We achieve long-range and continuous optical pulling in a periodic photonic crystal background, which supports a unique Bloch mode with the self-collimation effect. Most interestingly, the pulling force reported here is mainly contributed by the intensity gradient force originating from the self-induced backaction of the object to the self-collimation mode. This force is sharply distinguished from the widely held conception of optical tractor beams based on the scattering force. Also, this pulling force is insensitive to the angle of incidence and can pull multiple objects simultaneously.
Phys. Rev. Lett. 2018
a) Schematic of the optical pulling force enabled by the SC mode in a PC. The upper inset shows the intensity envelopes across the SC mode axis without (gray dashed line) and with (red solid line) the object. The green ellipse shows the object. (b) Detailed structure of the square lattice (lattice constant a) PC and the object. The parameters are na=3.4, nb=1.33, no=1.5, r=0.1a, and semiaxes of rx and ry.(c) The second band in the reduced Brillion zone for the TM mode (electric field perpendicular to the xy plane). For ω=0.5(2πc/a), the equifrequency contour is square, which is the distinguishing characteristic of the SC mode.(d) SC mode propagation analysis when a light beam is incident on the PC. Here, kin,r,t (vin,r,t, θin,r,t) are the wave vectors (group velocities, angles) of the incident, reflected, and transmitted beams, respectively. (e) Distribution of Ez(x,y) for the SC mode when excited by a Gaussian beam at normal incidence. The small circles show the position of the PC rods.