar approach as for mechanics problems 16 17 . However, metallic devices are different, due to the ohmic barrier problem : a small region of material is lossless in the limits of zero or infinite conductivity, whereas substantial ohmic losses appear for intermediate values.…”