Open AccessScalar and electromagnetic nonparaxial bases composed as superpositions of simple vortex fields with complex foci
Author(s) -
Rodrigo Gutiérrez-Cuevas,
Miguel A. Alonso
Publication year - 2017
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.25.014856
Subject(s) - orthogonality , scalar (mathematics) , vortex , simple (philosophy) , electromagnetic field , physics , basis (linear algebra) , orthogonal polynomials , scalar field , focus (optics) , optics , mathematical analysis , classical mechanics , mathematics , quantum mechanics , geometry , philosophy , epistemology , thermodynamics
We derive bases constructed from simple vortices and complex focus fields and show that they are useful in the description of strongly focused fields. Both scalar and electromagnetic fields are considered, and in each case two types of basis are discussed: bases that use standard polynomials but whose orthogonality condition requires a non-uniform directional weight factor, and bases that are orthogonal with uniform weight but that require new polynomials. Their performance is studied by fitting prescribed fields, where it is seen that the accuracy provided by both types of bases is comparable.