We develop a spatiotemporal mode decomposition technique to study the spatial and temporal mode power distribution of ultrashort pulses in long spans of graded-index multimode fiber, for different input laser conditions. We find that the beam mode power content in the dispersive pulse propagation regime can be described by the Bose–Einstein law, as a result of the process of power diffusion from linear and nonlinear mode coupling among nondegenerate mode groups. In the soliton regime, the output mode power distribution approaches the Rayleigh–Jeans law.

Characterization of the state of polarization (SOP) of ultrafast laser emission is relevant in several application fields such as field manipulation, pulse shaping, testing of sample characteristics, and biomedical imaging. Nevertheless, since high-speed detection and wavelength-resolved measurements cannot be simultaneously achieved by commercial polarization analyzers, single-shot measurements of the wavelength-resolved SOP of ultrafast laser pulses have rarely been reported. Here, we propose a method for single-shot, wavelength-resolved SOP measurements that exploits the method of division-of-amplitude under far-field transformation. A large accumulated chromatic dispersion is utilized to time-stretch the laser pulses via dispersive Fourier transform, so that spectral information is mapped into a temporal waveform. By calibrating our test matrix with different wavelengths, wavelength-resolved SOP measurements are achieved, based on the division-of-amplitude approach, combined with high-speed opto-electronic processing. As a proof-of-concept demonstration, we reveal the complex wavelength-dependent SOP dynamics in the build-up of dissipative solitons. The experimental results show that the dissipative soliton exhibits far more complex wavelength-related polarization dynamics, which are not shown in single-shot spectrum measurement. Our method paves the way for single-shot measurement and intelligent control of ultrafast lasers with wavelength-resolved SOP structures, which could promote further investigations of polarization-related optical signal processing techniques, such as pulse shaping and hyperspectral polarization imaging.

Multimode optical fibers are attracting a growing interest for their capability to transport high-power laser beams, coupled with novel nonlinear optics-based applications. However, optical fiber breakdown occurs when beam intensities exceed a certain critical value. Optical breakdown associated with irreversible modifications of the refractive index, triggered by multiphoton absorption, has been largely exploited for fiber material micro-structuration. Here we show that, for light beam intensities slightly below the breakdown threshold, nonlinear absorption strongly affects the dynamics of a propagating beam as well. We experimentally analyze this subthreshold regime and highlight the key role played by spatial self-imaging in graded-index fibers for enhancing nonlinear optical losses. We characterize the nonlinear power transmission properties of multimode fibers for femtosecond pulses propagating in the near-infrared spectral range. We show that an effective N-photon absorption analytical model is able to describe the experimental data well.

Dissipative solitons emerge as stable pulse solutions of nonintegrable and nonconservative nonlinear physical systems, owing to a balance of nonlinearity, dispersion, and loss/gain. A considerable research effort has been dedicated to characterizing amplitude and phase evolutions in the spatiotemporal dynamics of dissipative solitons emerging from fiber lasers. Yet, the picture of the buildup process of dissipative solitons in fiber lasers is incomplete in the absence of corresponding information about the polarization evolution. Here, we characterize probabilistic polarization distributions in the buildup of dissipative solitons in a net-normal dispersion fiber laser system, mode-locked by single-wall carbon nanotubes. The output optical spectra under different pump powers are filtered by a tunable filter, and are detected by a polarization state analyzer. The laser system operates from random amplified spontaneous emission into a stable dissipative soliton state as the cavity gain is progressively increased. Correspondingly, the state of polarization of each spectral wavelength converges towards a fixed point. To reveal the invariant polarization relationship among the various wavelength components of the laser output field, the phase diagram of the ellipticity angle and the spherical orientation angle is introduced. We find that, within the central spectral region of the dissipative soliton, the state of polarization evolves with frequency by tracing a uniform arc on the Poincaré sphere, whereas in the edges of the dissipative soliton spectrum, the state of polarization abruptly changes its path. Increasing cavity gain leads to spectral broadening, accompanied by a random scattering of the state of polarization of newly generated frequencies. Further increases of pump power result in dissipative soliton explosions, accompanied by the emergence of a new type of optical polarization rogue waves. These experimental results provide a deeper insight into the transient dynamics of dissipative soliton fiber lasers.