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In the past decade, self mode-locking was reported for a number of different semiconductor lasers. In contrast to theoretical predictions of the Haus master equation, there was no effective saturable absorber mechanism present to stabilize mode-locking. This deficiency has led to numerous discussions on the validity of the self mode-locking and FM comb reports.
Here we now offer a theoretical explanation for self mode-locking, based on the Haus master equation, which identifies three different solution regimes, depending on the complex sign of the nonlinearity. For a pure dissipative nonlinearity, we see the well-known regimes of phase turbulence and mode-locking. For a predominant reactive nonlinearity, however, we find a previously unreported locking mechanism between adjacent modes. In this regime, phases fluctuate, but remain bounded within a phase interval, i.e., a frequency lock rather than a phase lock emerges. While the total power remains perfectly constant, the power in the individual modes is heavily fluctuating, giving rise to the formation of a quasi-periodic breather. This breathing mechanism continuously transfers energy from the spectral center into the wings and back again.
Slowly increasing the phase nonlinearity, one sees a threshold-like onset of the frequency locking mechanism, which is indicated by sudden collapse of the intermode beatnote width and an increase of the coherence to near-unity values. While internal phase space dynamics are clearly chaotic, all observables of the system, including autocorrelations and rf spectra show little indication for this highly dynamic scenario. This unusual mode-locking mechanism is probably best understood as the liquid state of mode-locking in between the gaseous phase turbulence and the condensation into a solid soliton state. This previously unrecognized mechanism explains peculiar reports on mode-locking without an apparent saturable absorption mechanism and suggests the high utility of FM combs in the frequency domain, in particular for dual comb spectroscopy.
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