Nonlinear Multimode Research Articles

Time-Weighted Kernel-Sparse-Representation-Based Real-Time Nonlinear Multimode Process Monitoring

Real-time nonlinear multimode process monitoring of actual industrial systems has attracted increasing attention recently. In this article, the time-weighed kernel sparse representation (TWKSR) method is proposed to partition the mode of the training dataset by introducing the time-series-dependent characteristics into the kernel sparse representation algorithm. The alternating direction method of multipliers is utilized to solve the optimization problem of the proposed TWKSR method. Then, the representative samples from each identified mode are selected to update the dictionary matrix. Based on the updated dictionary matrix, the sparse coefficient is used for online mode identification, and the reconstruction error is utilized for fault detection. Finally, a numerical simulation case and the wastewater treatment process example verify the effectiveness of the proposed method.

Wavelength-switchable and multi-pulse bound state based on a hybrid mode-locked mechanism.

Relying on the nonlinear multimode interference in multimode fibers and the nonlinear polarization rotation, these two mode-locked techniques are combined in our proposed fiber laser. Stable optical soliton and multi-pulse regimes with a constant frequency of 11.44 MHz have been generated experimentally. Through altering intra-cavity conditions, bound-state pulses with diverse properties are observed. To the best of our knowledge, the obtained bound-state pulse constituted by more than thirty sub-pulses is achieved for the first time. Moreover, the center wavelength of bound-state pulse could be switched in a certain range covering the entire C band.

All-fiber erbium-doped dissipative soliton laser with multimode interference based on saturable-reserve saturable hybrid optical switch

Reverse saturable absorption is essential for the realization of dissipative solitons. In this paper, we introduce reverse saturable absorption by using nonlinear multimode interference (NL-MMI), for the first time, to the best of our knowledge, and obtain a stable dissipative soliton operation. By adjusting the coupling efficiency from multimode fiber to single mode fiber, the absorption properties of NL-MMI can be switched between saturation and reverse saturation. The dissipative soliton can be obtained with pulse width of 975 fs in the experiment, the 3-dB bandwidth at 1555 nm is 16 nm, and the maximum output power is 11.48 mW. The nonlinear absorption optical modulation and high damage threshold characteristics of the NL-MMI based ultrafast optical switch provide a new idea for realizing dissipative solitons.

Research progress of mode-locked pulsed fiber lasers with high damage threshold saturable absorber

As the basic hardware to promote the development of various fields, fiber laser has great development potential in rail transit, optical communication, new material manufacturing, power battery processing, military defense, medical treatment, and other fields. As the core device of passively mode-locked fiber laser, a high damage threshold saturable absorber plays a decisive role in achieving high power, ultrashort pulse duration, and high energy laser output for a fiber laser. For saturable absorbers of traditional materials and structures, the spot size of light acting on the material is almost the same as the exit diameter of the optical fiber, which is easy to exceed the damage threshold of the saturable absorber and lead to damage. To improve the damage threshold of saturable absorbers, the structure of saturable absorbers based on both real materials and traditional saturable absorbers can be optimized. On the one hand, the preparation technology of the saturable absorber is adjusted, such as using the sol-gel method, which has a good effect on improving the damage threshold of the saturable absorber. Moreover, different materials are selected and used as substrates, such as the use of inorganic materials as material substrates and the selection of a variety of insertion cavity structures, such as “sandwich” transmission structures, tapered fibers, and photonic crystal fibers. These methods are of great significance in improving the damage threshold of the real material saturable absorber and realizing pulsed laser with excellent performance and high stability. On the other hand, the equivalent saturable absorber structure is used to improve the damage threshold and optimize the laser performance, such as hybrid mode-locked structure and nonlinear multimode interference. The continuous optimization of the fiber laser damage threshold will further expand its application range. Therefore, it is important to adjust the preparation process and insert the cavity structure of saturable absorbers for improving the damage threshold of the saturable absorber and achieving high performance and stability of the pulsed laser. This paper reviews the research status of high damage threshold saturable absorbers at home and abroad, summarizes the latest methods to improve material damage threshold and the latest research progress of equivalent saturable absorbers, and also points out the future development direction of high damage threshold saturable absorbers.

