Nonlinear Pulse Research Articles

Spatiotemporal instability and optical filament formation in metamaterials

This study investigates the spatiotemporal instability in artificial metamaterials, with a focus on generating ultrashort pulses or light filaments. We identify the parametric regions where the metamaterial exhibits spatiotemporal instability, enabling the generation of ultrashort pulses. Our approach involves modeling nonlinear pulse propagation in the metamaterial using a (3+1)-dimensional nonlinear Schrödinger equation and performing a standard linear stability analysis to explore the spatiotemporal instability. Leveraging the engineering freedom to tailor the material parameters, we numerically demonstrate the generation of ultrashort pulses through spatiotemporal instability.

Generation of 1 MHz 15 fs pulses in the near-infrared with high energy and their application to time-resolved spectroscopy

Ultrashort pulses with a duration of ∼10 fs are crucial to fully resolve nuclear motions in molecules and materials. Here, we employ nonlinear pulse compression using photonic crystal fiber in the near-infrared region to generate ultrashort pulses at a high repetition rate with significant pulse energy. Femtosecond pulses centered around 1200 nm from a cavity-dumped optical parametric oscillator are compressed to a duration of 15 fs. The pulse energy reaches several tens of nanojoules, sufficient for wavelength conversion via nonlinear processes. Second harmonic generation produces clean 13 fs pulses at around 600 nm with pulse energy of 4 nJ. The effectiveness of nonlinear pulse compression using photonic crystal fiber for ultrafast time-resolved spectroscopy is demonstrated through time-resolved fluorescence (photoluminescence) and transient absorption apparatus, utilizing the second harmonic as pump pulses. Specifically, a time resolution of ∼20 fs is achieved in a time-resolved fluorescence experiment, enabling the recording of nuclear wave packets over 1200 cm−1 by spontaneous fluorescence. The high repetition rate at the megahertz level significantly improved the signal quality.

All-fiber GHz few-cycle pulse generation at 2 µm.

We demonstrate an all-fiber GHz mode-locked laser system with few-cycle duration operating at 2 µm. Based on a dispersion-managed mode-locked oscillator, a multi-stage fiber amplifier, and a nonlinear pulse compressor, the laser system can deliver watt-level few-cycle pulses at a fundamental repetition rate of 1.041 GHz. This 2-µm pulsed laser offers outstanding performance metrics, including a pulse duration of 33 fs (corresponding to ∼5 optical cycles) and an average power of 4.17 W. Moreover, the all-fiber laser system exhibits excellent power stability, and the integrated relative intensity noise (RIN) is only 0.052% (10 Hz-1 MHz). It is anticipated that this new, to the best of our knowledge, laser source is promising for frontier applications, including coherent supercontinuum generation, nonlinear frequency conversion, and laser-material interaction.

Highly coherent mid-infrared wideband supercontinuum generation by a silica cladded silicon nitride core buried waveguide

Abstract Optical waveguides with semiconductor cores are drawing considerable research interest in the domain of supercontinuum (SC) generation in recent times. In this work, we design a square-core silicon nitride buried waveguide with a silica-clad, aiming for a wideband spectrum generation in the mid-IR region when operated at the standard telecommunication wavelength of 1550 nm. Among different such silicon nitride square-core buried waveguides, we propose a typical design with dimensions of 400 nm × 400 nm along its height and width, capable of producing a highly coherent broadband intensity spectrum ranging from 810 nm to 5441 nm after propagating through just a few millimeters of the waveguide. The group velocity dispersion maintains minimal value over a broad wavelength range in the mid-IR region, while the nonlinear coefficient is estimated to be sufficiently high. The nonlinear pulse propagation through such a waveguide leads to achieving an SC spanning over 2.76 octaves, sufficiently broader than previously reported silicon nitride-based waveguides. Furthermore, our calculations confirm the highly coherent nature of the generated SC. To the best of our knowledge, this is the first report of SC generation maintaining a high degree of coherence over such a wide wavelength range in the mid-IR zone using a square-core silicon nitride buried waveguide.

