Spontaneous Pattern Formation in a Noise-Initiated Laser System Mediated by the Dissipative Faraday Instability

The pattern formation induced by modulation instabilities (MIs) is a universal phenomenon in nonlinear physical systems [1], and provides potential applications in the generation of localized structures with high repetition rate. The dissipative Faraday instability (DFI), as a novel type of MI, could occur within a system where dissipative parameter is periodically modulated along the longitudinal direction [2], [3]. The spontaneous pattern formation from longitudinal modulation of gain parameter has been demonstrated in a Raman fiber laser [4]. In rare-earth doped laser systems, the periodic modulation of gain naturally exists due to the pump depletion, gain saturation and etc. However, since the formation of stable patterns depends on continuous wave (CW) as transient solution, it is quite difficult to obtain high-repetition-rate pulse trains directly from rare-earth doped lasers using noise as the initial iterative condition, even if there exists the gain-guided DFI internally. Here, we show that introducing a spectral filter may overcome this limitation, enabling stable patterns to be generated directly from noise without the need for external CW driving. The small-signal gain coefficient inside the laser under study [Fig. 1(a)] is modulated longitudinally. The propagation of light field is described by the dimensionless nonlinear Schrödinger equation: