Spatiotemporal dynamics of multimode optical solitons

A High-Energy, Wide-Spectrum, Spatiotemporal Mode-Locked Fiber Laser

In this article, we demonstrate a high-energy, wide-spectrum, spatiotemporal mode-locked (STML) fiber laser. Unlike traditional single-mode fiber lasers, STML fiber lasers theoretically enable mode-locking with various combinations of transverse modes. The laser can deliver two different STML pulse sequences with different pulse widths, spectra and beam profiles, due to the different compositions of transverse modes in the output pulses. Moreover, we achieve a wide-spectrum pulsed output with a single-pulse energy of up to 116 nJ, by weakening the spectral filtering and utilizing self-cleaning. Strong spatial and spectral filtering are usually thought to be necessary for achieving STML. Our experiment verifies the necessity of spatial filtering for achieving STML, and we show that weakening unnecessary spectral filtering provides an effective way to increase the pulse energy and spectrum width of mode-locked fiber lasers.

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.

Periodically tunable multimode soliton pulsation in a spatiotemporal mode-locked fiber laser

Multimode fiber lasers have become a new platform for investigating nonlinear phenomena since the report on spatiotemporal mode-locking. In this work, the multimode soliton pulsation with a tunable period is achieved in a spatiotemporal mode-locked fiber laser. It demonstrates that the pulsation period drops while increasing the pump power. Moreover, it is found that different transverse modes have the same pulsation period, asynchronous pulsation evolution and different dynamical characteristics through the spatial sampling technique and the dispersive Fourier transform technique. To further verify the experimental results, we numerically investigate the influences of the gain and the loss on the pulsation properties. It is found that within a certain parameter range, the pulsation period drops and rises linearly with the increase of the gain and the loss, respectively. The obtained results contribute to understanding the formation and regulating of soliton pulsations in fiber lasers.

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.

Nonlinear dynamics of beam self-cleaning on LP11 mode in multimode fibers

We investigate the modal energy flow of the femtosecond-pulsed beam self-cleaning on LP₁₁ mode with the influence of different factors such as the initial fraction of LP₁₁ mode, initial peak power, distribution of high-order modes and the numerical aperture of the fiber. It is interesting that there is a critical value of the initial peak power, Pcr, which is the watershed, not only in the quantitatively dominant transverse mode converting from LP₁₁ mode to LP₀₁ mode, but also in the behavior of HOMs of the transition from Attractor to chaos. Our simulation results may provide a novel perspective to understanding the beam self-cleaning on LP₁₁ mode.

Synthesized spatiotemporal mode-locking and photonic flywheel in multimode mesoresonators

Dissipative Kerr soliton (DKS) frequency combs—also known as microcombs—have arguably created a new field in cavity nonlinear photonics, with a strong cross-fertilization between theoretical, experimental, and technological research. Spatiotemporal mode-locking (STML) not only adds new degrees of freedom to ultrafast laser technology, but also provides new insights for implementing analogue computers and heuristic optimizers with photonics. Here, we combine the principles of DKS and STML to demonstrate the STML DKS by developing an unexplored ultrahigh-quality-factor Fabry–Pérot (FP) mesoresonator based on graded index multimode fiber (GRIN-MMF). Complementing the two-step pumping scheme with a cavity stress tuning method, we can selectively excite either the eigenmode DKS or the STML DKS. Furthermore, we demonstrate an ultralow noise microcomb that enhances the photonic flywheel performance in both the fundamental comb linewidth and DKS timing jitter. The demonstrated fundamental comb linewidth of 400 mHz and DKS timing jitter of 500 attosecond (averaging times up to 25 μs) represent improvements of 25× and 2.5×, respectively, from the state-of-the-art. Our results show the potential of GRIN-MMF FP mesoresonators as an ideal testbed for high-dimensional nonlinear cavity dynamics and photonic flywheel with ultrahigh coherence and ultralow timing jitter.

Here the authors demonstrate spatiotemporal mode-locked dissipative Kerr soliton and enhanced photonic flywheel performances in both the fundamental comb linewidth and DKS timing jitter.

