  We report the first prediction of fully localized two-dimensional embedded
solitons. These solitons are obtained in a quasi-one-dimensional waveguide
array which is periodic along one spatial direction and localized along the
orthogonal direction. Under appropriate nonlinearity, these solitons are found
to exist inside the Bloch bands (continuous spectrum) of the waveguide, and
thus are embedded solitons. These embedded solitons are fully localized along
both spatial directions. In addition, they are fully stable under
perturbations. These results show that multidimensional embedded solitons may
find applications just like non-embedded (regular) solitons.
