Interaction between momentum-space and metasurface phase fields

Clarify the interaction mechanism between momentum-space phase fields in photonic crystal slabs and the phase fields generated by metasurface spatial arrangements, to enable their effective integration in photonic devices.

Background

The paper discusses the integration of photonic crystal slabs with metasurface-based optical phase control. Periodic perturbations in photonic crystal slabs can generate both real-space and momentum-space topological singularities, while metasurface arrangements can produce lasers with arbitrarily tunable wavefronts and tailored polarization topological charges. However, the relationship between these two types of phase-field engineering remains unresolved, limiting the rational design of integrated devices that combine metasurface spatial organization with momentum-space phase control.