Propagation Of Ultrafast Pulses Research Articles

Seq2Seq model with attention for predicting nonlinear propagation of ultrafast pulses in optical fibers

The propagation of ultrashort pulses in optical fibers exhibits highly complex nonlinear dynamics, which plays a central role in the development of light sources and photonic technologies. The mainstream of the existing methods for modeling and predicting complex nonlinear propagation dynamics of ultrashort pulses in optical fibers is based on recurrent neural networks (RNNs), which use a Multi-In-Single-Out (MISO) architecture to predict the optical pulse evolution recursively. This autoregressive model is severely limited by the error accumulation problem and also requires significant computational resources. Affected by the error accumulation problem, this method often leads to severe performance degradation in long sequence prediction tasks, thus limiting the practical application of the prediction model. In this work, we propose a new non-autoregressive model using a Single-In-Multi-Out (SIMO) architecture to simulate the highly nonlinear dynamics of ultrashort pulse propagation in optical fibers. Our model is validated on the public dataset. The results show that our model can significantly reduce the prediction error in modeling and predicting the complex nonlinear propagation of ultrashort pulses in optical fibers. In addition, the required computational resources and time spent are significantly reduced. As a whole, our proposed method comprehensively outperforms the mainstream methods in terms of efficiency, accuracy and practicality. We believe our work could bring new insights into the modeling and analysis of complex ultrafast nonlinear dynamics.

Dynamic interplay: unveiling inelastic breather collisions and modulation instability enhancement in a periodically gained inhomogeneous fiber optic communication system across temporal frequencies

Examining the impact of inhomogeneity on the propagation of femtosecond ultrafast optical pulses in fiber, we delve into the realm of the modified Hirota nonlinear Schrödinger equation (NLS) with inhomogeneity of variable coefficients (MIH-vc). Employing the Hirota bilinear method, we derive two soliton solutions for the modified Hirota NLS equation and analyze the effect of variable coefficients. The dynamical properties of these soliton solutions come to light as we meticulously analyze the corresponding plots. In our exploration, a noteworthy revelation unfolds as we witness the inelastic collision between two breathers, unleashing profound changes in the trajectory of femtosecond pulses. Furthermore, we showcase a detailed modulation instability analysis, unraveling the gain spectrum for our theoretical model. Through graphical illustrations, we elucidate how inhomogeneous functions intricately shape the modulation instability (MI) gain spectrum. A groundbreaking observation surfaces as, for the first time, we discern the periodic gain enhancement in relation to Group Velocity Dispersion along the fiber and its dynamic interactions.

Simultaneous temporal and spectral evolution of ultrafast optical pulse propagation using a single bidirectional LSTM network

Numerical simulations of optical pulse evolution are often a cumbersome task, mostly due to the presence of nonlinearities, and standard numerical approaches like splitting methods can be too complex and resource-hungry to compute them. However, under certain conditions, deep learning (DL) techniques can provide accurate alternative approaches to predict such propagation behavior. Here, we show a bidirectional long short-term memory (BiLSTM) network that predicts both temporal and spectral evolution of a short optical pulse going through a 13 m highly nonlinear fiber (HNLF). The BiLSTM performed an RMSE metric of 0.004 and 0.012 for temporal and spectral domains, respectively. A supercontinuum generation was also performed in a 20-cm photonic-crystal fiber, and the BiLSTM returns an RMSE metric of 0.018 and 0.013 for temporal and spectral domains, respectively.

Accurate modeling of ultrafast nonlinear pulse propagation in multimode gain fiber

The nonlinear propagation of picosecond or femtosecond optical pulses in multimode fiber amplifiers underlies a variety of intriguing physical phenomena as well as the potential for scaling sources of ultrashort pulses to higher powers. However, existing theoretical models of ultrashort-pulse amplification do not include some critical processes, and, as a result, they fail to capture basic features of experiments. We introduce a numerical model that combines steady-state rate equations with the unidirectional pulse propagation equation, incorporating dispersion, Kerr and Raman nonlinearities, and gain/loss-spectral effects in a mode-resolved treatment that is computationally efficient. This model allows investigation of spatiotemporal processes that are strongly affected by gain dynamics. Its capabilities are illustrated through examinations of amplification in few-mode gain fiber, multimode nonlinear amplification, and beam cleaning in a multimode fiber amplifier.

