Lorenz-Mie scattering of focused light via complex focus fields: an analytic treatment

TL;DR

This paper develops an analytic framework for Lorenz-Mie scattering of complex focused light fields, enabling precise calculations of scattering, forces, and torques on spherical particles with advanced beam structures.

Contribution

It introduces closed-form expressions for complex focused electromagnetic fields and their multipolar expansions, extending nonparaxial beam models for scattering analysis.

Findings

Derived analytic expressions for complex focus fields.

Provided closed-form multipolar expansions for scattering calculations.

Enabled computation of forces and torques on particles in complex fields.

Abstract

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.