Asymmetric phase modulation of light with parity-symmetry broken metasurfaces

The design of wavefront-shaping devices is conventionally approached using real-frequency modeling. However, since these devices interact with light through radiative channels, they are by default non-Hermitian objects having complex eigenvalues (poles and zeros) that are marked by phase singularities in a complex frequency plane. Here, by using temporal coupled mode theory, we derive analytical expressions allowing to predict the location of these phase singularities in a complex plane and as a result, allowing to control the induced phase modulation of light. In particular, we show that spatial inversion symmetry breaking—implemented herein by controlling the coupling efficiency between input and output radiative channels of two-port components called metasurfaces—lifts the degeneracy of reflection zeros in forward and backward directions, and introduces a complex singularity with a positive imaginary part necessary for a full 2 π -phase gradient. Our work establishes a general framework to predict and study the response of resonant systems in photonics and metaoptics.