## Inverse design of dielectric materials by topology optimization

Publication: Research › Journal article – Annual report year: 2012

### Standard

**Inverse design of dielectric materials by topology optimization.** / Otomori, M.; Andkjær, Jacob Anders; Sigmund, Ole; Izui, K.; Nishiwaki, S.

Publication: Research › Journal article – Annual report year: 2012

### Harvard

*Progress in Electromagnetics Research*, vol 127, pp. 93-120.

### APA

*Progress in Electromagnetics Research*,

*127*, 93-120.

### CBE

### MLA

*Progress in Electromagnetics Research*. 2012, 127. 93-120.

### Vancouver

### Author

### Bibtex

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### RIS

TY - JOUR

T1 - Inverse design of dielectric materials by topology optimization

AU - Otomori,M.

AU - Andkjær,Jacob Anders

AU - Sigmund,Ole

AU - Izui,K.

AU - Nishiwaki,S.

PY - 2012

Y1 - 2012

N2 - 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 con¯gurations. 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.

AB - 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 con¯gurations. 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.

M3 - Journal article

VL - 127

SP - 93

EP - 120

JO - Progress in Electromagnetics Research

T2 - Progress in Electromagnetics Research

JF - Progress in Electromagnetics Research

SN - 1043-626X

ER -