Harmonic mode-locked fiber laser based on microfiber-assisted nonlinear multimode interference

A novel harmonic mode-locked fiber laser based on nonlinear multimode interference (NL-MMI) in a microfiber-assisted ultrafast optical switch is proposed in this Letter. The microfiber-assisted ultrafast optical switch can be obtained by tapering the splicing point of the graded-index multimode fiber (GIMF) and single-mode fiber, which not only helps to shorten the self-imaging period in GIMF to relax the strict requirement of NL-MMI on the length of multimode fiber, but also improves the harmonic order. In the experiment, with the waist diameter of ∼15 µm, the repetition rates of the fiber laser can be stably locked at 285 MHz, corresponding to the 16th-order harmonic mode-locking, with the pulse duration of 1.52 ps. Our results provide novel insight into the design of a high-repetition-rate laser and the application of microfibers in the mode-locking device.

Ultrafast all-anomalous-dispersion Er-doped large-mode-area fiber lasers

Ultrafast Er-doped large-mode-area (LMA) fiber lasers are demonstrated in the all-anomalous-dispersion regime. With the assistance of a home-made carbon nanotube saturable absorber, stable and chirp-free solitons are always observed for output coupling ratios (OCRs) varying from 10% to 90%, leading to the simultaneous achievement of the maximum pulse energy and minimum pulse duration at the OCR of 70%. To validate the universality of the all-anomalous-dispersion mode-locking, an all-fiber saturable absorber based on nonlinear multimode interference effect is incorporated into the LMA fiber laser cavity, which can also generate chirp-free solitons. The influences of gain fiber dispersion on solitons are numerically simulated, revealing that the dispersion consistency of fibers in the laser cavity is in favor of generating stable and chirp-free solitons even at an ultrahigh OCR. This work paves the way for ultrafast Er-doped LMA fiber lasers in the all-anomalous-dispersion regime, which provides an alternative route to further improve the stability and output pulse energy of ultrafast LMA fiber lasers, i.e. ensuring the dispersion consistency and hence enlarging the OCRs.

Profile extrusion die design: A comparative study between elastic and inelastic fluids

AbstractComputational modeling is widely used to support the design of profile extrusion dies. However, despite the viscoelastic nature of the polymer melts, the majority of the computational approaches resort to inelastic models. With the aim of assessing the accuracy of the approach usually employed on the modeling of profile extrusion dies, this work aims at comparing the behavior of profile extrusion dies when interrelated viscoelastic (elastic) and generalized Newtonian (inelastic) constitutive models are used. For this purpose, the polymer melt employed in the study was experimentally characterized, being the data collected used to fit a nonlinear multimode viscoelastic (elastic) Giesekus constitutive model. Subsequently, the fitted model was used to generate the material shear flow curve, which was then used to fit a Bird‐Carreau (inelastic) constitutive model. The numerical studies undertaken were focused on the extrusion die of two profiles: a simple one, with a rectangular cross‐section, and a complex swimming pool cover profile. The results obtained showed that in realistic case studies, the effect of elasticity might be relevant, even when modeling just the flow in the extrusion die flow channel and, thus, should be considered when designing profile extrusion dies.

All-fiber saturable absorber based on nonlinear multimode interference with enhanced modulation depth.

We experimentally demonstrate a passively mode-locked fiber ring laser using a small-core fiber-graded index multimode fiber-single-mode fiber (SCF-GIMMF-SMF) structure as an effective saturable absorber based on the nonlinear multimode interference (NL-MMI) effect. A small-core fiber is used as an input single-mode fiber to improve the coupling of power into higher-order modes in a multimode fiber and to enhance the modulation depth of the structure. Stable fundamental mode-locked operation is obtained at a pump threshold of 166 mW and the output soliton pulses have a 647 fs duration at 1557.96 nm with a 5.2 nm spectral width at a repetition rate of 19.37 MHz. This NL-MMI SA can be applied to high-power mode-locked fiber lasers owing to its inherent high damage threshold, compact size, wavelength independent operation, and fabrication simplicity.

Common and specific deep feature representation for multimode process monitoring using a novel variable-wise weighted parallel network

Multimodal data are common in industrial processes because of switched operating conditions, varying feedstocks and changed product designs and so on. To guarantee process safety and improving process performance, a variable-wise weighted parallel stacked auto-encoder model is proposed for nonlinear multimode process monitoring. Considering the similarity and difference between multiple operating modes with complex process nonlinearities, mode-common and mode-specific deep features are parallelly extracted with the proposed new model. Since each variable distinctly contributes to the mode-common features, variable-wise weights are designed with an optimal transport distance between modes when the mode-common features are learned. Moreover, different from designing a unified monitoring index for all modes, three asymmetric indices are designed to not only trigger an alarm for an anomaly, but also indicate whether the anomaly is caused by mode-common factors, mode-specific factors or others. Thus, the real-time monitoring results, together with some diagnosis information are simultaneously presented. A numerical example and a real industry application are used to validate the monitoring efficacy of the proposed model.

