Numerical Study of Kerr Nonlinearity in Gold Nanoparticles under Dual-Wavelength Vectorial Focusing
Optical tweezers enable the non-contact trapping and manipulation of micro- and nanoparticles using highly localized optical fields, while the optical response of metallic nanoparticles is closely related to the spatial distribution, polarization state, and intensity of the focused light field. To investigate the effects of Kerr nonlinearity on vectorially focused optical fields and the optical trapping of gold nanoparticles, a three-dimensional full-wave electromagnetic model was developed in COMSOL Multiphysics. An 800 nm azimuthally polarized beam and a 532 nm left-circularly polarized beam were vectorially focused through a focusing system with a numerical aperture of 0.85 in water. Kerr nonlinearity was introduced through an intensity-dependent refractive index. The optical response of gold nanoparticles with a radius of 30 nm was described using their complex polarizability, and their optical trapping characteristics were analyzed under the electric dipole approximation. A parametric study was conducted by varying the incident electric-field amplitude to investigate the focused electromagnetic field at different excitation intensities. The simulation results show that as the incident field strength increases, the local electric-field amplitude increases significantly, while the spatial distribution of the focused optical field also undergoes pronounced changes. The position and spatial extent of the high-field region, the axial extension of the focal field, and the local multi-peak features all vary with excitation intensity. These results indicate that, in the presence of Kerr nonlinearity, the focused field is not simply an amplitude-scaled version of the corresponding linear field distribution, but instead exhibits pronounced intensity-dependent spatial reconstruction. By varying the incident field strength, the spatial distribution of the dual-wavelength vectorially focused optical field can therefore be controlled via Kerr nonlinearity, providing a numerical basis for tunable nonlinear optical trapping of gold nanoparticles.
