Self-similar Pulses Research Articles

Propagation of M-shaped and W-shaped similaritons in birefringent tapered graded-index nonlinear fiber amplifiers

We study the self-similar transmission of optical beams inside an inhomogeneous birefringent tapered graded-index nonlinear fiber amplifier within the framework of generalized coupled Schrödinger equations with spatially inhomogeneous nonlinearity, group velocity dispersion, tapering and gain or loss. New kinds of similariton solutions for the governing model are constructed by means of the similarity transformation method. Especially, the M-shaped and W-shaped similariton pulses are found successfully for the first time, which do not exist in single-mode waveguide amplifier. In addition, bright–dark similaritons are found in the presence of tapering effect. It is shown that these waveforms exhibit a quadratic phase structure, which leads to chirped self-similar pulses. In addition, we determine the relationships among the tapering profile, gain or loss distribution, nonlinearity, and similariton width, which provide the required conditions for controlling the self-similar wave dynamics. Moreover, we discuss the dynamical evolution of the similariton pulses under the influence of special tapering profiles, which are of physical importance in practical applications. The results show that through selecting the appropriate tapering, dispersion and nonlinearity profiles, we can control the dynamics of similaritons effectively.

Tapered photonic crystal fiber based on artificial intelligence-design for pulse compression

In this study, we employ a deep neural network(DNN) to achieve rapid prediction of dispersion and effective mode area in Pb-silicate photonic crystal fiber. Subsequently, this prediction model is used to drive a particle swarm optimization(PSO) algorithm to design tapered Pb-silicate photonic crystal fibers for pulse compression. The designed fibers exhibit an increasing nonlinear index profile, enabling self-similar pulse compression(SSPC) of pulses at a wavelength of 2μm. In compliance with fundamental soliton conditions, a 0.566 m tapered PCF achieves notable pulse compression. It reduces the initial pulse width of 1.76 ps to 52 fs, achieving a remarkable compression factor of 33.92, while maintaining a quality factor of 1.01 and less than 5.4% pedestal energy. In scenarios where fundamental soliton conditions are not met, a 1.74 m tapered PCF also achieves significant compression. It compresses a pulse with a width of 1.76 ps and a peak power of 1 kW to a pulse width of 13.7 fs and a peak power of 24.82 kW, resulting in a compression factor of 129. The proposed approach overcomes the empirical reliance inherent in manual design and significantly reduces computational demands, enabling the design of pulse compression fiber tapers tailored to input pulse shapes.

Nonlinear tunneling of self-similar periodic waves in inhomogeneous two mode optical fibers

Distinct types of self-similar periodic waveforms of the generalized coupled nonlinear Schrödinger equations with varying nonlinearity, gain or loss and group velocity dispersion are obtained. The coupled system applies to the description of light pulse propagation in an inhomogeneous two mode optical fiber. The self-similar solutions are expressed in terms of Jacobian elliptic functions, thus enabling us to identify various kinds of propagating self-similar soliton pulses in their long-wave limit. It is found that these periodic structures exhibit a linear chirp property, which can be utilized to achieve efficient pulse compression and amplification. As a physically relevant application, we discuss the nonlinear tunneling process of these linearly chirped self-similar periodic waves through both dispersion and nonlinear barriers.

Nearly Self-Similar Pulse Compression in Horizontally Slotted Waveguides at 2.0 μm

Nearly Self-Similar Pulse Compression in Horizontally Slotted Waveguides at 2.0 μm

Optimally design of amplifier self-similar pulse in thulium-doped multimode fiber laser

High-energy ultrashort pulses fiber lasers could be widely used in scientific research and industrial applications. Researchers often use two methods to boost the pulse energy, one is to achieve self-similar pulse (SSP) output in a single mode fiber (SMF) laser, and the other is to use multimode fiber (MMF) instead of SMF. Here we combine the above two methods to optimally design the output characteristics of SSP in thulium-doped MMF lasers. The influence of different parameters, including spectral filter bandwidth, fiber length, and gain saturation energy, on the output characteristics of SSP have been analyzed, and an optimal SSP with pulse energy of 63.48 nJ, spectrum width of 52.53 nm, dechirped pulse peak power of 283.34 kW, and dechirped pulse width of 219.74 fs has been obtained.

