Third-order Dispersion Research Articles

Distance controlled resonant radiation from modulated Airy pulses

We investigate the dynamic evolution of resonant radiation (RR) emitted from modulated Airy pulses in an optical fiber with emphasis on the third-order dispersion. We show that the process of RRs emission strongly depends on the parameters of the predesigned spectral phase imposed on the Airy pulses, which is attributed to its linear focusing behaviors. A localized pulse formed at the distance-controlled focusing can effectively generate a large amount of RR after a prescribed propagation distance. At variance with the case of fundamental soliton, the minimum value of third-order dispersion required for the onset of RRs emission becomes much smaller for the modulated Airy pulse. The conversion efficiency of RRs increases with an increasing linear focusing point, but decreases with an increasing truncated coefficient. There is an optimal value of the truncated coefficient for the RRs having highest peak intensity and largest frequency shift. The impact of Raman effects on the RRs is also revealed. Our results not only provide a simply route to actively manipulate the efficient emission of RRs in conventional optical fiber, also could have significant implications of pulse shaping technology in novel highly efficient light sources based on the RRs emission for a variety of application.

The distortion study of rogue waves of the generalized nonlinear Schrödinger equation under the third-order dispersion perturbation

The distortion study of rogue waves of the generalized nonlinear Schrödinger equation under the third-order dispersion perturbation

Delayed feedback control on wave dynamics in a nonlinear optical cavity with third-order chromatic dispersion

By taking into account third-order dispersion effects in the presence of feedback, we investigate the stability and nonlinear dynamic movements of waves created in microcavities and fiber cavities from numerical simulations of the extended Lugiato–Lefever equation. The current analysis emphasizes that third-order scattering, feedback strength, and feedback local and global components allow for the numerical observation of dissipative bound states of solitons and chaos with extended and antisymmetric interaction domains. In this regard, we demonstrate how the symmetry of the localized structural interactions is broken by the radiation that results from third-order dispersion.

Effective soliton order approach for scaling of pulse self-compression in hollow-core fibers

Optical solitons can undergo extreme temporal and spectral reshaping at high pulse intensities. These dynamics can be utilized to extract few-cycle pulses in the negative dispersion region in the case of higher-order spatial modes in hollow fibers. One can achieve self-compression up to few-cycle duration in hollow capillary fibers without any external optical post-compression schemes using this technique. These intense few-cycle pulses are an essential tool for revealing the ultrafast dynamics in the femtosecond to attosecond timescale, where the tunability and scalability of few-cycle pulses are a necessity. Utilizing the soliton dynamics, we can scale the pulses up to multi-millijoule energies as well as terawatts of peak power. Scaling relations are relations that can be used to produce propagation dynamics that are invariant and essentially identical for multiple sets of input conditions. But, for the same input soliton order, the scaling relations derived under different dispersion conditions, such as different gas pressure, result in somewhat different scaling laws. This leads to an ambiguity in the compression factor and compression length for any particular soliton order N. It is thus necessary to find an accurate soliton order which can scale the self-compression dynamics over different dispersion conditions. We numerically simulate soliton self-compression in an argon gas-filled HCF across a wide range of dispersion conditions and present a set of efficient scaling laws for soliton dynamics. We introduce an effective soliton order Neff for explaining the behavior of the dynamics in systems with high third-order dispersion (TOD) such as the HCF. The proficiency of the new scaling laws over the earlier scaling laws in literature is elucidated in this work. Thus, an inclusive set of scaling laws for generating high-energy few-cycle pulses are defined which are critical for generating single and trains of attosecond pulses, as well as electron and ion acceleration strategies in intense laser pulses.

