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We study trapping and propagation of a matter-wave soliton through theinterface between uniform medium and a nonlinear optical lattice (NOL).Different regimes for transmission of a broad and a narrow soliton areinvestigated. Reflections and transmissions of solitons are predicted asfunction of the lattice phase. The existence of a threshold in the amplitude ofthe nonlinear optical lattice, separating the transmission and reflectionregimes, is verified. The localized nonlinear surface state, corresponding tothe soliton trapped by the interface, is found. Variational approachpredictions are confirmed by numerical simulations for the originalGross-Pitaevskii equation with nonlinear periodic potentials.

Soliton dynamics at an interface between uniform medium and nonlinear optical lattice