Spatio-temporal-spectral imaging of non-repeatable dissipative soliton dynamics

The study investigates how to directly observe and characterize the dynamics of three-dimensional (3D) dissipative solitons (DSs) in multimode fiber (MMF) lasers. DSs form through balances among dispersion/diffraction, nonlinearity, gain and loss, and their 3D nature introduces complex spatio-temporal-spectral (STS) interactions. Conventional diagnostics largely address 1D or repeatable events and cannot fully capture non-repeatable, stochastic dynamics coupled across space, time, and spectrum. The authors aim to enable real-time, single-shot, multi-dimensional imaging of DSs—across space (x,y), discrete time (round trips), and wavelength—at ultrafast frame rates sufficient to resolve femtosecond pulse dynamics, thereby answering open questions about formation, stability, and modal interactions in STML (spatio-temporal mode-locking) multimode lasers.

Prior single-shot and real-time techniques (e.g., temporal stretching/dispersive Fourier transform, time-lens-based temporal imaging, and full-field approaches) have revealed important ultrafast laser phenomena such as rogue waves, soliton molecules and their internal motion, and mode-locking build-up. However, these studies largely focus on 1D or repeatable behaviors and do not fully capture STS-coupled, non-repeatable 3D solitons in multimode environments. Multimode fibers and STML lasers have recently shown complex 3D solitons where many transverse and longitudinal modes lock together, challenging intuitive expectations about strong modal dispersion. The need remains for single-shot, multi-DoF, high-temporal-resolution tools to directly visualize non-repeatable STS dynamics, including round-trip-to-round-trip evolution and spectral dependence of modal content.

System overview: The authors developed spatio-temporal-spectral compressed ultrafast photography (STS-CUP), combining a CUP unit with a free-space angular-chirp-enhanced delay (FACED) device. The system has two channels: (1) Round-trip pulses (RTP) channel to capture spatial profiles over successive cavity round trips, and (2) Spectrally resolved single-pulse (SRSP) channel to capture spectrally segmented modal profiles of a single femtosecond pulse. A 50:50 beamsplitter directs the event into both channels; complementary shutters select which channel is recorded.

CUP unit (RTP mode): The RTP path directly launches the event into the CUP unit, which uses complementary spatial encoding and a streak camera to temporally shear and integrate the scene for compressed-sensing reconstruction. Frame rate is adjustable from ~1 MHz to 2 THz; RTP operation here reached up to 2 THz (500 fs inter-frame), sufficient for resolving inter-round-trip timing but not intra-pulse femtosecond structures. Reconstruction yields volumetric x–y–t datasets of successive round trips.

FACED device and SRSP mode: In the SRSP path, the event is diffracted by a grating (600 grooves/mm, 1.0 µm blaze), relayed to a pair of long, slightly misaligned mirrors. Cardinal modes (discrete angles) undergo different zig-zag paths and return with distinct time delays (100s of ps between modes), effectively segmenting the input spectrum into sub-bands with known delays. The returned spectrally separated sub-pulses are relayed and captured by the same CUP unit, enabling single-shot spectrally resolved spatial profiling. Spectral resolution (number of cardinal modes) depends on the entrance cone angle and mirror misalignment; time delay depends on mirror separation. Potential spectral resolution can reach tens of pm with upgraded FACED.

Laser systems:

• Validation with single-mode (SM) DS fiber laser (1064 nm): NPR mode-locked, output frequency-doubled to ~532 nm (thin BBO ~20 µm) to match CUP photocathode sensitivity; pulses coupled into a short few-mode (FM) fiber (~1 m) using a scanning mirror and lens to selectively excite LP01/LP11/LP21 modes; collimated and sent to RTP channel for capture at up to 1 Gfps–2 Tfps.
• Dynamic mode control: A broadband electro-optic modulator (EOM, 30 MHz bandwidth) acted as an ultrafast variable wave plate. The SM DS train passed through the EOM and was then coupled into the FM fiber. The EOM was driven with a square wave at half the laser repetition rate (e.g., 8 MHz for a 16 MHz laser), producing alternating spatial modes each round trip (mode switching) or rotating patterns (mode rotation). Static verification used a CCD at 1 Hz modulation; dynamic sequences were captured by STS-CUP at 1 Gfps.
• Multimode DS (MM DS) STML fiber laser: A ring cavity combining few-mode (FM) and graded-index (GRIN) MM fibers, all-normal dispersion. Gain: FM double-clad Yb-doped fiber (~4.5 m), cladding-pumped by a high-power MM diode via a signal/pump combiner. The FM gain fiber (core ~10 µm) supports LP01, LP11, LP21, LP02. A GRIN MM fiber (62.5 µm core, ~1 m) is fusion-spliced with core offset (~20 µm) to promote strong multimode operation and reduce modal dispersion. Free-space section provides spectral filtering, signal extraction, polarization control, and NPR-based polarization-dependent transmission for mode-locking. A passive FM fiber with matched core serves as a spatial filter. A bandpass filter enforces spectral constraints, enabling partial or full STML.

