Dynamics of optical forces and torques in plasmonic systems: a surface integral equation

A novel approach is introduced to determine the time evolution of optical forces and torques on arbitrary shape nanostructures by combining Maxwell's stress tensor with the surface integral equation method (SIE). Conventional time averaging of Maxwell’s stress tensor allows obtaining an elegant form in terms of surface currents for the force exerted on nanostructures. Unfortunately, the information about the time dependence of the force – which can be very important in ultrafast photonics experiments and in nano-manipulation applications – is lost in such an approach. To overcome this, we have developed a time-domain method based on the inverse Fourier transform of the frequency-domain SIE. The calculations in the frequency domain allow accurately taking into account the dispersion of the permittivity function of the system and the use of surface currents enables the rigorous treatment of intricate geometries for the scatterer. Furthermore, the integration of Maxwell’s stress tensor directly on the scatterer’s boundary significantly reduces the required computation time and increases the accuracy of the method. We show quite unusual sum frequency-like terms in the dynamics of the force appearing in Maxwell’s stress tensor, which normally vanish for the time-averaged force. To illustrate this effect, we study how the pulse duration influences the dynamics of optical force in the case of a rectangular shape and Gaussian pulses illuminating thin film at normal incidence. In the framework of the developed numerical method, we study the influence of the sum-frequency-like terms on the dynamics of optical forces in the case of a spherical scatterer.