TW-scale few-cycle short-wave infrared laser based on nonlinear compression in a large-core gas-filled hollow core fiber

In this Letter, we present the generation of terawatt-scale few-cycle short-wave infrared (SWIR) lasers using nonlinear compression in a large-core gas-filled hollow core fiber. Through the experimental verification, we investigate the energy scaling properties and nonlinear pulse propagation in the argon-filled hollow core fiber. At static pressure, the system delivers pulses with 5.55 mJ/9.04 fs at a central wavelength of 1.45 μm, resulting in a peak power of about 0.5 TW. Subsequently, based on the chirped input pulses and pressure gradient, the system delivers terawatt-scale two-cycle SWIR pulses with 9.52 mJ/10.65 fs, resulting in a record peak power of about 0.7 TW. This study marks a crucial advancement in the field of SWIR ultra-intense, ultrashort pulse nonlinear interaction platforms. This high-energy, few-cycle SWIR source has significant applications in high-intensity THz radiation, x-ray generation, and other fields of strong-field physics.

Self-Focused Pulse Propagation Is Mediated by Spatiotemporal Optical Vortices.

We show that the dynamics of high-intensity laser pulses undergoing self-focused propagation in a nonlinear medium can be understood in terms of the topological constraints imposed by the formation and evolution of spatiotemporal optical vortices (STOVs). STOVs are born from pointlike phase defects on the sides of the pulse nucleated by spatiotemporal phase shear. These defects grow into closed loops of spatiotemporal vorticity that initially exclude the pulse propagation axis, but then reconnect to form a pair of toroidal vortex rings that wrap around it. STOVs constrain the intrapulse flow of electromagnetic energy, controlling the focusing-defocusing cycles and pulse splitting inherent to nonlinear pulse propagation. We illustrate this in two widely studied but very different regimes, relativistic self-focusing in plasma and nonrelativistic self-focusing in gas, demonstrating that STOVs mediate nonlinear propagation irrespective of the detailed physics.

Ultrafast reverse saturable absorption and all-optical computing with boron dipyrromethene (BODIPY) chromophore derivatives

Ultrafast reverse saturable absorption (RSA) in chromophore-based borondipyrro-methenes (BODIPYs) derivatives, 1,7-Diphenyl-3,5-bis(9,9-dimethyl-9H-fluoren-2-yl)-boron-diuoride-azadipyrromethene (ZL-61) and 1,7-Diphenyl-3,5-bis(4-(1,2,2-triphenyl-vinyl)phenyl)-boron-diuoride azadipyrromethene (ZL-22), has been theoretically analyzed with femtosecond (fs) laser pulses at 800 nm and 850 nm. The results are in good agreement with the reported experimental results. The effect of input pulse intensity, pulse width, nonlinear absorption (NLA) coefficients, sample thickness and laser pulse shaping on transmittance has been studied and optimized for high contrast and low-power operation. All-optical fs NOT and the universal NOR and NAND Boolean logic gates have been designed with ZL-61 and ZL-22. The logic gates with top-hat input pulse profile have a sharp switch ON/OFF time compared to the Gaussian input laser profile. Ultrafast operation at relatively low pump intensities opens up exciting prospects for the applicability of BODIPY derivatives for ultrafast low-power all-optical computing and information processing.

Spatial mode cleaning and efficient nonlinear pulse compression to sub-50 fs in a gas-filled multipass cell.

We demonstrate a gas-filled multipass cell (MPC) that cleaned the spatial mode of a spatial-filter-free 250 W, 100 kHz, 445 fs driven source based on an Innoslab amplifier and compressed the pulse duration to 41 fs simultaneously. The multipass cell acted as a spatial filter and benefited from its discrete waveguide nature, in which the input beam quality factor M2 was improved from 1.53 to a near-diffraction-limited value of 1.21 at 96% transmission.

Phase-locked and phase-unlocked multicolor solitons in a fiber laser.

