Self-induced back-action for aperture trapping: Bethe-Rayleigh theory

A dielectric (nano)particle can influence the local electromagnetic field and thereby alter its interaction with that field through the process of self-induced back-action. While this phenomenon is usually considered theoretically as a change in a cavity resonance frequency, such theoretical approaches are not as appropriate when considering systems away from resonance, such as with a subwavelength aperture in a metal film. Here we consider the interaction between an aperture, modelled with Bethe theory as a magnetic dipole, and a Rayleigh particle, modelled as an electric dipole. Using this magnetic dipole - electric dipole interaction, we quantify the self-induced back-action of the particle on the aperture transmission and the optical trapping potential. The model shows quantitative agreement with finite-difference time-domain simulations. This shows that the physics of self-induced back-action for an aperture and a nanoparticle can be understood in terms of dipole-dipole coupling.