Soliton solutions of fractional extended nonlinear Schrödinger equation arising in plasma physics and nonlinear optical fiber

In this research, we study traveling wave solutions to the fractional extended nonlinear SchrÖdinger equation (NLSE), and the effects of the third-order dispersion parameter. This equation is used to simulate the propagation of femtosecond, plasma physic and in nonlinear optical fiber. To accomplish this goal, we use the extended simple equation approach and the improved F-expansion method to secure a variety of distinct solutions in the form of dark, singular, periodic, rational, and exponential waves. Also, the stability of the outcomes is effectively examined. Several graphs have been sketched under appropriate parametric values to reinforce some reported findings. Computational work along with a graphical demonstration confirms the exactness of the proposed methods. The issue has not previously been investigated by taking into account the impact of the third order dispersion parameter. The main objective of this study is to obtain the different kinds of traveling wave solutions of fractional extended NLSE which are absent in the literature which justify the novelty of this study. We believe that these novel solutions hold a prominent place in the fields of nonlinear sciences and optical engineering because these solutions will enables a through understanding of the development and dynamic nature of such models. The obtained results indicate the reliability, efficiency, and capability of the implemented technique to determine wide-spectral stable traveling wave solutions to nonlinear equations emerging in various branches of scientific, technological, and engineering domains.

Dispersion Engineering for Advanced Temporal Imaging Modalities

Temporal imaging provides a promising platform for ultrafast signal processing in both spectral and temporal domains. Most temporal imaging systems consist of time-lens and temporal dispersion; while optical fibers are desirable to achieve the dispersion component by virtue of their acceptable losses. On the other hand, parametric mixing-based time-lens is commonly used in temporal imaging thanks to the high modulation depth. In those situations, highly nonlinear fiber (HNLF) is used as the nonlinear medium. However, third-order dispersion (TOD) exists in commercial fibers will incur temporal aberration on the system. For instance, the inherent dispersion in HNLF decreases the conversion bandwidth of the parametric process, which restricts the performance of time-lens. In this article, we present our recent efforts in dispersion engineering for temporal imaging systems, both in the temporal dispersion and the nonlinear medium. All these efforts could inspire more innovative applications of temporal imaging modalities in the future.

Investigation on different type of pulses due to strong third order dispersion effect in mode-locked fiber lasers

Here we have numerically investigated the pulse property in a wavelength switchable mode-locked fiber laser which is achieved with a tunable filter. Owing to the strong third-order dispersion (TOD) of dispersion-compensating fiber, the net cavity group velocity dispersion of the proposed fiber laser can be manipulated and exhibits wavelength-dependent feature. Our findings indicate that different types of pulses, including conventional solitons, dispersion-managed solitons, and dissipative solitons, can be achieved, and switched in various wavelengths. The pulse characteristics including pulse width and spectrum bandwidth have been investigated, in addition to with the intracavity dynamics. The influence of the length of dispersion-compensating fiber is also investigated. These results provide an excellent foundation for understanding the formation dynamics of various pulse waveforms in the laser cavity and help the development of a multi-wavelength fiber laser with a strong TOD cavity.

Higher-order rogue-wave fission in the presence of self-steepening and Raman self-frequency shift

Using the generalized nonlinear Schr\"odinger equation, we investigate how the effect of self-steepening and Raman-induced self-frequency shift impact higher-order rogue-wave solutions. We observe that each effect breaks apart the higher-order rogue wave, reducing it to its constituent fundamental parts, in a similar manner to how a higher-order soliton undergoes fission. Applying a local inverse-scattering technique, we show that under the effect of self-frequency shift, the emergence of a rogue wave significantly influences the surrounding wave background, triggering solitons, breathers, and new rogue waves. We demonstrate that under the combined effect of third-order dispersion, self-steepening, and Raman-induced self-frequency shift, the disintegrated elements of higher-order rogue waves become fundamental solitons, creating an asymmetrical spectral profile that generates both red- and blue-shifted frequency components. We also show the intermediary processes of the fission steps prior to soliton transformation which can only be observed in the presence of weak perturbations. These observations reveal the mechanisms that create a large number of solitons in the process of modulation instability-induced supercontinuum generation from a continuous-wave background in optical fibers.

