Generalized Rayleigh-Sommerfeld Diffraction Theory for Metasurface-Modulating Paraxial and Non-Paraxial Near-Field Pattern Estimation

In this paper, different diffraction theories for estimating the diffraction field patterns modulated by metasurfaces are firstly revisited. Further reformulation of these theories is performed to better reveal their inherent mechanisms and differences. To compute the metasurface-modulating paraxial and/or non-paraxial diffraction field patterns within the near-field region, including the evanescent area, a universal pattern-propagation Eigenfactor is introduced to generalize Rayleigh-Sommerfeld diffraction theory. To investigate its applicability and accuracy, a representative monofocal metasurface with an ultrahigh numerical aperture of 0.96, together with two coplanar and non-coplanar multifocal holographic metasurfaces, are constructed as illustrative examples. Their near-field patterns are calculated by the generalized Rayleigh-Sommerfeld (GRS) diffraction integral and compared with those extracted by the finite-different time-domain full wave analysis, generalized Huygens-Fresnel principle, and Huygens's Principle. It is demonstrated that within the near-field region including the non-paraxial and evanescent area, the GRS diffraction integral provides the best and satisfactory agreement with the full wave simulation, and thus offers a more accurate and efficient tool for quantitative analysis and iterative optimization.