Vector Slepian functions and the inverse problem of high numerical aperture focusing

Kornél Jahn, N. Bokor

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The vector Slepian multipole fields are recently published basis functions that are naturally suitable for approximating the focal electric field of a high numerical aperture lens, because their plane-wave amplitude spectrum shows an angular energy distribution that is highly confined to the spherical cap corresponding to the numerical aperture of the lens. Thus when solving inverse problems, no additional constraints are needed to ensure the directionality of the focused field, and the number of degrees of freedom can be reduced, as opposed to a representation using conventional multipole fields. In this paper we demonstrate the applicability of this new basis to an inverse problem of focusing where the three-dimensional intensity distribution is prescribed in some reasonably chosen volume around the focus. Using numerical optimization, an approximation of the focused electric field in terms of the vector Slepian multipole fields is obtained and the illuminating field is calculated in a straightforward way. Three examples from recent literature have been chosen to illustrate the method.

Original languageEnglish
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
Volume8550
DOIs
Publication statusPublished - 2012
EventOptical Systems Design 2012 - Barcelona, Spain
Duration: Nov 26 2012Nov 29 2012

Other

OtherOptical Systems Design 2012
CountrySpain
CityBarcelona
Period11/26/1211/29/12

Fingerprint

numerical aperture
Inverse problems
multipoles
Lenses
Inverse Problem
Electric fields
lenses
spherical caps
electric fields
Lens
Electric Field
illuminating
energy distribution
plane waves
degrees of freedom
Energy Distribution
Numerical Optimization
optimization
Plane Wave
Basis Functions

Keywords

  • High numerical aperture focusing
  • Inverse problem
  • Slepian's concentration problem
  • Vector diffraction theory

ASJC Scopus subject areas

  • Applied Mathematics
  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Jahn, K., & Bokor, N. (2012). Vector Slepian functions and the inverse problem of high numerical aperture focusing. In Proceedings of SPIE - The International Society for Optical Engineering (Vol. 8550). [855038] https://doi.org/10.1117/12.979311

Vector Slepian functions and the inverse problem of high numerical aperture focusing. / Jahn, Kornél; Bokor, N.

Proceedings of SPIE - The International Society for Optical Engineering. Vol. 8550 2012. 855038.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Jahn, K & Bokor, N 2012, Vector Slepian functions and the inverse problem of high numerical aperture focusing. in Proceedings of SPIE - The International Society for Optical Engineering. vol. 8550, 855038, Optical Systems Design 2012, Barcelona, Spain, 11/26/12. https://doi.org/10.1117/12.979311
Jahn K, Bokor N. Vector Slepian functions and the inverse problem of high numerical aperture focusing. In Proceedings of SPIE - The International Society for Optical Engineering. Vol. 8550. 2012. 855038 https://doi.org/10.1117/12.979311
Jahn, Kornél ; Bokor, N. / Vector Slepian functions and the inverse problem of high numerical aperture focusing. Proceedings of SPIE - The International Society for Optical Engineering. Vol. 8550 2012.
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