### 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 language | English |
---|---|

Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 8550 |

DOIs | |

Publication status | Published - 2012 |

Event | Optical Systems Design 2012 - Barcelona, Spain Duration: Nov 26 2012 → Nov 29 2012 |

### Other

Other | Optical Systems Design 2012 |
---|---|

Country | Spain |

City | Barcelona |

Period | 11/26/12 → 11/29/12 |

### Fingerprint

### 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

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Vector Slepian functions and the inverse problem of high numerical aperture focusing

AU - Jahn, Kornél

AU - Bokor, N.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - High numerical aperture focusing

KW - Inverse problem

KW - Slepian's concentration problem

KW - Vector diffraction theory

UR - http://www.scopus.com/inward/record.url?scp=84877889936&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84877889936&partnerID=8YFLogxK

U2 - 10.1117/12.979311

DO - 10.1117/12.979311

M3 - Conference contribution

AN - SCOPUS:84877889936

SN - 9780819493019

VL - 8550

BT - Proceedings of SPIE - The International Society for Optical Engineering

ER -