Array-mode far-field patterns for phase-locked diode-laser array: Coupled-mode theory versus simple diffraction theory

A simple, closed-form expression is derived for the far-field patterns corresponding to the modes of a phase-locked array of
N
identical elements. That allows a comparison between the correct array-mode far-field patterns (i.e., coupled-mode theory) and the heuristic, diffraction-grating-like far-field patterns generated by using simple diffraction theory. The correct diffraction-limited lobewidth is determined as a function of array-element number.