To design wavefront-shaping of metasurfaces, an analytic expression to predict the phase singularities in the complex plane and a general framework to predict and study these resonant systems are presented. It can be shown that breaking the out-of-plane symmetry allows for full-phase modulation with a single mode.
E. Mikheeva, et al. Asymmetric phase modulation of light with parity-symmetry broken metasurfaces, Optica 10, 1287-1294 (2023).