Effect of dispersion and nonlinearity on ultrashort optical pulse propagation in long-period fiber grating: An analytical investigation

Long-period fiber grating is widely used as an optical component in photonics communication technology. The optical pulse propagation in grating has been studied mostly numerically and some number of studies carried out experimentally. The detailed analytical investigation has not been reported due to the complexity of the mathematical equations. Here, we have investigated analytically the effect of dispersion and nonlinearity on ultrafast optical pulse propagation in long-period fiber grating and derived the expression for transmitted optical pulses because the detailed analytical investigation has not been reported by any authors. The results of the study show how grating-induced overall dispersion and nonlinearity-induced self-phase modulation (SPM) modify the shape of the ultrashort optical pulses when it’s propagating through a length of the grating. The combined effects of dispersion and SPM on the optical pulse evaluation are also analyzed. From the plotted graphs it is investigated that the dispersion of the grating distorted the pulse shape whereas SPM shifts the pulse towards the higher time scale. It is also investigated that the distorted optical pulse due to dispersion is reshaped by the nonlinearity introduced in the medium due to the combined effect of dispersion and SPM. Optical pulse compression, optical limiting and pulse reshaping are also illustrated as a function of excitation intensity.

Optical soliton solutions of (1 + 1)- and (2 + 1)-dimensional generalized Sasa–Satsuma equations using new Kudryashov method

In this paper, we aim to derive new soliton solutions of (1+1)- and (2+1)-dimensional generalized Sasa–Satsuma equations via the new Kudryashov method. In optical fiber transmission systems, the Sasa–Satsuma equation describes the effects of third-order dispersion, self-steepening and stimulated Raman scattering in the propagation of ultrafast pulses. The considered equations are encountered in various physical applications such as ultra-short and femto-second pulse propagation in optical fibers and dynamics of deep water waves. So, investigation of the novel solutions of the equations is one of the important topics. We have successfully extracted some soliton solutions for the considered equation. The various graphs of the obtained solutions have been depicted in the figures by selecting appropriate parameters. The singular and bright soliton solutions have been revealed in the figures. All acquired solutions have been confirmed to satisfy the considered equations. The results show that the approach may be used to find exact solutions to various nonlinear evolution equations. The new solutions and the paper results may enrich the understanding of the wave propagation in the optical fibers and may shed light on new studies.

Ultrafast pulse propagation in graphene-comprising nanophotonic waveguides considering nonperturbative electrodynamic nonlinearity

We outline a comprehensive model for ultrafast optical pulse propagation along nonlinear graphene-comprising integrated photonic waveguides. An electrodynamic graphene hot-electron model (GHEM) is used to capture the temporal dynamics and intertwined absorptive and refractive nonlinearity to explore a strongly nonperturbative photoconductivity regime that transcends third-order phenomena. We propose a formalism to abstract the 2D material-related modal properties of the waveguides in the static/continuous-wave regime that can also be plugged into a generalized nonlinear Schrödinger equation (NLSE) framework. Our model of optical pulse propagation consists of a coupled NLSE along with the nonlinear equation system of the GHEM. We demonstrate pulsed applications pertinent to integrated photonic components, namely, improvement of the extinction ratio (ER) of a nonreturn-to-zero (NRZ)-modulated bitstream, pulse shaping, spectral broadening, and optical-shock formation leading to pulse breaking and soliton formation. Our NLSE-GHEM extracts graphene nonlinearity from fundamental physics without resorting to phenomenological correction terms or fitted parameters, shows good agreement with recent experiments, and can potentially be used in the study of high-power on-chip applications such as pulsed lasers and frequency combs.