Multicolor solitons are nonlinear pulses composed of two or more solitons centered at different frequencies, propagating with the same group velocity. In the time domain, multicolor solitons consist of an envelope multiplying a more rapidly varying fringe pattern that results from the interference of these frequency components. Here, we report the observation in a fiber laser of a novel, to the best of our knowledge, type of dynamics in which different frequency components still have the same group velocity but have different propagation constants. This causes the relative phases between the constituent spectral components to change upon propagation, corresponding to the fringes moving under the envelope. This leads to small periodic energy variations that we directly measure. Our experimental results are in good agreement with realistic numerical simulations based on an iterative cavity map.

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.

Nonlinear propagation of chirped laser pulses through a dispersive and turbulent atmosphere

The evolution of ultrashort laser pulses in dispersive, turbulent, nonlinear, and dissipative media is discussed in connection with nonlinear self-focusing collapse and the onset of laser filamentation. In quiescent air, a laser pulse propagating with a peak power greater than a critical power for self-focusing will undergo a catastrophic, transverse collapse until the intensity is large enough for photoionization. At this point, self-focusing is arrested and balanced by plasma refraction, forming a laser filament. By applying an appropriate chirp, the dispersive properties of the medium can be used to enhance this process and control its onset, and to counter dissipative effects such as molecular absorption and atmospheric scattering. This paper presents an analysis of the effect of atmospheric turbulence on the propagation of nonlinear pulses with dispersion compensation (chirp). The analytical results are compared with wave optics simulations and found to be in reasonable agreement as long as the pulse maintains a near-Gaussian spatiotemporal profile.

Fractional Fokas-Lenells equation: analyzing travelling waves via advanced analytical method

In this paper, we consider the fractional Fokas-Lenells equation, which allows us to analyze how a nonlinear optic pulse spreads in time as single-mode fiber produces higher-order nonlinear effects. We have computed perfectly accurate travelling wave solutions for the Fokas-Lenells equation using the Riccati-Bernoulli sub-Ode approach. For the corresponding equation, we have established three distinct classes of perfectly accurate travelling wave solutions with different free parameters; hyperbolic, trigonometric, and rational. A sophisticated Backlund transformation is implemented to the equation to change it to ordinary differential equation domain, leading to many extra exact solutions.

Ternary ReS2(1-x)Se2xalloys of different composition for Q-switched and mode-locked all-fiber laser.

This paper systematically studied the composition-controlled nonlinear optical properties and pulse modulation of ternary ReS2(1-x)Se2xalloys for the first time. The compositionally modulated characteristics of ReS2(1-x)Se2xon the band gap were simulated based on the first principles. We investigated the effect of the band gap on the saturable absorption properties. In addition, we demonstrated the modulation characteristics of different components ReS2(1-x)Se2xon 1.5μm Q-switched pulse performance. The Q-switched threshold, repetition rate, and pulse duration increase as the S(sulfur)-element composition rise. And pulse energy also was affected by the S(sulfur)-element composition. The ReS0.8Se1.2SA was selected to realize a conventional soliton with high energy in the all-fiber mode-locked laser. The pulse was centered at 1562.9 nm with a pulse duration of 2.26 ps, a repetition rate of 3.88 MHz, and maximum pulse energy of 1.95 nJ. This work suggests that ReS2(1-x)Se2xhas great potential in laser technology and nonlinear optics, and widely extends the material applications in ultrafast photonics.

Dynamic analysis of a SIS epidemic model with nonlinear incidence and ratio dependent pulse control

Dynamic analysis of a SIS epidemic model with nonlinear incidence and ratio dependent pulse control

A new version of trial equation method for a complex nonlinear system arising in optical fibers

In this study, the dissipation problem of nonlinear pulse in mono mode optical fibers which is governed by the Fokas system (FS) is considered. The solutions of this system have an important role in comprehending the different wave structures in physical settings. Therefore, a new version of the trial equation method (NVTEM) is employed to present the new exact wave solutions of the FS. The advantage of the NVTEM is to use different root possibilities of a polynomial which shape the solutions of the related model. Primarily this system is converted to a nonlinear ordinary differential equation (NODE) via the traveling wave transform to apply the proposed method. Various exact wave solutions to the FS are obtained such as rational function, exponential function, hyperbolic function, and Jacobi elliptic function solutions. Thus, we have revealed solutions featly which are unlike the wave solutions previously found by other analytical methods. The present results depict the formation and development of such waves and their interactions. The exhibition of the solutions is given by 3D plots together with the corresponding 2D plots. The outcomes have shown that the proposed technique is abundant in achieving different wave solutions of many nonlinear differential equations in the field of optics.

