Nonlinear Multimode Research Articles

Generation of noise-like pulses in a linear-cavity Tm fiber mode-locked laser based on FMF saturable absorber

As a real saturable absorber (SA) based on the nonlinear multimode interference (NL-MMI) effect, the devices based on the few-mode fiber possess numerous exciting characteristics due to their all-fiber structure, straightforward manufacturing process. In this paper, by employing a SA with the SMF-FMF-SMF structure in a linear cavity, we demonstrate a stable mode-locked Tm-doped fiber laser. At the pump power of 1 W, a single noise-like pulse (NLP) with a pedestal pulse duration of 28 ps and coherent peak width of 0.77 ps is generated at a central wavelength of 1940 nm with a 3 dB bandwidth of 10.51 nm. The stable noise-like pulse can be sustained from the lasing pump threshold up to the maximum pump power of 2.2 W without experiencing pulse splitting. The experiment results in a peak average output power of 116 mW, along with a corresponding maximum pulse energy of 24.73 nJ at a repetition frequency of 4.69 MHz. The high stability of our fiber laser is confirmed by the signal-to-Noise Ratio (SNR) of 63 dB, and its enduring stability is additionally validated over an 8-hour period. The experimental findings suggest that the SMF-FMF-SMF structure has significant potential in the simple and robust all-fiber mode-locked lasers operating in the noise-like pulse regime.

In-fiber waveguide-based mode-locker for generating diverse ultrafast pulses

The pursuit of an optimal mode-locker in nonlinear photonics is crucial for advancing high-performance laser technologies. Addressing the market demands and technical complexities in creating highly integrated and robust saturable absorbers, we present a femtosecond laser-inscribed in-fiber straight waveguide, seamlessly integrating a few-mode fiber segment into a single-mode fiber. This design reduces costs, simplifies fabrication, and enhances system integration and stability. As a saturable absorber, it enables nonlinear polarization rotation and multimode interference, which are essential for ultrafast pulse generation. It exhibits slight polarization-dependent loss and significant modulation depth, effectively inducing mode-locking. Based on the waveguide, 1.36 ps soliton pulses with a 2.9 nm bandwidth at a central wavelength of 1573 nm are initially achieved in an anomalous dispersion regime. Transitioning to the normal dispersion regime, at 190 mW pump power, the system produces Q-switched mode-locked pulses at 1574 nm. Increasing the pump power to 295 mW results in 712 fs noise-like pulses at 1572 nm, featuring an 8 nm bandwidth and 4.57 MHz repetition rate. This advancement in fiber lasers, facilitated by hybrid nonlinear effects in the waveguide, represents a significant milestone, promising for nonlinear optics and photonics due to its simplicity, cost-effectiveness, compactness, robustness, and high damage threshold.

Tunable mode-locked holmium-doped fiber laser based on GIMF-SIMF-GIMF structure at 2.09 µm

In this study, a structure of graded-index multimode fiber-step index multimode fiber-graded index multimode fiber (GIMF-SIMF-GIMF) was used as a saturable absorber (SA) to generate mode-locking in a holmium-doped fiber laser (HDFL). The HDFL was pumped with a compact in-house thulium-doped fiber laser (TDFL) operating at 1943 nm with a maximum output power of 2.1 W. Mode-locked pulses with a pulse duration of 1.61 ps were successfully generated at the center wavelength of 2091.1 nm. The pulse had a repetition rate of 12.79 MHz with a bit of fluctuation of 2.09 %, indicating stable pulses. The mode-locked pulses were also tunable with a range from 2086.5 nm to 2091.1 nm by stretching the GIMF part of the SA. This first report demonstrated mode-locking using nonlinear multimode interference (NL-MMI) using GIMF-SIMF-GIMF structure as a saturable absorber in HDFL operating near 2.1 µm wavelength.

