Generation of three-dimensional dark spots with a perfect light shell with a radially polarized Laguerre-Gaussian beam

The theoretical analyses in this paper show that a highly focused double-ring radially polarized Laguerre-Gaussian beam with a topological charge of 1 (R-LG(11)) can generate a small three-dimensional (3D) dark spot surrounded by an almost 100% uniform light shell in all directions. The cleanness and size of the 3D dark spot, the uniformity and strength of the light shell surrounding the dark spot, and the light efficiency all depend on the truncation parameter β of the R-LG(11) beam and the numerical aperture (NA) of the system. When β=1.6 and the NA is close to its utmost, an almost 100% uniform light shell surrounding the 3D dark spot can be achieved and the dark spot is very clean. If the NA is lowered but β is increased to 1.95, we can also achieve an almost 100% uniform light shell and light efficiency can reach 90%, but the disadvantage is that the center of the dark spot is not too clean. A not-too-clean 3D dark spot, if the light shell surrounding it is very uniform, is acceptable for many applications. Therefore, 3D dark spots surrounded by a high uniform light shell, generated by simply adjusting the truncation parameter of the R-LG(11) beam and the NA of the system, are useful for superresolution fluorescence microscopy, dark spot microscopy, and the dark spot trap.