Active manipulation for Goos-Hänchen shift of guided-wave via a metasurface of silicon-nanoscale semi-spheres on SOI waveguide

Goos-Hänchen shift of total internal reflection (TIR) is the light beam movement without external driving, so envisioned to have potential manipulation of optical beams. In this article, with a silicon-on-insulator (SOI) waveguide corner structure, a variable equivalent permittivity of guided wave is modelled, and then the equivalent electric polarizabilities and the Goos-Hänchen shift of guided wave are modelled. Consequently, with a 2.0-µm SOI waveguide corner structure and an abrupt phase change of ∼0.5π caused by a vertically inserted metasurface of nanoscale semi-spheres having a 450-nm radius can reach the GH shifts of 2.1 µm for TE- and TM-mode, respectively, which are verified by both the FDTD simulation results of 1.93 µm with a reflectivity of about 62% and the experimental results of 2.0 µm with ∼60%. Therefore, this work has efficiently modelled the optical feature response of semi-sphere metasurface to guided wave and the active manipulation for the GH shifts of guided-wave, opening more opportunities to develop the new functionalities and devices for Si-based photonic integrated circuit (PIC) applications.