Higher-order Nonlinear Effects Research Articles

Impact of high-order effects on soliton explosions in the complex cubic-quintic Ginzburg-Landau equation

We investigate the impact of higher-order nonlinear and dispersive effects on the onset of soliton explosions in the complex cubic-quintic Ginzburg-Landau equation. We show how the interplay of the high order effects (HOEs) results in the splitting of symmetric explosion modes and to the formation of right- or left-side periodic explosions. In addition, we demonstrate that HOEs induce a series of pulsating instabilities, leading to a significant reduction of the stability region of the single soliton solution.

Role of higher order nonlinearities in the instability spectra of two core oppositely directed saturated coupler

We theoretically investigate the impact of modified form of saturable nonlinearity in the modulational instability (MI) spectra of an opposite directed two core coupler with a negative index material channel. Particularly, our emphasize is on the interplay between the nonlinear saturation and the higher order nonlinear effects in fibers such as self-steepening and intrapulse Raman scattering. Using the modified nonlinear Schrödinger equation we appropriately model the light propagation in the two core opposite coupler with saturation of nonlinearity. A standard approach like the linear stability analysis was used to derive the dispersion relation pertaining to the MI. For a comprehensive picture, we consider both the normal and the anomalous dispersion regimes and special attention is paid to understand the influence of system parameters such as the power, coupling coefficient, saturation parameter, and nonlinear coefficient on the MI. Effect of different combinations of self-steepening as well as the contribution of intrapulse Raman scattering are discussed and its role on the instability bands are highlighted. Thus we report new ways to generate and manipulate the MI in two core oppositely directed couplers with the effect of saturation of nonlinearity.

Lax pair, breather-to-soliton conversions, localized and periodic waves for a coupled higher-order nonlinear Schrödinger system in a birefringent optical fiber

A coupled higher-order nonlinear Schrodinger system, which describes the ultrashort pulses in a birefringent optical fiber, is analytically investigated. For the complex envelopes of the electric field in the fiber, we construct a Lax pair which is different from that in the existing literature, and derive out the corresponding first- and second-order breather solutions. We present the first- and second-order breather-to-soliton conversion conditions, related to the strength of the higher-order linear and nonlinear effects. We find that the strength affects the peak numbers of solitons, and see the multi-peak soliton, W-shaped soliton, M-shaped soliton, anti-dark soliton and two kinds of periodic waves. From the second-order breather solutions under the first-order breather-to-soliton conversion condition, interactions between the breather and a W-shaped soliton, an M-shaped soliton or periodic waves are given. From the second-order breather solutions under the second-order breather-to-soliton conversion conditions, we present the interactions between the two M-shaped solitons, the two anti-dark solitons, a W-shaped soliton and an M-shaped soliton, or a W-shaped soliton and two kinds of the periodic waves. Those results might provide certain assistance for the studies on the birefringent optical fibers.

Frequency Multiplication With Adjustable Waveform Shaping Demonstrated at 200 GHz

A frequency multiplier for the direct generation of the fourth, sixth, or eighth harmonic of an input signal in a single stage is presented. By analyzing the effect of clipping both half-waves in the output signal asymmetrically, beneficial clipping thresholds are identified. Based on the ideal signal analysis, circuit simulations are carried out to investigate and implement the proposed approach using a heterojunction bipolar transistor (HBT) push–push cascode amplifier, which enables the independent adjustment of the clipping thresholds. Finally, the circuit is combined with an input balun and an output amplifier and fabricated in a 130-nm SiGe BiCMOS process for verification. Measurement results of the prototype are compared with simulations based on available VBIC and HICUM models for the HBTs, providing insight on their capabilities to predict the high-order nonlinear effects essential for the operation of the presented multiplier. The circuit performs in general agreement with the HICUM model simulations and represents a versatile times-four, times-six, and times-eight frequency multiplier with a 37-GHz output-referred bandwidth from 173 to 210 GHz and an output power of up to −6 dBm. To the the best of the authors’ knowledge, the conversion gain of 10 dB is the highest in class reported up to date, even when compared to III/V-based circuits. A maximum harmonic suppression of 40 dB and a total dc power consumption of 63 mW are measured.

