Diode-laser array modes: discrete and continuous models and their stability

A new class of mode profiles appropriate to large one-dimensional evanescently coupled laser diode arrays can be conveniently approximated by solutions to a Riccatti equation derived from a continuous model of the discrete array. Solutions of the latter model are shown to agree with the continuous solutions in the large-N limit. The continuous model has the advantage that new types of discrete array modes can readily be identified. Stability analyses of the discrete array modes as a function of increasing N confirm that these laser systems are intrinsically unstable in the free-running mode.