Non-linear bistability in pulsed optical traps

Optical trapping, also known as optical tweezing or optical levitation, is a technique that uses highly focused laser beams to manipulate micro- and nanoscopic particles. In optical traps driven by high-energy pulses, material non-linearity can result in unusual opto-mechanical effects, such as displaced equilibrium points. However, existing theoretical models of non-linear optical force on small particles consider smooth material dependence on the incident field strength alone, and not the feedback between the particle permittivity and internal field strength, which is, in turn, a function of the permittivity. The hysteresis effects of optical bistability in pulsed optical traps, therefore, elude existing optical force models. Here, we investigate a bistable optical trap, set up by counter-propagating ultrashort pulses, in which the optical force exerted on a particle depends not only on the field at its current location but on the historic trajectory of the particle in the trap. The developed formalism will be important for designing optical traps and nanoparticle manipulation in pulsed field for various applications, including potentially time crystal demonstrations.