Plasmon-induced Lorentz forces of nanowire chiral hybrid modes

The light-induced motion of plasmonic materials differs fundamentally from that of dielectric media. We demonstrate that significant translation and torque arise via Lorentz forces and surface-bound currents when linearly-polarized light illuminates metallic nanowires. Optical trapping of plasmonic nanoparticles may provide great insight to light-matter interactions at the nanoscales yet the ability to trap arbitrary shaped nanoparticles present difficulty unlike dielectric media, in which the forces governing the motion are well understood. The mechanical forces on metallic nanostructures associated with surface currents are widely overlooked and point to a new family of plasmonically-driven processes [1, 2]. Here, we study plasmon-induced forces on metal nanowires, which are significant with the presence of chiral hybrid plasmon modes at longer wavelengths between longitudinal and transverse absorption resonances. Plasmonic activity underlies the mechanism that leads to nanowire rotation and explain prior experimental results [3-5]. We find that the presence of chiral hybrid plasmon modes yields the greatest net translation and torque forces when nanowires are illuminated with linearly-polarized light. The asymmetric plasmon behavior subsequently affects the complex nonlinear dynamics of plasmonic nonspherical nanoparticles in fluids. We examine the behavior with numerical simulations of a gold nanowire illuminated with linearly-polarized light at different orientations of a 1025nm-long, 75nm diameter gold nanowire in water. The time-averaged Lorentz force per volume is attributed to electric and magnetic fields: 〈f〉 = ε0(∇ ∙ E)E ∗ + J × B + c. c. = fE + fM (1) Where E is the electric field, and B is the magnetic, ρ is the charge density, v is the velocity of the electron gas, ε0 is the permittivity of free space, J is the current density. The net torque on a nanowire is calculated from the cross product of the radial distance from the origin and fEor fM as contributions from the electric dipole and surface currents respectively. Figures 1(a-c) shows the distribution of the Lorentz force [Eq. 1] on the surface of the nanowire at 3 different orientations when the illuminating wavelength is 1071nm; at different orientations, different chiral hybrid modes are present. Momentum is conserved in the system by scattering and absorption of the incident light. Directional reflection via oblique incidence produces translational motion. Due to the lossy nature of plasmonic materials in the optical regime the nanowire can be treated as a lossy Fabry-Perot cavity in which light couple in to one terminus of the nanowire and propagates the length, losing intensity, resulting in an asymmetrical profile. This loss of the propagating longitudinal mode coupled with the asymmetric nature of the chiral hybrid plasmon mode results in asymmetric force that can lead to significant translational and/or rotational motion that is an order of magnitude stronger larger than optical trapping forces. A phase portrait of the rotational motion of a nanowire can be computed from the torque around the respective axes. They exhibit complex and rich dynamics associated with chiral hybrid modes excited on metallic nanowires; orientations show stable, unstable, saddle points and even stable limit cycles that lead to and explain the complicated motion observed experimentally. Forces that arise from the surface currents in metallic nanowires are greater in magnitude than those produced from the electric field acting on the charge density. The Lorentz force produced from the electric field is consistent with the motion of dielectric nanoparticles that align perpendicular to incident polarization. The forces from the magnetic field acting on the surface currents are significantly stronger and lead to the highly nonlinear and complicated motion observed experimentally such as spinning, rocking and rapid reversals. Our model also identifies correctly the equilibrium orientations as well as stable limit cycles. In conclusion we have shown that plasmonically-induced Lorentz forces in metallic nanowires are fundamentally different from the optical trapping forces that lead to stable controlled behavior of dielectric media. Surface-bound plasmon currents interacting with the magnetic field dominate the Lorentz force that explains the complex dynamics associated with metallic nanowires in optical traps. Our work points to novel methods that manipulate conducting nanoparticles that do not result in the extreme absorption and heating generally associated with the excitation of plasmons. References [1] M. Moocarme et al., “Plasmon-induced Lorentz forces of nanowire chiral hybrid modes,” Optical Materials Express 4, 2355-2367 (2014). [2] N. Horiuchi “Research highlights (optomechanics) Plasmonic Lorentz force,” Nature Photonics 8, 880 (2014). [3] L. Tong et al., “Alignment, rotation, and spinning of single plasmonic nanoparticles and nanowires using polarization dependent optical forces ,” Nano Letters 10, 268-273 (2010). [4] C. Selhuber-Unkel et al., “Quantitative optical trapping of single gold nanowires,” Nano Letters 8, 2998-3003 (2008). [5] Z. Yan et al., “Why single beam optical tweezers trap gold nanowires in three dimension,” ACS Nano 7, 8794-8800 (2013). Fig. 1. Forces on the nanowire surface produced by the surface currents (red arrows) and the norm of the surface magnetic field (surface colormap) for oblique geometries that excite the chiral hybrid plasmonic mode, where (a) θ = 15◦, φ = 90◦, (b) θ = 30◦, φ = 75◦, (c) θ = 60◦, φ = 60◦ at λ = 1071nm. (d) The calculated azimuthal torque, T, as a function of azimuthal coordinate associated with electric dipole (dashed) and plasmons (solid).

