Modelocking beyond Haus theory: fast gain dynamics and coherent effects

Synchronisation of light waves with different frequencies oscillating in lasers cavities (mode-locking) leads to the generation of ultrashort coherent light pulses which find ubiquitous applications in technologies such as surgery, material processing, metrology, molecular fingerprinting and others.

A particular challenge which I am working to address, in a broad collaboration together with the group of Stephane Barland (University of Nice, France), German de Valcarcel (Universitat de Valencia, Spain) and Franco Prati (Universit√† dell’Insubria, Italy); is to obtain a general theory of mode-locking in lasers which is valid beyond the particular limitations of existing models. Such new theory should be able to successfully describe fast dynamics in the laser. Where by fast I mean collective relaxation process of the atoms inside the laser from an higher energy level to a lower one, which take place on the scale of the nanosecond (1 billionth of a second!).

Let us now be more technical. One of the giants of laser physics and nonlinear optics, Hermann Haus, laid the foundation of existing mode-locking theory establishing the celebrated Master Equation which bears his name back in 1975.
Haus Master Equation is a compact and elegant mean field model derived under the assumptions that the the gain saturates on the average intensity of the light pulse and does not suffer substantial variations on a time scale comparable with a pulse duration; it has been extremely successful in the description of mode-locking in slow gain lasers such as solid state or fiber lasers where the population inversion relaxes on time scales ranging from milliseconds to microseconds.

However in semiconductor lasers where the gain evolution is fast (on the nanosecond time scale) deviations from Haus theory may become more relevant: such deviations include the asymmetric pulse shape, appearance of satellite pulses and symmetry breaking of the pulse solution with respect to the sign of the detuning between modulation and the cavity free spectral range.

Another important case where Haus Master Equation fails is in capturing effects which arise due to coherent interaction between light and matter in the gain medium: such effects may lead to a dynamical power broadening of the gain line beyond its normal width (enabling pulses shorter than those predicted by Haus and Siegman & Kuizenga models), to coherent ringing with generation of satellite pulses and finally to spontaneous mode-locking induced by coherent instabilities, without the need of a further mode-locker element inside the cavity. Interestingly such spontaneous coherent mode-locking is one of the possibilities currently explored to achieve frequency comb generation in quantum cascade lasers!

We are developing a novel, compact and amenable to analytical treatment theoretical framework which is able to describe mode-locking outside the limit of validity of Haus model in particularly capturing fast gain dynamics and coherent effects, without requiring the use of first principle models such as Maxwell-Bloch equations.