Dynamic characteristics for 2 μm-self-similar pulse thulium-doped fiber laser

A passive mode-locked thulium-doped fiber laser is a generator for 2 μm ultra-short laser pulses. In addition, mode-locked self-similar pulses also exhibit rich nonlinear dynamic characteristics in thulium-doped fiber lasers. Therefore, this article studies the dynamic characteristics of self-similar pulses for the 2 μm passive mode-locked thulium-doped fiber laser. The research results also indicate that as the gain coefficient increases, the peak power of self-similar pulses increases, pulse width widens, and the linearity of chirp increases.

Chirped self-similar optical solitons with cubic–quintic–septic–nonic form of self-phase modulation

This study investigates the dynamics of ultrashort light pulses in an inhomogeneous optical medium exhibiting all orders of nonlinearity up to the ninth order. The research focuses on exploring the existence and properties of self-similar solitons while varying cubic, quintic, septic, and nonic nonlinearities, group velocity dispersion, and loss or gain. It is found that the transmission system supports the existence of novel types of self-similar bright and dark pulses in the presence of various physical processes. Importantly, these self-similar localized waves exhibit a linear chirp, a crucial factor for achieving effective pulse amplification or compression. Based on the chirp property, the dynamical behaviors of these self-similar waveforms are discussed in a periodically distributed amplification system. The findings highlight that the shape and dynamics of these chirped self-similar pulses can be precisely controlled by selecting appropriate profiles for gain or loss, nonlinearity, and dispersion. Additionally, the research numerically discusses the interaction dynamics between two and three adjacent solitons.

Self-similar pulse compression in a tapered Pb-silicate photonic crystal fiber at 2 µm

We report a 2-µm all-fiber nonlinear pulse compressor based on a tapered Pb-silicate photonic crystal fiber (PCF), which is capable of achieving large compression with low pedestal energy. A tapered Pb-silicate photonic crystal fiber with increased nonlinear coefficients is proposed for achieving self-similar pulse compression (SSPC) at 2 µm. The dynamic evolution of the fundamental order soliton is numerically analyzed based on the designed tapered fiber. After pulse compression in a tapered fiber with a length of 2.2 m, an initial 1.76 ps pulse can be compressed to 88 fs, increasing the peak power from 4.4 to 86 W with a compression factor of 20 and a quality factor of 98%. The results reveal that exponential variation yields superior compression performance and provides a promising solution for generating high-power femtosecond pulses at 2 µm.

Discriminating the existence regions and dynamics between quartic self-similar pulse and dissipative pure quartic soliton in ultrashort fiber laser

Recently, both quartic self-similar pulses (QSSPs) and dissipative pure-quartic-solitons (DPQSs) pulses have been theoretically demonstrated in mode-locked fiber laser with pure positive fourth-order dispersion (FOD). Here, we investigate the existence regions and dynamics of those two soliton pulses by numerically solving the cubic-quintic Ginzburg-Landau equation. We find the positive FOD fiber laser tends to emit QSSPs in the presence of high nonlinear gain, while it is apt to generate DPQS pulses in the case of low nonlinear gain. An unstable pulse region separates the QSSP region from the DPQS region. The characteristics of QSSP and DPQS pulses are dependent on the nonlinear gain and FOD. The QSSP can carry more energy than that of DPQS pulse, because the DPQS pulse with large energy could be unstable due to the excessive pulse pedestal. Our results are not only useful for understanding the dynamics of the DPQS pulse and QSSP in the cubic-quintic Ginzburg-Landau equation with pure FOD, but also provide a guideline for generating high-energy pulses from the positive FOD fiber laser.

Investigation of Multimode Self-Similar Pulse Compression in Tapered Photonic Crystal Fibers

In this paper, we theoretically investigate the multimode self-similar pulse compression (MM-SSPC) in tapered photonic crystal fibers. To expand the self-similar theory beyond single-mode scenarios, we have discovered through analytical analysis that the width of the input pulse has a significant impact on perturbing the MM-SSPC process. We proceed to solve the multimode generalized nonlinear Schrödinger equation using numerical methods for various input pulse widths, which leads to the observation of three distinct types of multimode pulse compression. MM-SSPC only takes place when the input pulse width is comparatively longer. Our numerical results are consistent with the predictions of analytical calculations. Our results demonstrate that by using input pulses of 2.5 ps in duration, three modes can be compressed in a self-similar manner to 200 fs, which corresponds to a compression factor of 12.5. Finally, We establish the minimum input pulse width required to enable the MM-SSPC to function for the three specific modes of interest. Our findings provide an effective guidance to design pulse compressor for the generation of pedestal-free, high-energy femtosecond pulses.

