Analytical techniques for the study of focused beams

The study of nonparaxial fields through the complex focus model is discussed. This model can be used to rep- resent fields with linear, circular, elliptical, radial, azimuthal, and full Poincar´e polarizations. Other interesting beam distributions include nonparaxial Airy-Gauss beams. Further, complete bases are proposed that allow the expansion of arbitrary focused fields. The Mie scattering for any of these fields is given in closed form, for any position of the particle, allowing analytic calculations of the forces and torques. Finally, these analytic expressions lend themselves to the study of the interaction between orbital and spin angular momenta in the nonparaxial regime.

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