Calculation of radiation force on a Kerr micrometer-sized sphere due to a highly-focused laser beam: Scalar wave-optics approximation

Abstract

Previous studies have shown that a dielectric microsphere experiences a mechanical recoil arising from a highly-focused Gaussian beam. In another work, we have analyzed the interaction of a highly-focused unpolarized pulsed laser beam on a non-absorbing Kerr-type microsphere whose refractive index is linearly dependent on the intensity of the Gaussian beam. Our previous approach was reliable only in the limit where the size parameter x ≥ 100 (geometrical optics approximation), where x = 2πa/λ, a = radius of microsphere, and λ = incident wavelength. In this present paper, we derive a workable radiation force equation within the confines of scalar wave theory, which will allow us to extend our analysis to the case where x ≥ 2π (diffraction limit analysis).
We first obtain a general EM field solution and then relate these field expressions for the incident, scattered, and internal EM fields by applying boundary conditions at the surface of the Kerr microsphere. The EM field inside the weakly nonlinear medium is iteratively calculated through a Rylov approximation. We can now write the component F_x, F_y and F_z of the radiation force on the sphere as a surface integral of the spatial components of T_1k of the EM energy-momentum tensor T_μν.