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Shape optimization for the strong directional scattering of dielectric nanorods
Umeå University, Faculty of Science and Technology, Department of Computing Science.ORCID iD: 0000-0002-0143-5554
Umeå University, Faculty of Science and Technology, Department of Computing Science. Department of Mathematics and Computer Science, Karlstad University, Karlstad, Sweden.ORCID iD: 0000-0001-8704-9584
2021 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 122, no 15, p. 3683-3704Article in journal (Refereed) Published
Abstract [en]

In this project, we consider the shape optimization of a dielectric scatterer aiming at efficient directional routing of light. In the studied setting, light interacts with a penetrable scatterer with dimension comparable to the wavelength of an incoming planar wave. The design objective is to maximize the scattering efficiency inside a target angle window. For this, a Helmholtz problem with a piecewise constant refractive index medium models the wave propagation, and an accurate Dirichlet-to-Neumann map models an exterior domain. The strategy consists of using a high-order finite element (FE) discretization combined with gradient-based numerical optimization. The latter consists of a quasi-Newton (BFGS) with backtracking line search. A discrete adjoint method is used to compute the sensitivities with respect to the design variables. Particularly, for the FE representation of the curved shape, we use a bilinear transfinite interpolation formula, which admits explicit differentiation with respect to the design variables. We exploit this fact and show in detail how sensitivities are obtained in the discrete setting. We test our strategy for a variety of target angles, different wave frequencies, and refractive indexes. In all cases, we efficiently reach designs featuring high scattering efficiencies that satisfy the required criteria.

Place, publisher, year, edition, pages
John Wiley & Sons, 2021. Vol. 122, no 15, p. 3683-3704
Keywords [en]
directional scattering, Helmholtz problem, light routing, scattering problem, shape optimization
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-183008DOI: 10.1002/nme.6677ISI: 000646710100001Scopus ID: 2-s2.0-85104290944OAI: oai:DiVA.org:umu-183008DiVA, id: diva2:1555203
Funder
The Kempe Foundations, SMK-1857eSSENCE - An eScience CollaborationAvailable from: 2021-05-18 Created: 2021-05-18 Last updated: 2022-01-12Bibliographically approved

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Araujo-Cabarcas, Juan CarlosWadbro, Eddie

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