Graded-index solitons in multimode fibers

Spectral-temporal-spatial customization via modulating multimodal nonlinear pulse propagation

Multimode fibers (MMFs) are gaining renewed interest for nonlinear effects due to their high-dimensional spatiotemporal nonlinear dynamics and scalability for high power. High-brightness MMF sources with effective control of the nonlinear processes would offer possibilities in many areas from high-power fiber lasers, to bioimaging and chemical sensing, and to intriguing physics phenomena. Here we present a simple yet effective way of controlling nonlinear effects at high peak power levels. This is achieved by leveraging not only the spatial but also the temporal degrees of freedom during multimodal nonlinear pulse propagation in step-index MMFs, using a programmable fiber shaper that introduces time-dependent disorders. We achieve high tunability in MMF output fields, resulting in a broadband high-peak-power source. Its potential as a nonlinear imaging source is further demonstrated through widely tunable two-photon and three-photon microscopy. These demonstrations provide possibilities for technology advances in nonlinear optics, bioimaging, spectroscopy, optical computing, and material processing.

Statistics of modal condensation in nonlinear multimode fibers

Optical pulses traveling through multimode optical fibers encounter the influence of both linear disturbances and nonlinearity, resulting in a complex and chaotic redistribution of power among different modes. In our research, we explore the phenomenon where multimode fibers reach stable states marked by the concentration of energy into both single and multiple sub-systems. We introduce a weighted Bose-Einstein law, demonstrating its suitability in describing thermalized modal power distributions in the nonlinear regime, as well as steady-state distributions in the linear regime. We apply the law to experimental results and numerical simulations. Our findings reveal that, at power levels situated between the linear and soliton regimes, energy concentration occurs locally within higher-order modal groups before transitioning to global concentration in the fundamental mode within the soliton regime. This research broadens the application of thermodynamic principles to multimode fibers, uncovering previously unexplored optical states that exhibit characteristics akin to optical glass.

Nature of Optical Thermodynamic Pressure Exerted in Highly Multimoded Nonlinear Systems

The theory of optical thermodynamics provides a comprehensive framework that enables a self-consistent description of the intricate dynamics of nonlinear multimoded photonic systems. This theory, among others, predicts a pressurelike intensive quantity (p[over ^]) that is conjugate to the system's total number of modes (M)-its corresponding extensive variable. Yet at this point, the nature of this intensive quantity is still nebulous. In this Letter, we elucidate the physical origin of the optical thermodynamic pressure and demonstrate its dual essence. In this context, we rigorously derive an expression that splits p[over ^] into two distinct components, a term that is explicitly tied to the electrodynamic radiation pressure and a second entropic part that is responsible for the entropy change. We utilize this result to establish a formalism that simplifies the quantification of radiation pressure under nonlinear equilibrium conditions, thus eliminating the need for a tedious evaluation of the Maxwell stress tensor. Our theoretical analysis is corroborated by numerical simulations carried out in highly multimoded nonlinear optical structures. These results may provide a novel way in predicting and controlling radiation pressure processes in a variety of nonlinear electromagnetic settings.

Spatiotemporal mode-locking and dissipative solitons in multimode fiber lasers

Multimode fiber (MMF) lasers are emerging as a remarkable testbed to study nonlinear spatiotemporal physics with potential applications spanning from high energy pulse generation, precision measurement to nonlinear microscopy. The underlying mechanism for the generation of ultrashort pulses, which can be understood as a spatiotempoal dissipative soliton (STDS), in the nonlinear multimode resonators is the spatiotemporal mode-locking (STML) with simultaneous synchronization of temporal and spatial modes. In this review, we first introduce the general principles of STML, with an emphasize on the STML dynamics with large intermode dispersion. Then, we present the recent progress of STML, including measurement techniques for STML, exotic nonlinear dynamics of STDS, and mode field engineering in MMF lasers. We conclude by outlining some perspectives that may advance STML in the near future.

Deformation of optical solitons in a variable-coefficient nonlinear Schrödinger equation with three distinct PT-symmetric potentials and modulated nonlinearities

We investigate deformed/controllable characteristics of solitons in inhomogeneous parity-time (PT)-symmetric optical media. To explore this, we consider a variable-coefficient nonlinear Schrödinger equation involving modulated dispersion, nonlinearity, and tapering effect with PT-symmetric potential, which governs the dynamics of optical pulse/beam propagation in longitudinally inhomogeneous media. By incorporating three physically interesting and recently identified forms of PT-symmetric potentials, namely, rational, Jacobian periodic, and harmonic-Gaussian potentials, we construct explicit soliton solutions through similarity transformation. Importantly, we investigate the manipulation dynamics of such optical solitons due to diverse inhomogeneities in the medium by implementing step-like, periodic, and localized barrier/well-type nonlinearity modulations and revealing the underlying phenomena. Also, we corroborate the analytical results with direct numerical simulations. Our theoretical exploration will provide further impetus in engineering optical solitons and their experimental realization in nonlinear optics and other inhomogeneous physical systems.