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.

Tunable mode-locked fiber laser based on nonlinear multimode interference with double offset-splicing step-index few-mode fiber

A tunable mode-locked all-fiber Yb-doped laser with a double offset-splicing step-index few-mode fiber (DOS-SIFMF) is demonstrated, to the best of our knowledge, for the first time. The structure of DOS-SIFMF, which constructs a micro Mach-Zehnder interferometer as a consequence of introducing offset splicing, has characteristics of both a saturable absorber and filter and is more accessible to obtain mode-locking operation in an all-normal dispersive region. The results of simulation show that interference with fewer modes is more reliable to acquire mode-locking operation of the fiber laser. The central wavelength, spectrum, and pulse widths are 1032 nm, 6.15 nm, and 28.8 ps, respectively. The output pulse in time and spectrum domains can be tuned in the range of 168.7 ps and 10.7 nm, respectively. This structure has effects of both mode-locking and filtering, showing potential application in communication and sensing. Furthermore, the influence on mode number to interference is generally discussed in the end.

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.

Multimode solitons in step-index fibers

We experimentally generate multimode solitons in step-index fibers, where nonlinearity compensates for both chromatic and modal dispersion. These solitons are subject to Raman self-frequency shift, and their energy is gradually transfered to the fundamental fiber mode. We compare multimode soliton dynamics in both step-index and graded index fibers, in excellent agreement with numerical predictions.

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.

Observation of spatial nonlinear self-cleaning in a few-mode step-index fiber for special distributions of initial excited modes

In this paper, we experimentally demonstrate that a nonlinear Kerr effect in suitable coupling conditions can introduce a spatially self-cleaned output beam for a few-mode step-index fiber. The impact of the distribution of the initial excited modes on spatial beam self-cleaning has been demonstrated. It is also shown experimentally that for specific initial conditions, the output spatial pattern of the pulsed laser can be reshaped into the LP11 mode due to nonlinear coupling among the propagating modes. Self-cleaning into LP11 mode required higher input powers with respect to the power threshold for LP01 mode self-cleaning. Our experimental results are in agreement with the results of numerical calculations.

Spatial Beam Self-Cleaning in Bi-Tapered Multimode Fibers

We report the spatial beam self-cleaning in bi-tapered conventional multimode fibers (MMFs) with different tapered lengths. Through the introduction of the bi-tapered structure in MMFs, the input beam with poor beam quality from a high-power fiber laser can be converted to a centered, bell-shaped beam in a short length, due to the strengthened nonlinear modes coupling. It is found that the bi-tapered MMF with longer tapered length at the same waist diameter shows better beam self-cleaning effect and larger spectral broadening. The obtained results offer a new method to improve the beam quality of high-power laser at low cost. Furthermore, it may be interesting for manufacturing bi-tapered MMF-based devices to obtain the quasi-fundamental mode beam in spatiotemporal mode-locked fiber lasers.

Modal dynamics in multimode optical fibers: an attractor of high-order modes

Multimode fibers (MMFs) support abundant spatial modes and involve rich spatiotemporal dynamics, yielding many promising applications. Here, we investigate the influences of the number and initial energy of high-order modes (HOMs) on the energy flow from the intermediate modes (IMs) to the fundamental mode (FM) and HOMs. It is quite surprising that random distribution of high-order modes evolves to a stationary one, indicating the asymptotic behavior of orbits in the same attraction domain. By employing the Lyapunov exponent, we prove that the threshold of the HOMs-attractor is consistent with the transition point of the energy flow which indicates the HOMs-attracotr acts as a "valve" in the modal energy flow. Our results provide a new perspective to explore the nonlinear phenomena in MMFs, such as Kerr self-cleaning, and may pave the way to some potential applications, such as secure communications in MMFs.

Origin of spontaneous wave mixing processes in multimode GRIN fibers

We show that geometric parametric instability (GPI) in graded-index multimode fibers is strongly influenced by higher-order dispersion. By measuring the output spectrum for different core radii, we distinguish peaks generated by GPI from other coexisting parametric processes using phase-matching arguments and numerical simulations. We highlight for the first time a non-degenerate GPI process involving two pumps at different wavelengths.

