Phase-gradient metasurfaces (PGMs) have gained significant attention due to their exceptional ability to control light propagation. However, previous studies primarily focused on the diffraction characteristics of propagating waves, while the diffraction behavior of evanescent waves in PGMs remains largely unexplored. In this work, we systematically explore the interaction of the evanescent wave with PGMs, unveiling the diffraction rule and underlying mechanism. We demonstrate that integer parity plays a crucial role in the diffraction of evanescent waves with large wave vectors. Moreover, the parity-reversed diffraction rules exhibit a unique periodic nature of the PGM response within momentum space, leading to the emergence of a momentum zone with a width of $K=m\xi$ (where $m$ is the number of unit cells over supercell and $\xi$ is phase gradient). Notably, the diffraction behavior remains invariant when the incident wave vector is shifted by integer multiples of $K$. The periodic diffraction rules establish a theoretical framework for manipulating evanescent waves, enabling the perfect conversion of an arbitrary evanescent wave into a propagating wave in free space. This study provides a theoretical foundation for extracting evanescent wave information and designing far-field superresolution devices.

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• Evanescent waves
• Optical & microwave phenomena