Multimode nonlinear dynamics in spatiotemporal mode-locked anomalous-dispersion lasers

Spatiotemporal mode-locking in a laser with anomalous dispersion is investigated. Mode-locked states with varying modal content can be observed, but we find it difficult to observe highly-multimode states. We describe the properties of these mode-locked states and compare them to the results of numerical simulations. Prospects for the generation of highly-multimode states and lasers based on multimode soliton formation are discussed.

Two octave supercontinuum generation in a non-silica graded-index multimode fiber

The generation of a two-octave supercontinuum from the visible to mid-infrared (700-2800 nm) in a non-silica graded-index multimode fiber is reported. The fiber design is based on a nanostructured core comprised of two types of drawn lead-bismuth-gallate glass rods with different refractive indices. This yields an effective parabolic index profile and ten times increased nonlinearity when compared to silica fibers. Using femtosecond pulse pumping at wavelengths in both normal and anomalous dispersion regimes, a detailed study is carried out into the supercontinuum generating mechanisms and instabilities seeded by periodic self-imaging. Significantly, suitable injection conditions in the high power regime are found to result in the output beam profile showing clear signatures of beam self-cleaning from nonlinear mode mixing. Experimental observations are interpreted using spatio-temporal 3+1D numerical simulations of the generalized nonlinear Schrödinger equation, and simulated spectra are in excellent agreement with experiment over the full two-octave spectral bandwidth. Experimental comparison with the generation of supercontinuum in a silica graded-index multimode fiber shows that the enhanced nonlinear refractive index of the lead-bismuth-gallate fiber yields a spectrum with a significantly larger bandwidth. These results demonstrate a new pathway towards the generation of bright, ultrabroadband light sources in the mid-infrared.

All-fiber high-power spatiotemporal mode-locked laser based on multimode interference filtering

Multimode interference (MMI) has been considered to be critical and investigated extensively in mode-locked laser based on single transverse mode systems, whereas there are few researches related to three-dimensional nonlinear dynamics within lasers. In this paper, we demonstrate all-fiber high-power spatiotemporal mode-locked (STML) laser by optimizing MMI filtering, where we find that the MMI filtering plays an important role in counteracting the coupling of high-order modes and improving output power of STML laser. The results under weak coupling condition when the length of graded-index multimode fiber (GIMF) is integral multiple of beat length show that the oscillator generates dissipative soliton pulses at 1036.86 nm with pulse width of 5.65 ps, and the slope efficiency of pump-signal is up to 10.3% with average power/energy of 215 mW/6 nJ, which is the highest among all-fiber STML lasers in normal dispersion regime. Besides, the multiple-soliton of STML, including multiple pulses and harmonic mode-locking can be observed in the experiment. Our work significantly broadens the dimensions of design for all-fiber high-power STML and makes them much more accessible for being put into applications.

High-Peak Power Frequency Modulation Pulse Generation in Cascaded Fiber Configurations with Inscribed Fiber Bragg Grating Arrays

We explored the dynamics of frequency-modulated (FM) pulses in a cascaded fiber configuration comprising one active and one passive optical fiber with multiple fiber Bragg gratings (FBGs) of different periods inscribed over the fiber configuration length. We present a theoretical formalism to describe the mechanisms of the FM pulse amplification and pulse compression in such fiber cascades resulting in peak powers up to ~0.7 MW. In combination with the decreasing dispersion fibers, the considered cascade configuration enables pico- and sub-picosecond pulse trains with a sub-terahertz repetition rate and sub-kW peak power generated directly from the continuous optical signal.

Conditions for walk-off soliton generation in a multimode fiber

It has been recently demonstrated that multimode solitons are unstable objects which evolve, in the range of hundreds of nonlinearity lengths, into stable single-mode solitons carried by the fundamental mode. We show experimentally and by numerical simulations that femtosecond multimode solitons composed by non-degenerate modes have unique properties: when propagating in graded-index fibers, their pulsewidth and energy do not depend on the input pulsewidth, but only on input coupling conditions and linear dispersive properties of the fiber, hence on their wavelength. Because of these properties, spatiotemporal solitons composed by non-degenerate modes with pulsewidths longer than a few hundreds of femtoseconds cannot be generated in graded-index fibers.

