Shape optimization for the strong routing of light in periodic diffraction gratings
(2023) In Journal of Computational Physics 472.- Abstract
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... (More)
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.
(Less)
- author
- Araújo C., Juan C. ; Engström, Christian LU and Wadbro, Eddie
- publishing date
- 2023-01-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Diffraction grating, Helmholtz problem, Light routing, Scattering problem, Shape optimization
- in
- Journal of Computational Physics
- volume
- 472
- article number
- 111684
- publisher
- Elsevier
- external identifiers
-
- scopus:85140226291
- ISSN
- 0021-9991
- DOI
- 10.1016/j.jcp.2022.111684
- language
- English
- LU publication?
- no
- additional info
- Funding Information: Juan C. Araújo thanks all the members of the Design Optimization Group at the Umit research lab for several enlightening discussions on numerical optimization for Helmholtz problems. This work was financially supported by the Kempe Foundations under Grant No. SMK-1857 , the Swedish strategic research programme eSSENCE , and the Swedish Research Council under Grant No. 2021-04537 . Publisher Copyright: © 2022 The Author(s)
- id
- 8098950c-4239-4c2d-ac69-7dfb58853cec
- date added to LUP
- 2023-03-24 11:02:49
- date last changed
- 2023-03-24 13:18:24
@article{8098950c-4239-4c2d-ac69-7dfb58853cec,
abstract = {{<p>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.</p>}},
author = {{Araújo C., Juan C. and Engström, Christian and Wadbro, Eddie}},
issn = {{0021-9991}},
keywords = {{Diffraction grating; Helmholtz problem; Light routing; Scattering problem; Shape optimization}},
language = {{eng}},
month = {{01}},
publisher = {{Elsevier}},
series = {{Journal of Computational Physics}},
title = {{Shape optimization for the strong routing of light in periodic diffraction gratings}},
url = {{http://dx.doi.org/10.1016/j.jcp.2022.111684}},
doi = {{10.1016/j.jcp.2022.111684}},
volume = {{472}},
year = {{2023}},
}