  A lattice-induced opacity is identified in the scattering process of a
normally-incident matter wave from a two dimensional lattice of atoms. This
system can be treated as an analogue of a confinement induced resonance.
Specifically by modifying the s-wave scattering length between atoms in the
incident matter wave and the lattice-confined atoms, the transmission of the
matter wave can be tuned controllably from zero to one. Based on this, we
propose a possible scheme for a matter wave transistor. When the transmission
of the matter wave is tuned to zero, a matter wave cavity can be formed by
placing two such lattice planes of atoms parallel to one another. At higher
kinetic energies, the two dimensional lattice of atoms can also serve as a
matter wave beam splitter and a wave plate.