Acquisition and reconstruction: CUP reconstructions yield 3D x–y–t data for RTP sequences or spectrally tagged x–y maps for SRSP of single pulses. Frame rates were chosen to trade off temporal span (number of round trips captured) and spatial resolution, keeping sufficient sparsity for compressed-sensing recovery. External CCD images provided time-integrated reference spatial profiles.

• STS-CUP capability: Achieved single-shot multi-dimensional imaging across space (x,y), discrete time (round trips), and wavelength. Operated up to 2 trillion frames per second (2 THz; 500 fs inter-frame) in SRSP; flexible from ~1 MHz to 2 THz overall.
• Validation of spatial modes: Successfully reconstructed sequences of 27 round-trip DSs with distinct LP modes (LP01, LP11, LP21) excited in an FM fiber. Measured repetition rate was 16 MHz from reconstructed data (62 ns period), matching photodetector measurements.
• Dynamic mode control: Using an EOM driven at half the pulse repetition rate (8 MHz for 16 MHz laser), STS-CUP captured alternating spatial modes (mode switching) and continuous rotation (~40°) of LP21 on successive round trips at 1 Gfps, demonstrating single-shot visualization of engineered per-round-trip modal changes.
• Multimode STML laser dynamics: Real-time STS-CUP revealed complex, stochastic modal dynamics indicative of partially detuned STML conditions. Observed behaviors included periodic switching between spatial profiles over round trips and random-periodicity changes over microsecond timescales. The number of coexisting 3D solitons varied with cavity parameters/pump power (examples with 1, 2, and 3 coexisting solitons), with instances of as few as two distinguished pulses.
• Spectrally resolved single-pulse imaging: At 2 THz, SRSP captured spectrally segmented spatial profiles of a single 3D DS using FACED cardinal modes. Clear wavelength dependence of modal composition was observed across distinct spectral components, evidencing that STML pulses are spectrally multimode with wavelength-varying modal amplitudes/phases. Potential spectral resolution can be improved to tens of pm with FACED upgrades.
• Recording span: With reduced streak rate (500 MHz), dynamics of up to 60 consecutive round-trip events were reconstructed, illustrating trade-offs among frame rate, temporal span, and spatial resolution.

The results directly address the challenge of observing non-repeatable, stochastic 3D DS dynamics by enabling single-shot, multi-dimensional imaging. By combining RTP and SRSP modes, STS-CUP reveals per-round-trip spatial evolution and intra-pulse spectral-modal structure, providing insights into how spatio-temporal and spectral degrees of freedom couple in multimode DS formation and stability. Observations of periodic and random modal switching, varying numbers of coexisting solitons, and strong wavelength dependence of modal content illuminate the underlying nonlinear interactions in STML multimode lasers, including roles of modal dispersion, chromatic dispersion, and nonlinear effects (SPM, XPM, FWM, Raman). These measurements validate that STML pulses are inherently spectrally multimode and that round-trip modal dynamics can be rich and non-repeatable in partially detuned regimes. The technology thus offers a path to disentangle complex DS behaviors and inform the design and control of multimode laser cavities and related nonlinear systems.

This work introduces STS-CUP as a single-shot, ultrafast, multi-dimensional imaging platform for non-repeatable dissipative soliton dynamics, integrating RTP capture of round-trip evolution with SRSP spectrally resolved single-pulse imaging. The system operates up to 2 THz and reveals (i) per-round-trip spatial mode dynamics (including engineered mode switching/rotation), (ii) stochastic and periodic modal behaviors in multimode STML lasers with variable numbers of coexisting solitons, and (iii) strong wavelength dependence of modal composition within a single DS. These contributions provide new tools and observations to understand and control 3D solitons in multimode fibers. Future directions include increasing spectral resolution (tens of pm) via FACED upgrades, enhancing volumetric refresh rate for longer continuous observations, applying STS-CUP to probe soliton collisions and molecule dynamics, and extending to studies of optical turbulence, random lasers, disordered media, and high-capacity STS-multiplexed communications.

• Compressed sensing requirements: Successful reconstruction relies on temporal sparsity (very low duty cycle of mode-locked lasers, ~10^-5). Events with prolonged or dense activity reduce sparsity and reconstruction fidelity.
• Frame-rate vs span trade-off: Capturing longer dynamics (many round trips) necessitates reducing the streak rate, which lowers temporal resolution of inter-round-trip dynamics and may require reducing spatial magnification, diminishing spatial detail.
• Spatial resolution trade-off: Compressing more information into a single CUP frame can reduce pixel resolution for each spatial profile, limiting the ability to resolve fine features of complex solitons.
• Maximum consecutive events: In this study, up to 60 consecutive round-trip events were reconstructed at a 500 MHz streak rate; larger spans further exacerbate trade-offs.
• Refresh rate: The maximum volumetric (x,y,t) refreshing rate is ~50 Hz, limiting continuous observation of long-term evolutions.
• Photocathode spectral sensitivity: The CUP unit used a visible-sensitive photocathode, necessitating SHG to 532 nm for some experiments; replacing with an NIR photocathode could improve directness and efficiency.