Nonlinear Landau-Zener tunneling under higher-order dispersion

We studied nonlinear Landau-Zener tunneling under the effect of higher-order dispersion, transformed the Gross-Pitaevskii (GP) equation with higher-order dispersion terms into a nonlinear two-energy level form using a two-mode approximation, and comprehensively analyzed the loop structure of the lowest-energy band and the nonlinear Landau-Zener tunneling. The results show that, when third-order dispersion coefficient is not zero, there is a spatial inversion symmetry breaking of the energy band structure and unbalanced Landau-Zener tunneling. By analyzing the fixed point's nature of the classical Hamiltonian, we obtain a law for the variation of the loop structure and adiabatic tunneling probability with the dispersion coefficient, consistent with our numerical analysis results. In addition, we analyzed the real-time evolution of solitons with transverse bias and observed the tunneling phenomenon. Consistent with our analysis, the adjustment of the dispersion term can effectively control optical tunneling, which provides an alternative idea for optical switching.

Soliton-sinc optical pulse propagation in the presence of high-order effects.

We investigate the propagation dynamics of the soliton-sinc, a kind of novel hybrid pulse, in the presence of higher-order effects with emphasis on the third-order dispersion (TOD) and Raman effects. At variance with the fundamental sech soliton, the traits of the band-limited soliton-sinc pulse can effectively manipulate the radiation process of dispersive waves (DWs) induced by the TOD. The energy enhancement and the radiated frequency tunability strongly depend on the band-limited parameter. A modified phase-matching condition is proposed for predicting the resonant frequency of the DWs emitted by soliton-sinc pulses, which is verified by the numerically calculated results. In addition, Raman-induced frequency shift (RIFS) of the soliton sinc pulse increases exponentially with a decrease of the band-limited parameter. Finally, we further discuss the simultaneous contribution of the Raman and TOD effects to the generation of the DWs emitted from the soliton-sinc pulses. The Raman effect can then either reduce or amplify the radiated DWs depending on the sign of the TOD. These results show that soliton-sinc optical pulses should be relevant for practical applications such as broadband supercontinuum spectra generation as well as nonlinear frequency conversion.

Soliton stabilization in microresonators with high order dispersion via pump phase modulation

We theoretically and numerically investigate the effects of third-order dispersion on microresonator solitons in anomalous dispersion with an extended normalized Lugiato–Lefever equation. The temporal position drift of solitons in the microresonator induced by the third-order dispersion is observed. The soliton temporal location stabilization is realized via pump phase modulation. Moreover, the final stable cavity soliton temporal position is deviated to the maxima of the pump phase modulation field profile which is the stable position of the solitons without high-order dispersion. We also study the effectiveness of the pump phase modulation in different modulation parameters. The research method sheds light on the cavity soliton stabilization, on-chip ultrashort pulse formation and optical information processing.

Rational solitons for non-local Hirota equations: Robustness and cascading instability

The Hirota equation is a higher-order non-linear Schrödinger equation by incorporating third-order dispersion. Two pairs of non-local Hirota equations are studied. One is a parity transformed conjugate pair, and the other is a conjugate PT-symmetric pair. For the first pair, rational solitons are derived by the Darboux transformation, and are shown computationally to exhibit robust propagation properties. These rational solitons can exhibit both elastic and inelastic interactions. One particular case of an elastic collision between dark and “anti-dark” solitons is demonstrated. For the second pair, a “cascading mechanism” illustrating the growth of higher-order sidebands is elucidated explicitly for these non-local, conjugate PT-symmetric equations. These mechanisms provide a theoretical confirmation of the initial amplification phase of the growth-and-decay cycles of breathers. Such repeated patterns will serve as a manifestation of the classical Fermi-Pasta-Ulam-Tsingou recurrence.

