On the physical realizability of highly focused electromagnetic field distributions.

A method to evaluate the physical realizability of an arbitrary three-dimensional vectorial field distribution in the focal area is proposed. A parameter that measures the similarity between the designed (target) field and the physically achievable beam is provided. This analysis is carried out within the framework of the closest electromagnetic field to a given vectorial function, and the procedure is applied to two illustrative cases.

[1]  Nir Davidson,et al.  High-numerical-aperture focusing of radially polarized doughnut beams with a parabolic mirror and a flat diffractive lens. , 2004, Optics letters.

[2]  Susumu Noda,et al.  Sub-wavelength focal spot with long depth of focus generated by radially polarized, narrow-width annular beam. , 2010, Optics express.

[3]  Rosario Martínez-Herrero,et al.  Characterization of Partially Polarized Light Fields , 2009 .

[4]  F Kenny,et al.  Complete polarization and phase control for focus-shaping in high-NA microscopy. , 2012, Optics express.

[5]  S. Khonina,et al.  Controlling the contribution of the electric field components to the focus of a high-aperture lens using binary phase structures. , 2010, Journal of the Optical Society of America. A, Optics, image science, and vision.

[6]  Colin J R Sheppard,et al.  Annular pupils, radial polarization, and superresolution. , 2004, Applied optics.

[7]  S Bosch,et al.  Vectorial structure of nonparaxial electromagnetic beams. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[8]  E. Wolf,et al.  Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system , 1959, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[9]  Xu Liu,et al.  Phase encoding for sharper focus of the azimuthally polarized beam. , 2010, Optics letters.

[10]  Luping Shi,et al.  Creation of a needle of longitudinally polarized light in vacuum using binary optics , 2008 .

[11]  G Leuchs,et al.  Sharper focus for a radially polarized light beam. , 2003, Physical review letters.

[12]  Shunichi Sato,et al.  Sharper focal spot formed by higher-order radially polarized laser beams. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[13]  Uriel Levy,et al.  Effect of radial polarization and apodization on spot size under tight focusing conditions. , 2008, Optics express.

[14]  Jianping Ding,et al.  Polarization structuring of focused field through polarization-only modulation of incident beam. , 2010, Optics letters.

[15]  B. Hecht,et al.  Principles of nano-optics , 2006 .