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Robust topology optimization of optical cloaks under uncertainties in wave number and angle of incident wave
Author(s) -
Sato Yuki,
Izui Kazuhiro,
Yamada Takayuki,
Nishiwaki Shinji
Publication year - 2020
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6393
Subject(s) - topology optimization , mathematics , topology (electrical circuits) , optimization problem , norm (philosophy) , taylor series , mathematical analysis , minification , sensitivity (control systems) , mathematical optimization , finite element method , physics , electronic engineering , combinatorics , political science , law , thermodynamics , engineering
Summary This article presents a robust topology optimization method for optical cloaks under uncertainties in the wave number and angle in the incident wave. We first discuss the governing equation derived from Maxwell's equation, and extend it to the entire domain including the dielectric material and air, based on the level set‐based topology optimization method. Next, a robust optimization problem is formulated as a minimization problem of the weighted sum of the scattered wave norm and its standard deviation with respect to the wave number and angle of the incident wave. The standard deviation is mathematically expressed by the Taylor series approximation and the use of the adjoint variable method. The design sensitivity of the objective functional is also derived by the adjoint variable method. An optimization algorithm is then constructed, based on the proposed formulation for robust designs of optical cloaks. Several numerical examples are finally provided to demonstrate the validity and utility of the proposed method.