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Upper bounds on absorption and scattering

Gustafsson, Mats LU orcid ; Schab, Kurt LU ; Jelinek, Lukas and Capek, Miloslav LU (2020) In New Journal of Physics 22(7).
Abstract

A general framework for determining fundamental bounds in nanophotonics is introduced in this paper. The theory is based on convex optimization of dual problems constructed from operators generated by electromagnetic integral equations. The optimized variable is a contrast current defined within a prescribed region of a given material constitutive relations. Two power conservation constraints analogous to the optical theorem are utilized to tighten the bounds and to prescribe either losses or material properties. Thanks to the utilization of matrix rank-1 updates, modal decompositions, and model order reduction techniques, the optimization procedure is computationally efficient even for complicated scenarios. No dual gaps are observed.... (More)

A general framework for determining fundamental bounds in nanophotonics is introduced in this paper. The theory is based on convex optimization of dual problems constructed from operators generated by electromagnetic integral equations. The optimized variable is a contrast current defined within a prescribed region of a given material constitutive relations. Two power conservation constraints analogous to the optical theorem are utilized to tighten the bounds and to prescribe either losses or material properties. Thanks to the utilization of matrix rank-1 updates, modal decompositions, and model order reduction techniques, the optimization procedure is computationally efficient even for complicated scenarios. No dual gaps are observed. The method is well-suited to accommodate material anisotropy and inhomogeneity. To demonstrate the validity of the method, bounds on scattering, absorption, and extinction cross sections are derived first and evaluated for several canonical regions. The tightness of the bounds is verified by comparison to optimized spherical nanoparticles and shells. The next metric investigated is bi-directional scattering studied closely on a particular example of an electrically thin slab. Finally, the bounds are established for Purcell's factor and local field enhancement where a dimer is used as a practical example.

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Absorption, Bounds, Convex optimization, Field enhancement, Plasmonics, Scattering
in
New Journal of Physics
volume
22
issue
7
article number
073013
publisher
IOP Publishing
external identifiers
  • scopus:85089814528
ISSN
1367-2630
DOI
10.1088/1367-2630/ab83d3
language
English
LU publication?
yes
id
5d6d53ff-4c5b-483e-8878-1874f30e7db1
date added to LUP
2020-12-29 13:40:35
date last changed
2022-04-26 22:52:48
@article{5d6d53ff-4c5b-483e-8878-1874f30e7db1,
  abstract     = {{<p>A general framework for determining fundamental bounds in nanophotonics is introduced in this paper. The theory is based on convex optimization of dual problems constructed from operators generated by electromagnetic integral equations. The optimized variable is a contrast current defined within a prescribed region of a given material constitutive relations. Two power conservation constraints analogous to the optical theorem are utilized to tighten the bounds and to prescribe either losses or material properties. Thanks to the utilization of matrix rank-1 updates, modal decompositions, and model order reduction techniques, the optimization procedure is computationally efficient even for complicated scenarios. No dual gaps are observed. The method is well-suited to accommodate material anisotropy and inhomogeneity. To demonstrate the validity of the method, bounds on scattering, absorption, and extinction cross sections are derived first and evaluated for several canonical regions. The tightness of the bounds is verified by comparison to optimized spherical nanoparticles and shells. The next metric investigated is bi-directional scattering studied closely on a particular example of an electrically thin slab. Finally, the bounds are established for Purcell's factor and local field enhancement where a dimer is used as a practical example.</p>}},
  author       = {{Gustafsson, Mats and Schab, Kurt and Jelinek, Lukas and Capek, Miloslav}},
  issn         = {{1367-2630}},
  keywords     = {{Absorption; Bounds; Convex optimization; Field enhancement; Plasmonics; Scattering}},
  language     = {{eng}},
  number       = {{7}},
  publisher    = {{IOP Publishing}},
  series       = {{New Journal of Physics}},
  title        = {{Upper bounds on absorption and scattering}},
  url          = {{http://dx.doi.org/10.1088/1367-2630/ab83d3}},
  doi          = {{10.1088/1367-2630/ab83d3}},
  volume       = {{22}},
  year         = {{2020}},
}