Efficient Method for the Electrodynamics Langevin-Dynamics Simulation of Multiple Nanoparticles Based on the Coupling Theory of Quasinormal Mode

We propose an efficient method for simulating the motion of multiple nanoparticles under light-field excitation. By exploiting a recently reported method based on the coupling theory of quasinormal mode (QNM) for an efficient electrodynamics (ED) calculation of optical force, this method can achieve a fast Langevin dynamics (LD) simulation of multiple nanoparticles, which incorporates not only the routinely considered optical force, viscous resistance and Brownian motion of nanoparticles but also the electrostatic double-layer force between particles. Compared to the ED-LD methods that rely on full-wave numerical calculations of optical force (such as the finite element method), our method has the advantage that when changing the particle positions, the incident light distribution or the wavelength, the employed QNM-coupling theory does not need to repetitively solve Maxwell's equations, but only needs to perform analytical calculations of the QNM-expansion coefficients to obtain the electromagnetic field required for calculating optical force, which significantly reduces computation time by at least 2 orders of magnitude while maintaining accuracy. The high computational efficiency of our method makes it possible for simulations that are difficult for the full-wave numerical methods. For example, by simulations with a large number of time steps, multiple repetitive simulations, or simulations involving a large spatial range and a large number of particles, this method can predict the probability distributions of positions, the probability of path selection, or the controlled motion for gold nanoparticles. The proposed method and results can be used for an efficient design of optical tweezers with various applications.