Normal modes of N coupled lasers

The normal modes of an arbitrary number, N, of longitudinally (end-to-end) coupled lasers are derived for simple coupling configurations. Eigenfrequencies and the relative phases and amplitudes of the lasers are obtained from a weak-coupling model. The spacing of the eigenfrequencies is important for the ease of mode selection. In all cases, the frequency spacing is found to increase with coupling and to diminish with increasing N. But in the case in which each laser is coupled to every other in the array, the frequency spacing decreases as N/(N - 1); whereas for cases in which each laser is coupled only to its nearest neighbors, the spacing goes rapidly to zero with increasing N.