Fig. 1. Schematic of the generation of a donut-like photonic nanojet (PNJ). Incident light has circular polarization σ and topological charge m.

Fig. 2. Electric field intensity distribution |E|² of the PNJ generated by a dielectric sphere (R = λ) under illumination by left circularly polarized Laguerre–Gaussian beams with topological charges (a) m = 2 and (b) m = 0. For each case, the top plot is the |E|² of the PNJ, while the bottom one is the longitudinal intensity profile. The inset is the transverse profile with marked full width at half-maximum, corresponding to the dashed red line that crosses the maximum intensity point of the PNJ. (c) and (d) plot |E|² at the focal planes of the PNJs in (a) and (b), respectively.

Fig. 3. Longitudinal energy flow P_z at the focal plane of the PNJs generated by left circularly polarized Laguerre–Gaussian beams with (a) fixed topological charge m = 2 and refractive index n = 1.5 but different microsphere radii R; (b) fixed m = 2, R = 6λ but different n; and (c) fixed n = 1.5, R = 6λ but different m. Insets: P_z at x = 6.

Fig. 4. Energy flow of the PNJs generated by a dielectric sphere (R = 6λ, n = 1.5) illuminated by left circularly polarized Laguerre–Gaussian beams with topological charges (a) m = 2 and (b) m = 0, corresponding to Figs. 2(a) and 2(b), respectively. The blue arrows depict the forward energy flow, and the red arrows depict the reverse flow.

Fig. 5. Longitudinal component of the Poynting vector along the x axis in the focal plane of the proposed donut-like PNJ (red curve) compared to that predicted from the RW integral (blue curve). The incident light is a left circularly polarized Laguerre–Gaussian beam with topological charge m = 2. The dielectric microsphere has R = 6λ and n = 1.5, and the NA of the lens is one.