Study on the Effect of Climate Change on Ship Responses Based on Nonlinear Simulations

Hull girder ultimate strength governs sagging and hogging failures, which is one of the most critical failure modes for a ship hull. The structural reliability analysis methodology has been used to develop common structural rules for tankers and bulk carriers. A linear model for bending moment in extreme weather with a nonlinear correction factor has been adopted in the analysis. It is difficult to conclude on the model uncertainty associated with nonlinear effects of bending moment as, until now, there are few studies addressing this topic. In this paper, the nonlinear effect on ship responses is analyzed, and the potential effect of climate change on ship responses is investigated with the improved three-dimensional (3D) Rankine Panel method using nonlinear wave input. The nonlinear wave input is generated by the higher-order spectral method (HOSM) wave model incorporating higher-order nonlinear effects, including nonlinear free-wave modulation as well as higher-order bound harmonics. The past and projected future wave climates of selected locations in the North Atlantic and North Norwegian Sea are considered.

Analyzing the effect of higher order nonlinearity on dispersion relation and optical multistability generation in oppositely directed coupler

We report the influence of higher order nonlinearity on dispersion relation and multistability in oppositely directed coupler with negative index material channel. The study shows that the high intensity electric field shifts the photonic bandgap down in energy. When the positive index material channel of the coupler is influenced by quintic nonlinearity the group velocity of upper branch of dispersion curve (δ–q curve) falls to zero in positive q region and the loop in the lower branch shifts to positive q region. But the minima in upper branch and loop in the lower branch are observed at negative q region when the negative index material channel is influenced by χ(5) nonlinearity. As the curvature of the dispersion relation determines the group velocity dispersion the study report the possibility for dispersion engineering in oppositely directed coupler. Also we observed that the quintic nonlinearity enhances formation of multi stable states.

Empirical sensitivity of two-dimensional nonlinear wake–cylinder oscillators in cross-flow/in-line vortex-induced vibrations

Phenomenological wake–cylinder oscillators have been extensively implemented for vortex-induced vibration (VIV) predictions. Although such models capture fundamental VIV phenomena, the maximum response estimations and comparisons with different experimental data reveal some quantitative discrepancies due to the model empiricism embedding some uncertainties through system variables. This vital issue has not been well addressed in the literature of VIV modelling. This paper presents a new comprehensive investigation into the sensitivity to empirical input variables of nonlinear wake–cylinder oscillators simulating the two-dimensionally coupled cross-flow/in-line VIV and amplified mean displacements of a flexibly mounted circular cylinder in uniform flows. The fluid–structure coupling terms are advanced by accounting for the higher-order nonlinear effects of fluctuating lift–drag forces and steady-drag dynamic magnifications, depending on the relative flow-cylinder velocities. A random sampling and variance-based sensitivity studies are carried out using Monte Carlo simulations which are computationally efficient based on the reduced-order model. This enables a large series of parametric examinations. Individual contribution, relative importance, coupling and interdependence of multiple input variables affecting output uncertainties are qualitatively and quantitatively evaluated. The Reynolds number dependence is also captured by correlating the wake and hydrodynamic coefficients with experimental data. Parametric studies highlight greater variations in the predicted amplitudes and mean displacements of the cylinder two-degree-of-freedom VIV with a lower mass ratio. Numerical findings allow for the identification of a few most influential variables to be treated as the empirically tuned coefficients. The improved understanding of model versatility and sensitivity enhances the calibration confidence and the response predictability with a reduced computational effort.

