Design andanalysis of interlayer spacing in cascaded metasurfaces for beam steering

Cascaded metasurfaces have been considered to introduce interlayer propagation as an additional degree of freedom, by which a viable route is provided for extending the wavefront-control capability of single-layer planar optical devices. In this study, a phase-design method based on reverse ray tracing was proposed for cascaded bilayer metasurfaces intended for large-angle beam steering. By this method, rays were traced backward from the target wavefront specified on the second metasurface to determine their corresponding positions on the first metasurface (MS1), on which a phase term was pre-encoded to compensate for interlayer propagation. The effects of interlayer spacing on the phase distribution, higher-order radial components, and effective optical aperture of MS1 were investigated through theoretical derivation and geometrical-optics modeling. Under the specified aperture and deflection conditions, it was found that the required compensation phase becomes increasingly nonlinear and the effective aperture contracts as the interlayer spacing increases. Therefore, the simple phase-superposition model based on the zero-spacing approximation cannot be directly applied to designs with large interlayer spacing. The resulting analytical framework is shown to link interlayer spacing, compensation phase, and effective aperture, by which a basis is provided for subsequent full-wave optimization and experimental design of cascaded metasurfaces.