Theory of laser array phase locking by Fourier coupling

The type of coupling in a fibre laser array phase locked with the help of an external mirror located at the focal distance from the plane of output ends of individual lasers is studied analytically. The explicit expression is derived for the eigenvalue of the resonator and the restriction on the width of the tuning range in which laser array phase locking is preserved is determined. The influence of the spread in the optical lengths of fibres on the phase-locking efficiency is considered. The phase-locking efficiency is analysed for the spread of optical lengths of fibres considerably exceeding the radiation wavelength.