Study of wavelength-dependent pulse self-compression for high intensity pulse propagation in gas-filled capillaries

We theoretically investigate the wavelength-dependent pulse self-compression dynamics of intense femtosecond laser pulses in gas-filled capillaries. Simulations with λ = 1, 2, 3 and 4 µm using the multimode carrier-resolved unidirectional pulse propagation equation reveal pulse self-compression or pulse broadening depending on plasma and modal dispersion. Our study shows that the pulse at 1 µm exhibits better pulse self-compression compared with longer wavelengths due to smaller group velocity mismatch between fundamental and higher-order capillary modes.

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.

Depolarization of Light in Optical Fibers: Effects of Diffraction and Spin-Orbit Interaction

Polarization is measured very often to study the interaction of light and matter, so the description of the polarization of light beams is of both practical and fundamental interest. This review discusses the polarization properties of structured light in multimode graded-index optical fibers, with an emphasis on the recent advances in the area of spin-orbit interactions. The basic physical principles and properties of twisted light propagating in a graded index fiber are described: rotation of the polarization plane, Laguerre–Gauss vector beams with polarization-orbital angular momentum entanglement, splitting of degenerate modes due to spin-orbit interaction, depolarization of light beams, Berry phase and 2D and 3D degrees of polarizations, etc. Special attention is paid to analytical methods for solving the Maxwell equations of a three-component field using perturbation analysis and quantum mechanical approaches. Vector and tensor polarization degrees for the description of strongly focused light beams and their geometrical interpretation are also discussed.

Generation of coherent multicolor noise-like pulse complex in Yb-doped fiber laser mode-locked by GIMF-SA

We have demonstrated the generation of multicolor noise-like pulse complex in a passively Yb-doped mode-locked fiber laser based on a single mode-graded index multimode-single mode fiber (SMF-GIMF-SMF) device as the saturable absorber (SA). The stimulated Raman scattering (SRS) effect leads to the cascaded generation of the main noise-like pulse (NLP) at 1028.8 nm together with the noise like Raman pulse (RP) at 1076.1 nm. The generated dual wavelength pulses demonstrate the unique properties of mutually synchronization and coherence. The autocorrelation traces show that each of the synchronously mode-locked pulses exhibits a double-scale structure with a narrow peak which consists of a train of quasi-periodic beat pulses with a 35.7 fs pulse width and a pulse separation of about 77.2 fs. The total output power reaches 102.5 mW with 34% of it belonging to the RP. And furthermore, by separating the two pulses with spectral filters, the modulation fringes cannot be observed anymore. These results indicate that the Raman component participates in the mode-locking operation as a 'signal' instead of 'noise'. Such a coherent Raman pulse source provides a novel platform for numerous applications, such as frequency comb spectroscopy and so on.

Real-time multispeckle spectral-temporal measurement unveils the complexity of spatiotemporal solitons

The dynamics of three-dimensional (3D) dissipative solitons originated from spatiotemporal interactions share many common characteristics with other multi-dimensional phenomena. Unveiling the dynamics of 3D solitons thus permits new routes for tackling multidisciplinary nonlinear problems and exploiting their instabilities. However, this remains an open challenge, as they are multi-dimensional, stochastic and non-repeatable. Here, we report the real-time speckle-resolved spectral-temporal dynamics of a 3D soliton laser using a single-shot multispeckle spectral-temporal technology that leverages optical time division multiplexing and photonic time stretch. This technology enables the simultaneous observation on multiple speckle grains to provide long-lasting evolutionary dynamics on the planes of cavity time (t) - roundtrip and spectrum (λ) - roundtrip. Various non-repeatable speckly-diverse spectral-temporal dynamics are discovered in both the early and established stages of the 3D soliton formation.

