Three-dimensional fully-structured light by counter-propagation of self-similar beams

So-called fully-structured light fields are characterized by a spatial variation in their amplitude, phase, and, simultaneously, polarization. Along with the technological progress of light-shaping methods based on q-plates or spatial light modulators, the variety of accessible structures has significantly increased and has proven being advantageous for high resolution imaging [1] , quantum communication [2] and particle manipulation [3] . For the vast majority of implemented light fields, the actually accessible customization is limited to two dimensions, i.e. the transverse plane of the light field to be modulated. Only a few approaches have recently been developed towards a full control of all degrees of freedom of the light field in all three spatial dimensions [4] , [5] . A common approach to structure light along its propagation direction takes advantage of tight focusing [6] . However, the resulting non-paraxial situation as well as the short longitudinal distance of the focal volume make it difficult to obtain an equal partition of fully structured light in all three dimensions. Thus, tailoring the longitudinal direction of a light field in the same effective manner than the transverse direction is an actual unsolved challenge. Counter-propagating light approaches that structure the longitudinal direction by interference at the same scale than transverse dimensions is a promising approach to this question. However, though being theoretically appealing, its experimental realization and detection meets unsolved challenges since the detection of a field in one direction is disturbed by the counterpropagating field.