Dynamics of solitons in NOLM based all-normal dispersion Yb-doped mode-locked fiber laser

The properties of the saturable absorber are critical to the soliton dynamics in the all-normal dispersion Yb-doped mode-locked fiber laser based on the nonlinear optical loop mirror (NOLM). In this paper, it is found that by adjusting the splitting ratio f and cavity length L of the NOLM, self-similar pulse (SSP), soliton molecule (SM), dissipative soliton resonance (DSR), dissipative soliton (DS) and dissipative soliton pair (DSP) can be obtained in such fiber laser system. In addition, the mechanisms and characteristics of these solitons are discussed. These findings will facilitate the in-depth understanding of the characteristics of nonlinear pulses generated by NOLM-based all-normal dispersion Yb-doped mode-locked fiber laser.

Passive Self-similar Pulse Fiber Laser Constructed by Anomalous Dispersion Gain Fiber

Passive Self-similar Pulse Fiber Laser Constructed by Anomalous Dispersion Gain Fiber

Generation of dissipative solitons and self-similar pulses by a mode-locked fiber laser using a bandwidth tunable Mach-Zehnder interferometer filter

We suggest and demonstrate a scheme to generate dissipative solitons and self-similar pulses in a fiber laser mode-locked by nonlinear polarization rotation (NPR). The scheme is based on inserting a bandwidth tunable Mach-Zehnder interferometer (MZI) filter in the cavity. The MZI filter is fabricated by cascading two 3 dB optical couplers (OCs). The propagating light is split into two arms in the first OC and is combined again in the second OC. The free spectral range of the MZI, and the corresponding bandwidth of the MZI filter, depend on the optical path difference between these two arms. By applying stretching on one of the arms, both dissipative solitons and self-similar pulses have been obtained both numerically and experimentally. Furthermore, upon exploiting the dependence of the peak wavelength of the MZI filter on the amount of stretching, dissipative solitons with tunable wavelength have also been obtained.

Numerical modeling of the self-similar mode-locked Er3+-doped fluoride fiber laser around 3 µm

At present, generating sub-100 fs ultrafast pulse in the mid-infrared (mid-IR) region around 3 µm is very challenging. In this work, we have numerically investigated self-similar mode-locking of an Er3+-doped fluoride fiber laser with dispersion compensation. The simulation results show that stable self-similar pulse with 3 dB spectral bandwidth of 100 nm can be achieved. The self-similar pulse has a large linear chirp with the corresponding time bandwidth product (TBP) of about 5.81, which can be easily compressed to a near-Fourier-transform-limited pulse as short as 92 fs via de-chirping technology outside the cavity. In addition, optimal investigations of the mode-locked fiber laser have been conducted. This work provides an attractive alternative scheme for generating sub-100 fs ultrafast fiber laser in the mid-IR region.

Chirped self-similar localized pulses on a continuous wave background in presence of cubic–quintic nonlinearity and self-frequency shift

We investigate the nonlinear pulse propagation through an inhomogeneous single-mode optical fiber where the evolution dynamics is governed by the generalized higher-order nonlinear Schrödinger equation with varying group velocity dispersion, cubic and quintic nonlinearities, self-frequency shift arising from stimulated Raman scattering, and linear gain or loss. A new class of soliton pulse solutions for a wave field is constructed based on the similarity transformation connecting with the constant-coefficient Kundu–Eckhaus equation. This class describes soliton structures that propagate self-similarity on a continuous-wave (cw) background, and acquires a nonlinear chirp as it propagates in the inhomogeneous fiber medium. It is found that the nonlinear chirp associated with these self-similar pulses originates essentially from the self-frequency shift effect. The conditions on fiber parameters for the existence of those nonlinearly chirped self-similar localized pulses are also given. As a practical example, we studied their evolution dynamics in a specified soliton control system. The solution stability against perturbation is checked by direct numerical simulation.