Calorimetry of Photon Gases in Nonlinear Multimode Optical Fibers

Recent studies have shown that light propagating in a nonlinear, highly multimode system can thermalize in a manner totally analogous to that encountered in traditional statistical mechanics. At thermal equilibrium, the system’s entropy is at a maximum, in full accord with the second law of thermodynamics. In such arrangements, the entropy is extremized once the statistical power allocation among modes associated with this photon gas attains a Rayleigh-Jeans distribution that is fully characterized by an optical temperature T and a chemical potential μ. However, it has been theoretically argued that the variables T and μ represent actual thermodynamic forces that control the exchange of the respective conjugate quantities between two subsystems. In this work, we report, for the first time, optical calorimetric measurements in nonlinear multimode fibers, which unambiguously demonstrate that both the temperature T and the chemical potential μ dictate the flow of their associated extensive quantities, i.e., the energy and the optical power. Specifically, we study the process of light thermalization associated with two orthogonally polarized laser beams. Our observations are enabled by recently developed techniques that allow one to judiciously multiplex/demultiplex the optical power within various mode groups. Our results indicate that because of photon-photon collisions, “heat” only flows from a hot to a cold photon gas subsystem—thus providing an unequivocal demonstration of the second law in such all-optical thermodynamic arrangements. In addition to being fundamental, our findings provide a new approach to manipulate laser beams using thermodynamic principles. Published by the American Physical Society 2024

Optical solitons for 2D-NLSE in multimode fiber with Kerr nonlinearity and its modulation instability

This paper deals with the soliton solutions for beam movement within a multimode optical fiber featuring a parabolic index shape. It is considered that a Two-Dimensional Nonlinear Schrödinger Equation (2D-NLSE) with an instantaneous Kerr nonlinearity of the kind can represent the beam dynamics. Nonlinear Multimode Optical Fibers (MMFs) of this kind are gaining popularity because they provide novel approaches to control the spectral, temporal, and spatial characteristics of ultrashort light pulses. We gain the optical soliton solutions for the nonlinear evolution beam dynamics using the Jacobi Elliptic Function Expansion (JEFE) method. The exact analytical solution of Nonlinear Partial Differential Equations (NLPDEs) can be achieved with wide application using the effective JEFE approach. These solutions are obtained in the form of dark, bright, combined dark–bright, complex combo, periodic, and plane wave solutions. Additional solutions for Jacobi elliptic functions, encompassing both single and dual function solutions, have been acquired. This approach is based on Jacobi elliptic functions, which will provide us the exact soliton solutions to nonlinear problems. Additionally, we will analyze the Modulation Instability (MI) for the underlying model. Moreover, we show the physical behavior of the beam propagation in a multimode optical fiber the three-dimensional, two-dimensional, and their corresponding contour plots are dispatched using the different values of parameters.

Nanosecond pulse generation mode-locked by an artificial saturable absorber based on SMF-MMF-SMF structure

We present a noteworthy demonstration of nanosecond pulse generation utilizing an all-fiber artificial saturable absorber (SA) structure, composed of single-mode multimode single-mode fiber (SMF-MMF-SMF), integrated into a passively mode-locked erbium-doped fiber laser (EDFL). The SMS-based SA effectively phase-locked the longitudinal modes within the elongated EDFL cavity, resulting in the production of mode-locked pulses operating at 1567 nm. Mode-locking is achieved through the Kerr effect of nonlinear multimode interference. The pulse repetition rate is synchronized with the fundamental frequency at 1.28 MHz. At a pump power of 269.1 mW, the laser achieves a remarkable peak average pulse energy of 6.0 nJ. Demonstrating outstanding stability, the laser operation exhibits a peak-to-pedestal extinction ratio of 70 dB for the fundamental frequency. We are confident in the substantial potential of this SMS structure, positioning it as a compelling candidate for integration into ultrafast fiber lasers, with promising prospects in the field.

Generation of Different Mode-Locked States in Nonlinear Multimodal Interference-Based Fiber Lasers

A novel mode-locking method based on nonlinear multimode interference (NLMI) using a distributed large-core (105 μm) graded-index multimode fiber (GIMF)-based saturable absorber (SA) capable of generating four pulse modes is proposed. The distributed SA geometry consists of two GIMFs located at different positions in the resonant cavity. The coupling and joint operation not only facilitate resistance to pulse fragmentation but also provide a sophisticated and widely tunable transmission with saturable and reverse saturable absorption phenomena. Based on this, dissipative soliton (DS), dissipative soliton resonance (DSR), wedge-shaped, and staircase pulses are achieved without additional filters. The DS has accessible output power, pulse energy, bandwidth, and duration of up to 15.33 mW, 2.02 nJ, 22.63 nm, and ~1.68 ps. The DSR has an achievable pulse duration and energy of ~32.39 ns, 30.3 nJ. The dispersion range that allows DS operation is studied, and the dynamics of the evolution from DS to DSR are observed. The versatility, flexibility, and simplicity of the SA device, combined with the possibility of scaling the pulse energy, make it highly attractive for ultrafast optics and nonlinear dynamics.

