Interaction of spatial solitons with a localized spatially-modulated medium

The propagation of solitons through spatially-modulated media is studied numerically as a function of the amplitude, frequency and length of the spatial nonuniformities. It is shown that for a fixed amplitude and length of modulation, an increase in frequency may result in a soliton that propagates in the opposite direction to the one encountering the nonuniform medium because of reflection, whereas, for a fixed frequency and length, an increase in the amplitude of the spatial modulation results in a surface wave and a soliton that may propagate towards either the right or left boundary. In either case, the radiation increases as the amplitude of the spatial modulation is increased. For fixed amplitude and frequency, an increase in the length of nonuniformities results in both surface waves whose amplitude decreases and right-traveling solitons whose velocity decreases as the length of these nonuniformities is increased. A comparison between space and time variations of the dispersion index is also presented.