Analysis and design of arbitrary 3D curved Pancharatnam-Berry phase THz metasurface with high aperture efficiency

In recent years, there has been extensive research on two-dimensional (2D) planar metasurfaces (MTSs), and there is a growing interest in curved MTSs driven by the need to integrate radiators with specific structures such as aircraft, trains, cars, or missiles. However, current curved designs are mostly limited to spherical or cylindrical MTSs, and research on arbitrary three-dimensional (3D) curved MTSs remains limited due to their complex geometric shapes and radiation characteristics. In this paper, the effects of curvature, oblique incidence, distorted shape, and local diverging normal vectors on scattering amplitude degradation and the nonlinear phase of MTSs are thoroughly analyzed. Based on these analyses, a general design strategy for arbitrary 3D curved Pancharatnam-Berry (PB) phase terahertz (THz) MTSs with high aperture efficiency (AE) is proposed. As an example, two arbitrary 3D curved PB phase THz orbital angular momentum (OAM) MTSs are designed: (1) MTS-I: Dual beam (right hand circular polarization (RHCP), l₁ = 1, α₁ = 30°, φ₁ = 0°), (RHCP, l₂ = -1, α₂ = -30°, φ₂ = 0°), (2) MTS-II: Single beam (RHCP, l₃ = 1, α₃ = 30°, φ₃ = 0°), where l, α and φ represent the OAM mode, elevation and azimuth, respectively. The following advantages are demonstrated: the feasibility of designing arbitrary 3D curved MTSs; high OAM conversion efficiency (>95.4%); high OAM mode purity (>75%); and high AE for OAM MTSs (29% for simulated MTS-I, 15.7% for simulated MTS-II, and 11.1% for measured MTS-II). The proposed design methodology can be applied to arbitrarily shaped conformal devices in fields such as wearable electronics and aerial vehicles.