Phase-coherence dynamics of frequency-comb emission via high-order harmonic generation in few-cycle pulse trains

Frequency-comb emission via high-order harmonic generation(HHG)provides an alternative method for the coherent vacuum ultraviolet(VUV)and extreme ultraviolet(XUV)radiation at ultrahigh repetition rates.In particular,the temporal and spectral features of the HHG were shown to carry profound insight into frequency-comb emission dynamics.Here we present an ab initio investigation of the temporal and spectral coherence of the frequency comb emitted in HHG of He atom driven by few-cycle pulse trains.We find that the emission of frequency combs features a destructive and constructive coherences caused by the phase interference of HHG,leading to suppression and enhancement of frequency-comb emission.The results reveal intriguing and substantially different nonlinear optical response behaviors for frequency-comb emission via HHG.The dynamical origin of frequency-comb emission is clarified by analyzing the phase coherence in HHG processes in detail.Our results provide fresh insight into the experimental realization of selective enhancement of frequency comb in the VUV–XUV regimes.

Intravascular photoacoustic and optical coherence tomography imaging dual-mode system for detecting spontaneous coronary artery dissection: A feasibility study

In this work,we present an intravascular dual-mode endoscopic system capable of both intravascular photoacoustic imaging(IVPAI)and intravascular optical coherence tomography(IVOCT)for recognizing spontaneous coronary artery dissection(SCAD)phantoms.IVPAI provides high-resolution and high-penetration images of intramural hematoma(IMH)at different depths,so it is especially useful for imaging deep blood clots associated with imaging phantoms.IVOCT can readily visualize the double-lumen morphology of blood vessel walls to identify intimal tears.We also demonstrate the capability of this dual-mode endoscopic system using mimicking phantoms and biological samples of blood clots in ex vivo porcine arteries.The results of the experiments indicate that the combined IVPAI and IVOCT technique has the potential to provide a more accurate SCAD assessment method for clinical applications.

Tunable spectral continuous shift of high-order harmonic generation in atoms by a plasmon-assisted shaping pulse

We delve into the phenomenon of high-order harmonic generation within a helium atom under the influence of a plasmon-assisted shaping pulse.Our findings reveal an intriguing manipulation of the frequency peak position in the harmonic emission by adjusting the absolute phase parameter within the frequency domain of the shaping pulse.This phenomenon holds potential significance for experimental setups necessitating precisely tuned single harmonics.Notably,we observe a modulated shift in the created harmonic photon energy,spanning an impressive range of 1.2 eV.This frequency peak shift is rooted in the asymmetry exhibited by the rising and falling edges of the laser pulse,directly influencing the position of the peak frequency emission.Our study quantifies the dependence of this tuning range and the asymmetry of the laser pulse,offering valuable insights into the underlying mechanisms driving this phenomenon.Furthermore,our investigation uncovers the emergence of semi-integer order harmonics as the phase parameter is altered.We attribute this discovery to the intricate interference between harmonics generated by the primary and secondary return cores.This observation introduces an innovative approach for generating semi-integer order harmonics,thus expanding our understanding of high-order harmonic generation.Ultimately,our work contributes to the broader comprehension of complex phenomena in laser-matter interactions and provides a foundation for harnessing these effects in various applications,particularly those involving precise spectral control and the generation of unique harmonic patterns.

Aflibercept combined with triamcinolone acetonide in the treatment of diabetic macular edema:optical coherence tomography and optical coherence tomography angiography

AIM:To analyze the relationship between optical coherence tomography(OCT)and OCT angiography(OCTA)imaging in patients with diabetic macular edema(DME)who are treated with a combination of aflibercept and triamcinolone acetonide(TA).METHODS:A total of 76 eyes newly diagnosed DME were included in this study.They were randomly assigned to receive either aflibercept or a combination of aflibercept and TA.Injections once a month for a total of three injections.Central macular thickness(CMT),number of hyperreflective foci(HRF),height of subretinal fluid(SRF),and area of foveal avascular zone(FAZ)were evaluated using OCT and OCTA at baseline and after each monthly treatment.RESULTS:Both groups showed improvement in best corrected visual acuity(BCVA)and reduction in macular edema after treatment,and the difference in BCVA between the two groups was statistically significant after each treatment(P<0.05).The difference in CMT between the two groups was statistically significant after the first two injections(P<0.01),but not after the third injection(P=0.875).The number of HRF(1mo:7.41±8.25 vs 10.86±7.22,P=0.027;2mo:5.33±6.13 vs 9.12±8.61,P=0.034;3mo:3.58±3.00 vs 6.37±5.97,P=0.007)and height of SRF(1mo:82.39±39.12 vs 105.77±42.26μm,P=0.011;2mo:36.84±10.02 vs 83.59±37.78μm,P<0.01;3mo:11.57±3.29 vs 45.43±12.60μm,P<0.01)in combined group were statistically significant less than aflibercept group after each injection,while the area of FAZ showed no significant change before and after treatment in both groups.CONCLUSION:The combination therapy of aflibercept and TA shows more significant effects on DME eyes with decreased HRF and SRF.However,both aflibercept and combination therapy show no significant change in the area of FAZ.

