Divide and focus: generating novel focal polarization modalities by symmetry-based phase tailoring in one dimension

Symmetry-based tailoring of photonic systems recently heralded the advent of novel concepts, such as photonic topological insulators and bound states in the continuum. In optical microscopy systems, similar tailoring was shown to result in tighter focusing, spawning the field of phase- and polarization-tailored light. Here, we show that even in the fundamental case of 1D focusing using a cylindrical lens, symmetry-based phase tailoring of the input field can result in novel features. Dividing the beam or utilizing a π phase shift for half the input light along the non-invariant focusing direction, these features include a transverse dark focal line and a longitudinally polarized on-axis sheet. While the former can be used in dark-field light-sheet microscopy, the latter, similar to the case of a radially polarized beam focused by a spherical lens, results in a z polarized sheet with reduced lateral size when compared with the thickness of a transversely polarized sheet produced by focusing a non-tailored beam. Moreover, the switching between these two modalities is achieved by a direct 90° rotation of the incoming linear polarization. We interpret these findings in terms of the requirement to adapt the symmetry of the incoming polarization state to match the symmetry of the focusing element. The proposed scheme may find application in microscopy, probing anisotropic media, laser machining, particle manipulation, and novel sensor concepts.