Dynamics Of Pulse Propagation Research Articles

Dynamics of pulse propagation with solitary waves in monomode optical fibers with nonlinear Fokas system

In this study, a unified auxiliary equation method, which is one of the powerful methods for exploring nonlinear model solutions, is used in the Fokas system, with complex functions representing nonlinear pulse propagation in monomode optical fibers. As a result, we get some solutions, including dark–bright, singular, periodic, bright–dark, Jacobi elliptic functions, trigonometric, hyperbolic and exponential ones. In addition, we use a computer program to generate 3D, 2D and counterplot graphics from the obtained solutions by assigning specific values to the involved parameters. While discussing, the graphs for various values of an arbitrary constant are examined. These findings constitute an important step in understanding how solitary waves are generated in nonlinear media. Since the studied model is used in many domains, including Bose–Einstein condensates and plasma physics, these results improve our theoretical knowledge and open up new avenues for potential real-world applications and the development of cutting-edge technologies.

Linear and Nonlinear Optics of Broad-Band Laser Pulses: Diffraction.

The typical spectrally limited laser pulse in the near-infrared region is narrow-band up to 40-50 fs. Its spectral width Δk is much smaller than the carrying wavenumber k0 (Δk ≪ k0) . For such kinds of pulses, on distances of a few diffraction lengths, the diffraction is of a Fresnel's type and their evolution can be described correctly in the frame of the well-known paraxial evolution equation. The technology established in 1985 of amplification through chirping of laser pulses triggered remarkable progress in laser optics along with the construction of femtosecond (fs) laser facilities producing high intensity fields of the order of 1015-1021 W/cm2. However, the duration of the pulse was quickly shortened from picoseconds down to 5-6 fs, which have a broad-band nature (Δk ∼ k0). The linear and nonlinear propagation dynamics of broad-band pulses is quite different form their narrow-band counterparts. Here, we review the appropriate theoretical approach to study the evolution of the pulse. Moreover, we shed light on the different diffraction regimes inherent to both narrow-band and broad-band laser pulses and compare them to unveil the main differences. Using this very method, in subsequent papers, we will investigate the influence of the dispersion and nonlinearity on the laser pulse propagation in isotropic media.

The periodic soliton solutions for a nonlocal nonlinear Schrödinger equation with higher-order dispersion

A nonlocal nonlinear Schr¨odinger (NNLS) equation with fourth-order dispersion and cubic-quintic nonlinearities has been studied analytically and numeri- cally. Under the constraint conditions, auxiliary functions are introduced, and explicit one- and two-soliton solutions are obtained by the Hirota bilinear method. Accord- ing to the solutions, the propagation dynamics of soliton pulses are investigated. The influences of different parameters on the dynamics of one- and two-soliton solutions have been analyzed. The results show that the two-soliton solution exhibits diverse dy- namic characteristics under the suitable parameter selections. In addition, the stability of one- and two-soliton solutions against the constraint conditions deviations and under the initial perturbations are also studied numerically.

Simulation of laser-induced ionization in wide bandgap solid dielectrics with a particle-in-cell code.

Modeling the laser-plasma interaction within solids is crucial in controlling ultrafast laser processing of dielectrics, where the pulse propagation and plasma formation dynamics are highly intricate. This is especially important when dealing with nano-scale plasmas where specific phenomena of plasma physics, such as resonance absorption, can significantly impact the energy deposition process. In this article, we report on adapting of a Particle-In-Cell code, EPOCH, to model the laser-plasma interaction within solids. This is performed by implementing a background permittivity and by developing and validating adapted field ionization and impact ionization modules. They are based on the Keldysh ionization theory and enable the modeling of ionization processes within solids. The implementation of these modules was validated through comparisons with a hydrodynamic code and existing literature. We investigate the necessary number of super-particles per cell to model realistic ionization dynamics. Finally, we apply the code to explore the dynamics of plasma formation in the regime of of quantized structuring of transparent films. Our study elucidates how a stack of nano-plasma layers can be formed by the interference of a pulse with its reflection on the exit surface of a high refractive index material.

