Axial optical trap stiffness influenced by retro-reflected beam

We studied experimentally how the beam retro-reflected from a planar interface (microscope slide) influences the axial stiffness of a single beam trap. Since the incident and retro-reflected beams interfere, weak intensity maxima and minima form a standing wave superposed on the axial single focused beam intensity envelope. Therefore there exists competition between the single beam trap and the weak standing wave traps. It results in microsphere hops to a new stable position at certain distances of the beam focus from the retro-reflecting surface. We analysed the behaviour of two polystyrene spheres of different sensitivities to the weak standing wave (diameters 690 and 820 nm) placed close to surfaces with different reflectivities (common glass R = 0.4% and reflective coating R = 13%). We used quadrant photodiode placed in a back focal plane of the microscope objective to track the position of the particle trapped in the single beam trap. Analyses of the thermal motion of trapped bead provided trap stiffnesses at different distances of the beam focus from the retro-reflecting surface and it also revealed a non-harmonic shape of the axial potential profile at the distances where the bead hops. We compared the experimental results with theoretical simulations based on Lorentz-Mie scattering theory.