Effects of Donepezil on Nonlinear Arterial Pressure and Pulse Interval Dynamics in Spontaneously Hypertensive Rats (SHR)

Objectives: This study aimed to evaluate the effects of donepezil, an anticholinesterase agent that potentiates parasympathetic function, in the nonlinear dynamics of blood pressure (BP) and pulse interval (PI) from spontaneously hypertensive rats (SHR). Entropy-based approaches which quantify the irregularity or unpredictability of time series were employed. Additionally, detrended fluctuation analysis (DFA) was applied to estimate the degree of self-similarity in the time series. We hypothesized that donepezil improves both entropy and DFA indices of BP and PI. Methods: Male SHR or Wistar-Kyoto (WKY) rats (5 weeks old) were implanted with subcutaneous osmotic mini-pumps for donepezil (DON) administration (1.4 mg/kg/day) or vehicle. At the end of the treatment (16 weeks), conscious WKY (N=12) and SHR treated with donepezil (N=8), or vehicle (N=9), had their BP directly recorded during 1h. Time series (15 min) from systolic BP and PI were generated and used to calculate sample (SampEn), fuzzy (FuzzyEn), and dispersion (DispEn) entropy, as well as DFA scale exponents in short (α1; 5≤n≤15), mid (α2; 20≤n≤100) and long (α3; 100≤n≤500) windows. The results are shown as mean ± SD. One-Way ANOVA, followed by Tukey’s post-test, evaluated differences between the WKY, SHR, and SHR+DON groups. Results: The data are displayed in the table. Lower PI DispEn was observed in SHR treated with DON compared to WKY. Entropy values of BP series were found smaller in SHR and SHR+DON compared to WKY rats. For DFA of the PI series, SHR+DON showed higher α1 compared to the WKY. Moreover, SHR displayed higher α3 when compared to the WKY. In the series of BP values, the results showed higher α2 and α3 in SHR compared to WKY. [Formula: see text] Conclusion: These findings showed that SHR exhibited lower BP entropy and higher DFA of BP and IP compared with WKY. However, donepezil did not prevent these changes of non-linear indices from BP and PI variability in SHR. Funding Sources: FAPESP, Process 2020/06043-7. CNPq, Process 306994/2021-6 and 423999/2021-4. FAEPA. CAPES. This is the full abstract presented at the American Physiology Summit 2024 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

The impact of resource limitation on the pest-natural enemy ecosystem with anti-predator behavior and fear effect

Research on agricultural pest control data indicates that the actual effectiveness of insecticides may exhibit slight variations, influenced by factors such as the type and quantity of pests. Additionally, the development of resistance by pests, as a result of adaptation to the environment, can impact the precision of pest control strategies. Hence we suggest implementing a nonlinear pulse state-dependent feedback control system, considering resource limitations, to investigate the influence of varying pesticide fatality rates on pest outbreaks. This paper takes into account the fear effect and anti-predator behavior to accurately portray the farmland ecosystem. We assessed the phase set and Poincaré map under the conditions for the existence of order-k (where k=1,2,3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$k=1,2,3$\\end{document}) periodic solutions and examined their stability behavior. Remarkably, the system exhibited diverse bifurcation phenomena associated with pesticide-related parameters. Furthermore, the system demonstrated a multistability phenomenon involving the coexistence of the order-1 periodic solution and the limit cycle. This suggests that altering control strategies can disturb the initial coexistence status of pests and natural enemies. It also underscores that resource limitations can indeed impact the outbreak patterns and frequencies of pests. In addition to the variability in pesticide fatality rates, the inclusion of natural enemy releases in the nonlinear pulse strategy contributes to the model exhibiting complex dynamic characteristics. All these findings are substantiated by numerical simulations.

