Hierarchical self-assembly of trapped Brownian pulses in a modelocked laser

Passive modelocking is when the optical modes of a laser cavity spontaneously lock mutually, localizing all energy into one or more pulses, each far narrower than the cavity. These diffuse like Brownian particles due to intrinsic noise and form various patterns via emergent pulse-to-pulse interactions. If identical and equally spaced, the pulses constitute harmonic modelocking with many applications, but they exhibit bifurcated and multistable, often uncontrollable states due to the vast dimensionality of their phase space, and no model has been simple yet accurate enough to enable their control. We recognize that these degrees of freedom evolve in a hierarchy of timescales, which we separate into a hierarchy of lower-dimensional subsystems describing the evolutions of the pulse shape, the pulse energy, the laser gain medium's excitation and acoustic oscillations, and the relative pulse spacings. Variables evolving in one timescale are simultaneously order parameters for lower subsystems and slaved to higher ones. This perspective yields recipes to create and annihilate laser pulses and steer them to a perfect harmonic pattern with over 100 pulses limited only by the available power.