Single-shot chirped pulse digital holography for observing the propagation of ultrafast optical pulses in liquid

The propagation of intense ultrafast optical pulses in liquid was observed using single-shot chirped pulse digital holography for measuring the sequence of ultrafast optical wavefronts. In this method, two non-collinear ultrafast object pulses and a chirped reference pulse were interfered to record the digital hologram of optical wavefronts at two different times. The phase difference images of the propagation of intense optical pulses in water as well as carbon disulfide separated by 0.67 ps were obtained and the densities of generated plasma were estimated.

Dispersive wave propagation of the nonlinear Sasa-Satsuma dynamical system with computational and analytical soliton solutions

The Sasa-Satsuma equation on a continuous background describes a nonlinear fiber system with higher-order effects including the third-order dispersion and Kerr dispersion. The Sasa-Satsuma equations describe the simultaneous propagation of two ultrashort pulses in the birefringent or two-mode fiber with the third-order dispersion, self-steepening, and stimulated Raman in scattering effects, and govern the propagation of ultra-fast pulses in optical fiber transmission systems. We consider the Sasa-Satsuma equation, which is one of the integrable extensions of the nonlinear Schrödinger equations. We find the functional integral and the Lagrangian of this model. We derived the computational and analytical soliton solutions of the nonlinear Sasa-Satsuma dynamical system. We discuss the stability analysis for our solutions.

Resonance-affected high-order harmonic emission from atomic and molecular chromium laser-induced plasmas

The resonance enhancement of single-harmonic emission during the propagation of ultrafast pulses through chromium-contained plasmas is reexamined. We compare atomic (Cr) and molecular (Cr2O3, Cr3C2) plasmas to demonstrate a distinction in the enhancement factor of the single harmonic. We show how, in the case of 806 nm pump, the enhancement of the 29th harmonic (λ=27.8 nm) in Cr-contained plasma depends on the constituency of the plasma components at different conditions of target ablation. The application of tunable (1280–1440 nm) radiation allows the demonstration of notable variations of single harmonic (46 to 49 orders) enhancement using a two-color pump of Cr-contained plasma.

Reexamining Different Factors of the Resonance-Enhanced High-Order Harmonic Generation in Atomic and Nanoparticle Laser-Induced Tin Plasmas

We reexamine the resonance enhancement of a single harmonic emission during the propagation of ultrafast pulses through atomic and nanoparticle tin-containing laser-induced plasma (LIP). We compare the single atomic Sn and Sn nanoparticle plasmas to demonstrate a distinction in the enhancement factor of the single harmonic in the case of fixed and tunable near-infrared pulses. The analysis of the dynamics of Sn LIP shows the range of optimal delays between heating and driving pulses (130–180 ns), at which the maximal harmonic yield can be achieved. The enhancements of the 17th and 18th harmonics of 806 nm pulses were analyzed in the case of single-color and two-color pumps of LIP, showing up to a 12-fold enhancement of even harmonics in the two-color pump case. We show the enhancement of a single harmonic in the vicinity of the 4d105s25p2P3/2→4d95s25p2 transitions of Sn II ions and demonstrate how this process depends on the constituency of the plasma components at different conditions of target ablation. The application of tunable (1280–1440 nm) radiation allows for demonstrating the variations of single harmonic enhancement using a two-color pump of Sn-containing LIP.

Measurement of propagation of ultrafast surface plasmon polariton pulses using dual-probe scanning near-field optical microscopy.

