Invariant optical properties of dielectric nanofins in geometric phase metasurfaces

While the geometric phase shift imparted by C2-symmetric meta-atoms is intrinsically independent of shape, depending solely on the rotation angle or orientation, the invariance of other critical optical properties has remained unexplored. Here, we demonstrate that dielectric nanofins exhibit significant additional invariances by analyzing the influence of nanofin geometry on polarization conversion efficiency, transmission and phase shift. We studied nanofins, or anisotropic meta-atoms, with rectangular and elliptical geometries, which are commonly used to control light propagation in geometric or Pancharatnam-Berry phase metasurfaces. This analysis was conducted using the finite-difference time-domain (FDTD) method, for three different wavelengths (405, 532, and 660 nm), across the visible spectrum. Our results show that when both the effective transverse area and aspect ratio (defined as the ratio between the long and short axes) of the nanofins are preserved, both geometries exhibit nearly identical polarization conversion efficiency, transmission and phase responses. This behaviour of rectangular and elliptical meta-atoms suggests that the optical properties of nanofins are independent of their shape as long as their geometry maintains C2 rotational symmetry, and both the transverse area and aspect ratio are preserved. In contrast, significant differences emerge when only the aspect ratio is matched, highlighting the critical role of effective area preservation. These findings provide design flexibility, enabling geometry selection based on fabrication constraints without compromising optical performance.