Gradient force acting from a Gaussian light beam on a dielectric transparent microsphere: Rayleigh–Gans approximation

Abstract

An expression for the gradient force acting in a Gaussian beam of optical radiation on a transparent dielectric microsphere is derived within the Rayleigh–Gans approximation, which imposes a constraint on the phase shift of the wave as it passes through the microsphere. The approximation of an undamped beam is assumed. The inhomogeneity of the incident radiation within the microsphere is taken into account. The resulting expression for the gradient force in the Rayleigh–Gans approximation reduces to the known expressions for the gradient force in the Rayleigh approximation. The expression for the gradient force is radially symmetric, regardless of the direction of light wave polarization in the beam cross section. It is shown that for particles satisfying the Rayleigh–Gans approximation, the gradient force acting in the transverse direction of the beam is smaller than the gradient force calculated in the Rayleigh approximation. This difference increases with increasing particle size.

A correction factor for the Rayleigh–Gans theory is computed as a function of twice the square of the ratio of the microsphere radius to the light beam radius. It is shown that even for a microsphere radius of 3.5 wavelengths, the gradient force in the Rayleigh–Gans approximation is half that in the Rayleigh approximation.