Ultrashort pulse breaking in optical fiber with third-order dispersion and quintic nonlinearity

The optical wave breaking （OWB） characteristics in terms of the pulse shape, spectrum, and frequency chirp, in the normal dispersion regime of an optical fiber with both the third-order dispersion （TOD） and quintic nonlinearity （QN） are numerically calculated. The results show that the TOD causes the asymmetry of the temporal- and spectral-domain, and the chirp characteristics. The OWB generally appears near the pulse center and at the trailing edge of the pulse, instead of at the two edges of the pulse symmetrically in the case of no TOD. With the increase of distance, the relation of OWB to the TOD near the pulse center increases quickly, leading to the generation of ultra-short pulse trains, while the OWB resulting from the case of no TOD at the trailing edge of the pulse disappears gradually. In addition, the positive （negative） QN enhances （weakens） the chirp amount and the fine structures, thereby inducing the OWB phenomena to appear earlier （later）. Thus, the TOD and the positive （negative） QN are beneficial （detrimental） to the OWB and the generation of ultra-short pulse trains.

Suppression and Compensation of the Third-Order Dispersion Effect on Polarization Modes in Birefringent Fibres

The influence of the third-order dispersion (TOD) on the polarization mode dispersion (PMD) is investigated. It is found that the TOD effect destroys orthogonal polarization modes in optical birefringent fibres. A new method is proposed to compensate for the PMD by means of cascading the fibres with the positive and negative TOD. This has proven to be practicable in long transmissions.

Effect of Third-order Dispersion of Birefringent Fiber on Pulse Transmission

The effect of third order dispersion on pulse transmission is discussed. The coupled nonlinear Schrdinger equations characterizing the birefringent single mode fibers is solved numerically with combined consideration on chromatic dispersion, including second and third order dispersions, polarization mode dispersion (PMD) and nonlinearity. Various simulation results are presented.

Dissipative Kerr solitons in optical microresonators with Raman effect and third-order dispersion

Using the mean-field normalized Lugiato-Lefever equation,we theoretically investigate the dynamics of cavity soliton and comb generation in the presence of Raman effect and the third-order dispersion.Both of them can induce the temporal drift and frequency shift.Based on the moment analysis method,we analytically obtain the temporal and frequency shift,and the results agree with the direct numerical simulation.Finally,the compensation and enhancement of the soliton spectral between the Raman-induced self-frequency shift and soliton recoil are predicted.Our results pave the way for further understanding the soliton dynamics and spectral characteristics,and providing an effective route to manipulate frequency comb.

Bi-Soliton Propagation in Dispersion-Managed Line under the Influence of Third-Order Dispersion

We show that bi-soliton which is a periodically stationary pulse consisting of two peaks can propagate in a dispersion-managed line under the influence of third-order dispersion. Numerical averaging method is used to extract bi-soliton from a couple of Gaussian pulses and its stability is studied by a free propagation for a long distance.

Performance evaluation for 160-Gb/s optical phase conjugation systems considering dispersion mapping and third-order dispersion

The impact of third-order dispersion （TOD） is investigated by numerical simulations in 160-Gb/s singlechannel systems incorporated with dispersion mapping and optical phase conjugation （OPC）. System performances using retrun-to-zero （RZ） or carrier-suppressed RZ （CSRZ） modulation format are evaluated on the optimized dispersion map. The results indicate that even though TOD has been fully compensated, the intra-channel nonlinearity induced by local TOD would degrade the system performance in nonlinear regime. The scheme with an optimized dispersion map provides a much higher performance and offers a larger tolerance on a variation of pre-compensation. CSRZ modulation format is more robust due to its tradeoff between tolerances on intra-channel nonlinearity and dispersion.

Effect of third-order dispersion on breathing localized solutions in the quintic complex Ginzburg-Landau equation

The effect of third-order dispersion on breathing localized solutions in the quintic complex GinzburgLandau (CGL) equation is investigated. It is found that even small third-order dispersion can cause dramatic changes in the behavior of the solutions, such as breathing solution asymmetrically and travelling slowly towards the right for the positive third-order dispersion. A little larger third-order dispersion causes the solution breathing only on one side and the other side keeping the soliton profile. For the negative dispersion, the same results can be obtained except for the change of the traveling direction. Otherwise, we analyzed the interaction of two breathing solitons and found a simple method to inhibit this interaction.