Simultaneous Pulse Combination and Nearly Self-Similar Pulse Compression in Tapered Silicon Waveguides at Around 2.0 μm

Nonlinear pulse compression technology permits practitioners to produce ultrashort pulses for integrated frequency comb generation and optical coherence tomography. However, on-chip simultaneous combination and compression of two pulses at 2.0 μm is a complex nonlinear dynamic that has never been reported. Here, we demonstrate that two raised cosine pulses with the same center wavelengths of 2.0 μm are firstly coalesced into a single combined pulse and then realize nearly self-similar compression in the dispersion exponentially decreasing silicon waveguide, where the final compressed pulse was reduced from 200 fs to 49 fs with a compression factor of 4.08. Additionally, the peak power of the compressed pulse steadily rises to 2.16 times of the initial peak power. For further development, we also illustrate two input pulses with different center wavelengths to realize effective combination and self-similar compression. These results shed new insights into the potential of dispersion engineering waveguides for low-power integrated applications at 2.0 μm.

Chirped self-similar pulses and envelope solutions for a nonlinear Schrödinger's in optical fibers using Lie group method

In this work, we present an application of Lie group analysis to study the generalized derivative nonlinear Schrödinger equation, which governs the evolution of a nonlinear wave and plays an important role in the propagation of short pulses in optical fiber systems. To construct Lie group reductions, we study the symmetry properties and introduce various infinitesimal operators. Further, we obtain self-similar solutions and periodic soliton solutions of the generalized derivative nonlinear Schrödinger equation. This type of solution plays a vital role in the study of the blow-up and asymptotic behavior of non-global solutions. And at the end, we present graphs for each solution by considering the physical meaning of the solutions.

Spatiotemporal dynamics of self-similar parabolic pulse evolution in multimode fibers

In this paper, we have investigated for the first time, the spatiotemporal dynamics of self-similar parabolic pulse evolution in multimode fibers. Two types of fiber are considered, graded-index and step-index MMFs. For the quality of the generated parabolic pulse, the mismatch parameter is used. A thorough study of the evolution of the pulse parameters as a function of the initial parameters has been carried out. As a result, the initial pulse evolved into a linearly chirped pulse with a parabolic intensity shape in both fibers, under the predominantly excitation of the fundamental mode. It has been shown, in particular, that the pulse can be compressed to a temporal duration of about 40 fs. Moreover, a spatiotemporal nonlinear dynamic, beam auto-selection, of one specific mode, is investigated through graded-index MMF, under the different initial modes excitation. The parabolic pulse formation process plays a critical role in this nonlinear dynamic. This approach provides another framework to understand the complex nonlinear dynamics in MMFs.

New chirped gray and kink self–similar waves in presence of quintic nonlinearity and self–steepening effect

We demonstrate new types of chirped self-similar waves for a generalized derivative nonlinear Schrödinger equation with varying dispersion, self–steepening effect, cubic–quintic nonlinearity, and gain or loss. The equation arises in modeling femtosecond light propagation in an optical fiber with spatial parameter variations. The newly found self-similar structures take the shape of gray and kink pulses. It is observed that the frequency chirp accompanying these self-similar pulses depends crucially on the intensity of the wave and its amplitude can be effectively governed by adjusting the self-steepening parameter. The dynamical behaviors of the chirped self-similar gray and kink waves are analyzed in a periodic distributed amplification system. The acquired self-similar structures display rich dynamical evolutions that are important in practical applications.

Femtosecond fiber oscillator based on a 3×3-coupler-NALM: numerical model and realizations at 1 and 2 µm.

In this article, we present robust passively mode-locked femtosecond lasers operating at 1030 and approximately 2000 nm, respectively. The all-fiber, all-polarization-maintaining (PM) lasers are mode-locked by a nonlinear amplifying loop mirror (NALM) which is attached to the cavity by a 3×3-coupler. The NALM is phase-biased by the coupler, enabling turn-key operation of the oscillator. Femtosecond pulse generation is demonstrated using Ytterbium and Thulium doped active fibers. Depending on the wavelength and the installed dispersive elements, pulse formation can be aided by a range of attractors including self-similar pulse evolution, soliton, or dispersion-managed soliton formation.