We report the construction of diagnostics for ultrafast surface plasmon polariton (SPP) pulses that evolve spatiotemporally in femtosecond and nanometer scales. We constructed two types of scanning near-field optical microscopes (SNOMs) and verified that the temporal waveform of ultrafast SPP pulses can be measured by combining spectral interferometry (SI). In the illumination-collection (I-C) mode SNOM, which uses a single fiber probe to excite samples and collect optical responses, a lock-in detection scheme using a lock-in camera detects SI fringes even for extremely weak signal light pulses. With this I-C SI-SNOM scheme, we measured the complex plasmon response functions of gold (Au) nanorods on Ge2Sb2Te5 thin film, both in the crystal and amorphous phases. For a dual-probe SNOM (DSNOM), a dual-band modulation technique was introduced to independently control the probe-sample and probe-probe distances. With the DSNOM and by employing femtosecond SPP pulse excitation, we successfully measured the temporal waveform of an ultrafast SPP pulse that is propagating on an Au thin layer.

Multioctave supercontinuum from visible to mid-infrared and bend effects on ultrafast nonlinear dynamics in gas-filled hollow-core fiber.

Broadband supercontinuum generation is numerically investigated in a Xe-filled nested hollow-core antiresonant (HC-AR) fiber pumped at 3μm with pulses of 100fs duration and 15μJ energy. For a 25cm long fiber, under 7bar pressure, the supercontinuum spectrum spans multiple octaves from 400nm to 5000nm. Furthermore, the influence of bending on ultrafast nonlinear pulse propagation dynamics is investigated for two types of HC-AR fibers (nested and non-nested capillaries). Our results predict similar nonlinear dynamics for both fiber types and a significant reduction of the spectral broadening under tight bending conditions.

Discontinuous solutions for the short-pulse master mode-locking equation

The short-pulse master mode-locking equation is a model for ultrafast pulse propagation in a mode-locked laser cavity in the few-femtosecond pulse regime, that is a nonlinear evolution equation. In this paper, we prove the wellposedness of the Cauchy problem associated with this equation within a class of discontinuous solutions.

Guided-Wave Properties of Mode-Selective Transmission Line

The so-called mode-selective transmission line or simply “MSTL” is studied theoretically and experimentally. This low-loss and low-dispersion transmission line operates with a frequency-dependent mode-switching behavior. This self-adaptive mode-selective guided-wave structure begins with the propagation of electromagnetic waves over the lower frequency range in the form of a quasi-TEM fundamental mode similar to the microstrip line case, then followed by a fundamental quasi-TE10 mode with reference to rectangular waveguide over the higher frequency region. To gain insight into the physical mechanism and fundamental features of this mode-selective transmission line, a detailed semi-analytical hybrid-mode analysis is developed through the application of a method of lines. This method allows accurate and effective modeling of MSTL guided-wave properties. Propagation characteristics of this proposed mode-agile structure in terms of dispersion, modal, and loss properties are examined, which leads to the establishment of some basic MSTL design guidelines. Numerical results confirm the expected mode conversion and low-loss behavior through the observation of field evolutions along the structure. For experimental verification, a set of MSTL prototypes are fabricated on two different substrates through dissimilar fabrication processes. Measurements are carried out from dc-to-500 GHz using a vector network analyzer. Excellent agreement between theoretical and experimental results is observed. It is confirmed that the low-dispersion and low-loss behavior of MSTL makes it an outstanding integrated waveguide in support of high-performance super-broadband signal transmission and/or ultra-fast pulse propagation in a fully-integrated platform.

Controlling nonlinear instabilities in Bessel beams through longitudinal intensity shaping.

During ultrafast laser pulse propagation in dielectrics, the nonlinear generation of new spatial frequencies can be deleterious to reach high intensities and to generate uniform plasma channels. In this context, diffraction-free Bessel beams have attracted major recent interest because of their enhanced stability when compared to conventional Gaussian beams. However, Bessel beams can still suffer from significant modulation instability arising from noise-induced nonlinear four-wave mixing (FWM). In this Letter we report control of the nonlinear instability growth by shaping the longitudinal intensity profile of the incident field. Our results show that tailored longitudinal intensity shaping of a nondiffracting Bessel beam can strongly reduce FWM-induced oscillations and stabilize nonlinear propagation at ablation-level intensities.

