Fig. 2. Design strategy and simulated focusing performance of the on-fibre UNM.

a Detailed view of the functionalized fibre consisting of a single-mode fibre, spliced multimode fibre section for beam expansion, and the meta-lens on its facet that is used to create a tight focus for trapping particles. b Meta-lens design map: Limiting factors for UNM design (λ₀ = 660 nm). Low spatial resolution results in aliasing, while limited laser source bandwidth leads to incoherent interference of the Fresnel zones. c Simulated focal spot of an on-fibre meta-lens including wavefront curvature correction. The inset shows the radial focal plane (scale bar: 500 nm, dashed line: with the fitted Airy function; note that the scale of both axes is the same as that in the inset and in (e)). The colour scale ranges linearly from zero (dark blue) to unity (yellow). d Radial and (e) axial (upper axis) intensity profiles (solid) along the symmetry axes and the corresponding fits (dashed). The vertical dotted lines indicate the full-width-half-maximum of the fits. Note that in (e), the uncompensated fibre wavefront curvature (blue, lower axis) leads to a strong focal shift and spherical aberration compared to the wavefront-corrected design (green, upper axis)