Bright soliton of Stochastic perturbed Biswas-Milovic equation with cubic-quintic-septic law having multiplicative white noise

For the first time, the adopted stochastic form of the perturbed Biswas-Milovic equation with cubic-quintic-septic law having spatio-temporal and chromatic dispersion in the presence of multiplicative white noise in Ito sense was presented and examined. The Biswas-Milovic equation ˆ models numerous physical phenomena occurring in optical fiber. We analyzed the optical soliton solutions of the stochastic model with the aid of a subversion of the new extended auxiliary equation method. Furthermore, we investigated the evaluation of the noise impacts and the effects of some model parameters on the dynamics of the generated soliton. Finally, graphical depictions of the derived soliton types were represented for some solution functions. The stochastic model and the derived results will contribute to the comprehension of the nonlinear dynamics of pulse propagation in optical fibers which has great importance for the advancement of optical communication engineering.

Unveiling optical soliton solutions and bifurcation analysis in the space–time fractional Fokas–Lenells equation via SSE approach

The space–time fractional Fokas–Lenells (STFFL) equation serves as a fundamental mathematical model employed in telecommunications and transmission technology, elucidating the intricate dynamics of nonlinear pulse propagation in optical fibers. This study employs the Sardar sub-equation (SSE) approach within the STFFL equation framework to explore uncharted territories, uncovering a myriad of optical soliton solutions (OSSs) and conducting a thorough analysis of their bifurcations. The discovered OSSs encompass a diverse array, including bright-dark, periodic, multiple bright-dark solitons, and various other types, forming a captivating spectrum. These solutions reveal an intricate interplay among bright-dark solitons, complex periodic sequences, rhythmic breathers, coexistence of multiple bright-dark solitons, alongside intriguing phenomena like kinks, anti-kinks, and dark-bell solitons. This exploration, built upon meticulous literature review, unveils previously undiscovered wave patterns within the dynamic framework of the STFFL equation, significantly expanding the theoretical understanding and paving the way for innovative applications. Utilizing 2D, contour, and 3D diagrams, we illustrate the influence of fractional and temporal parameters on these solutions. Furthermore, comprehensive 2D, 3D, contour, and bifurcation analysis diagrams scrutinize the nonlinear effects inherent in the STFFL equation. Employing a Hamiltonian function (HF) enables detailed phase-plane dynamics analysis, complemented by simulations conducted using Python and MAPLE software. The practical implications of the discovered OSS solutions extend to real-world physical events, underlining the efficacy and applicability of the SSE scheme in solving time–space nonlinear fractional differential equations (TSNLFDEs). Hence, it is crucial to acknowledge the SSE technique as a direct, efficient, and reliable numerical tool, illuminating precise outcomes in nonlinear comparisons.

Bidirectional mode-locked erbium-doped fiber laser based on an all-fiber gold nanofilm saturable absorber.

We demonstrate a bidirectional mode-locked erbium-doped fiber laser by incorporating gold nanofilm as a saturable absorber (SA). The gold nanofilm SA has the advantages of high stability and high optical damage threshold. Besides, the SA exhibits a large modulation depth of 26% and a low saturation intensity of 1.22 MW/cm2 at 1.56 μm wavelength band, facilitating the mode-locking of bidirectional propagating solitons within a single laser cavity. Bidirectional mode-locked solitons are achieved, with the clockwise pulse centered at 1568.35 nm and the counter-clockwise one at 1568.6 nm, resulting in a slight repetition rate difference of 19 Hz. Moreover, numerical simulations are performed to reveal the counter-propagating dynamics of the two solitons, showing good agreement with the experimental results. The asymmetric cavity configuration gives rise to distinct buildup and evolution dynamics of the two counter-propagating pulses. These findings highlight the advantage of the gold nanofilm SA in constructing bidirectional mode-locked fiber lasers and provide insights for understanding the bidirectional pulse propagation dynamics.

