Tunability of double foci of a circular Airyprime beam achieved by a movable thin convex lens

The circular Airyprime beam (CAPB) is a Janus wave that, in the absence of a lens, has mirrored real focus and virtual focus in free space propagation. Under the action of a thin convex lens, its double foci are directly observed, denoted as foci 1 and 2, which are the images of the real and virtual foci through the lens, respectively. This paper proposes a scheme to determine the placement position of the thin convex lens through the lens imaging formula, and quantitatively analyzes the positions of foci 1 and 2, as well as the variation rules of their focusing abilities. Compared to the real focus, the strongest focusing ability of one of the double foci can be enhanced to more than tenfold, with the upper limit of enhancement depending on the focal length of the thin convex lens. The tunability of position and focusing ability for double foci can be effectively achieved by moving the lens. What's even more interesting is that when the sum of the two positions of the lens is twice the focal length of the lens, the focal spots of foci 1 and 2 are interchangeable. The tunability of double foci by moving the lens is successfully demonstrated in experiment. Double foci double the stable equilibrium points for capturing Rayleigh particles, and the tunability of double foci allows for a wider range of Rayleigh particles to be captured. Therefore, the tunability of double foci of a CAPB through the movement of a lens is expected to be applied in many scenarios.