First-order nonconservative motion of optically trapped nonspherical particles

Stephen H. Simpson and Simon Hanna

It is well known that optical force fields are not conservative. This has important consequences for the thermal motion of optically trapped dielectric spheres. In particular, the spheres do not reach thermodynamic equilibrium. Instead, a steady state is achieved in which the stochastic trajectory contains an underlying deterministic bias toward cyclic motion, and the energy of the sphere deviates from that implied by the equipartition theorem. Such effects are second order and only observed at low trap powers when the sphere is able to explore regions of the trap beyond the linear regime. Analogous effects may be expected for particles of less than spherical symmetry. However, in this case the effects are first order and depend on the linear term in the optical force field. As such they are not suppressed by increases in beam power, although the frequency and amplitude of the cyclic motion will be affected by it. In this paper, we present an analysis of the first-order nonconservative behavior of nonspherical particles in optical traps. The analysis is supported by optical force calculations and Brownian dynamics simulations of dielectric microrods held vertically in Gaussian optical traps.

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