Efficient Prediction and Analysis of Optical Trapping at Nanoscale via Finite Element Tearing and Interconnecting Method

Abstract

Numerical simulation plays an important role for the prediction of optical trapping based on plasmonic nano-optical tweezers. However, complicated structures and drastic local field enhancement of plasmonic effects bring great challenges to traditional numerical methods. In this article, an accurate and efficient numerical simulation method based on a dual-primal finite element tearing and interconnecting (FETI-DP) and Maxwell stress tensor is proposed, to calculate the optical force and potential for trapping nanoparticles. A low-rank sparsification approach is introduced to further improve the FETI-DP simulation performance. The proposed method can decompose a large-scale and complex problem into small-scale and simple problems by using non-overlapping domain division and flexible mesh discretization, which exhibits high efficiency and parallelizability. Numerical results show the effectiveness of the proposed method for the prediction and analysis of optical trapping at nanoscale.

Plasmonic Optical Tweezers for Particle Manipulation: Principles, Methods, and Applications

“…For harmonic electromagnetic fields, the time-averaged Maxwell stress tensor can be expressed as , Hence, the optical force of an object in electromagnetic field can be written as , where n is the unit normal vector to the particle surface. Then the trapping potential energy for a particle located at r 0 can be obtained as follows: , This is a very important figure of merit to define the stableness of an optical trap which has been used in numerous investigations. − When other forces are not considered, the depth of the potential well should satisfy exp­(− U / k B T ) ≪ 1 (normally U > 10 k B T is applied) to suppress the Brownian motion of a particle …”

“…For harmonic electromagnetic fields, the time-averaged Maxwell stress tensor can be expressed as 49,50 Re…”

“…Hence, the optical force of an object in electromagnetic field can be written as 49,50 where n is the unit normal vector to the particle surface. Then the trapping potential energy for a particle located at r 0 can be obtained as follows: 37,51 U r r d r F ( ) ( )…”