Dynamics of twin pulse propagation and dual-optical switching in a Λ + Ξ atomic medium

Optical bistability (OB) and optical multistability (OM) as well as optical soliton and all-optical switching have been successfully established in a lambda + cascade-type five-level atomic medium under electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) regimes. For this configuration, three laser fields are required to excite atomic transitions. The probe laser field with two circularly left- and right-polarized components excites atoms in a lambda-type configuration. Meanwhile, two coupling laser fields excite atoms in a ladder-type configuration. In this way, the above optical phenomena can occur with two frequency channels corresponding to the circularly left- and right-polarized light components. By adjusting the strength/direction of the static magnetic field in the presence of the driving field, the EIT and EIA effects can be swapped, at the same time, OB and OM effects can also be converted. In the EIT regime, the propagation of the probe pulse easily achieves the soliton state, whereas it can be completely extinguished in the EIA regime. This makes it easy to create an all-optical switching mechanism. Especially, both components of the probe field (cw) can be modulated into a synchronous or asynchronous square pulse according to the modulation of the driving field. The results obtained from the investigated model may provide merits of the applications for optical storage and all-optical switching for multi-channel optical communications.

Acceleration-free propagation of Airy pulses in pure-quartic dispersion media

We investigate the propagation dynamics of Airy pulses in pure-quartic dispersion media both numerically and analytically. For linear propagation, our results show that Airy pulses will keep the acceleration-free propagation behaviors under the action of pure-quartic dispersion, quite different from the case in the presence of only quadratic or cubic dispersion. Another notable observation is that the optical fields will evolve to become a symmetric-shaped pulse and the oscillatory tail is gradually suppressed over long propagation. For nonlinear propagation, the Airy pulse having high powers will be shed into multiple soliton dynamics through the physical balance between anomalous pure-quartic dispersion and the Kerr nonlinear effect.

Distinguishing the nonlinear propagation regimes of vortex femtosecond pulses in fused silica by evaluating the broadened spectrum.

The nonlinear propagation dynamics of vortex femtosecond laser pulses in optical media is a topic with significant importance in various fields, such as nonlinear optics, micromachining, light bullet generation, vortex air lasing, air waveguide and supercontinuum generation. However, how to distinguish the various regimes of nonlinear propagation of vortex femtosecond pulses remains challenging. This study presents a simple method for distinguishing the regimes of nonlinear propagation of femtosecond pulses in fused silica by evaluating the broadening of the laser spectrum as the input pulse power gradually increases. The linear, self-focusing and mature filamentation regimes for Gaussian and vortex femtosecond pulses in fused silica are distinguished. The critical powers for self-focusing and mature filamentation of both types of laser pulses are obtained. Our work provides a rapid and convenient method for distinguishing different regimes of nonlinear propagation and determining the critical powers for self-focusing and mature filamentation of Gaussian and structured laser pulses in optical media.

Optical Solitons and Modulation Instability Analysis with Lakshmanan–Porsezian–Daniel Model Having Parabolic Law of Self-Phase Modulation

This paper seeks to find optical soliton solutions for Lakshmanan–Porsezian–Daniel (LPD) model with the parabolic law of nonlinearity. The spatiotemporal dispersion is included to the model, as it can contribute to handling the problem of internet bottleneck. This study was performed analytically using the traveling wave hypothesis to reduce the model to an integrable form. Then, the resulting equation was handled with two approaches, namely, the auxiliary equation method and the Bernoulli subordinary differential equation (sub-ODE) method. With an intentional focus on hyperbolic function solutions, abundant optical soliton waves including W-shaped, bright, dark, kink-dark, singular, kink, and antikink solitons were derived with the existing conditions. Furthermore, the behaviors of some optical solitons are illustrated. The spatiotemporal dispersion was found to significantly affect the pulse propagation dynamics. Finally, the modulation instability (MI) of the LPD model is explained in detail along with the extraction of the expression of MI gain.

