UTD-Type Solution of Physical Optics Approximation for Reconfigurable Intelligent Surface Modeled by a Continuous Planar Surface

An accurate and fast prediction technique is necessary for the radiation pattern of the reconfigurable intelligent surface (RIS) to quantitatively and efficiently evaluate the performance of RIS. Based on the uniform theory of diffraction (UTD), this paper proposes a UTD-type solution of the physical optics approximation (PO) for RIS modeled by a continuous planar surface in a two-dimensional environment. The authors validate the proposal under different scenarios in an indoor environment (0.1 - 20 m) at the terahertz bands (100 - 300 GHz), by comparing them with those computed using the Fresnel approximation, the Fraunhofer approximation, PO, and the full-wave approach based on the method of moment (MoM). The simulated results show that compared to MoM, the proposal and PO achieve good accuracy with a smaller error of less than 1 dB, while the Fresnel and Fraunhofer approximations present imperfect accuracy with an error of larger than 1 dB in the near-field region. Moreover, the proposal outperforms the PO in terms of faster calculation time by approximately 70% - 76%, and the computational time of the proposal is improved by approximately 46, 190 - 125, 460 times compared to MoM. Furthermore, the computational complexities of the proposal, the Fresnel approximation and the Fraunhofer approximation are O(N-0), compared to that of PO and MoM by O(N) and O(N-2), respectively, where N and O() are the number of sampling points and the notation of order, respectively. Therefore, the proposal can achieve a good balance between accuracy and computational cost.