Single-beam high-accuracy longitudinal position measurement using spiralling beams

The shaping of light fields spans research areas from the foundations of optics to optical communication, materials processing, quantum optics, and microscopy [1] . The azimuthal phase structure contains transverse phase of the form exp( −iℓφ ), where φ is the azimuthal coordinate and ℓ defines the quanta of orbital angular momentum (OAM) each photon carries [2] . Bessel beams, whose higher orders can have an azimuthal phase, are comparatively easy to generate using a ring aperture at the back focal plane of a lens ( k -space). Complex superpositions of these modes with multiple rings of different radii and different orders give rise to radially spiralling beam patterns [3] – [5] .