Weak beam self-cleaning of femtosecond pulses in the anomalous dispersion regime

Kerr beam cleaning in graded-index multimode fiber has been investigated in experiments with sub-nanosecond pulses and in experiments with femtosecond pulses at wavelengths where the dispersion is normal. We report a theoretical and experimental study of this effect with femtosecond pulses and anomalous dispersion. In this regime, only weak beam cleaning is observed experimentally, along with strong temporal evolution of the pulse. Numerical simulations exhibit the qualitative trends of the experiments.

Correlation between geometric parametric instability sidebands in graded-index multimode fibers

The spectral analysis of the light propagating in normally dispersive graded-index multimode fibers is performed under initial noisy conditions. Based on the obtained spectra with multiple simulations in the presence of noise, we investigate the correlation in energy between the well-separated spectral sidebands through both the scattergrams and the frequency-dependent energy correlation map and find that conjugate couples are highly correlated while cross-combinations exhibit a very poor degree of correlation. These results reveal that the geometric parametric instability processes associated with each sideband pair occur independently from each other, which can provide significant insights into the fundamental dynamical effect of the geometric parametric instability and facilitate the future implementation of high-efficiency photon pair sources with reduced Raman decorrelations.

High-energy soliton fission dynamics in multimode GRIN fiber

The process of high-energy soliton fission is experimentally and numerically investigated in a graded-index multimode fiber. Fission dynamics is analyzed by comparing experimental observations and simulations. A novel nonlinear propagation regime is observed, where solitons produced by the fission have a nearly constant Raman wavelength shift and same pulse width over a wide range of soliton energies.

2 kW high-efficiency Raman fiber amplifier based on passive fiber with dynamic analysis on beam cleanup and fluctuation

In this paper, we study the power scaling in high power continuous-wave Raman fiber amplifier employing graded-index passive fiber. The maximum output power reaches 2.087 kW at 1130 nm with an optical conversion efficiency of 90.1% (the output signal power versus the depleted pump power). To the best of our knowledge, this is the highest power in the fields of Raman fiber lasers based merely on Stokes radiation. The beam quality parameter M² improves from 15 to 8.9 during the power boosting process, then beam spot distortion appears at high power level. This is the first observation and analysis on erratic dynamic properties of the transverse modes in high power Raman fiber amplifier.

Spatiotemporal dissipative solitons and vortices in a multi-transverse-mode fiber laser

We introduce a model for spatiotemporal modelocking in multimode fiber lasers, which is based on the (3+1)-dimensional cubic-quintic complex Ginzburg-Landau equation (cGLE) with conservative and dissipative nonlinearities and a 2-dimensional transverse trapping potential. Systematic numerical analysis reveals a variety of stable nonlinear modes, including stable fundamental solitons and breathers, as well as solitary vortices with winding number n = 1, while vortices with n = 2 are unstable, splitting into persistently rotating bound states of two unitary vortices. A characteristic feature of the system is bistability between the fundamental and vortex spatiotemporal solitons.

Graded-index breathing solitons from Airy pulses in multimode fibers

Breathing solitons, as localized wave packets with a periodic evolution in amplitude and duration, are able to model extreme wave events in complex nonlinear dispersive systems. We have numerically studied the formation and manipulation of graded-index breathing solitons embedded in nonlinear multimode fibers based on a single nonlinear Schrödinger equation that includes the spatial self-imaging effect through a periodically varying nonlinear parameter. Through changing specific parameters of the input optical field, we can manipulate the period and depth of graded-index breathing soliton dynamics under different relative strengths between the dispersion length and the self-imaging period of the multimode fiber. Our study can explicitly derive a robust mechanism to control the behavior of the breathing localized structure directly and contribute to a better understanding of the much more complex nonlinear graded-index soliton dynamics in multimode fibers.

Fate of a Soliton in a High Order Spatial Mode of a Multimode Fiber

We show numerically that under certain conditions noise-induced soliton self-mode conversion dominates over soliton self-frequency shift for a soliton in a high order spatial mode of a multimode optical fiber. The input soliton has to be group index matched to a lower order mode for a frequency separation for which the Raman gain is non-negligible, and this condition determines the wavelength of the pulse growing from noise. The phenomenon has no known analogs in single-mode or graded-index fibers. The results demonstrate that it is possible for a noise-induced physical process to dominate over a seeded one even for noise levels at the fundamental limit.