A vectorial model for the nonlinear gradient force exerted on metallic Rayleigh nanoparticles

Optical tweezers have proved to be a powerful tool with a wide range of applications. The gradient force plays a vital role in the stable optical trapping of nano-objects. The scalar method is convenient and effective for analyzing the gradient force in traditional optical trapping. However, when the third-order nonlinear effect of the nano-object is stimulated, the scalar method cannot adequately present the optical response of the metal nanoparticle to the external optical field. Here, we propose a theoretical model to interpret the nonlinear gradient force using the vector method. By combining the optical Kerr effect, the polarizability vector of the metallic nanoparticle is derived. A quantitative analysis is obtained for the gradient force as well as for the optical potential well. The vector method yields better agreement with reported experimental observations. We suggest that this method could lead to a deeper understanding of the physics relevant to nonlinear optical trapping and binding phenomena.