  The Lorenz-Mie scattering of a wide class of focused electromagnetic fields
off spherical particles is studied. The focused fields in question are
constructed through complex focal displacements, leading to closed-form
expressions that can exhibit several interesting physical properties, such as
orbital and/or spin angular momentum, spatially-varying polarization, and a
controllable degree of focusing. These fields constitute complete bases that
can be considered as nonparaxial extensions of the standard Laguerre-Gauss
beams and the recently proposed polynomials-of-Gaussians beams. Their analytic
form turns out to lead also to closed-form expressions for their multipolar
expansion. Such expansion can be used to compute the field scattered by a
spherical particle and the resulting forces and torques exerted on it, for any
relative position between the field's focus and the particle.
