Frequency modulated (FM) frequency combs constitute an exciting alternative to generate equidistant spectra. The full set of Maxwell-Bloch equations is reduced to a single master equation for FM combs with fast dynamics to provide insight into the governing mechanisms behind phase-locking. It reveals that the recently observed linear frequency chirp is caused by the combined effects of spatial hole burning, group velocity dispersion and Kerr due to asymmetric gain. The comparison to observation in various semiconductor lasers suggests that the linear chirp is general to self-starting FM combs.

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Coupled clocks are a classic example of a synchronization system leading to periodic collective oscillations. This phenomenon already attracted the attention of Christian Huygens back in 1665, who described it as a kind of "sympathy" among oscillators. In this work we describe the formation of two types of laser frequency combs as a system of oscillators coupled through the beating of the lasing modes. We experimentally show two completely different types of synchronizations in a quantum dot laser -in-phase and splay states. Both states can be generated in the same device, just by varying the damping losses of the system. This effectively modifies the coupling among the oscillators. The temporal output of the laser is characterized using both linear and quadratic autocorrelation techniques. Our results show that both pulses and frequency-modulated states can be generated on demand. These findings allow to connect laser frequency combs produced by amplitude-modulated and frequency-modulated lasers, and link these to pattern formation in coupled systems such as Josephson-junction arrays.

Quantum cascade lasers (QCL) have revolutionized the generation of mid-infrared light. Yet, the ultrafast carrier transport in mid-infrared QCLs has so far constituted a seemingly insurmountable obstacle for the formation of ultrashort light pulses. Here, we demonstrate that careful quantum design of the gain medium and control over the intermode beat synchronization enable transform-limited picosecond pulses from QCL frequency combs. Both an interferometric radio-frequency technique and second-order autocorrelation shed light on the pulse dynamics and confirm that mode-locked operation is achieved from threshold to rollover current. Furthermore, we show that both anti-phase and in-phase synchronized states exist in QCLs. Being electrically pumped and compact, mode-locked QCLs pave the way towards monolithically integrated non-linear photonics in the molecular fingerprint region beyond 6 μm wavelength.

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