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

The modulation instability conditions are studied for a wave packet consist ing of two strongly coupled modes co-propagating in a two-mode fibre. The t wo modes are linearly coupled by the phase matching conditions, which take the longitudinal periodicity of the fibre into account. The nonlinear coupl ing of the modes is provided by the cross-modulation interaction. The influ ence of the initial conditions of the fibre excitation on the subsequent de velopment of the modulation instability is analysed. It is shown that the m odulation instability can exist in a region of normal material dispersion o f the fibre.