Solitary vortex dynamics of two-dimensional harmonically trapped Bose-Einstein condensates with higher-order nonlinear interactions

We studied the evolutionary patterns of two-dimensional Bose-Einstein condensates incorporating higher-order nonlinear interactions in harmonic potential. Using the Gross-Pitaevskii equation model with higher-order nonlinear corrections, we derived the analytical solitary vortex solutions via the variational method. The impact of the higher-order nonlinear interaction on the vortex dynamics is quantitatively analyzed, showing its key nonlinear feature contribution in the asymmetric vortex evolution with more precise evolutionary pattern generated. We found that, for the circular symmetric solution, if the nonlinear strength is not high, the higher-order nonlinear corrections essentially have only a tiny perturbative effect on the system’s quasi-static oscillation state, whereas for asymmetric evolution of the solitary vortex, incorporating higher-order corrections will generate an evolution pattern that better matches the results of numerical simulation. The theoretical results derived here can be used to guide relevant experimental studies of higher-order nonlinear effects in ultracold atomic systems.

Optimal control for soliton breathers of the Lakshmanan–Porsezian–Daniel, Hirota, and cmKdV models

We apply the method for systematic construction of the two-soliton (and in principal, N-soliton) breather solutions on the zero background to the Lakshmanan–Porsezian–Daniel model with varying dispersion and nonlinearity, gain or loss, and derive the specific conditions for the appearance of the so-called standing and moving soliton breathers. We show that both all parameters of constituent solitons forming the breather and the varying dispersion and nonlinearities should be appropriately chosen in accordance with the exact integrability conditions of the Lakshmanan–Porsezian–Daniel equation with vanishing boundary conditions. We compare the details of periodic breather dynamics for the complex modified KdV, Hirota, and Lakshmanan–Porsezian–Daniel models with the classical Satsuma–Yajima breather behavior. We derive simple formulas for the soliton breather periods and use them to understand the possibilities to control breather dynamics, and, in particular, to realize the so-called regimes of “artificial breathing”, when periods of soliton breathing in space and time are controlled by choosing appropriate complex spectral parameters defining the amplitudes and velocities of constituent solitons. Of fundamental importance is the remarkable theoretical fact that the higher-order nonlinear and dispersion effects included into (or removed from) the new higher-order equations of the AKNS hierarchy, as a rule, do not destroy soliton breathers discovered here and do not transform them into dispersive waves. On the contrary, we demonstrate that novel and novel soliton breathers can appear in the framework of the next, more and more higher orders of the AKNS and NLSE hierarchies.

Multidimensional Vibrational Coherence Spectroscopy.

Multidimensional vibrational coherence spectroscopy has been part of laser spectroscopy since the 1990s and its role in several areas of science has continuously been increasing. In this contribution, after introducing the principals of vibrational coherence spectroscopy (VCS), we review the three most widespread experimental methods for multidimensional VCS (multi-VCS), namely femtosecond stimulated Raman spectroscopy, pump-impulsive vibrational spectroscopy, and pump-degenerate four wave-mixing. Focus is given to the generation and typical analysis of the respective signals in the time and spectral domains. Critical aspects of all multidimensional techniques are the challenges in the data interpretation due to the existence of several possible contributions to the observed signals or to optical interferences and how to overcome the corresponding difficulties by exploiting experimental parameters including higher-order nonlinear effects. We overview how multidimensional vibrational coherence spectroscopy can assist a chemist in understanding how molecular structural changes and eventually photochemical reactions take place. In order to illustrate the application of the techniques described in this chapter, two molecular systems are discussed in more detail in regard to the vibrational dynamics in the electronic excited states: (1) carotenoids as a non-reactive system and (2) stilbene derivatives as a reactive system.

Broadband and highly coherent supercontinuum generation in a suspended As2S3, ridge waveguide

Abstract In this paper, a chalcogenide-based ridge waveguide with a suspended structure on the substrate of Si 3 N 4 , is designed, which is demonstrated to have low and flat dispersion profiles. Simulation results show that when the higher-order nonlinear effects and linear loss are considered, a broadband supercontinuum with high coherence ranging from 1.0 to 5. 6 μ m is obtained after a 3.1-mm long propagation when pumping wavelength 2. 65 μ m and peak power 450 W. Our proposed scheme provides a promising solution to realize broadband and highly coherent SC in mid-infrared region for nonlinear photonics and spectroscopy.