Generation of spatiotemporal dark pulse or polarization domain wall solitons in a partial multimode mode-locked fiber laser

In this paper, we have experimentally investigated different operational states of a partial multimode Er-doped spatiotemporal mode-locked (STML) fiber laser. The STML is enabled by nonlinear multimode interference (NL-MMI) effect from the partial multimode cavity structure. It is found that by adjusting the multimode polarization controller (PC) and the pump power, the STML dark pulses, bright pulses, as well as the polarization domain wall solitons can all be obtained, alternatively. The fused-tapered multimode coupler is responsible for the dark pulses generation via the enhanced modal cross-phase coupling. It is believed that the present findings can offer an important insight into the spatiotemporal dynamics of the STML solitons.

Mode-locked thulium-doped fiber laser using a stretched few-mode fiber as a saturable absorber

In this work, an all-fiber saturable absorber (SA) based on nonlinear multimode interference in a short few-mode fiber (FMF) was proposed. Saturable absorption in this all-fiber device was demonstrated with an absorption modulation depth and a saturation fluence of 14.3% and 55.6 μJ cm−2, respectively. A stable mode-locking operation was observed in a thulium-doped passively mode-locked fiber laser using the FMF-based FMF SA. Ultrafast pulses were generated at 1911 nm with a pulse width of 1.96 ps and a 15.69 MHz repetition rate, respectively. The output average power was 2.8 mW, corresponding to a pulse energy of 178 pJ, which was significantly improved compared to graded-index multimode fiber-based SA. The experimental results demonstrate that FMF SA has great potential in eye-safe ultrafast photonics.

Wavelength-tunable quasi-unidirectional spatiotemporal mode-locked solitons in an isolator-free Er-doped fiber laser

In this letter, we have demonstrated the realization of the wavelength-tunable spatiotemporal mode-locked (STML) operation in an Er-doped partial multimode fiber laser without the intracavity isolator. The laser adopts an all-fiber structure and the saturable absorption effect is attributed to nonlinear multimode interference (NL-MMI) from the single mode fiber-graded index multimode fiber-single mode fiber (SMF-GIMF-SMF) design. The STML laser can operate in the quasi-unidirectional regime with an emission strength difference of larger than 30 dB for the two counter-propagating lasers. And the switching between the dominating operating directions in the clockwise (CW) or counter-clockwise (CCW) directions can be easily achieved by adjusting the MM polarization controller (PC). Both STML conventional solitons (CSs) and the STML soliton molecules are obtained with a similar tunable wavelength from ∼1.56 μm to ∼1.58 μm for the opposite operating directions. Furthermore, the spatial dynamics of the STML soliton are also investigated in detail. The experimental results are of great help for us to explore nonlinear spatiotemporal dynamics and provide potential applications in fields of all-optical signal processing, fiber sensing and information coding.

Diverse mode operation fiber laser mode-locked by nonlinear multimode interference

We present an all-fiber passively mode-locked (ML) laser with a nonlinear multimode interference (NLMI)-based saturable absorber (SA) capable of generating five pulse modes. The SA consists of two centrally aligned graded index multimode fiber (GIMF) with different diameters (105-50 µm) and features a widely adjustable transmission with saturable/reverse-saturable absorption. Based on this, dissipative soliton (DS), Q-switched rectangular pulse (QRP), dissipative soliton resonance (DSR), noise-like pulse (NLP) and bright-dark pulse pairs (BDP) are observed at three dispersions without additional filter. The DS has a pulse energy, bandwidth and duration of up to 1.15 nJ, 17.98 nm and ∼2.78 ps. The achievable pulse duration and energy of DSR and NLP are 5.21, 48.06 ns and 4.53, 5.12 nJ, respectively. Furthermore, it is demonstrated that the BDP is superimposed by a chair-case pulse (CP) and a rectangular pulse (RP) belonging to orthogonal polarization states. The versatility, flexibility, simplicity and energy scalability of the large-core hybrid GIMF-SA, make it interesting and highly attractive in ultrafast photonics.