Designing an ultrafast laser virtual laboratory using MATLAB GUIDE

In this work we present a virtual simulator developed using the MATLAB GUIDE environment based on the numerical resolution of the nonlinear Schrödinger equation (NLS) and using the split step method for the study of the spatial–temporal propagation of nonlinear ultrashort laser pulses. This allows us to study the spatial–temporal propagation of ultrafast pulses as well as the influence of high-order spectral phases such as group delay dispersion and third-order dispersion on pulse compression in time. The NLS can describe several nonlinear effects, in particular in this paper we consider the Kerr effect, cross-polarized wave generation and cubic–quintic propagation in order to highlight the potential of this equation combined with the GUIDE environment. Graphical user interfaces are commonly used in science and engineering teaching due to their educational value, and have proven to be an effective way to engage and motivate students. Specifically, the interactive graphical interfaces presented provide the visualization of some of the most important nonlinear optics phenomena and allows users to vary the values of the main parameters involved.

Modelling a nonlinear optical switching in a standard photonic crystal fiber infiltrated with carbon disulfide

In this letter, a numerical analysis is developed for the propagation of ultrafast optical pulses through a standard photonic crystal fiber (PCF) consisting of two infiltrated holes using carbon disulfide (CS2). This material is a good choice since it has highly nonlinear properties, what makes it a good candidate for optical switching and broadband source at low power compared to traditional nonlinear fiber coupler. Based on supermodes theory, a set of generalized nonlinear equations is presented in order to study the propagation characteristics. It is shown in this letter that it is possible to get optical switching behavior at low power and how the dispersion, as well as, the two infiltrated holes separation influence this effect. Finally, we see that supercontinuum generation can be induced equally in both infiltrated holes despite no initial excitation at one hole.

Ultra-fast pulse propagation in nonlinear graphene/silicon ridge waveguide.

We report the femtosecond laser propagation in a hybrid graphene/silicon ridge waveguide with demonstration of the ultra-large Kerr coefficient of graphene. We also fabricated a slot-like graphene/silicon ridge waveguide which can enhance its effective Kerr coefficient 1.5 times compared with the graphene/silicon ridge waveguide. Both transverse-electric-like (TE-like) mode and transverse-magnetic-like (TM-like) mode are experimentally measured and numerically analyzed. The results show nonlinearity dependence on mode polarization not in graphene/silicon ridge waveguide but in slot-like graphene/silicon ridge waveguide. Great spectral broadening was observed due to self-phase modulation (SPM) after propagation in the hybrid waveguide with length of 2 mm. Power dependence property of the slot-like hybrid waveguide is also measured and numerically analyzed. The results also confirm the effective Kerr coefficient estimation of the hybrid structures. Spectral blue shift of the output pulse was observed in the slot-like graphene/silicon ridge waveguide. One possible explanation is that the blue shift was caused by the ultra-fast free carrier effect with the optical absorption of the doped graphene. This interesting effect can be used for soliton compression in femtosecond region. We also discussed the broadband anomalous dispersion of the Kerr coefficient of graphene.

Ultrafast multi-wavelength switch based on dynamics of spectrally-shifted solitons in a dual‑core photonic crystal fiber

Nonlinear propagation of ultrafast near infrared pulses in anomalous dispersion region of dual-core photonic crystal fiber was studied. Polarization tunable soliton-based nonlinear switching at multiple non-excitation wavelengths was demonstrated experimentally for fiber excitation by 100 fs pulses at 1650 nm. The highest-contrast switching was obtained with the fiber length of just 14 mm, which is significantly shorter compared to the conventional non-solitonic in-fiber switching based on nonlinear optical loop mirror. Advanced numerical simulations show good agreement with the experimental results, suggesting that the underlying dual-core soliton fission process supports nonlinear optical switching and simultaneous pulse compression to few-cycle durations at the level of 20 fs.