Network model for two-dimensional coupled laser arrays

We have developed a network model for two-dimensional phase-locked arrays of coupled lasers that provides a basis for modeling arrays incorporating mixed coupling schemes. With this network approach we show that the modes of two-dimensional arrays that are evanescently coupled in the lateral direction and injection coupled in the longitudinal direction can be expressed in terms of the eigenvalues of matrices separately representing the lateral and longitudinal coupling. As an example, the modes and grating-coupled near-field patterns of a 3 x 3 array injection coupled through surface-emitting second-order Bragg reflectors are determined explicitly.