Turbulence in detuned mode-locked lasers

Summary form only given. The theory of actively mode-locked lasers (AML), with and without detuning, is an old subject in itself. Such devices are key elements in modern optical communication systems, especially in soliton storage rings for future high bit rate systems. Despite the importance of ALMs and the vast amount of literature on this subject, the type of instability occurring for a large detuning was never investigated theoretically. The reason is that a linear stability analysis indicates stability independent of the detuning. However, for a large enough detuning T/sub d/ between the period of the active mode locker and the cavity round-trip time, the AML is surprisingly unstable, a fact that is well known from both experiment and numerical simulations. We show that detuned ALMs undergo a transition to turbulence similar to a hydrodynamics instability, as explained by a recently proposed theory. This type of instability cannot be detected by a linear stability analysis. We model the AML by a master equation, which includes the saturated gain with the finite gain bandwidth and a parabolic loss modulation, resulting in Gaussian pulses. Without detuning, the Gaussian pulses are located at the point of minimum loss. With detuning, the stationary pulse shifts away from the point of minimum loss, until the reshaping of the pulse due to the modulator balances the mismatch between the modulation period and the cavity round-trip time.