3D time-domain beam mapping for studying nonlinear dynamics in multimode optical fibers

Characterization of the complex spatiotemporal dynamics of optical beam propagation in nonlinear multimode fibers requires the development of advanced measurement methods, capable of capturing the real-time evolution of beam images. We present a new space-time mapping technique, permitting the direct detection, with picosecond temporal resolution, of the intensity from repetitive laser pulses over a grid of spatial samples from a magnified image of the output beam. By using this time-resolved mapping, we provide, to the best of our knowledge, the first unambiguous experimental observation of instantaneous intrapulse nonlinear coupling processes among the modes of a graded index fiber.

Recent progress in all-fiber ultrafast high-order mode lasers

Ultrafast high-order mode (HOM) lasers are a relatively new class of ultrafast optics. They play a significant role in the fieldsof scientific research and industrial applications due to the high peak power and unique properties of spatial intensity and polarization distribution. Generation of ultrafast HOM beams in all-fiber systems has become an important research direction. In this paper, all-fiber mode conversion techniques, pulsed HOM laser strategies, and few-mode/multi-mode fiber (FMF/MMF) lasers are reviewed. The main motivation of this review is to highlight recent advances in the field of all-fiber ultrafast HOM lasers, for example, generating different HOM pulses based on fiber mode converters and mode-locking in the FMF/MMF lasers. These results suggest that mode selective coupler can be used as a broad bandwidth mode converter with fast response and HOM can be directly oscillated in the FMF/MMF laser cavity with high stability. In addition, spatiotemporal mode-locking in the FMF/MMF is also involved. It is believed that the development of all-fiber ultrafast HOM lasers will continue to deepen, thus laying a good foundation for future applications.

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-power synchronous multi-wavelength solitons from a multimode mode-locked fiber laser system

In this Letter, we implement a multimode fiber (MMF) laser system mode-locked by a nonlinear polarization rotation technique for controllable synchronous multi-wavelength soliton generation. The synchronization of the repetition rates for different wavelengths is realized by the special mode transmission in MMF. For dual-wavelength mode-locking at 1566.7 nm and 1617.2 nm, each of the synchronously mode-locked solitons consists of a train of quasi-periodic beat pulses with a pulse width of 84 fs and period of 162 fs. The total output power reaches 532 mW with optimally balanced two-color intensities. Furthermore, switchable dual- and tri-wavelength synchronized femtosecond pulses are also obtained. In contrast to previous reports, this synchronously mode-locked multi-wavelength is output directly from a laser oscillator, which provides a simpler candidate to achieve pulse synchronization.

Recent advances in real-time spectrum measurement of soliton dynamics by dispersive Fourier transformation

Mode-locking lasers have not only produced huge economic benefits in industrial fields and scientific research, but also provided an excellent platform to study diverse soliton phenomena. However, the real-time characterization of the ultrafast soliton dynamics remains challenging for traditional electronic instruments due to their relatively low response bandwidth and slow scan rate. Consequently, it is urgent for researchers to directly observe these ultrafast evolution processes, rather than just indirectly understand them from numerical simulations or averaged measurement data. Fortunately, dispersive Fourier transformation (DFT) provides a powerful real-time measurement technique to overcome the speed limitations of traditional electronic measurement devices by mapping the frequency spectrum onto the temporal waveform. In this review, the operation principle of DFT is discussed and the recent progress in characterizing the ultrafast transient soliton dynamics of mode-locking lasers is summarized, including soliton explosions, soliton molecules, noise-like pulses, rogue waves, and mode-locking buildup processes.

Fragility of a soliton's shot-to-shot coherence

We show that a soliton in a high-order spatial mode of a multi-mode fiber can completely lose its shot-to-shot coherence due to a noise seed with energy orders of magnitude below that of the soliton. The total degradation of shot-to-shot coherence is caused by a very strong recently demonstrated intermodal nonlinear effect, soliton self-mode conversion. The results indicate that the robustness of solitons against perturbations is not entirely applicable in the presence of intermodal nonlinearities, and, more generally, that certain single-mode results cannot be trivially extrapolated to multi-mode fibers.

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.

