Robust synchronization in fiber laser arrays

Abstract

Synchronization of coupled fiber lasers has been reported in recent experiments [Bruesselbach, Opt. Lett. 30, 1339 (2005); Minden, Proc. SPIE 5335, 89 (2004)]. While these results may lead to dramatic advances in laser technology, the mechanism by which these lasers synchronize is not understood. We analyze a recently proposed [Rogers, IEEE J. Quantum Electron. 41, 767 (2005)] iterated map model of fiber laser arrays to explore this phenomenon. In particular, we look at synchronous solutions of the maps when the gain fields are constant. Determining the stability of these solutions is analytically tractable for a number of different coupling schemes. We find that in the most symmetric physical configurations the most symmetric solution is either unstable or stable over insufficient parameter range to be practical. In contrast, a lower symmetry configuration yields surprisingly robust coherence. This coherence persists beyond the pumping threshold for which the gain fields become time dependent.

Effect of Gain-Dependent Phase Shift on Fiber Laser Synchronization

“…In this section, we present a summary of some numerical results we generated by direct simulation of the governing dynamical equations. As with our earlier investigations of fiber laser arrays [10]- [12], we find that the derived properties of the CW state provide a useful guide even as the system displays far more complicated dynamics, though some differences arise. We have no deep understanding of this apparent correspondence.…”

“…At first blush, one might expect to see σ = 1 whenever µ max dips below unity since the latter implies that the inphase fixed point is stable. But it happens that the basin of attraction of the inphase state is very small [12], and for a typical initial condition, the system evolves into a poorly synchronized state [11]. In contrast, we see that when the inphase fixed point is locally unstable, the array behavior may be complicated but is reasonably synchronized.…”

“…We further assume that the coupler is lossless, in which case S is unitary [12]. This property of the coupling matrix S requires both M and m to have unit modulus.…”

“…This property of the coupling matrix S requires both M and m to have unit modulus. Under these circumstances, there exist fully symmetric, constant intensity solutions [10]- [12]. Equations (4) and (5) can be rewritten to identify solutions using E n = E and…”

Theoretical study on phase locking of the array of fiber lasers coupled by bi-dimensional mutual injection

“…27 The main difference between two arrays is that the fiber loop is used as the mode-selection component in the latter array, 27 while no mode-selection component is utilized in the former one. Besides that, the array of the mutually-injected fiber lasers is also different from the array coupled by evanescent coupling [32][33][34] because a loss mechanism is induced by mutual injection (see Fig. 1) but on loss mechanism is induced by evanescent coupling.…”