Tailoring photonic forces on a magnetodielectric nanoparticle with a fluctuating optical source

We address the forces exerted by the random electromagnetic field emitted by a fluctuating optical source on a kind of dielectric nanoparticles that have arisen much interest because of their recently shown magnetodielectric behavior. The illumination with light, or other electromagnetic wave, of a given state of coherence allows us to create photonic forces, a particular case of which are optical analogous to the Casimir-Polder and van der Waals forces, as well as of thermal forces out of thermodynamic equilibrium. This leads to a deeper understanding of the conditions and limitations under which some theories of these forces were established. We also study the effects of the coherence length and of sharp changes in the particle differential scattering cross section due to Kerker minimum forward or zero backward conditions. We show how the nanoparticle Mie resonances, constituted by the induced electric and magnetic dipoles, lead to long distance attractions to the source, as well as to the possible predominance of magnetic forces. In addition, it is shown how, by manipulating the fluctuating source, either pushing or tractor beams are obtained, even in the far zone. These effects are specially relevant when quasimonochromatic emission is employed, and manifest the possibility of performing a monitoring of these mechanical interactions, in particular by a photonic analogy of those aforementioned classical thermal forces. This opens paths to nanoparticle ensembling and manipulation. The influence of the excitation of surface waves of the source is also considered.