Investigation on saturable absorbers based on nonlinear Kerr beam cleanup effect

We experimentally investigate characteristics of saturable absorbers (SAs) based on nonlinear Kerr beam cleanup effect (NL-KBC). The SAs are formed by a long graded-index multimode fiber (GRIN MMF) with a short single-mode fiber served as a diaphragm. We studied the evolution of output spectrum and beam profiles from the GRIN MMF in order to investigate the mechanism of these SAs. We further performed saturable absorption measurements to evaluate their modulation depths and saturation intensities. We experimentally observed and first theoretically analyzed the "relaxation oscillation" behavior of the optical transmittance with increasing input intensity. We also studied their nonlinear polarization dynamics and observed the repolarized effect in NL-KBC regime. Our results confirm the optical properties of the SAs based on NL-KBC, and these SAs can find applications in Q-switched and mode-locked lasers.

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.

Spatial beam self-cleaning and supercontinuum generation with Yb-doped multimode graded-index fiber taper based on accelerating self-imaging and dissipative landscape

We experimentally demonstrate spatial beam self-cleaning and supercontinuum generation in a tapered Ytterbium-doped multimode optical fiber with parabolic core refractive index profile when 1064 nm pulsed beams propagate from wider (122 µm) into smaller (37 µm) diameter. In the passive mode, increasing the input beam peak power above 20 kW leads to a bell-shaped output beam profile. In the active configuration, gain from the pump laser diode permits to combine beam self-cleaning with supercontinuum generation between 520-2600 nm. By taper cut-back, we observed that the dissipative landscape, i.e., a non-monotonic variation of the average beam power along the MMF, leads to modal transitions of self-cleaned beams along the taper length.

Selective wavelength conversion in a few-mode fiber

We experimentally demonstrate a means to selectively enhance wavelength conversion of WDM channels on a 100 GHz grid exploiting nonlinear effects between the spatial modes of a few mode fiber. The selectivity of parametric gain is obtained by dispersion design of the fiber such that the inverse group velocity curves of the participating modes are parallel and their dispersion is suitably large. We describe both theoretically and experimentally the observed dependence of the idler gain profile on pump mode (quasi) degeneracy.

Continuously wavelength-tunable mode-locked Tm fiber laser using stretched SMF-GIMF-SMF structure as both saturable absorber and filter

We demonstrate, for the first time, use of a stretched single mode-graded-index multimode-single mode fiber (SMF-GIMF-SMF) structure as a saturable absorber (SA) for a passively mode-locked Tm fiber laser. Such an all-fiber SA was based on the nonlinear multimode interference (NL-MMI). Stable fundamentally mode-locking operation was obtained at a pump threshold of 100mW. The output soliton pulses had a center wavelength, spectral width, pulse duration, and repetition rate of 1931 nm, 3.77 nm, 1.2ps, and 19.94 MHz, respectively. Furthermore, the SMF-GIMF-SMF structure can also be used as a filter to tune the laser. Continuously tunable mode-locking was experimentally demonstrated only by varying the stretched length of GIMF. Our results indicate that the stretched SMF-GIMF-SMF structure could serve as a SA together with a bandpass filter, which makes it advantageous for wavelength-tunable mode locking lasers.

Accelerated nonlinear interactions in graded-index multimode fibers

Multimode optical fibers have recently reemerged as a viable platform for addressing a number of long-standing issues associated with information bandwidth requirements and power-handling capabilities. As shown in recent studies, the complex nature of such heavily multimoded systems can be effectively exploited to observe altogether novel physical effects arising from spatiotemporal and intermodal linear and nonlinear processes. Here, we study for the first time, accelerated nonlinear intermodal interactions in core-diameter decreasing multimode fibers. We demonstrate that in the anomalous dispersion region, this spatiotemporal acceleration can lead to relatively blue-shifted multimode solitons and blue-drifting dispersive wave combs, while in the normal domain, to a notably flat and uniform supercontinuum, extending over 2.5 octaves. Our results pave the way towards a deeper understanding of the physics and complexity of nonlinear, heavily multimoded optical systems, and could lead to highly tunable optical sources with very high spectral densities.

Multimode optical fibers can be used to observe complex intermodal processes like optical solitons. Here, Eftekhar et al. study accelerated nonlinear interaction in multimode fibers with a tapered core diameter and its effect on the temporal and spectral behavior of the multimode 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.