Vector multi-rogue waves for the three-coupled fourth-order nonlinear Schrödinger equations in an alpha helical protein

In this paper, we investigate the vector multi-rogue waves for the three-coupled fourth-order nonlinear Schrödinger equations, which describe the dynamics of an alpha helical protein with the nearest and next-nearest neighbor interactions and interspine coupling. Via the Darboux-dressing transformation, the vector multi-rogue-wave solutions are derived. Based on such solutions, we present the single vector rogue wave, vector rogue wave pair and triple vector rogue wave graphically. We show that a four-petaled rogue wave with two humps and two valleys appears in two components, while the other component has an eye-shaped rogue wave. Existing time of the rogue wave decreases with the strength of higher-order linear and nonlinear effects in the alpha helical protein. We also obtain the separated and interacting vector rogue wave pairs, as well as the triple vector rogue waves. Moreover, we verify the baseband modulation instability through the linear stability analysis.

Influence of spatial delay on the modulational instability in a composite system with a controllable nonlinearity.

A theoretical investigation of the modulational instability (MI) in a composite system with a nonlocal response function is presented. A composite system of silver nanoparticles in acetone is chosen, whose nonlinearity can be delicately varied by controlling the volume fraction of the constituents, thus enabling the possibility of nonlinearity management. A pump-probe counterpropagation configuration has been assumed, and the interplay between the competing nonlinearities and the nonlocalities in the MI dynamics is systematically explored. A different class of nonlocalities have been considered, and the study reveals that the nonlocality critically depends on the kind of nonlocal function. However, the general behavior is that the strength of nonlocality suppresses the MI gain, while for a rectangular function it assists the emergence of new spectral windows. We also show that the cross coupling effects are significant in enhancing MI, especially in the defocusing nonlinearity. We also emphasize the impact of the relative strength of the nonlinearities in the MI dynamics at different settings of competing nonlinearities. Thus, we emphasize the importance of the different class of nonlocal response in the MI dynamics and explore the interplay between the higher order nonlinear effects and nonlocalities in the counterpropagating configurations.

Continuous-wave multiphoton photoemission from plasmonic nanostars

Highly nonlinear optical processes require high intensities, typically achieved with ultrashort laser pulses, and hence, they were first observed with the advent of picosecond laser technology. An alternative approach for reaching the required field intensities is offered by localized optical resonances in tailored plasmonic nanostructures, enabling the enhancement of a multitude of nonlinear phenomena. However, so far, plasmon-enhanced high-order nonlinear effects have been restricted to experiments involving short-pulsed and ultrafast laser sources. Here, we demonstrate localized three-photon photoemission from chemically synthesized plasmonic gold nanostars under continuous-wave illumination at sub-MWcm−2 incident intensities. Intensity- and polarization-dependent measurements confirm the nonlinearity of the photoemission process and agree with quantum mechanical calculations of the electron yield from nanostar tips with features smaller than 5 nm, which facilitate local intensity enhancement factors exceeding 1000. Our results open up new avenues for the design of accessible nanoscale coherent electron sources, with potential applications in microscopy, spectroscopy, sensing, and signal processing.

Dark solitons in an extended nonlinear Schrödinger equation with higher-order odd and even terms

An extended nonlinear Schrödinger equation that includes terms accounting for higher-order odd (third order) and even (fourth order) terms is investigated. The model contains a variety of higher-order dispersion and nonlinear terms that are important for applications in fiber optics, the Heisenberg spin chain, plasma physics and ocean waves. We derive a nonlinear structural equation with fifth-degree nonlinear term describing the evolution of the wave amplitude in the nonlinear media by means of the coupled amplitude-phase formulation. We find the exact analytical dark soliton solution of the model in the presence of all the physical parameters. The results show that these structures characteristically exist due to a balance among higher-order nonlinear and dispersive effects of different nature. Particular cases are also discussed. We also investigate numerically the parametric stability of the solitary dark wave solution. We further calculate the power required for generating dark solitons in the nonlinear media together with their width.

