Tapered N-helical metamaterials with three-fold rotational symmetry as improved circular polarizers

Chiral helix-based metamaterials can potentially serve as compact and broadband circular polarizers. We have recently shown that the physics of structures composed of multiple intertwined helices, so called N-helices with N being an integer multiple of 4, is distinct from that of structures made of single circular helices (N = 1). In particular, undesired circular polarization conversion is strictly eliminated for N = 4 helices arranged on a square lattice. However, the fabrication of such structures for infrared/visible operation wavelengths still poses very significant challenges. Thus, we here revisit the possibility of reducing N from 4 to 3, which would ease micro-fabrication considerably. We show analytically that N = 3 helices arranged on a hexagonal lattice exhibit strictly vanishing circular polarization conversion. N = 3 is the smallest option as N = 2 obviously leads to linear birefringence. To additionally improve the circular-polarizer operation bandwidth and the extinction ratio while maintaining high transmission for the wanted polarization and zero conversion, we also investigate by numerical calculations N = 3 helices with tapered diameter along the helix axis. We find operation bandwidths as large as 2.4 octaves.