Abstract
We present an efficient method for determining the T-matrix of axisymmetric particles using the finite element method (FEM) in conjunction with an analytical approach that expands the scattered field using vector spherical harmonics (VSHs). To tailor the response of nanoparticles under complex optical field excitation, we design the incident field based on the T-matrix, which comprehensively describes the relationship between the incident and scattered fields. The sensitivity of scattering field to environmental refractive index can be effectively controlled by introducing the concepts of principal modes (PMs) and anti-principal modes (anti-PMs), which used to be utilized to control frequency dispersion of multi-channel light scattering. Our approach diverges from previous research by emphasizing the manipulation of refractive index sensitivity in Mie particles, rather than focusing on controlling scattering response in the frequency domain. Additionally, we employ an inverse design method to determine the light field distribution on the entrance pupil plane, which can be used to generate the designed PMs and anti-PMs after tightly focusing by high-NA objective. This work presents new degrees of freedom for controlling light-matter interactions in modern optics It is expected to find wide-ranging applications in the fields of optical sensing and measurement.