Modulation instability of the wave packet in a periodically inhomogeneous nonlinear fibre

The modulation instability conditions are studied for a wave packet consisting of two strongly coupled modes co-propagating in a two-mode fibre. The two modes are linearly coupled by the phase matching conditions, which take the longitudinal periodicity of the fibre into account. The nonlinear coupling of the modes is provided by the cross-modulation interaction. The influence of the initial conditions of the fibre excitation on the subsequent development of the modulation instability is analysed. It is shown that the modulation instability can exist in a region of normal material dispersion of the fibre.