  A new scheme for building two dimensional laser arrays that operate in the
single supermode regime is proposed. This is done by introducing an optical
coupling between the laser array and a lossy pseudo-isospectral chain of
photonic resonators. The spectrum of this discrete reservoir is tailored to
suppress all the supermodes of the main array except the fundamental one. This
spectral engineering is facilitated by employing the Householder transformation
in conjunction with discrete supersymmetry. The proposed scheme is general and
can in principle be used in different platforms such as VCSEL arrays and
photonic crystal laser arrays.