Nonlinear autoregressive with external input neural network for predicting the nonlinear dynamics of supercontinuum generation in optical fibers

Full characterization of the propagation dynamics of ultra-short pulses in optical fibers is of fundamental importance in designing optical devices for several applications in the nonlinear optics field. Such applications range from basic descriptions of the light–matter dynamics to Bose–Einstein condensates, plasma physics, hydrodynamics, high-resolution imaging, and remote sensing, among many others. Nevertheless, ultra-short pulse propagation is a highly nonlinear process, so correctly describing all temporal and spectral features of these pulses is a big challenge, consuming extensive computational resources. Looking for simple solutions to this problem, we present in this paper, for the first time, to the best of our knowledge, a nonlinear autoregressive with external input neural network (NARXNET) capable of predicting the nonlinear dynamics of supercontinuum generation in optical fibers. The NARXNET structure allows low prediction error, fast training as short as 1.45 min, satisfactory generalization ability, and low computational resources for the training and testing stages.

Curve-shaped ultrashort laser pulses with programmable spatiotemporal behavior

Structured ultrashort laser pulses with controlled spatiotemporal properties are emerging as a key tool for the study and application of light–matter interactions in different fields such as microscopy, time-resolved imaging, laser micro-machining, particle acceleration, and attosecond science. In practice, a structured ultrashort pulse focused along a target trajectory with controlled pulse dynamics is required, e.g., to set the trajectory and velocity of the resulting intensity peak. Here, to address this challenging problem, we present a technique and experimental setup that allows straightforward engineering of structured ultrashort laser pulses with control of their spatiotemporal properties enabling tailored pulse propagation dynamics along the target trajectory. Our theoretical framework describes the design and control of this kind of curve-shaped laser pulse in terms of the curve geometry and phase prescribed along it. We have derived a closed-form expression that describes the interplay between the curve geometry and prescribed phase governing the pulse dynamics, including the temporal behavior of the pulse peak intensity while preserving the pulse duration. The theoretical results and the corresponding numerical simulations allow us to analyze the pulse dynamics on the example of femtosecond curve-shaped vortex pulses, including contour-shaped pulses created to follow the outline of objects at micrometer scale. The experimental results demonstrate the generation of these structured ultrashort pulses. These findings could pave the way for the next generation of ultrashort laser-based optical tools for the study and control of light–matter interactions.

Pure–quartic optical solitons and modulational instability analysis with cubic–quintic nonlinearity

We analyze the propagation dynamics of intense light pulses in an optical medium exhibiting cubic–quintic nonlinearity and pure fourth-order dispersion. We show that this physical system may support a rich variety of periodic wave solutions in the presence of all physical processes. Interestingly, in the long-wave limit, two different types of quartic dark solitons with equal amplitudes and wave numbers but different widths are identified for the first time. The obtained dark soliton solutions are shown to be independent of any free parameters and their characteristics are uniquely determined by system parameters. The numerical examples are presented for illustrating the soliton evolution dynamics in the waveguiding system. The formation of these quartic dark solitons occurs in normal pure fourth-order dispersion when the quintic and cubic nonlinearities are competitive. The modulational instability of a continuous wave is also analyzed under the combined effects of quartic dispersion and cubic–quintic nonlinearities. Additionally, the role of quintic nonlinearity and fourth-order dispersion effects on the modulational instability has been discussed.

Design and analysis of recurrent neural networks for ultrafast optical pulse nonlinear propagation.

In this work, we analyze different types of recurrent neural networks (RNNs) working under several different parameters to best model the nonlinear optical dynamics of pulse propagation. Here we studied the propagation of picosecond and femtosecond pulses under distinct initial conditions going through 13 m of a highly nonlinear fiber and demonstrated the application of two RNNs returning error metrics such as normalized root mean squared error (NRMSE) as low as 9%. Those results were further extended for a dataset outside the initial pulse conditions used on the RNN training, and the best-proposed network was still able to achieve a NRMSE below 14%. We believe that this study can contribute to a better understanding of building RNNs employed for modeling nonlinear optical pulse propagation and of how the peak power and nonlinearity affect the prediction error.

