Figure 2
From: Enhancement of the ‘tractor-beam’ pulling force on an optically bound structure
(a) Stable configurations of the particle pair. The first particle is placed at the origin of the coordinate system (big black dot), and the steady-state positions of the second particle are marked by yellow dots. The calculated optical intensity is shown as the background. Due to the interference between the incident and reflected beam, the horizontal interference fringes are formed. As the result of the interference between the incident and scattered light, the intensity lobes are formed, and their maxima are highlighted by thin solid white curves. The y axis is normalized to the length of two fringes λSW=λm/cosα. (b) The total force F2,z acting upon the second particle can be written as F2,z=Fisol2,z+Fint2,z, where the force Fisol2,z acts on the particle if the first particle is absent (denoted by unfilled black arrows), and Fint2,z denotes the interaction force due to the presence of the first particle (filled black arrows). The open gray circles denote stable configurations that were not studied here. (c and d) The direction of the interaction force Fint,z, which determines the total tractor force, is given by the position of particles with respect to the scattering lobe maxima. (c) In the formed optically bound structures, the particles are localized on the left-hand side of the lobe maxima and pulled toward the runaway lobe maximum. Analogously for pushing in d, where the bound particles are pushed toward the lobe intensity maximum. The color of the lobe pattern follows the color of the particle. (e–h) Plots compare the calculated optical intensity profiles along the z axis (filled green/red), their gradients along the z axis (thin green/red) and the optical forces (full black) acting on the particular particle. The particles are drawn at the positions corresponding to the stable equilibrium configuration of the particle pair. See Supplementary Media 2 for more details. Parameters of the calculations: λm=400 nm, incident angle of the S-polarized tractor beam α=2.15 °, polystyrene particles with an 820-nm diameter.
