Abstract
A series expansion method is proposed for high numerical aperture focusing problems. The angular spectrum of the focused field is expressed using orthogonal vector basis functions that are obtained by solving Slepian's concentration problem for a spherical cap and expressed in terms of the vector spherical harmonics. This newly obtained Slepiantype basis automatically satisfies the transversality condition and a subset exhibits excellent energy concentration inside the solid angle of illumination. This property makes the Slepiantype basis very useful in inverse focusing problems. The corresponding vector basis for focused fields is constructed as well. Examples are presented for linearly and radially polarized illumination, revealing the fact that, compared to an expansion using the vector spherical harmonics themselves, a lower number of terms is sufficient to achieve the same accuracy, suggesting that the Slepiantype basis is preferable even in direct focusing problems.
Original language  English 

Pages (fromto)  20282038 
Number of pages  11 
Journal  Optics Communications 
Volume  285 
Issue number  8 
DOIs 

Publication status  Published  Apr 15 2012 
Fingerprint
Keywords
 High numerical aperture focusing
 Multipole field
 Slepian's concentration problem
ASJC Scopus subject areas
 Electronic, Optical and Magnetic Materials
 Atomic and Molecular Physics, and Optics
 Physical and Theoretical Chemistry
 Electrical and Electronic Engineering