Single-cavity bidirectional Raman-assisted mode-locked fiber laser

Bidirectional mode-locked fiber lasers are promising dual-comb light sources. Stimulated Raman scattering (SRS) effect can significantly extend the wavelength range of mode-locked fiber lasers. In this work, we propose and demonstrate a single-cavity bidirectional Raman-assisted mode-locked fiber laser based on nonlinear multimode interference effect. By adjusting the polarization of the cavity, we obtain synchronous and asynchronous pulse trains in counterclockwise (CCW) direction and clockwise (CW) direction, as a consequence of changes in the dispersion and nonlinear effects. Due to the extension of the wavelength range of single-cavity bidirectional mode-locked fiber laser, we believe that this work will hold potential for future applications in dual-comb spectroscopy, asynchronous sampling and other areas.

A Nonlinear Multimode Controller for Seamless off-Grid of Energy Storage Inverter Under Unintentional Islanding

A nonlinear multimode controller (NMC) is proposed to achieve the whole process seamless off-grid of energy storage inverter (ESI) from the grid-connected state of current control mode (CCM) to the islanded state of voltage control mode (VCM) under unintentional islanding. Based on the presented design idea of intelligent equivalent substitution, NMC is composed of multimode voltage controller (MVC), multimode power compensator (MPC) and multimode current controller (MCC). MVC can control load voltage in islanding and maintain manipulated variables of load current in other modes. MPC can compensate the power flowing into grid and help inner loop reference value achieve the smooth drop, and also compensate for load current variation during grid-connection. MCC can track the given current during grid-connection and make MPC quickly obtain the compensation of load power variation. The reference values of inner loop are logically split into the output of MVC, MPC and MCC, so that the manipulated variables can be combined nonlinearly to achieve seamless off-grid of ESI under unintentional islanding. This paper also analyzes the ESI stability with NMC during the off-grid process, and analyzes the relationship between manipulated variables by simulations. Finally, the correctness and effectiveness of proposed NMC are verified by experiments.

Mode attraction, rejection and control in nonlinear multimode optics

Novel fundamental notions helping in the interpretation of the complex dynamics of nonlinear systems are essential to our understanding and ability to exploit them. In this work we predict and demonstrate experimentally a fundamental property of Kerr-nonlinear media, which we name mode rejection and takes place when two intense counter-propagating beams interact in a multimode waveguide. In stark contrast to mode attraction phenomena, mode rejection leads to the selective suppression of a spatial mode in the forward beam, which is controlled via the counter-propagating backward beam. Starting from this observation we generalise the ideas of attraction and rejection in nonlinear multimode systems of arbitrary dimension, which paves the way towards a more general idea of all-optical mode control. These ideas represent universal tools to explore novel dynamics and applications in a variety of optical and non-optical nonlinear systems. Coherent beam combination in polarisation-maintaining multicore fibres is demonstrated as example.

High repetition frequency spatiotemporal mode-locked fiber laser based on cavity induced modulation instability

Intermodal dispersion and modal instability have been the primary challenges for achieving spatiotemporal mode-locked (STML) in multimode fiber. This paper utilizes the nonlinear multimode interference effect to redistribute the mode energy and suppress the intermodal dispersion. By building on this approach and combining it with cavity-induced modulation instability (CIMI), we experimentally demonstrate the STML pulse with a high repetition frequency of 1.116 GHz, corresponding to a harmonic order of 93. Our research not only significantly expands the application of spatiotemporal mode-locked lasers in high repetition frequency systems, but also provides valuable insights for further understanding the dynamics of spatiotemporal mode-locking.

All-fiber spatiotemporal mode-locked based on Mamyshev mechanism with high energy noise-like pulse generation at 1550 nm

Intermodal dispersion is the main problem restricting the establishment and stability of spatiotemporal mode-locking (STML) in the anomalous dispersion region. In the experiment, we employ the multimode Er-Yb double-clad fiber to carry out the multimode operation as a gain medium. The nonlinear multimode interference is used to enhance the mode coupling and spatial filtering in the cavity, achieve the purpose of suppressing the intermodal dispersion, and successfully realize the 1550 nm spatiotemporal noise-like solitons of Mamyshev oscillator based on the multimode gain fiber. The noise-like spatiotemporal soliton pulse energy reaches ∼171.29 nJ, and the corresponding peak power is ∼30.32 kW. The intermodal dispersion suppression based on nonlinear multimode interference performance makes this laser an attractive tool for practical applications.

