Single-Gaussian-beam interaction with a dielectric microsphere: radiation forces, multiple internal reflections, and caustic structures

We analyze the generation of radiation forces in the various internal reflections that occur when a tightly focused, unpolarized Gaussian beam interacts with a dielectric microsphere. The Euler transformation is used to compute the relevant axial-force vectors that are associated with the internal reflections rapidly. The net force is computed as the average of the forces generated by the s- and p-polarization components of the electric-field vector. The force characteristics are strongly dependent on the algebraic value of the index mismatch Δn at the sphere interface. For the two cases of Δn = 0.65, 0.32 with a sphere index n(2) = 1.65, the inclusion of the contributions from the second and third internal reflections after the magnitude of the effective force by at least 10%. For Δn < 0, the individual force contributions from internal reflections beyond the first are at least 4 orders of magnitude less than those of the first interaction. The caustic structures produced by the internal reflections are also profiled for both cases of Δn = ±0.32.