  The physical mechanism underlying scattering properties of matter wave
gap-solitons by linear optical lattice defects is investigated. The occurrence
of repeated reflection, transmission and trapping regions for increasing
strengths of an optical lattice defect are shown to be due to impurity modes
inside the defect potential with chemical potentials and numbers of atoms
matching corresponding quantities of an incoming gap-soliton. For gap-solitons
with chemical potentials very close to band edges, the number of resonances
observed in the scattering coincides with the number of bound states which can
exist in the defect potential for the given defect strength. The dependence of
the positions and widths of the transmission resonant on the incoming
gap-soliton velocities are investigated by means of a defect mode analysis and
effective mass theory. The comparisons with direct integrations of the
Gross-Pitaevskii equation provide a very good agreement confirming the
correctness of our interpretation. The possibility of multiple resonant
transmission through arrays of optical lattice defects is also demonstrated. In
particular, we show that it is possible to design the strength of the defects
so to balance the velocity detunings and to allow the resonant transmission
through a larger number of defects. The possibility of using these results for
very precise gap-soliton dynamical filters is suggested.
