We study experimentally and theoretically the interactions among ultrashort optical pulses in the soliton rain multiple-pulse dynamics of a fiber laser. The laser is mode-locked by a graphene saturable absorber fabricated using the mechanical transfer technique. Dissipative optical solitons aggregate into pulse bunches that exhibit complex behavior, which includes acceleration and bi-directional motion in the moving reference frame. The drift speed and direction depend on the bunch size and relative location in the cavity, punctuated by abrupt changes under bunch collisions. We model the main effects using the recently proposed noise-mediated pulse interaction mechanism, and obtain a good agreement with experiments. This highlights the major role of long-range Casimir-like interactions over dynamical pattern formations within ultrafast lasers.Dissipative solitons are localized waves in open systems far from equilibrium, whose existence results from a balance of dissipative and dispersive effects. They appear in numerous physical areas including reaction-diffusion systems, neurological and ecological sciences, fluid dynamics, and photonics [1,2]. In photonics, spatial dissipative solitons are stabilized by dynamical attractors and evolve like discrete particles in effective media [3]. A major challenge in their study is the distillation of an effective low-dimensional dynamical system governing pulse position and speed [4], which would determine the temporal evolution of multiple-pulse patterns. This implies an effective modeling of pulse interactions whose range and complexity are determined by the physical system. Mode-locked fiber lasers exhibit an extensive pallet of short and long-range pulse interactions. The former take place when pulse tails overlap [5][6][7][8], and the latter when pulses interact over separations orders of magnitude beyond their individual extension -and are hence mediated. In fiber lasers, where slow gain depletion and recovery dynamics create an effective long-range repulsive force [9] solitons pulses distribute equally along the cavity (harmonic mode-locking) [10]. Other interactions can be mediated by perturbations of an extended background field or propagation medium (e.g. electrostriction [11,12]).

Fiber lasers are convenient for studying extreme and rare events, such as rogue waves, thanks to the lasers' fast dynamics. Indeed, several types of rogue wave patterns were observed in fiber lasers at different time-scales: single peak, twin peak, and triple peak. We measured the statistics of these ultrafast rogue wave patterns with a time lens and developed a numerical model proving that the patterns of the ultrafast rogue waves were generated by the non-instantaneous relaxation of the saturable absorber together with the polarization mode dispersion of the cavity. Our results indicate that the dynamics of the saturable absorber is directly related to the dynamics of ultrafast extreme events in lasers.

We present a novel method for compensating scattering of entangled photons in real-time, by using feedback from the classical pump beam that stimulates their creation, paving the way for implementing wavefront shaping in quantum technologies.

Quantum technologies hold great promise for revolutionizing photonic applications such as cryptography. Yet, their implementation in real-world scenarios is challenging, mostly because of sensitivity of quantum correlations to scattering. Recent developments in optimizing the shape of single photons introduce new ways to control entangled photons. Nevertheless, shaping single photons in real time remains a challenge due to the weak associated signals, which are too noisy for optimization processes. Here, we overcome this challenge and control scattering of entangled photons by shaping the classical laser beam that stimulates their creation. We discover that because the classical beam and the entangled photons follow the same path, the strong classical signal can be used for optimizing the weak quantum signal. We show that this approach can increase the length of free-space turbulent quantum links by up to two orders of magnitude, opening the door for using wavefront shaping for quantum communications.

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