Calculation of radiation forces on an expanding ellipsoidal polystyrene illuminated by a focused Gaussian beam
Kristine Faith J. Roque ^{1*}, Giovanni A. Tapang^{1}, Caesar A. Saloma^{1}^{1}National Institute of Physics, University of the Philippines, Diliman, Quezon City, Philippines* presenting author:Kristine Faith Roque, email:kroque@nip.upd.edu.ph The interaction of light with matter gives rise to radiation forces which for optimal conditions enable the optical trapping of a particle in the region of the beam focus. Optical trapping using highly focused laser sources are usually employed for non-contact manipulation of biological specimens or handles. However, continuous exposure to highly focused light can cause changes in the samples like deformation and expansion due to heating which affect the resultant trapping forces. In this work we examine the effect of expansion to the axial trapping force experienced by an ellipsoidal polystyrene bead. We solve the new index of refraction of the particle after expansion using the Lorentz-Lorenz formula under the assumption that the polarizability and molecular weight do not change. We limit the calculations to a uniform expansion of the particle.
Calculations were made in the ray optics regime by modeling the beam as a Gaussian ray distribution focused by an objective. The ray-particle interactions were determined and the changes in the momentum of the reflected and refracted rays at each point of interaction were determined. The force is computed using information on the change in momentum and the incident photon rate. The net force is determined by summing the forces due to the rays. The contributions of the first eight internal reflections were considered in the net force. For the initial parameters used (λ = 632.8 nm, NA = 0.65, P = 100 mW, V _{0} = 2309.6 μm), the calculated forces are positive for both negative and positive axial displacements so the particle tends to be pushed in the +z direction. As the particle expands, the magnitude of the forces decrease and negative axial forces arise for a range of positive particle displacements. At around V = 1.5V_{0}, the force versus displacement curve becomes symmetric which suggests that the particle may be trapped at the equilibrium position (z = 0). However, further expansion causes the particle’s index of refraction to be less than the medium’s index of refraction (V = 1.75 V_{0}) so the forces flip their signs and the tendency is for the particle to be pushed away from the focus in the same direction as its displacement.Keywords: Radiation force, Geometrical optics, Ellipsoid |