A nanosecond Q-switched fiber laser based on step-index multimode fiber

A nanosecond passively Q-switched fiber laser using a single mode-step-index-multimode-single mode fiber (SMF–SIMF–SMF) device as the saturable absorber (SA) is demonstrated. Such SMF–SIMF–SMF device operates based on nonlinear multimode interference. A stable Q-switched erbium-doped fiber laser at 1546 nm was realized with a repetition rate varying from 99 kHz to 150 kHz and the shortest pulse duration of 740 ns. At the maximum pump power of 800 mW, the maximum pulse energy of 97.86 nJ at an average output power of ∼14.7 mW was obtained. Our results indicate that the SMF–SIMF–SMF structures can be used as effective SAs for nanosecond pulse generation.

All-normal dispersion ytterbium-doped fiber laser mode locked by nonlinear multimode interference.

We report a mode-locking operation using a nonlinear multimode interference (MMI)-based saturable absorber in an ytterbium-doped fiber laser under an all-normal dispersion configuration. The MMI is observed in a step-index single mode-multimode-single mode (SMS) fiber structure. The intensity and wavelength-dependent transmission of the SMS structure has been studied numerically to understand the Kerr-induced saturable absorber properties of MMI in a step-index fiber. Numerical investigations show that presence of a narrow-band wavelength-tunable spectral filter is necessary for a nonlinear MMI-based saturable absorber to be effective for mode locking. A single-pulse mode-locking operation in the laser is realized at a very low pump power of ${\sim}{56.3}\;{\rm mW}$ at which the laser generates 180 ps duration pulses at ${\sim}{9}\;{\rm MHz}$ repetition rate with measured signal-to-noise ratio of ${\sim}{50}\;{\rm dB}$. This all-fiber integrated laser operates in multi-pulse and noise-like rectangular pulse regimes at increased pump power.

SPA-Based Modified Local Reachability Density Ratio wSVDD for Nonlinear Multimode Process Monitoring

Many industrial processes are operated in multiple modes due to different manufacturing strategies. Multimodality of process data is often accompanied with nonlinear and non-Gaussian characteristics, which makes data-driven monitoring more complicated. In this paper, statistics pattern analysis (SPA) is introduced to extract low- and high-order statistics from raw process data. Support vector data description (SVDD), which can deal with nonlinear and non-Gaussian problems, is applied to monitor multimode process in this paper. To improve detection performance of SVDD for training multimode data with outliers, modified local reachability density ratio (mLRDR) is proposed as a weight factor to be embedded in the weighted-SVDD (wSVDD) model, in which the local neighbors in terms of both space and time are considered. Finally, the effectiveness and superiority of our proposed method are demonstrated by the Tennessee-Eastman (TE) process and wastewater treatment process (WWTP).

Wavelength switchable all-fiber mode-locked laser based on nonlinear multimode interference

We report a switchable single wavelength and dual-wavelength all-fiber ultrafast mode-locked lasers based on nonlinear multimode interference (NL-MMI) effect of graded-index multimode fiber (GIMF). The saturable absorber (SA) used in the laser is composed of tapered fiber-GIMF-tapered fiber. The use of tapered fibers not only reduces the dependence on the length of GIMF, but also simplifies the fabrication of SA. The modulation depth of the SA was measured to be 9%. By adjusting intra-cavity loss and the polarization controllers properly, traditional switchable single wavelength and dual-wavelength mode-locking can be realized. Meanwhile, a single wavelength harmonic soliton molecule mode-locking can be observed, and the central wavelength with the same modulation period can be switched between 1558 nm and 1531 nm. Such a switchable harmonic soliton molecules mode-locked laser with wide wavelength intervals could be useful in measuring chemical reactions, and has rarely been reported.

