Brownian diffusion of nano-particles in optical traps

The effect of thermal-induced motion on nano-particles in optical traps is examined theoretically. We derive the steady-state probability density for particles trapped by evanescent waves above a surface. In particular we investigate the enhancement of the gradient force by surface plasmon resonance in a gold film and its application to trapping nano-particles in solution. An expression is derived for the lifetime of nano-particles in the trap in terms of the ratio of the trap energy to the thermal energy. It is shown that this ratio should be 10 or greater for the nano-particles to remain in the trap.