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.

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We present fusing of a fiber micro-knot by a CO₂ laser beam. We demonstrate tuning of the coupling strength and tuning of the spectral resonance of the micro-knot by the fusing process. The experimental results reveal that fusing the fiber micro-knots increases the coupling efficiency and improves the robustness and the stability of the micro-knots.

We present long period fiber gratings with off-resonance spectral response. Our long period fiber gratings are created by the periodic structure of large perturbations in the fiber diameter. These perturbations result in unique spectral response, even in off-resonance frequencies. Writing these long period fiber gratings is based on utilizing the mechanical vibrations of tapered fibers during the tapering process. This writing method is simple and robust; it has high efficiency, high reproducibility, and low polarization dependency; and it enables real-time tunability of the periodicity, efficiency, and length of the grating. We also demonstrate a complex grating by writing multiple gratings one on top of the other. Finally, we utilize the formation of the gratings in different fiber diameters to investigate the Young's modulus of tapered fibers.

We present the polarization dependence of strong asymmetric long period fiber gratings written on tapered fibers. We found that for off-resonance conditions the spectral response and the output mode strongly depend on the input state of polarization. We utilize this dependence to obtain a mode selective device and demonstrate radially polarized and azimuthally polarized fiber lasers based on these asymmetric long period fiber gratings.

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We investigated ultrafast rogue waves in fiber lasers and found three different patterns of rogue waves: singlepeaks, twin-peaks, and triple-peaks. The statistics of the different patterns as a function of the pump power of the laser reveals that the probability for all rogue waves pattens increase close to the laser threshold. We developed a numerical model which prove that the ultrafast rogue waves patterns result from both the polarization mode dispersion in the fiber and the non-instantaneous nature of the saturable absorber. This discovery reveals that there are three different types of rogue waves in fiber lasers: slow, fast, and ultrafast, which relate to three different timescales and are governed by three different sets of equations: the laser rate equations, the nonlinear Schrodinger equation, and the saturable absorber equations, accordingly. This discovery is highly important for analyzing rogue waves and other extreme events in fiber lasers and can lead to realizing types of rogue waves which were not possible so far such as triangular rogue waves.