Propagation of periodic and solitary waves in a highly dispersive cubic–quintic medium with self-frequency shift and self-steepening nonlinearity

We study the dynamics of femtosecond light pulse propagation in a cubic–quintic medium exhibiting dispersive effect up to the fourth order as well as self-frequency shift and self-steepening nonlinearity. A rich variety of periodic and solitary wave solutions are derived for the governing generalized higher-order nonlinear Schrödinger equation in the presence of self-frequency shift and self-steepening effects. It is found that the frequency shift, inverse velocity, amplitude and wave number of both periodic and solitary waves depend on dispersion coefficients and nonlinearity parameters as well. The conditions on optical fiber parameters for the existence of these structures are presented. The stability of these periodic and solitary wave solutions is studied numerically by adding white noise. It is proved by using the numerical split-step Fourier method that the derived exact solutions are stable by Lyapunov criteria.

Controllable transmission of Airy pulses in nonlinear dissipative system

The propagation characteristics of truncated Airy pulses have been numerically investigated in complex cubic-quintic Ginzburg-Landau equation and some interesting nonlinear phenomena are observed. The results show that the transmission trajectory and amplitude of the Airy pulses can be controlled by changing the gain dispersion. Due to the complex interaction between the side lobes, the double Airy pulses evolve into single soliton, double solitons and triple solitons, respectively. The interaction between linear loss and nonlinear gain has a significant effect on the propagation dynamics of Airy pulses, which can obtain stable bound state solitons or pulsating-like solitons. In addition, the period, structure and number of solitons can be controlled by properly choosing the parameters of the quintic nonlinear correction term.

Spatio-temporal characterization of ultrashort vector pulses

Ultrafast vectorially polarized pulses have found many applications in information and energy transfer owing mainly to the presence of strong longitudinal components and their space-polarization non-separability. Due to their broad spectra, such pulses often exhibit space–time couplings, which significantly affect the pulse propagation dynamics. Although such couplings usually result in reduced energy density at the focal spot, they have been utilized to demonstrate pulse shaping as in the case of a rotating or sliding wavefront as the pulse travels through its focal point. Here, we present a new method for the spatiotemporal characterization of ultrashort cylindrical vector pulses based on a combination of spatially resolved Fourier transform spectroscopy and Mach–Zehnder interferometry. The method provides access to spatially resolved spectral amplitudes and phases of all polarization components of the pulse. We demonstrate the capabilities of the method by completely characterizing a 10 fs radially polarized pulse from a Ti:sapphire laser centered at 800 nm.

Optical wave patterns of nonlinear Schrödinger equation with anti-cubic nonlinearity in optical fiber

This paper studies the anti-cubic nonlinear Schrödinger equation which describes the nonlinear dynamics of pulse propagation in optical metamaterials. Three different types of optical soliton solutions are obtained through the complete polynomial discriminant system method, and their topological stability is analyzed. Under specific parameters, we give three-dimensional diagrams of solutions to prove the existence of solutions.

Nonlinear spatial reshaping of pulsed beam in a step-index few-mode optical fiber.

In this paper we demonstrate the spatial and spectral dynamics of pulse propagation in a step-index few-mode optical fiber, through an experimental and numerical analysis. The Kerr induced spatial self-cleaning is demonstrated by coupling a sub-nanosecond pulsed laser at 532nm into the fiber supporting above 10 modes. A bell-shaped and approximately single mode beam can be obtained for peak powers above 6kW and it remained relatively unchanged up to 25kW. But at significantly higher input peak powers, the spatial contents of spectral sidebands change dramatically, because of intermodal four wave mixing effect.