Tightly autofocusing beams along the spherical surface

We theoretically demonstrate different propagation trajectories of tightly autofocusing beams (TABs) along the spherical surface. The generalized expression of the TAB with spherical trajectory is given based on the nonparaxial accelerating Bessel beam. The effect of the spherical trajectory on the focusing performance of the TAB is analyzed. It reveals that the focal field with strong longitudinally polarized component and sub-diffraction-limit focal spot can be further enhanced by shortening the focal length of TAB. Theoretically, the minimum size of the focal spot can be close to 0.096λ2, and the proportion of longitudinal field can go up to 98.36%.