Analysis of bending effects in long period gratings in fibres with parabolic refractive index profile of the cladding

Bending effects of a long period grating inscribed into the core of a single-mode fibre with the cladding having a parabolic-index profile are theoretically investigated. Fully vectorial bend mode solver is used to calculate field distributions of both core and cladding modes. A simplified mode expansion and propagation theory is used to calculate the spectrally dependent transmission in bent fibres. Theoretical results show that the parabolic-index profile of the cladding should help dramatically reduce the sensitivity of the grating to fibre bending.