Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent

Optical beams exhibiting a long depth of focus and a minimum spot size can be obtained with the tight focusing of a narrow annulus of radially polarized light, leading to a needle of longitudinally polarized light. Such beams are of increasing interest for their applications, for example in optical data storage, particle acceleration, and biomedical imaging. Hence one needs to characterize the needles of longitudinally polarized light obtained with different focusing optics and incident beams. In this paper, we present analytical expressions for the electric field of such a nearly nondiffracting, subwavelength beam obtained with a parabolic mirror or an aplanatic lens. Based on these results, we give expressions of the transverse and longitudinal full widths at half maximum of the focal lines as a function of the width of the incident annular beam and we compare the performances of the two focusing systems. Then, we propose a practical solution to produce a needle of longitudinally polarized light with a tunable axial extent and a transverse width reaching the theoretical limit of 0.36λ.