High-Q microwave photonic filter with self-phase modulation spectrum broadening and third-order dispersion compensation

We propose and experimentally demonstrate a scheme of high-Q microwave photonic filter （MPF） using the techniques of self-phase modulation （SPM） spectrum broadening and third-order dispersion （TOD） compensation. The optical pulses from a mode-locking laser are spectrally broadened by the SPM in the highly nonlinear fiber. A wideband optical frequency comb with 365 spectral lines within 10-dB power variation from the highest spectral power is obtained. By applying a cubic phase modulation via a waveshaper, the effect of TOD which broadens the MPF passband is eliminated. The final implemented MPF has a Q-value as high as 296 and a tuning range of 700 MHz.

Independent and continuous third-order dispersion compensation using a pair of prisms

The dispersion of a pair of prisms is analyzed by means of a ray-tracing method operating at other than tip-to-tip propagation of the prisms, taking into consideration the limited spectral bandwidth. The variations of the group delay dispersion and the third-order dispersion for a pair of prisms are calculated with respect to the incident position and the separation between the prisms. The pair of prisms can provide a wide range of independent and continuous third-order dispersion compensation. The effect of residual third-order dispersion on the pulse contrast ratio and pulse duration is also calculated. The residual third-order dispersion not only worsens the pulse contrast ratio, but also increases the pulse duration to the hundreds of femtosecond range for a tens of femtosecond pulse, even when the residual thirdorder dispersion is small. These phenomena are helpful in compensating for the residual high-order dispersion and in understanding its effect on pulse contrast ratios and pulse durations in ultrashort laser systems.

Tunable dispersion relations manipulated by strain in skyrmion-based magnonic crystals

We theoretically investigate the propagation characteristics of spin waves in skyrmion-based magnonic crystals. It is found that the dispersion relation can be manipulated by strains through magneto-elastic coupling. Especially, the allowed bands and forbidden bands in dispersion relations shift to higher frequency with strain changing from compressive to tensile,while shifting to lower frequency with strain changing from tensile to compressive. We also confirm that the spin wave with specific frequency can pass the magnonic crystal or be blocked by tuning the strains. The result provides an advanced platform for studying the tunable skyrmion-based spin wave devices.

Pipeline thickness estimation using the dispersion of higher-order SH guided waves

Thickness measurement plays an important role in the monitoring of pipeline corrosion damage. However, the requirement for prior knowledge of the shear wave velocity in the pipeline material for popular ultrasonic thickness measurement limits its widespread application. This paper proposes a method that utilizes cylindrical shear horizontal(SH) guided waves to estimate pipeline thickness without prior knowledge of shear wave velocity. The inversion formulas are derived from the dispersion of higher-order modes with the high-frequency approximation. The waveform of the example problems is simulated using the real-axis integral method. The data points on the dispersion curves are processed in the frequency domain using the wave-number method. These extracted data are then substituted into the derived formulas. The results verify that employing higher-order SH guided waves for the evaluation of thickness and shear wave velocity yields less than1% error. This method can be applied to both metallic and non-metallic pipelines, thus opening new possibilities for health monitoring of pipeline structures.

Broadband third-order optical nonlinearities of layered franckeite towards mid-infrared regime

The study of nonlinear optical responses in the mid-infrared(mid-IR)regime is essential for advancing ultrafast mid-IR laser applications.However,nonlinear optical effects under mid-IR excitation are rarely reported due to the lack of suitable nonlinear optical materials.The natural van derWaals heterostructure franckeite,known for its narrow bandgap and stability in air,shows great potential for developing mid-IR nonlinear optical devices.We have experimentally demonstrated that layered franckeite exhibits a broadband wavelength-dependent nonlinear optical response in the mid-IR spectral region.Franckeite nanosheets were prepared using a liquid-phase exfoliation method,and their nonlinear optical response was characterized in the spectral range of 3000 nm to 5000 nm.The franckeite nanosheets exhibit broadband wavelengthdependent third-order nonlinearities,with nonlinear absorption and refraction coefficients estimated to be about 10^(-7)cm/W and 10^(-11)cm^(2)/W,respectively.Additionally,a passively Q-switched fluoride fiber laser operating around a wavelength of 2800 nm was achieved,delivering nanosecond pulses with a signal-to-noise ratio of 43.6 dB,based on the nonlinear response of franckeite.These findings indicate that layered franckeite possesses broadband nonlinear optical characteristics in the mid-IR region,potentially enabling new possibilities for mid-IR photonic devices.

