A multipole expansion, based on spherical harmonics, provides an efficient method for calculating the field in the focal region of a lens for radially polarized illumination, or other illumination polarization and phase distributions, including vortex beams. The multipole approach also has the benefit of providing a simple measure of the purity of the longitudinal field mode. The method is also convenient for calculation of fields scattered by particles and calculation of optical trapping forces.
© 2012 Optical Society of America
Diffraction and Gratings
Original Manuscript: September 15, 2011
Manuscript Accepted: October 9, 2011
Published: December 7, 2011
Vol. 7, Iss. 3 Virtual Journal for Biomedical Optics
Thanh Xuan Hoang, Xudong Chen, and Colin J. R. Sheppard, "Multipole theory for tight focusing of polarized light, including radially polarized and other special cases," J. Opt. Soc. Am. A 29, 32-43 (2012)