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Abstract
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.
Highlights
Chiral effects like optical activity or circular dichroism require both electric and magneticdipole responses and are usually weak in natural substances
If we combine the restrictions for the Jones reflection matrix derived from three-fold rotational symmetry with the constraints given by reciprocity, we find that ryx = rxy = 0 and the Jones reflection matrix can be written as rlin = rcirc =
We have shown that, just as in the case of N = 4 helices, losses are essential to obtain circular dichroism
Summary
Chiral effects like optical activity or circular dichroism require both electric and magneticdipole responses and are usually weak in natural substances. To fully eliminate circular polarization conversions it is important that N-fold rotational symmetry must be recovered by the structure, and by the lattice [14, 15]. We have shown that the four-fold rotational symmetry strictly eliminates off-diagonal elements in the Jones transmission and reflection matrices in circular polarization basis, provided that no diffracted orders other than the two 0-th orders occur. To fully eliminate circular polarization conversion for N = 3, we propose hexagonal N-helix arrays, recovering three-fold rotational symmetry for the individual unit cell and for the array and for the overall structure. We assume that non-linear effects as well as static magnetic fields are absent Under these conditions, the Jones reflection matrix can be written as: Er = rlin Ei =. If a polarizing effect is desired, the difference in transmittance must necessarily be achieved through absorption/losses (or, in principle, by applying an additional static magnetic field)
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