Model of the Self-Q-Switching Instability of Passively Phased Fiber Laser Arrays

Abstract

We present a simple model for self-pulsation instability in passively phased high power optical fiber amplifier arrays with external feedback. Its key features are, first, the feedback level's sensitivity, and thus that of the cavity Q-value, to small phase changes of the array fields, and, second, the effect of refractive index nonlinearity in the amplifiers. The model's prediction of an instability threshold for arrays of at least two amplifiers is confirmed by a linearized stability analysis of a system in ring-cavity geometry, and the magnitudes of predicted power levels are well within the domain of recent experiments.

Dynamics of Passively Phased Ring Oscillator Fiber Laser Arrays

“…From Fig. 7c, we see that the frequency spacing between the centers of two adjacent lobes is f ≈ 1.86 GHz, which is equivalent to a wavelength spacing of λ = λ 2 /c · f ≈ 7.2 pm in agreement with [4]. In these simulations we have assumed there are no external path delays due to the coupling optics.…”

“…Table I summarizes the important parameters/values used for all simulations. The coefficient of the Kerr nonlinearity is γ = 0.003 W −1 m −1 (n 2 = 3.2 × 10 −20 m 2 /W) [4], [9]; however, for our simulations, the value has been varied over a large range to study the effect of nonlinearity on the system. The chosen computational time window spans roughly two roundtrips for each individual fiber.…”

“…7 illustrates the dependence of the output power and the "order parameter" on the detuning from the operating wavelength of 1080 nm, as generated by our simulation results. We adopt the definition from [4]: the order parameter is equal to | N n=1 E n |/ N n=1 |E n |, where E n is the near-field amplitude at the output of the n th fiber in the array. The order parameter aims to characterize the degree of phasing in the array; if all fibers are coherently in phase at a specific frequency, then | N n=1 E n | = N n=1 |E n |, and thus the order parameter equals unity.…”

“…In these simulations we have assumed there are no external path delays due to the coupling optics. Inclusion of such delays does not affect the dynamics but results in a small shift of the order parameter spectrum from the power spectrum [4].…”

“…The initial models required a fixed phase difference as an input and did not yield spectral information [1], [2]. A more recent model focused on a Q-switching instability found from a linear stability analysis and presented only a few preliminary results from the numerical solution of the propagation equations [3], [4]. In the case of internally-coupled arrays [5], Wu, et al have presented a dynamic model based on the amplifying Nonlinear Schrödinger Equation (NLSE) that incorporates the multiple longitudinal modes of a fiber laser [6] and allows for the natural selection of the resonant array modes that experience the minimum loss [7], [8].…”