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Shape optimization for the strong routing of light in periodic diffraction gratings
Umeå University, Faculty of Science and Technology, Department of Science and Mathematics Education. Umeå University, Faculty of Science and Technology, Department of Computing Science.ORCID iD: 0000-0002-0143-5554
Department of Mathematics, Linnaeus University, Sweden.
Umeå University, Faculty of Science and Technology, Department of Computing Science. Department of Mathematics and Computer Science, Karlstad University, Sweden.ORCID iD: 0000-0001-8704-9584
2023 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 472, article id 111684Article in journal (Refereed) Published
Abstract [en]

In the quest for the development of faster and more reliable technologies, the ability to control the propagation, confinement, and emission of light has become crucial. The design of guide mode resonators and perfect absorbers has proven to be of fundamental importance. In this project, we consider the shape optimization of a periodic dielectric slab aiming at efficient directional routing of light to reproduce similar features of a guide mode resonator. For this, the design objective is to maximize the routing efficiency of an incoming wave. That is, the goal is to promote wave propagation along the periodic slab. A Helmholtz problem with a piecewise constant and periodic refractive index medium models the wave propagation, and an accurate Robin-to-Robin map models an exterior domain. We propose an optimal design strategy that consists of representing the dielectric interface by a finite Fourier formula and using its coefficients as the design variables. Moreover, we use a high order finite element (FE) discretization combined with a bilinear Transfinite Interpolation formula. This setting admits explicit differentiation with respect to the design variables, from where an exact discrete adjoint method computes the sensitivities. We show in detail how the sensitivities are obtained in the quasi-periodic discrete setting. The design strategy employs gradient-based numerical optimization, which consists of a BFGS quasi-Newton method with backtracking line search. As a test case example, we present results for the optimization of a so-called single port perfect absorber. We test our strategy for a variety of incoming wave angles and different polarizations. In all cases, we efficiently reach designs featuring high routing efficiencies that satisfy the required criteria.

Place, publisher, year, edition, pages
Elsevier, 2023. Vol. 472, article id 111684
Keywords [en]
Diffraction grating, Helmholtz problem, Light routing, Scattering problem, Shape optimization
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-200659DOI: 10.1016/j.jcp.2022.111684ISI: 000879217600002Scopus ID: 2-s2.0-85140226291OAI: oai:DiVA.org:umu-200659DiVA, id: diva2:1709074
Funder
The Kempe Foundations, SMK-1857eSSENCE - An eScience CollaborationSwedish Research Council, 2021-04537Available from: 2022-11-07 Created: 2022-11-07 Last updated: 2023-09-05Bibliographically approved

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Araujo-Cabarcas, Juan CarlosWadbro, Eddie

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