Tight focusing of a double-ring-shaped, azimuthally polarized beam through a dielectric interface

We investigate the tight focusing properties of a double-ring-shaped, azimuthally polarized vector beam (DRS-APVB) by use of vectorial Debye theory. It is shown that a dark channel with an ultralong depth of focus (~106λ) and subwavelength focal holes (~0.5λ) can be generated by focusing a DRS-APVB through a dielectric interface with an annular high-numerical aperture (NA) objective lens. The influence of the NA of the objective, the relative refractive indices of two dielectric media, and the probe depth of the system on the focusing properties of the dark channel has been studied in detail. Such a non-diffracting dark channel could find potential applications in atom optical experiments, such as with atomic lenses, atom traps, and atom switches.