Efficient multimode vectorial nonlinear propagation solver beyond the weak guidance approximation

In this paper, we present an efficient numerical model able to solve the vectorial nonlinear pulse propagation equation in circularly symmetric multimode waveguides. The algorithm takes advantage of the conservation of total angular momentum of light upon propagation and takes into account the vectorial nature of the propagating modes, making it particularly relevant for studies in ring-core fibers. While conventional propagation solvers exhibit a computational complexity scaling as Nmode4, where Nmode is the number of considered modes, the present solver scales as Nmode3/2. As a first example, it is shown that orbital angular momentum modulation instability processes take place in ring-core fibers in realistic conditions. Finally, it is predicted that the modulation instability process is followed by the appearance of breather-like angular structures.

A polynomial-correction Navier-Stokes characteristic boundary condition

In an effort to assess the efficacy of different non-reflecting boundary conditions (NRBCs) in high-order solvers, several NRBCs have been implemented in the context of the discontinuous Galerkin (DG) discretization. The methods considered are based on buffer zone techniques and boundary-imposed conditions. The former mainly utilizes the sponge layer (SL), the perfectly matched layer (PML) and the supersonic layer (SSL), while the latter uses a Riemann extrapolation (RE) technique and a novel polynomial-correction Navier-Stokes characteristic boundary condition (PC-NSCBC). The developed PC-NSCBC method reconstructs an explicit boundary state, instead of modifying the equations on the boundary or specifying ad hoc compatibility conditions on corners and edges. This property pairs well with a Riemann solver, as is typical in a DG method. Moreover, the boundary state can be assembled either from a one-dimensional perspective (NSCBC1D) or using partial knowledge of multi-dimensional effects (NSCBC3D).Four different benchmark problems are considered: a 1D linear acoustic pulse in a quiescent flow, a 2D non-linear pressure pulse in a quiescent flow, an isentropic vortex and a shear-flow vortex shedding instability. Results imply that mainly the PML performs better than most other approaches. This is especially true for acoustically-dominated flows. Alternatively, for flow conditions predominantly less acoustic in nature and strongly non-linear, instabilities in the PML may arise. The SL and SSL both suggest that a larger layer is required to deliver comparable results to the PML. The proposed (PC-)NSCBC methods demonstrate reasonable success with no instabilities reported, which is impressive given the comparatively less computational effort required. Partial inclusion of the transverse terms in the NSCBC3D noticeably enhances the output of the NSCBC1D, albeit further investigation is required to determine an optimal, universal expression for its transverse tuning coefficient.

Fundamental frequency and second harmonic mode-locked operations in an erbium-doped fiber laser based on Cr2Sn2Te6 saturable absorbers

With the rapid development of ultrafast photonics, the need for optical modulators is expanding. In particular, the optical modulator with a high damage threshold and the ability to generate multiple soliton states. This has prompted an ongoing search for optical modulators based on two-dimensional (2D) materials. Therefore, in this work, a novel 2D material Cr2Sn2Te6 (CSnT) with modulation depth of 6.17% and saturation intensity of 15.97 MW/cm2 is prepared as saturable absorber (SA). The nonlinear optical absorption characteristics and pulse modulation applications of CSnT are showed in the Erbium-doped fiber laser (EDFL). The fundamental frequency mode-locked operation and the second harmonic mode-locked operation are realized simultaneously in the ring cavity. Moreover, CSnT SA has a high damage threshold and high stability, the damage threshold reaches 467 mW and the signal-to-noise ratio (SNR) is higher than 70 dB. The experimental findings demonstrate that the CSnT-based saturable absorber possesses remarkable nonlinear optical properties, indicating its considerable potential in the realm of ultrafast photonics.