Efficient third-harmonic generation in composite aluminum nitride/silicon nitride microrings

Aluminum nitride and silicon nitride have recently emerged as important nonlinear optical materials in integrated photonics for their quadratic and cubic optical nonlinearity, respectively. A composite aluminum nitride and silicon nitride waveguide structure, if realized, will simultaneously allow highly efficient second- and third-harmonic generation on the same chip platform and therefore assists 2f-3f self-referenced frequency combs. On-chip third-harmonic generation, being a higher-order nonlinear optics effect, is more demanding than second-harmonic generation due to the large frequency difference between the fundamental- and third-harmonic frequencies, which implies a large change of refractive indices and more stringent requirements on phase matching. In this work we demonstrate high-efficiency third-harmonic generation in a high-Q composite aluminum nitride/silicon nitride ring cavity. By carefully engineering the microring resonator geometry of the bilayer structure to optimize the quality factor, mode volume, and modal overlap of the optical fields, we report a maximum conversion efficiency of 180% W−2, corresponding to an absolute conversion efficiency of 0.16%. This composite photonic chip design provides a solution for efficient frequency conversion over a large wavelength span, broadband comb generation, and self-referenced frequency combs.

Impact of higher order dispersion and nonlinearities on modulational instability in a dual-core optical fiber

In this investigation, we examine theoretically modulational instability (MI) in a dual-core optical fiber with higher order dispersion as well as higher order nonlinear effects. For dual-core or multicore optical fiber the investigation of MI analysis extends with parameters like linear coupling coefficient and coupling coefficient dispersion using extended coupled nonlinear Schrodinger equation. We analyze the impact of these parameters on MI gain spectrum at anomalous and normal dispersion regime along with higher order parameters. Our results show that the combined effect of higher order dispersion like fourth order dispersion and nonlinear parameter like self-steepening effect due to cubic–quintic nonlinearity, stimulated Raman response which is inevitable for the study of ultrashort pulse propagation and generation of the soliton. The study reveals that the frequency selection of MI gain is primarily controlled by the dispersion parameters while nonlinear parameters restrict the intensity and bandwidth of the MI gain. Though most of the distinguishable effects are observed in anomalous dispersion regime due to the presence of higher order parameters decent gain is also visible in the normal dispersion regime.

Bright, dark and W-shaped solitons with extended nonlinear Schrödinger's equation for odd and even higher-order terms

We present solitary wave solutions of an extended nonlinear Schrödinger equation with higher-order odd (third-order) and even (fourth-order) terms by using an ansatz method. The including high-order dispersion terms have significant physical applications in fiber optics, the Heisenberg spin chain, and ocean waves. Exact envelope solutions comprise bright, dark and W-shaped solitary waves, illustrating the potentially rich set of solitary wave solutions of the extended model. Furthermore, we investigate the properties of these solitary waves in nonlinear and dispersive media. Moreover, specific constraints on the system parameters for the existence of these structures are discussed exactly. The results show that the higher-order dispersion and nonlinear effects play a crucial role for the formation and properties of propagating waves.

Multi-dark soliton solutions for the higher-order nonlinear Schrödinger equation in optical fibers

In optical fibers with the higher-order dispersive and nonlinear effects, the propagation of the ultrashort pulse can be governed by the higher-order dispersive nonlinear Schrodinger equation. In this paper, the binary Darboux transformation is applied to this higher-order model, and the n-times iterative transformation is expressed in terms of the determinants. By the limit technique, the multi-dark soliton solutions are derived from the nonzero background. Based on obtained solution, the elastic collisions between two and among three-dark solitons with different velocities are presented. The bound-state dark solitons can be also formed when two-dark solitons with the same velocity propagate in parallel.

Conversions and interactions of the nonlinear waves in a generalized higher-order nonlinear Schrödinger equation

In this paper, we investigate a generalized higher-order nonlinear Schrödinger (NLS) equation with two free parameters, including the third-order and fourth-order dispersion with matching higher-order nonlinear effects. The results show that the breather solution can be converted into some types of localized and periodic waves under specified parameter conditions. Coupled with rich graphical examples, the coexistence and interaction of different nonlinear structures are displayed. Further, we demonstrate the explicit relation on the parallel propagation of the second-order breather solution.