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PIER PIER B PIER C PIER M PIER Letters
2012-04-10
Inverse Design of Dielectric Materials by Topology Optimization
By
Masaki Otomori,

    Mr. Masaki Otomori

    Kyoto University

    Japan

    Homepage

Jacob Andkjaer,

    Dr. Jacob Andkjaer

    Tech Univ Denmark

    Denmark

    Homepage

Ole Sigmund,

    Dr. Ole Sigmund

    Technical University of Denmark

    Denmark

    Homepage

Kazuhiro Izui,

    Dr. Kazuhiro Izui

    Kyoto University

    Japan

    Homepage

Shinji Nishiwaki

    Dr. Shinji Nishiwaki

    Kyoto University

    Japan

    Homepage

Progress In Electromagnetics Research, Vol. 127, 93-120, 2012
doi:10.2528/PIER12020501
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.
Citation
Masaki Otomori, Jacob Andkjaer, Ole Sigmund, Kazuhiro Izui, and Shinji Nishiwaki, "Inverse Design of Dielectric Materials by Topology Optimization," Progress In Electromagnetics Research, Vol. 127, 93-120, 2012.
doi:10.2528/PIER12020501
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