Characterization of the ultrafast fiber laser mode-locked by nonlinear multimode interference

A passively mode-locked fiber laser with switchable output states is demonstrated by using an all-fiber saturable absorber (SA) based on a hybrid single mode fiber-graded index multimode fiber-single mode fiber-graded index multimode fiber-single mode fiber (SMSMS) incorporated into a ring cavity. We investigate the vectorial characteristics of the output soliton in order to analyze the influence of polarization dependence of the SMSMS structure on solitons generation. Due to the appearance of vector solitons, it is proved that nonlinear multimode interference (NL-MMI) plays a dominant role in solitons generation but not nonlinear polarization rotation (NPR). Meanwhile, abundant mode-locked states are achieved in the laser, such as fundamental soliton, higher-order harmonics, bound twin-pulse solitons, and quasi-harmonic bound states. This configuration provides a useful platform for investigating ultrafast soliton dynamics.

Few-mode fiber based saturable absorber for ultra-fast fiber laser at 2 μm

The saturable absorption of the single mode-few-mode-single mode fiber (SMF-FMF-SMF) structure with respect to its passive mode-locking performance is still largely unexploited, although it is more conducive to the design and performance of the saturable absorber (SA) based on the nonlinear multimode interference effect. A series of FMF-based saturable absorbers with different FMF lengths are employed in passively mode-locked Tm fiber lasers for ultrafast pulse generations at 2 μm. The mode-locking performances using different FMF-based saturable absorbers were demonstrated. By comparing the saturable absorption characteristics and the respective mode-locking performances, we can conclude that it is easier to obtain the stable mode-locking output using saturable absorbers with the FMF lengths of 15.12 cm and 30.2 cm. The FMF saturable absorber with a 15.12 cm FMF has a large modulation depth of 40% and a saturation fluence of 108.23 μJ /cm2 which delivers ultrafast pulses with pulse width of 1.96 ps at 1878 nm. In addition, the harmonic mode-locking with stable and well-organized pulse trains could also be instantaneously achieved by increasing the pump power within the same cavity. Our results indicate that the SMF-FMF-SMF structure could operate as a SA while tuning its saturable absorption properties by changing the FMF length making it advantageous for mode locking fiber lasers.

Theory of localization-hindered thermalization in nonlinear multimode photonics

Our society’s appetite for ultra-high bandwidth communication networks and high-power optical sources, together with recent breakthroughs in mode multiplexing/demultiplexing schemes, forced the photonics community to reconsider the deployment of nonlinear multimode systems. These developments pose fundamental challenges stemming from the complexity of nonlinear mode-mode mixing by which they exchange energy in the process towards an equilibrium Rayleigh-Jeans (RJ) distribution. Here we develop a universal one-parameter scaling theory for the relaxation rates of out-of-equilibrium excitations towards their RJ thermal state. The theory predicts an exponential suppression of the rates with increasing disorder due to the formation of stable localization clusters resisting the nonlinear mode-mode interactions that tend to separate them. For low optical temperatures, the rates experience a crossover from linear to nonlinear temperature dependence which reflects a disorder-induced reorganization of the low frequency eigenmodes. Our theory will guide the design of nonlinear multimode photonic networks with tailored relaxation-scales.

Investigation of the transverse mode instability in an isolator-free quasi-unidirectional spatiotemporal self-mode locked fiber laser

A spatiotemporal (ST) self-mode locked (ML) Er-doped fiber laser based on the nonlinear multimode interference (NL-MMI) effect without an intracavity isolator has been proposed. Such a STML laser could operate in a quasi-unidirectional regime in both clockwise (CW) and counter-clockwise (CCW) directions. Different spatial dynamics of the STML solitons in the opposite directions are observed. For the STML solitons in the CCW direction, the beam profile is discretely distributed and the transverse mode instability (TMI) is observed. While for the STML solitons in the CW direction, the beam profile is relatively concentrated and can be partially controlled by adjusting the intracavity multimode (MM) fiber at the front-end of the MM coupler. These investigations would help to gain further understanding of the spatial and temporal dynamics and mechanism in the STML lasers.