Dynamics of Dark Pulse Affected by Higher-Order Effects in Microresonators

We theoretically investigate dynamics of dark pulse and Raman-Kerr microcombs generation influenced by higher-order effects, including high-order dispersion (HOD), stimulated Raman scattering (SRS) and self-steepening (SS) effects in silicon microresonators. These three effects cause the delay of dark pulse individually, or interact with each other to alter the drift velocity and direction of pulses. HOD effect can change pulse shift direction and even cause bifurcation. The temporal drift induced by SS or SRS effects could be balanced by the simultaneous third-order dispersion (TOD) engineering. In spectral domain, stable Raman-Kerr frequency comb will be generated due to the competition between strong SRS and Kerr effects. The Raman comb components are suppressed when HOD effect coexists, while SS effect has ignorable effect on the distribution of the Raman comb. Furthermore, the SS effect will increase the total energy of the spectrum by shifting the dispersive wave (DW) generation to the longer wavelength side. Our findings could deepen the understanding of intracavity nonlinear dynamics and provide theoretical guidance to precisely control the stabilization of dark pulse and the generation of broadband mid-infrared (MIR) microcomb.

From rogue wave solution to solitons.

Using a generalized nonlinear Schrödinger equation, we investigate the transformation of a fundamental rogue wave solution to a collection of solitons. Taking the third-order dispersion, self-steepening, and Raman-induced self-frequency shift as the generalizing effects, we systematically observe how a fundamental rogue wave has an impact on its surrounding continuous wave background and reshapes its own characteristics while a group of solitons are created. Applying a local inverse scattering technique based on the periodization of an isolated structure, we show that the third-order dispersion and Raman-induced self-frequency shift generates a group of solitons in the neighborhood where the rogue wave solution emerges. Using a volume interpretation, we show that the self-steepening effect stretches the rogue wave solution by reducing its volume. Also, we find that with the Raman-induced self-frequency shift, a decelerating rogue wave generates a red-shifted Raman radiation while the rogue wave itself turns into a slow-moving soliton. We show that when third-order dispersion, self-steepening, and Raman-induced self-frequency shift act together on the rogue wave solution, each of these effects favor the rogue wave to generate a group of solitons near where it first emerges while the rogue wave itself also becomes one of these solitons.

Phase properties of several nonlinear optical waves described by rational solutions

Phase plays an essential role in both classical and quantum wave dynamics, which has motivated many scientists to study the phases of many different nonlinear waves. Among those nonlinear waves, the ones described by rational solutions have been given much attention, partly because some of them can describe rogue wave dynamics. We revisit the phase of several well-known one-dimensional rational solutions and clarify that sudden phase inversion processes indeed exist for rogue waves, in contrast to the ones reported before. Moreover, we investigate the phase properties of rogue waves and rational W-shaped solitons in the Hirota and Sasa-Satsuma model, for which some high-order physical effects are considered, i.e., the third-order dispersion delayed nonlinear response and self-steeping effects. The quite distinctive phases are uncovered for the rational W-shaped solitons with similar density profiles in the two models, by limitation analysis on the underlying topological vector potentials of other related nonlinear waves. These results indicate that the underlying topological vector potentials can be used to identify the phases of nonlinear waves, especially for localized waves with abrupt phase jumps.

Bright and dark modulated optical solitons for a (2+1)-dimensional optical Schrödinger system with third-order dispersion and nonlinearity

This work studies the dynamics of an extended nonlinear (2+1)-dimensional evolution Schrödinger equation having third-order nonlinearity and dispersion. We employ distinct efficient schemes to furnish analytical bright and dark soliton modulated solutions that can describe the propagation of ultra-short pulses in nonlinear dispersive mediums. We investigate the model parameters that admit appropriate constraint conditions on a variety of solutions. Further, we obtain other solitonic solutions such as exponential solutions, singular, periodic, and rational solutions. The work shows the relevant contribution of third-order dispersion and nonlinearity to the derived solutions of the examined Schrödinger system.

