Theoretical analysis of phase locking in an array of globally coupled lasers

A model of an array of globally coupled fibre lasers, with the same fraction of the total output beam power injected into each laser, is considered. Phase self-locking of the laser array makes it possible to increase the brightness of the total output beam without any devices for controlling the phases of output beams, which significantly complicate the laser system. The spread of the laser optical lengths is several hundreds of wavelengths (or even more); within the theory of hollow cavities, this spread should lead to a fast decrease in the total power with an increase in the number of lasers. The presence of the active medium may reduce this drop to a great extent due to the self-tuning of the laser array radiation wavelength to a value providing a maximum gain for the array lasing mode. The optical length of each element is assumed to be random. The increase in the phase-locking efficiency due to the gain saturation is explained based on the probabilistic approach. An iterative procedure is developed to find the array output power in the presence of steady-state phase locking. Calculations for different values of small-signal gain and the output-power fraction spent on global coupling are performed. It is shown that, when this fraction amounts to similar to 20%-30%, phase locking of up to 20 fibre lasers can be implemented with an efficiency as high as 70%.