Transfers of the OAM and SAM densities of Bessel beam into the orbital and spin torques upon gold nanorod

Abstract

The optomechanical interplay of a Bessel beam (an optical vortex) with a gold nanorod (GNR) in water is theoretically studied. The optical force and torque exerted on the GNR are analyzed using Maxwell's stress tensor to investigate the transfer rates of the orbital angular momentum (OAM) and the spin angular momentum (SAM) densities of Bessel beam into the orbital and spin torques upon GNR, respectively. From the numerical analysis, we find that the ratio of the orbital torque to the spin torque on the GNR matches the ratio of OAM to SAM of Bessel beam, corresponding to the order (topological charge) of the Bessel beam. This is to say that the transfer rate of the OAM density of Bessel beam into the orbital torque exerted on GNR nearly equals that of the SAM density into the spin torque. It implies that the spin-orbit interaction (SOI) of the optical vortex beam via a GNR is very weak. In addition, the spin torque is nearly equal to the corresponding zilch torque, the surface integral of Lipkin's zilch stress tensor. This could be because a GNR can be regarded as a perfect electric dipole particularly when the wavelength of the incident light is close to and little longer than the longitudinal surface plasmon resonance of GNR; the dipole's orientation is along the long axis of GNR. In contrast, the SOI via a spherical gold nanoparticle (GNP) is strong due to no preferred orientation for the equivalent dipole; a part of SAM of the optical vortex is transferred to the orbital torque upon GNP. Our results demonstrate that GNR, functioning as an ideal electric dipole, is a highly effective probe for detecting the OAM and SAM densities of an optical vortex individually through its distinct orbital and spin motions, without any crosstalk.