Optical trapping of plasmonic nanoparticles may provide great insight to light-matter interactions at the nanoscales yet the ability to trap arbitrary shaped nanoparticles present difficulty unlike dielectric media, in which the forces governing the motion are well understood.The mechanical forces on metallic nanostructures associated with surface currents are widely overlooked and point to a new family of plasmonically-driven processes [1,2].
Here, we study plasmon-induced forces on metal nanowires, which are significant with the presence of chiral hybrid plasmon modes at longer wavelengths between longitudinal and transverse absorption resonances.Plasmonic activity underlies the mechanism that leads to nanowire rotation and explain prior experimental results [3][4][5].We find that the presence of chiral hybrid plasmon modes yields the greatest net translation and torque forces when nanowires are illuminated with linearly-polarized light.The asymmetric plasmon behavior subsequently affects the complex nonlinear dynamics of plasmonic nonspherical nanoparticles in fluids.
We examine the behavior with numerical simulations of a gold nanowire illuminated with linearly-polarized light at different orientations of a 1025nm-long, 75nm diameter gold nanowire in water.The time-averaged Lorentz force per volume is attributed to electric and magnetic fields: Where E is the electric field, and B is the magnetic, ρ is the charge density, v is the velocity of the electron gas, ε 0 is the permittivity of free space, J is the current density.The net torque on a nanowire is calculated from the cross product of the radial distance from the origin and   or   as contributions from the electric dipole and surface currents respectively.
Figures 1(a-c) shows the distribution of the Lorentz force [Eq.1] on the surface of the nanowire at 3 different orientations when the illuminating wavelength is 1071nm; at different orientations, different chiral hybrid modes are present.Momentum is conserved in the system by scattering and absorption of the incident light.Directional reflection via oblique incidence produces translational motion.Due to the lossy nature of plasmonic materials in the optical regime the nanowire can be treated as a lossy Fabry-Perot cavity in which light couple in to one terminus of the nanowire and propagates the length, losing intensity, resulting in an asymmetrical profile.This loss of the propagating longitudinal mode coupled with the asymmetric nature of the chiral hybrid plasmon mode results in asymmetric force that can lead to significant translational and/or rotational motion that is an order of magnitude stronger larger than optical trapping forces.
A phase portrait of the rotational motion of a nanowire can be computed from the torque around the respective axes.They exhibit complex and rich dynamics associated with chiral hybrid modes excited on metallic nanowires; orientations show stable, unstable, saddle points and even stable limit cycles that lead to and explain the complicated motion observed experimentally.
Forces that arise from the surface currents in metallic nanowires are greater in magnitude than those produced from the electric field acting on the charge density.The Lorentz force produced from the electric field is consistent with the motion of dielectric nanoparticles that align perpendicular to incident polarization.The forces from the magnetic field acting on the surface currents are significantly stronger and lead to the highly nonlinear and complicated motion observed experimentally such as spinning, rocking and rapid reversals.Our model also identifies correctly the equilibrium orientations as well as stable limit cycles.
In conclusion we have shown that plasmonically-induced Lorentz forces in metallic nanowires are fundamentally different from the optical trapping forces that lead to stable controlled behavior of dielectric media.Surface-bound plasmon currents interacting with the magnetic field dominate the Lorentz force that explains the complex dynamics associated with metallic nanowires in optical traps.Our work points to novel methods that manipulate conducting nanoparticles that do not result in the extreme absorption and heating generally associated with the excitation of plasmons.