Graded-index solitons in multimode fibers

We investigate stability of optical solitons in graded-index (GRIN) fibers by solving an effective nonlinear Schrödinger equation that includes spatial self-imaging effects through a length-dependent nonlinear parameter. We show that this equation can be reduced to the standard NLS equation for optical pulses whose dispersion length is much longer than the self-imaging period of the GRIN fiber. Numerical simulations are used to reveal that fundamental GRIN solitons as short as 100 fs can form and remain stable over distances exceeding 1 km. Higher-order solitons can also form, but they propagate stably over shorter distances. We also discuss the impact of third-order dispersion on a GRIN soliton.

Normal and anomalous random walks of 2-d solitons

Solitons, which describe the propagation of concentrated beams of light through nonlinear media, can exhibit a variety of behaviors as a result of the intrinsic dissipation, diffraction, and the nonlinear effects. One of these phenomena, modeled by the complex Ginzburg-Landau equation, is chaotic explosions, transient enlargements of the soliton that may induce random transversal displacements, which in the long run lead to a random walk of the soliton center. As we show in this work, the transition from nonmoving to moving solitons is not a simple bifurcation but includes a sequence of normal and anomalous random walks. We analyze their statistics with the distribution of generalized diffusivities, a novel approach that has been used successfully for characterizing anomalous diffusion.

Photon pair generation with tailored frequency correlations in graded-index multimode fibers

We study theoretically the generation of photon pairs with controlled spectral correlations via the four-wave mixing process in graded-index multimode optical fibers (GIMFs). We show that the quantum correlations of the generated photons in GIMFs can be preserved over a wide spectral range for a tunable pump source. Therefore, GIMFs can be utilized as quantum-state-preserving tunable sources of photons. In particular, we have shown that it is possible to generate factorable two-photon states, which allow for heralding of pure-state single photons without the need for narrowband spectral post filtering. We also elaborate on the possibility of simultaneously generating correlated and uncorrelated photon pairs in the same optical fiber.

Stretched graded-index multimode optical fiber as a saturable absorber for erbium-doped fiber laser mode locking

A novel mode-locking method based on the nonlinear multimode interference in the stretched graded-index multimode optical fiber (GIMF) is proposed in this Letter. The simple device geometry, where the light is coupled in and out of the stretched GIMF via single-mode fibers, is demonstrated to exhibit the temporal intensity discrimination required for mode locking. The nonlinear saturable absorber (SA) characteristics of the device are controllable by simply adjusting the strength of the stretching applied. The modulation depth of the device, which consists of ∼23.5  cm GIMF, is tuned from 10.37% to 22.27%. Such a simple SA enables the wavelength-switchable mode-locking operation in a ring Er-doped fiber laser, and ultrafast pulses with a pulse width of 506 fs at 1572.5 nm and 416 fs at 1591.4 nm were generated. The versatility and simplicity of the SA device, together with the possibility of scaling the pulse energy, make it highly attractive in ultrafast photonics.

Observation of soliton molecules in a spatiotemporal mode-locked multimode fiber laser

We report on the first experimental observation, to the best of our knowledge, of soliton molecules in a spatiotemporal mode-locked multimode fiber (MMF) laser. By adjusting the waveplates inside the cavity, not only the spatiotemporal mode-locking state with a stable single pulse but also soliton molecules are observed. Various soliton molecules, including soliton pairs, soliton triplets, and soliton quartets with different pulse separations, are achieved. Transition of different operation states with pump power is given. The results would be beneficial for further understanding of the nonlinear dynamics in spatiotemporal mode-locked MMF lasers.