Discontinuities of Banana Integrals in Dispersion Relation Representation

We derive the discontinuities of banana integrals using the dispersion relation iteratively,and find a series of identities between the parameterized discontinuities of banana integrals(p-DOBIs).Similar to elliptic integrals,these identities enable the reduction of various p-DOBIs to be a linear combination of some fundamental ones.We present a practical application of p-DOBIs for deriving the Picard–Fuchs operator.Then we establish the expression of generalized dispersion relation,which enables us to obtain the dispersion relation representation of arbitrary banana integrals.Moreover,we propose a hypothesis for generalized dispersion relation and p-DOBIs,which provides a simple way to calculate the discontinuities and transform dispersion relation representation to p-DOBIs.

A simple atomization approach enables monolayer dispersion of nano graphenes in cementitious composites with excellent strength gains

Carbon nano additives(CNAs)are critical to achieving the unique properties of functionalized composites,however,controlling the dispersion of CNAs in material matrix is always a challenging task.In this study,a simple atomization approach was successfully developed to promote the dispersion efficiency of graphene nanoplatelets(GNPs)in cement composites.This atomization approach can be integrated with the direct,indirect and combined ultrasonic stirrings in a homemade automatic stirring-atomization device.Mechanical and microstructure tests were performed on hardened cement pastes blended with GNPs in different stirring and mixing approaches.Results show that the direct ultrasonic stirrings enabled more homogeneous dispersions of GNP particles with a smaller size for a longer duration.The atomized droplets with the mean size of~100μm largely mitigated GNPs’agglomerations.Monolayer GNPs were observed in the cement matrix with the strength gain by up to 54%,and the total porosity decrease by 21%in 0.3 wt%GNPs dosage.The greatly enhanced dispersion efficiency of GNPs in cement also raised the cement hydration.This work provides an effective and manpower saving technique toward dispersing CNAs in engineering materials with great industrialization prospects.

Dispersion Relations in Diffraction in Time

In agreement with Titchmarsh’s theorem, we prove that dispersion relations are just the Fourier-transform of the identity, g(x′)=±Sgn(x′)g(x′), which defines the property of being a truncated functions at the origin. On the other hand, we prove that the wave-function of a generalized diffraction in time problem is just the Fourier-transform of a truncated function. Consequently, the existence of dispersion relations for the diffraction in time wave-function follows. We derive these explicit dispersion relations.

Real-time data processing method for CO_(2) dispersion interferometer on EAST

A real-time data processing system is designed for the carbon dioxide dispersion interferometer(CO_(2)-DI)on EAST.The system utilizes the parallel and pipelining capabilities of an fieldprogrammable gate array(FPGA)to digitize and process the intensity of signals from the detector.Finally,the real-time electron density signals are exported through a digital-to-analog converter(DAC)module in the form of analog signals.The system has been successfully applied in the CO_(2)-DI system to provide low-latency electron density input to the plasma control system on EAST.Experimental results of the latest campaign with long-pulse discharges on EAST(2022–2023)demonstrate that the system can respond effectively in the case of rapid density changes,proving its reliability and accuracy for future electron density calculation.

CFD-PBM coupled modeling of the liquid-liquid dispersion characteristics and structure optimization for Kenics static mixer

