Weak-link synchronization

We describe a mutual synchronization mechanism observed in a model of fiber laser arrays. Though suboptimal in terms of total coherent power, the weak-link-synchronized state is far more robust than the in-phase state of a uniformly pumped array, with respect to parameter mismatch among the individual elements. We find similar dynamical behavior in a more general system of coupled oscillators where the amplitude dynamics is crucial.

Figure 1

Schematic summarizing the regions of stability for the various fixed point solutions: $A$: weak link solutions. $B$: well-pumped solutions, Eq. (12). $C$: near-threshold transitional solutions.

Figure 2

Power spectrum $P\left(\omega \right)$ for the linear array of 19 lasers with near-neighbor coupling, with $r=0.2$, $ϵ=0.005$, $\delta \sim {10}^{-4}$, $\kappa =0.015$, and $z_c=1$. Initial conditions were chosen randomly with ${ϵ}_n∊(0,1)$, ${\psi }_n∊(0,2\pi )$, and $G_n∊(1.6,2.3)$. The upper plot is for the case when all lasers are strongly pumped, with $G^p=1.9$. The lower plot is for the case when instead every other laser is underpumped, with $G^p=0.4$ (weak-link synchronization).

Figure 3

Cross section of the 37-fiber system and the pumping scheme used to achieve weak-link synchronization. Black and gray circles represent the well-pumped and underpumped lasers, respectively.

Figure 4

Same as Fig. 2 but for the two-dimensional $(N=37)$ array. The upper plot is for the all-pumped configuration; the lower plot is for the weak-link arrangement.