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Publication# Multipolar origin of electromagnetic transverse force resulting from TE/TM wave interference

Abstract

In this paper, we aim at unveiling the underlying physical mechanism for transversal optical forces, appearing due to the simultaneous illumination of a spherical object with two plane waves possessing different polarizations. The appearance of such a transversal force is quite counterintuitive since it seems to contradict the law of momentum conservation. We consider the cases of perfect electric conductor (PEC) and silver spheres illuminated by two orthogonally polarized plane waves propagating obliquely with respect to each other. Interestingly, the Poynting vector in these cases acquires a nonzero component transverse to the plane of propagation. Since the momentum transfer is related to the energy transfer, or equivalently, to non-negligible Poynting vector pointed in a particular direction, an arbitrary object placed in such external field is expected to experience a transversal force. To cast light upon this peculiar effect, we use a surface integral equation method and, along with the Maxwell stress tensor formalism, find the optical force acting on various spheres. We observe this effect for PEC spheres of different sizes and find that they are indeed subject to such transversal force. We find an explanation for this phenomenon via interference effects between selected multipoles excited in the structure. With recently developed methods, we expand the optical force into contributing pairs of selected multipoles and show that, depending on the phase between each multipole pair, the sign and direction of the force can be controlled. We also compare the results for silver and PEC spheres and find that the transversal force magnitude in silver has higher values for more limited range of sphere radii, as compared to PEC.

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Karim Achouri, Andrei Kiselev, Olivier Martin

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.