Elliptically polarized high-order harmonic generation of Ar atom in an intense laser field

High-order harmonic generation(HHG) of Ar atom in an elliptically polarized intense laser field is experimentally investigated in this work.Interestingly,the anomalous ellipticity dependence on the laser ellipticity(ε) in the lower-order harmonics is observed,specifically in the 13rd-order,which displays a maximal harmonic intensity at ε ≈ 0.1,rather than at ε = 0 as expected.This contradicts the general trend of harmonic yield,which typically decreases with the increase of laser ellipticity.In this study,we attribute this phenomenon to the disruption of the symmetry of the wave function by the Coulomb effect,leading to the generation of a harmonic with high ellipticity.This finding provides valuable insights into the behavior of elliptically polarized harmonics and opens up a potential way for exploring new applications in ultrafast spectroscopy and light–matter interactions.

High-order Bragg forward scattering and frequency shift of low-frequency underwater acoustic field by moving rough sea surface

Acoustic scattering modulation caused by an undulating sea surface on the space-time dimension seriously affects underwater detection and target recognition.Herein,underwater acoustic scattering modulation from a moving rough sea surface is studied based on integral equation and parabolic equation.And with the principles of grating and constructive interference,the mechanism of this acoustic scattering modulation is explained.The periodicity of the interference of moving rough sea surface will lead to the interference of the scattering field at a series of discrete angles,which will form comb-like and frequency-shift characteristics on the intensity and the frequency spectrum of the acoustic scattering field,respectively,which is a high-order Bragg scattering phenomenon.Unlike the conventional Doppler effect,the frequency shifts of the Bragg scattering phenomenon are multiples of the undulating sea surface frequency and are independent of the incident sound wave frequency.Therefore,even if a low-frequency underwater acoustic field is incident,it will produce obvious frequency shifts.Moreover,under the action of ideal sinusoidal waves,swells,fully grown wind waves,unsteady wind waves,or mixed waves,different moving rough sea surfaces create different acoustic scattering processes and possess different frequency shift characteristics.For the swell wave,which tends to be a single harmonic wave,the moving rough sea surface produces more obvious high-order scattering and frequency shifts.The same phenomena are observed on the sea surface under fully grown wind waves,however,the frequency shift slightly offsets the multiple peak frequencies of the wind wave spectrum.Comparing with the swell and fully-grown wind waves,the acoustic scattering and frequency shift are not obvious for the sea surface under unsteady wind waves.

Distal-scanning common path probe for optical coherence tomography

In this paper,we present a distal-scanning common path probe for optical coherence tomography(OCT)equipped with a hollow ultrasonic motor and a simple and specially designed beam-splitter.This novel probe proves to be able to effectively circumvent polarization and dispersion mismatch caused by fiber motion and is more robust to a variety of interfering factors during the imaging process,experimentally compared to a conventional noncommon path probe.Furthermore,our design counteracts the attenuation of backscattering with depth and the fall-off of the signal,resulting in a more balanced signal range and greater imaging depth.Spectral-domain OCT imaging of phantom and biological tissue is also demonstrated with a sensitivity of∼100dB and a lateral resolution of∼3μm.This low-cost probe offers simplified system configuration and excellent robustness,and is therefore particularly suitable for clinical diagnosis as one-off medical apparatus.

Deep learning-based inpainting of saturation artifacts in optical coherence tomography images

Limited by the dynamic range of the detector,saturation artifacts usually occur in optical coherence tomography(OCT)imaging for high scattering media.The available methods are difficult to remove saturation artifacts and restore texture completely in OCT images.We proposed a deep learning-based inpainting method of saturation artifacts in this paper.The generation mechanism of saturation artifacts was analyzed,and experimental and simulated datasets were built based on the mechanism.Enhanced super-resolution generative adversarial networks were trained by the clear–saturated phantom image pairs.The perfect reconstructed results of experimental zebrafish and thyroid OCT images proved its feasibility,strong generalization,and robustness.

High-order harmonic generation of ZnO crystals in chirped and static electric fields

High harmonic generation in ZnO crystals under chirped single-color field and static electric field are investigated by solving the semiconductor Bloch equation(SBE). It is found that when the chirp pulse is introduced, the interference structure becomes obvious while the harmonic cutoff is not extended. Furthermore, the harmonic efficiency is improved when the static electric field is included. These phenomena are demonstrated by the classical recollision model in real space affected by the waveform of laser field and inversion symmetry. Specifically, the electron motion in k-space shows that the change of waveform and the destruction of the symmetry of the laser field lead to the incomplete X-structure of the crystal-momentum-resolved(k-resolved) inter-band harmonic spectrum. Furthermore, a pre-acceleration process in the solid four-step model is confirmed.

