Fast Calculation Method And Analysis Of The Optical Force Based On The Quasinormal Mode Theory

Optical tweezers can use the laser to hold or move micro-nano particles.As a precise and contactless experimental technique,they have been widely used in many fields such as optical manipulation,force transducers,biology science,and laser cooling.The general approach to evaluate the optical force on a mesoscopic particle is integrating the Maxwell stress tensor(MST)over a surface enclosing the particle.However,the traditional numerical calculation methods such as FEM or FDTD are generally time-consuming to solve the electromagnetic field.To improve the computational efficiency,a semi-analytical method for the calculation of the optical forces based on QNM theory is proposed.QNMs are the eigensolutions of source-free Maxwell’s equations at complex frequencies and satisfy the outgoing-wave condition at infinity.The presented calculation method assumes that the electric field distribution is divided into a background field and a scattered component.The scattered field distribution is expressed as a linear combination of a series of QNMs.And the background field distribution is calculated using diffraction theory or full-wave computations.Optical force is then obtained through the integration of the MST.We first propose an efficient method for the calculation of the optical force of a single nanoparticle based on the QNM expansion.For a single particle in a homogeneous space,the background field(ie,the incident field)in the absence of particles can be calculated analytically using the diffraction theory.Once a few dominant QNMs have been calculated by numerically solving the Maxwell equations,the optical force can be calculated analytically when varying the particle’s location,frequency,or polarization of the illumination without repeatedly solving the Maxwell equations.This advantage is not available in traditional optical force calculation methods.This method still works for single particles on substrates(such as metal or glass),where the background field needs to be calculated numerically.The dependence between the optical force of a single micro-nano particle and the position is analyzed using this method.And the results of the optical force analysis are experimentally verified.Secondly,this paper proposes a fast method for the optical force of multiple micro-nano particles based on the QNM coupling theory.As long as the QNMs of each particle are obtained by numerically solving the Maxwell equations,the optical force can be calculated analytically without repeatedly solving the Maxwell equations when changing the particle spacing,incident light frequency,or,polarization state.This advantage is also not available in traditional optical force calculation methods.Compared with the QNM expansion theory,the QNM coupling theory expands the scattering field of the multi-particle system with the QNMs of each particle,which avoids the repeated solution of the QNMs for the multi-particle system when the particle gap changes.The proposed method is suitable for the calculation of multi-particle optical force in a uniform space or in the presence of a substrate.In summary,two kinds of methods based on the QNM theory are proposed for a fast calculation of the optical force of single particle and multiple particles.The calculation results and time of the fast method based on the QNM theory proposed in this paper are compared with the finite element method(implemented by the commercial software COMSOL Multiphysics),verifying the calculation accuracy and efficiency of the method.This method is especially suitable for optical force calculation that requires a large number of sampling points of micro-nano particle positions and can provide an efficient numerical analysis tool for optical force-related applications(such as plasmonic tweezers and photoinduced force microscopy).