Fig. 1. (a) Annular vortex filter composed of two annular belts with π shift radially between adjacent belts; (b) an azimuthally divided annular vortex filter with additional phase for moving the magnetization needle along the positive and negative direction of the z axis.

Fig. 2. Longitudinal magnetization distribution along the z axis at different θ1, θ2, and Δz. The green line is obtained when θ1=1.19, θ2=1.21; blue line is obtained when θ1=1.19, θ2=1.23; red line is obtained when θ1=1.17, θ2=1.21; and yellow line is obtained when θ1=1.17, θ2=1.19. (a) Δz=1.90λ; (b) Δz=1.95λ; (c) Δz=2.00λ; (d) Δz=2.05λ.

Fig. 3. Normalized longitudinal magnetization distribution along the radial direction at z=0 and z=9λ. The red line is obtained when θ1=1.17, θ2=1.21 and. The green line is obtained when θ1=1.19, θ2=1.21 and Δz=2.00λ. The FWHM in all cases are 0.27λ.

Fig. 4. Two-dimensional intensity distribution of (a) the electric field and (b) longitudinal magnetization in the longitudinal plane of the focal volume. The parameters are θ1=1.17, θ2=1.21, and Δz=1.95λ.

Fig. 5. Three-dimensional half-maximum surface of the electric field (left panel) and longitudinal magnetization needle (right panel) in the focal volume.