Multipolar origin of electromagnetic transverse force resulting from TE/TM waves interference

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.