Several new directions for ultrafast fiber lasers [Invited]

Ultrafast fiber lasers have the potential to make applications of ultrashort pulses widespread - techniques not only for scientists, but also for doctors, manufacturing engineers, and more. Today, this potential is only realized in refractive surgery and some femtosecond micromachining. The existing market for ultrafast lasers remains dominated by solid-state lasers, primarily Ti:sapphire, due to their superior performance. Recent advances show routes to ultrafast fiber sources that provide performance and capabilities equal to, and in some cases beyond, those of Ti:sapphire, in compact, versatile, low-cost devices. In this paper, we discuss the prospects for future ultrafast fiber lasers built on new kinds of pulse generation that capitalize on nonlinear dynamics. We focus primarily on three promising directions: mode-locked oscillators that use nonlinearity to enhance performance; systems that use nonlinear pulse propagation to achieve ultrashort pulses without a mode-locked oscillator; and multimode fiber lasers that exploit nonlinearities in space and time to obtain unparalleled control over an electric field.

Design for a high birefringence photonic crystal fiber with multimode and low loss

In this work, a novel design of a high birefringence photonic crystal fiber (HB-PCF) with multimode and low confinement loss is proposed. To achieve high birefringence, the core is designed as an elliptical region, which is enclosed by twelve small holes. Based on this design, replacing the two circular holes at the top and bottom of the core region with two elliptical holes can further improve the birefringence. At the wavelength of 1.55 μm, the birefringence of the fundamental mode (LP₀₁) and the second-order mode (LP₁₁) are 1.70×10^-2 and 1.85×10^-2, respectively. Meanwhile, the confinement losses maintain on orders of 1×10^-5  dB/km (LP₀₁) and 1×10^-1  dB/km (LP₁₁). After the effective refractive indices of two types of the proposed HB-PCF are calculated by the finite element method, the birefringence, confinement loss, bending loss, dispersion, and nonlinear coefficient are studied. These results reveal that the HB-PCF might be applied for polarization-maintaining and nonlinear optics.

Mode-locked Tm fiber laser using SMF-SIMF-GIMF-SMF fiber structure as a saturable absorber

We demonstrate a mode-locked all-fiber Tm laser using a single mode-step index multimode-graded-index multimode-single mode fiber structure as a saturable absorber based on the nonlinear multimodal interference. Stable fundamentally mode-locking operation was obtained at a pump threshold of 180mW. The output soliton pulses had a center wavelength, spectral width, pulse duration, and repetition rate of 1888 nm, 3.6 nm, 1.4 ps, and19.82 MHz, respectively. This is a simple, low-cost, stable, and convenient laser oscillator with many potential applications in eye-safe ultrafast photonics.

Spatiotemporal mode-locking in multimode fiber lasers

A laser is based on the electromagnetic modes of its resonator, which provides the feedback required for oscillation. Enormous progress has been made toward controlling the interactions of longitudinal modes in lasers with a single transverse mode. For example, the field of ultrafast science has been built on lasers that lock many longitudinal modes together to form ultrashort light pulses. However, coherent superposition of longitudinal and transverse modes in a laser has received little attention. We show that modal and chromatic dispersions in fiber lasers can be counteracted by strong spatial and spectral filtering. This allows locking of multiple transverse and longitudinal modes to create ultrashort pulses with a variety of spatiotemporal profiles. Multimode fiber lasers thus open new directions in studies of nonlinear wave propagation and capabilities for applications.

Fast and accurate modeling of nonlinear pulse propagation in graded-index multimode fibers

We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists of a 1+1D generalized nonlinear Schrödinger equation with a periodic nonlinear coefficient, which can be solved in an extremely fast and efficient way. The model is able to quantitatively reproduce recently observed phenomena like geometric parametric instability and broadband dispersive wave emission. We envisage that our equation will represent a valuable tool for the study of spatiotemporal nonlinear dynamics in the growing field of multimode fiber optics.

Instant and efficient second-harmonic generation and downconversion in unprepared graded-index multimode fibers

We show that germanium-doped graded-index multimode silica fibers can exhibit relatively high conversion efficiencies (∼6.5%) for second-harmonic generation when excited at 1064 nm. This frequency-doubling behavior is also found to be accompanied by an effective downconversion. As opposed to previous experiments carried out in single- and few-mode fibers where hours of preparation were required, in our system, these χ⁽²⁾ related processes occur almost instantaneously. The efficiencies observed in our experiments are, to the best of our knowledge, among the highest ever reported in unprepared fibers.