Analysis of Problem of High Power Fiber LaserCombining for Arbitrary Large Optical PhaseDifferences

摘要

Coherent laser beam combining is potentially attractive way to increase the combined beam brightness beyond the limits imposed on single-mode lasers by technological bounds. The active control of every individual laser beam characteristics is more flexible but essentially more complicated in both, necessary equipment and service. Passive phase locking is an attractive alternative, since it does not need external management and leads to strong simplification of the system. A specific feature of fiber amplifiers and lasers is that they possess optical path differences (OPD) of many wavelengths magnitude. Cold-cavity theory predicts in this case fast decline in efficiency of coherent fiber laser beam combining with number of lasers. Experiments, in contrast, demonstrated in such systems that high degree of phasing takes place for laser arrays of up to 16 lasers. As lasers are strong non-linear systems, explanation of this discrepancy should rely on a role of non-linear effects: gain saturation and intensity-dependent index. Besides, since the gain band width is significantly broader than the distance between spectral lines responding to different longitudinal modes, it is a freedom in adjusting laser wavelength to a value, which corresponds to a best balance between gain and loss of laser radiation. As a first step, we consider a fiber laser array with external global coupling, which means that the same fraction of the combined laser beam is returned into the each element of the array. In this case, every laser in the array is operated as an injection controlled (slave) laser. The specific features of Yb-doped fiber lasers were taken into account in our model: 1) existence of multiple longitudinal modes; 2) typically low-Q cavity used in these lasers. This approach allows us to quantify the mechanism of laser wavelength self-adjustment taking into account the effect of gain saturation. Taking the injection signal intensity within limits of locking range, the output signal was studied as a function of wavelength detuning and small signal gain magnitude.Then the maximal phase locking efficiency is found numerically as a function of coupling strength and of optical pumping intensity at random values of the OPD for laser arrays of variable size. Just the gain saturation effect taken into account in our model leads to comparatively slow reduction of the maximal phase locking efficiency with the laser array size.