Direct laser writing of helical Bragg gratings in vortex silica fibre

Helical Bragg gratings (HBGs) are formed in silica-based multimode ring-core optical fibres by direct laser writing with a femtosecond laser beam. The structure of the field reflected by HBRs with linearly polarised Bessel beam fibre coupling is experimentally studied. It is shown that the reflected light carries orbital angular momentum in some resonances. A generalised condition for angular phase matching is presented for mode coupling in HBRs. The condition takes into account the angular azimuthal dependence of the induced refractive index in the helical structure. The generalised phase-matching condition explains multiple resonances in the HBR reflection spectra and gives an additional degree of freedom in writing helical gratings with desirable properties.