Multi-helix chiral fibre filters of higher-order optical vortices

Abstract

We study theoretically the propagation of higher-order (l>1) optical vortices (OVs) in multi-helix chiral weakly guiding optical fibres, in which the pitch value is comparable with the wavelength. We employ a simple mathematical model, in compliance with which the profile function of a multi-helix chiral fibre is obtained from the profile function of an ideal fibre through certain harmonic deformation in the radial direction in a cross section. We study the transmitting properties of such fibres and obtain the structure of their modes, which prove to be circularly polarized higher-order OVs. We obtain the spectra of propagation constants and demonstrate that some mode spectra exhibit the presence of a bandgap, whose position is determined by the modified Bragg condition. We also show that within the spectrum gap such fibres can filter out OVs with a certain sign of the topological charge l (depending on the handedness of the thread), while reflecting oppositely charged OVs, provided the number of treads coincides with l. We demonstrate that, if a broadband beam containing a mixture of OVs with different topological charges is incident on the fibre input, the reflected beam would comprise the OV with |l| equal to the number of fibre threads, so that such a fibre can serve also as a narrowband reflective vortex filter.