The generation of optical needle and magnetization needle with tunable longitudinal depth

Based on vector diffraction theory and inverse Faraday effect, we report on the generation of optical needle and magnetization needle with tunable longitudinal depth by focusing a narrow annulus of azimuthally polarized beams using optmagnetic materials and an elliptical mirror. In this paper, we present the expression of the approximate result between the angular thickness Δθ and the longitudinal depth when the annulus is assumed to be sufficiently narrow (Δθ<<π/2). We theoretically demonstrate that the induced magnetization needle has the same longitudinal depth as optical needle, but with different distributions. The results are applied to the specific cases of the elliptical mirror and the parabolic mirror, then we further theoretically demonstrate that the longitudinal depth is equally long in the elliptical mirror focusing system and the parabolic mirror focusing system.