Dynamical and phase-diagram study on stable optical pulling force in Bessel beams

Based on the generalized Lorenz-Mie theory and Maxwell stress tensor formulism, we calculate the transverse force constant matrix and perform a linear stability analysis on a spherical particle that is subject to negative longitudinal optical force (NLOF) under the illumination of Bessel beams. Phase diagrams with respect to the material parameters are presented, which exhibit the possibility of the appearance of NLOF. From dynamical simulations of the particle performed both in the transverse plane and along the longitudinal direction, an even clearer picture of the realization of stable NLOF is presented. It is shown that, due to rotation induced by the orbital angular-momentum of light, higher order Bessel beams cannot stably confine a particle to the beam center where NLOF occurs in the absence of ambient damping, which largely limits their applications for long-distance, stable, backward particle transportation. On the other hand, zero-order Bessel beams can achieve stable transverse confinement of the manipulated particle and act as an optical tractor beam per se. In addition, for a nonmagnetic particle with relative permeability mu = 1, a Bessel beam with transverse electric polarization is more favorable for the realization of NLOF than a transverse magnetic beam. Finally, a brief discussion is also presented of the conditions under which an off-beam-axis particle could be suitable for backward transportation using NLOF.