Modeling Rotational Equilibrium in Nanoparticle-Light Interactions

Light exerts optical forces on materials it illuminates, causing both rotation and translation of anisotropic dipolar nanoscale particles when in the path of an arbitrarily polarized laser beam. We find that below a certain polarization ellipticity threshold, anisotropic nanoparticles of arbitrary composition find a rotational equilibrium along the major axis of the polarization ellipse. We derive the force exerted on the particle at rotational equilibrium, expressing in terms of the two well-known contributions: the intensity gradient force that traps the particle where the light is most intense, and the phase gradient scattering force, which translates the particle in the direction of the beam's phase flow. We plot the translational force as a function of the light's polarization ellipticity at all possible equilibrium conditions, finding analytic expressions for the polarization ellipticities where the particle experiences its maximum and minimum translational velocities. Applying this model to the case of a weakly focused 1 mW 420 nm laser impinging upon an ellipsoidal gold nanoparticle, our model predicts a maximum translational velocity of around 10 microns/second when submerged in water. Our model suggests an experimental method of measuring the absorption properties of particles of anisotropic shape by comparing their maximum and minimum velocities at a given wavelength of illumination.