All-Fiber Femtosecond Mode-Locked Yb-Laser With Few-Mode Fiber as a Saturable Absorber

A novel few-mode fiber (FMF) based saturable absorber (SA) that works on the principle of nonlinear multimode interference has been proposed. To optimize the FMF parameters for the fabrication of SA, which is a combination of FMF with two single mode fibers (SMFs), a detailed numerical simulation is performed. The developed SMF-FMF-SMF structure exhibits a modulation depth and saturation intensity of 30.6% and 11.01 MW $/$ cm2, respectively. By inserting the fabricated SA in an all-normal dispersion Ytterbium doped cavity, we have been able to generate a laser pulse duration of 300 fs with an average power/pulse energy of 2.4 mW/64.8 pJ and a repetition rate of 37 MHz as an output. Thus, the proposed SA helps in generating stable pulses from the laser with enhanced output characteristics. We envisage that the fabricated SA would play an indispensable role in the development of ultrafast fiber lasers.

All-normal-dispersion dissipative soliton fiber laser using an offset-splicing graded-index-multimode-fiber-based saturable absorber.

All-normal-dispersion (ANDi) dissipative soliton mode-locking is realized based on nonlinear multimode interference (NMI), which is implemented by offset-splicing three pieces of graded-index multimode fibers (GIMFs) and acts as a saturable absorber. The higher-order modes can be excited by offset-splicing GIMFs (OS-GIMFs), which eliminates adding the step multimode fiber (SIMF) into the resonant cavity and the precise length requirement of the SIMF. In the experiment, the stable dissipative soliton mode-locking at 1030 nm can be obtained with the pulse width of 7.3 ps and the repetition rate of 20.52 MHz, and the bandwidth is 6.98 nm. The maximum output is 3.2 mW with the pump power of 257 mW. The OS-GIMFs can significantly improve the saturated absorption and can easily realize dissipative soliton mode-locking in ANDi regions, which makes it attractive in ultrafast photonics.

Strategies for wideband light generation in nonlinear multimode integrated waveguides

In this paper we discuss two strategies to achieve wideband light generation through intermodal nonlinear parametric processes in multimode integrated waveguides. We outline how the interplay among intermodal interactions and high dispersion may lead to the generation of light characterized by substantial power spectral density if compared to supercontinuum sources. These results are valid independently of the waveguide material; however, our numerical simulations focus on silicon waveguides, which are nowadays at the core of integrated photonics. The long-term vision is that by exploiting an adequate number of intermodal processes, widely tunable radiation having high-power spectral density can be generated in a broad portion of the transparency window of silicon.

A Robust Infinite Gaussian Mixture Model and Its Application in Fault Detection of Nonlinear Multimode Processes

A Robust Infinite Gaussian Mixture Model and Its Application in Fault Detection of Nonlinear Multimode Processes

Generation of a noise-like pulse from an erbium-doped fiber laser based on nonlinear multimode interference

A noise-like pulse (NLP) is generated in an anomalous-dispersion passively mode-locked erbium-doped fiber laser using graded-index multimode fiber (GIMF) as the all-fiber saturable absorber (SA) for the first time. By splicing two sections of bending GIMF at both ends of a single mode fiber and optimizing the birefringence and nonlinear parameters, stable NLP mode-locking operation can be achieved within a wide pump power range. Meanwhile, the performances of NLP mode-locking have been analyzed experimentally by changing the length of the GIMF.

Nonlinear Non-Gaussian and Multimode Process Monitoring-Based Multi-Subspace Vine Copula and Deep Neural Network

This paper proposes a robust copula double-subspace (CDS) model based on a sparse robust autoencoder (SRAE) named SRAE-CDS. By reconstructing training data with SRAE, the resulting SRAE-CDS model i...

Mode-locked Er-doped fiber laser based on nonlinear multimode interference

We demonstrated an all fiber passively mode-locked fiber laser by using one single mode fiber-graded index multimode fiber-single mode fiber (SMF-GIMF-SMF) structure as a saturable absorber (SA) based on the nonlinear multimode interference. The proposed SA with the modulation depth of 9.58%, saturation intensity of 36.50 MW cm−2 and nonsaturable loss of ∼ 21% was inserted into an Er-doped fiber laser cavity. Then the conventional soliton laser at 1566 nm was realized at a pump threshold of 180 mW. The output pulses had a pulse duration and repetition rate of 520 fs and 33.7 MHz, respectively. And the maximum pulse energy was 256 pJ. Our results further indicated that the SMF-GIMF-SMF structure can be used as an effective SA for ultrashort pulse generation.