Dynamics of temporal Kerr cavity solitons in the presence of rapid parameter inhomogeneities: From bichromatic driving to third-order dispersion

Temporal Kerr cavity solitons are pulses of light that can persist in coherently driven, dispersive resonators with Kerr-type nonlinearity. Many studies have shown that such solitons can react to parameter inhomogeneities (e.g., variations in the complex amplitude of the driving field) by experiencing a temporal drift. The vast majority of such studies assume that the inhomogeneity varies slowly across the soliton, leading to the prediction that the soliton drift rate is linearly proportional to the gradient of the inhomogeneity at the soliton position. However, the assumption of a slowly varying inhomogeneity may not hold true in all situations, e.g., when using bichromatic driving or in the presence of third-order dispersion that gives rise to an extended dispersive wave tail. Here we report on theoretical and numerical results pertaining to the behavior of dissipative temporal Kerr cavity solitons under conditions where parameter inhomogeneities vary nonlinearly across the width of the soliton. In this case, the soliton velocity is dictated by the full overlap between its so-called adjoint neutral mode and the parameter perturbation, which we show can yield dynamics that are manifestly at odds with the common wisdom of motion dependent solely upon the gradient of the inhomogeneity. We also investigate how the presence of third-order dispersion and the associated dispersive wave tail changes the motion induced by parameter inhomogeneities. We find that the dispersive wave tail as such does not contribute to the soliton motion; instead, higher-order dispersion yields counterintuitive influences. Our results provide new insights into the behavior of temporal cavity solitons in the presence of parameter inhomogeneities and can impact systems employing pulsed or bichromatic pumping and/or resonators with non-negligible higher-order dispersion.

Active Control Technology of Petawatt Laser Signal-to-Noise Ratio Based on Third-Order Dispersion

Active Control Technology of Petawatt Laser Signal-to-Noise Ratio Based on Third-Order Dispersion

Decade-long Timing Study of the Black Widow Millisecond Pulsar J1544+4937

Results from 11 yr of radio timing for the eclipsing black widow millisecond pulsar (MSP) binary J1544+4937 is presented in this paper. We report a phase-connected timing model for this MSP, using observations with the Giant Metrewave Radio Telescope (GMRT) at multiple frequencies and with the Green Bank Telescope. This is the longest-duration timing study of any galactic-field MSP with the GMRT. While extending the timing baseline from the existing 1.5 yr to about a decade we report the first detection for a significant value of proper motion (μ T ∼ 10.14(5) mas yr−1) for this pulsar. Temporal variations of dispersion measure (ΔDM ∼ 10−3 pc cm−3) manifested by significant determination of first-, second-, and third-order dispersion measure (DM) derivatives are observed along the line of sight to the pulsar. We also noticed frequency-dependent DM variations of the order of 10−3 pc cm−3, which could arise due to spatial electron density variations in the interstellar medium. This study has revealed a secular variation of the orbital period for this MSP for the first time. We investigated possible causes and propose that variation in the gravitational quadrupole moment of the companion could be responsible for the observed temporal changes in the orbital period.

Sideband-free dispersion-managed Yb-doped mode-locked fiber laser with Gires–Tournois interferometer mirrors

High-order dispersion introduced by Gires–Tournois interferometer mirrors usually causes spectral sidebands in the near-zero dispersion region of mode-locked fiber lasers. Here, we demonstrate a sideband-free Yb-doped mode-locked fiber laser with dispersion-compensating Gires–Tournois interferometer mirrors. Both the simulation and the experiment demonstrate that the wavelength and energy of the sidebands can be tuned by changing the transmission coefficient of the output mirror, the pump power, and the ratio of the net cavity dispersion to the net third-order dispersion in the cavity. By optimizing these three parameters, the laser can generate a sideband-free, Gaussian-shaped spectrum with a 13.56-nm bandwidth at -0.0232 ps2 net cavity dispersion, which corresponds to a 153-fs pulse duration.