Duecorresponding author guidelines for details."?> to the electronic bottleneck limited real-time measurement speed of common temporal-spectral detection and the particle-like nature of optical soliton enabled nonrepeatable transient behaviors, capturing the ultrafast laser pulses with unknown times of arrival and synchronously characterizing their temporal-spectral dynamic evolution is still a challenge. Here, using the Raman soliton frequency shift based temporal magnifier and dispersive Fourier transform based spectral analyzer, we demonstrate a self-synchronized, ultrafast temporal-spectral characterization system with a resolution of 160 fs and 0.05 nm, and a recording length above milliseconds. The synchronized nonlinear process makes it possible to image full-filled temporal sub-picosecond pulse trains regardless of their arrival times and without extra pump lasers and photoelectric conversion devices. To demonstrate the significance of this improvement, a buildup dynamic process of a soliton laser with a complex breakup and collisions of multisolitons is visually displayed in the spectral and temporal domains. The soliton dynamic evolution processes observed by our characterization system are in one-to-one correspondence with the numerical simulation results. We believe this work provides a new multidimensional technique to break the electronic bottleneck to gain additional insight into the dynamics of ultrafast lasers and nonlinear science.

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.

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.

Acousto-optic interactions, employed in the ultrafast laser regulation, possess remarkable advantages for fast tuning performance in a wide spectral range. Here, we propose an ultrafast fiber laser whose wideband tunability is provided by an acousto-optic structure fabricated with an etched single-mode fiber. Because of the laser polarization conversion induced by the coupling between the core and cladding vector modes in the etched fiber, a band-pass characteristic of the acousto-optic interaction is achieved to effectively regulate the inner-cavity gain range. Cooperating with a saturable absorber based on single-wall carbon nanotubes (SWCNTs) with polarization robustness, a soliton operating state is achieved in the tunable erbium-doped fiber laser. By controlling the acoustical wave frequency from 1.039 to 1.069 MHz, this soliton laser can be conveniently tuned in a wide spectral range from 1571.52 to 1539.26 nm. Meanwhile, the laser pulses have near-transform-limited durations stably maintaining less than 2 ps at different wavelength channels, owing to the broadband nonlinear absorption of SWCNTs.