Self-dissimilarity, irreversibility and robustness in mode-locked lasers

Passive mode-locking of lasers corresponds to a self-organized far-from-thermal-equilibrium steady state. These lasers also generate ultrafast pulses, which have a diverse range of scientific and industrial applications. Given their importance it is perhaps surprising that a fundamental question of great practical importance has remained unanswered to this date: When is a mode-locked laser robust against noise? When is it fragile? What is the origin of different levels of robustness of different lasers, such as soliton and similariton lasers? Here, we borrow the concept of self-dissimilarity from complexity science and apply it as a measure of complexity of the phase space of mode-locking. Robustness is shown to be directly linked to low self-dissimilarity and irreversibility of noise-induced transitions. Further, we show that all laser types develop low self-dissimilarity as nonlinearity is increased (higher power), but at different paces. At even higher powers, they all eventually approach a critical transition, where the phase space evolves into a random fractal, exhibiting scale independence, measured over 7 decades. Thus, the well known but hitherto unexplained differences in robustness are intuitively explained and quantified.