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Proceedings Paper

Vector Slepian functions and the inverse problem of high numerical aperture focusing
Author(s): Kornél Jahn; Nándor Bokor
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Paper 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.

Paper Details

Date Published: 18 December 2012
PDF: 8 pages
Proc. SPIE 8550, Optical Systems Design 2012, 855038 (18 December 2012); doi: 10.1117/12.979311
Show Author Affiliations
Kornél Jahn, Budapest Univ. of Technology and Economics (Hungary)
Nándor Bokor, Budapest Univ. of Technology and Economics (Hungary)


Published in SPIE Proceedings Vol. 8550:
Optical Systems Design 2012
Laurent Mazuray; Rolf Wartmann; Andrew P. Wood; Marta C. de la Fuente; Jean-Luc M. Tissot; Jeffrey M. Raynor; Daniel G. Smith; Frank Wyrowski; Andreas Erdmann; Tina E. Kidger; Stuart David; Pablo Benítez, Editor(s)

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