Upper bounds on focusing efficiency
Schab, Kurt ; Jelinek, Lukas ; Capek, Miloslav and Gustafsson, Mats LU
(2022)
In Optics Express
30(25).
p.45705-45723
- Abstract
Upper bounds on the focusing efficiency of aperture fields and lens systems are formulated using integral equation representations of Maxwell’s equations and Lagrangian duality. Two forms of focusing efficiency are considered based on lens exit plane fields and optimal polarization currents within lens design regions of prescribed shape and available materials. Bounds are compared against the performance of classical prescriptions of ideal lens aperture fields, hyperbolic lens designs, and lenses produced by inverse design. Results demonstrate that, without regularization, focusing efficiency based solely on lens exit plane fields is unbounded, similar to the problem of unbounded antenna directivity. Additionally, results considering... (More)
Upper bounds on the focusing efficiency of aperture fields and lens systems are formulated using integral equation representations of Maxwell’s equations and Lagrangian duality. Two forms of focusing efficiency are considered based on lens exit plane fields and optimal polarization currents within lens design regions of prescribed shape and available materials. Bounds are compared against the performance of classical prescriptions of ideal lens aperture fields, hyperbolic lens designs, and lenses produced by inverse design. Results demonstrate that, without regularization, focusing efficiency based solely on lens exit plane fields is unbounded, similar to the problem of unbounded antenna directivity. Additionally, results considering extruded two-dimensional dielectric geometries driven by out-of-plane electric fields for the calculation of bounds and inverse design demonstrate that aperture fields based on time-reversal do not necessarily yield optimal lens focusing efficiency, particularly in the case of near-field (high numerical aperture) focusing.
(Less)
- author
- Schab, Kurt
; Jelinek, Lukas
; Capek, Miloslav
and Gustafsson, Mats
LU
- organization
- publishing date
- 2022-12-05
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Optics Express
- volume
- 30
- issue
- 25
- pages
- 19 pages
- publisher
- Optical Society of America
- external identifiers
-
- pmid:36522970
- scopus:85144165825
- ISSN
- 1094-4087
- DOI
- 10.1364/OE.472558
- language
- English
- LU publication?
- yes
- id
- 4f86923a-a906-42cf-9c1e-b9b2305b6fd5
- date added to LUP
- 2023-01-16 08:52:54
- date last changed
- 2024-04-03 18:01:23
@article{4f86923a-a906-42cf-9c1e-b9b2305b6fd5,
abstract = {{<p>Upper bounds on the focusing efficiency of aperture fields and lens systems are formulated using integral equation representations of Maxwell’s equations and Lagrangian duality. Two forms of focusing efficiency are considered based on lens exit plane fields and optimal polarization currents within lens design regions of prescribed shape and available materials. Bounds are compared against the performance of classical prescriptions of ideal lens aperture fields, hyperbolic lens designs, and lenses produced by inverse design. Results demonstrate that, without regularization, focusing efficiency based solely on lens exit plane fields is unbounded, similar to the problem of unbounded antenna directivity. Additionally, results considering extruded two-dimensional dielectric geometries driven by out-of-plane electric fields for the calculation of bounds and inverse design demonstrate that aperture fields based on time-reversal do not necessarily yield optimal lens focusing efficiency, particularly in the case of near-field (high numerical aperture) focusing.</p>}},
author = {{Schab, Kurt and Jelinek, Lukas and Capek, Miloslav and Gustafsson, Mats}},
issn = {{1094-4087}},
language = {{eng}},
month = {{12}},
number = {{25}},
pages = {{45705--45723}},
publisher = {{Optical Society of America}},
series = {{Optics Express}},
title = {{Upper bounds on focusing efficiency}},
url = {{http://dx.doi.org/10.1364/OE.472558}},
doi = {{10.1364/OE.472558}},
volume = {{30}},
year = {{2022}},
}