Enhanced control of transmission/reflection amplitudes using a closed-form slowly varying phase-gradient metasurface GSTC framework

Abstract Although the generalized Snell’s law qualitatively predicts the effect of the phase gradient on wave impedance and parasitic diffractions, a closed-form quantitative relationship among transmission/reflection coefficients, phase gradient, incidence angle, and polarizabilities enables better control over scattering coefficients. In phase-gradient metasurface design, the impact of the phase gradient on scattering coefficients is often treated as a nuisance factor. This work proposes a closed-form GSTC-based relationship linking these parameters, allowing designers to treat amplitude as a design parameter rather than an unwanted side effect. The formulation is validated through full-wave simulations of two metasurface examples with different phase distributions. Unlike classical metasurfaces without special unit cell design, the conditions for total transmission and total reflection no longer depend solely on incidence angle and polarizabilities. The results show that under slow phase gradient conditions and near-normal incidence angles, the proposed model’s predictions closely match simulations; for steeper gradients or larger angles, it serves as a reliable zero order approximation. Furthermore, by tailoring the phase gradient, the maximum transmission can be maintained over a broader range of incidence angles, in contrast to conventional metasurfaces with uniform unit cells. This framework provides a quantitative tool for systematic metasurface design, reducing reliance on computationally expensive full-wave optimization.