Optical forces on an oscillating dipole near VO$_2$ phase transition

We investigate optical forces on oscillating dipoles close to a phase-change vanadium dioxide (VO$_2$) film, which exhibits a metal-insulator transition around $340$ K and low thermal hysteresis. This configuration is related to one composed of an excited two-level quantum emitter and we employ a classical description to capture important aspects of the radiation-matter interaction. We consider both electric and magnetic dipoles for two different configurations, namely, with the dipole moments parallel and perpendicular to the VO$_2$ film. By using Bruggeman theory to describe the effective optical response of the material, we show that, in the near-field regime, the force on the dipoles can change from attractive to repulsive just by heating the film for a selected frequency range. We demonstrate that the thermal hysteresis present in the VO$_2$ transition clearly shows up in the behavior of the optical forces, setting the grounds for alternative approaches to control light-matter interactions using phase-change materials.