Kenics static mixers(KSM)are extensively used in industrial mixing-reaction processes by virtue of high mixing efficiency,low power homogenization and easy continuous production.Resolving liquid droplet size and its distribution and thus revealing the dispersion characteristics are of great significance for structural optimization and process intensification in the KSM.In this work,a computational fluid dynamics-population balance model(CFD-PBM)coupled method is employed to systematically investigate the effects of operating conditions and structural parameters of KSM on droplet size and its distribution,to further reveal the liquid-liquid dispersion characteristics.Results indicate that higher Reynolds numbers or higher dispersed phase volume fractions increase energy dissipation,reducing Sauter mean diameter(SMD)of dispersed phase droplets and with a shift in droplet size distribution(DSD)towards smaller size.Smaller aspect ratios,greater blade twist and assembly angles amplify shear rate,leading to smaller droplet size and a narrower DSD in the smaller range.The degree of impact exerted by the aspect ratio is notably greater.Notably,mixing elements with different spin enhance shear and stretching efficiency.Compared to the same spin,SMD becomes 3.7-5.8 times smaller in the smaller size range with a significantly narrower distribution.Taking into account the pressure drop and efficiency in a comprehensive manner,optimized structural parameters for the mixing element encompass an aspect ratio of 1-1.5,a blade twist angle of 180°,an assembly angle of 90°,and interlaced assembly of adjacent elements with different spin.This work provides vital theoretical underpinning and future reference for enhancing KSM performance.

Effect of trigger system on experimental dispersion characteristics of active surface wave testing

A trigger system is typically employed in active seismic testing to trigger and synchronize multichannel surface wave data acquisition.The effect of the trigger system on the dispersion image of surface waves is empirically known to be negligible,however,theoretical explanation regarding the effect of the trigger system is insufficient.This study systematically examines the theory for surface wave dispersion analysis and proves that the effect of the trigger system on a dispersion image is negligible via a solid theoretical explanation.Subsequently,based on the new theoretical explanation,an alternative method that uses only the relative phase difference between sensors to extract dispersion characteristics with better conceptual clarity is proposed.Two active surface wave testing cases are considered to validate the theory and method.The results indicate that(1)an accurate trigger system is not necessary for surface wave data acquisition,and(2)it is unnecessary to assume that the impact point is the generation point of the surface waves for the experimental dispersion analysis.

A seismic elastic moduli module for the measurements of low-frequency wave dispersion and attenuation of fluid-saturated rocks under different pressures

Knowledge about the seismic elastic modulus dispersion,and associated attenuation,in fluid-saturated rocks is essential for better interpretation of seismic observations taken as part of hydrocarbon identification and time-lapse seismic surveillance of both conventional and unconventional reservoir and overburden performances.A Seismic Elastic Moduli Module has been developed,based on the forced-oscillations method,to experimentally investigate the frequency dependence of Young's modulus and Poisson's ratio,as well as the inferred attenuation,of cylindrical samples under different confining pressure conditions.Calibration with three standard samples showed that the measured elastic moduli were consistent with the published data,indicating that the new apparatus can operate reliably over a wide frequency range of f∈[1-2000,10^(6)]Hz.The Young's modulus and Poisson's ratio of the shale and the tight sandstone samples were measured under axial stress oscillations to assess the frequency-and pressure-dependent effects.Under dry condition,both samples appear to be nearly frequency independent,with weak pressure dependence for the shale and significant pressure dependence for the sandstone.In particular,it was found that the tight sandstone with complex pore microstructure exhibited apparent dispersion and attenuation under brine or glycerin saturation conditions,the levels of which were strongly influenced by the increased effective pressure.In addition,the measured Young's moduli results were compared with the theoretical predictions from a scaled poroelastic model with a reasonably good agreement,revealing that the combined fluid flow mechanisms at both mesoscopic and microscopic scales possibly responsible for the measured dispersion.

Overview of computation strategies on the dispersion analysis for explicit finite difference solution of acoustic wave equation

Finite-difference(FD)method is the most extensively employed numerical modeling technique.Nevertheless,when using the FD method to simulate the seismic wave propagation,the large spatial or temporal sampling interval can lead to dispersion errors and numerical instability.In the FD scheme,the key factor in determining both dispersion errors and stability is the selection of the FD weights.Thus,How to obtain appropriate FD weights to guarantee a stable numerical modeling process with minimum dispersion error is critical.The FD weights computation strategies can be classified into three types based on different computational ideologies,window function strategy,optimization strategy,and Taylor expansion strategy.In this paper,we provide a comprehensive overview of these three strategies by presenting their fundamental theories.We conduct a set of comparative analyses of their strengths and weaknesses through various analysis tests and numerical modelings.According to these comparisons,we provide two potential research directions of this field:Firstly,the development of a computational strategy for FD weights that enhances stability;Secondly,obtaining FD weights that exhibit a wide bandwidth while minimizing dispersion errors.