Automatic diagnosis of diabetic retinopathy using vision transformer based on wide-field optical coherence tomography angiography

Diabetic retinopathy(DR)is one of the major causes of visual impairment in adults with diabetes.Optical coherence tomography angiography(OCTA)is nowadays widely used as the golden criterion for diagnosing DR.Recently,wide-field OCTA(WF-OCTA)provided more abundant information including that of the peripheral retinal degenerative changes and it can contribute in accurately diagnosing DR.The need for an automatic DR diagnostic system based on WF-OCTA pictures attracts more and more attention due to the large diabetic population and the prevalence of retinopathy cases.In this study,automatic diagnosis of DR using vision transformer was performed using WF-OCTA images(12 mm×12 mm single-scan)centered on the fovea as the dataset.WF-OCTA images were automatically classified into four classes:No DR,mild nonproliferative diabetic retinopathy(NPDR),moderate to severe NPDR,and proliferative diabetic retinopathy(PDR).The proposed method for detecting DR on the test set achieves accuracy of 99.55%,sensitivity of 99.49%,and specificity of 99.57%.The accuracy of the method for DR staging reaches up to 99.20%,which has been proven to be higher than that attained by classical convolutional neural network models.Results show that the automatic diagnosis of DR based on vision transformer and WF-OCTA pictures is more effective for detecting and staging DR.

Observer-based robust high-order fully actuated attitude autopilot design for spinning glide-guided projectiles

This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glideguided projectile(SGGP),addressing model uncertainties and external disturbances.Based on fixed-time stable theory,a disturbance observer with integral sliding mode and adaptive techniques is proposed to mitigate total disturbance effects,irrespective of initial conditions.By introducing an error integral signal,the dynamics of the SGGP are transformed into two separate second-order fully actuated systems.Subsequently,employing the high-order fully actuated approach and a parametric approach,the nonlinear dynamics of the SGGP are recast into a constant linear closed-loop system,ensuring that the projectile's attitude asymptotically tracks the given goal with the desired eigenstructure.Under the proposed composite control framework,the ultimately uniformly bounded stability of the closed-loop system is rigorously demonstrated via the Lyapunov method.Validation of the effectiveness of the proposed attitude autopilot design is provided through extensive numerical simulations.

Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.

Repeatability,interocular correlation and agreement of optic nerve head vessel density in healthy eyes:a sweptsource optical coherence tomographic angiography study

AIM:To assess the repeatability,interocular correlation,and agreement of quantitative swept-source optical coherence tomography angiography(OCTA)optic nerve head(ONH)parameters in healthy subjects.METHODS:Thir ty-three healthy subjects were enrolled.The ONH of both eyes were imaged four times by a swept-source-OCTA using a 3 mm×3 mm scanning protocol.Images of the radial peripapillary capillary were analyzed by a customized Matlab program,and the vessel density,fractal dimension,and vessel diameter index were measured.The repeatability of the four scans was determined by the intraclass correlation coefficient(ICC).The most well-centered optic disc from the four repeated scans was then selected for the interocular correlation and agreement analysis using the Pearson correlation coefficient,ICC and Bland-Altman plots.RESULTS:All swept-source-OCTA ONH parameters exhibited certain repeatability,with ICC>0.760 and coefficient of variation(CoV)≤7.301%.The obvious interocular correlation was observed for papillary vessel density(ICC=0.857),vessel diameter index(ICC=0.857)and fractal dimension(ICC=0.906),while circumpapillary vessel density exhibited moderate interocular correlation(ICC=0.687).Bland-Altman plots revealed an agreement range of-5.26%to 6.21%for circumpapillary vessel density.CONCLUSION:OCTA ONH parameters demonstrate good repeatability in healthy subjects.The interocular correlations of papillary vessel density,fractal dimension and vessel diameter index are high,but the correlation for circumpapillary vessel density is moderate.

Detecting early changes in choroidal vascularity and thickness using optical coherence tomography in patients with corneal crosslinking for keratoconus

AIM:To investigate changes in choroidal thickness and vascularity in keratoconus patients treated with corneal crosslinking.METHODS:This study evaluated 28 eyes of 22 patients with keratoconus who underwent corneal crosslinking.The choroidal thicknesses were evaluated on enhanced depth imaging optical coherence tomography at the preoperative and postoperative 3d,1,and 3mo.Choroidal thickness in the four cardinal quadrants and the fovea were evaluated.The choroidal vascularity index was also calculated.RESULTS:There was no significant difference in central choroidal thickness between the preoperative and postoperative 3d,1mo(P>0.05).There was a significant increase in the 3mo(P=0.034)and a significant decrease in the horizontal choroidal vascularity index on the postoperative 3d(P=0.014),there was no statistically significant change in vertical axes and other visits in horizontal sections(P>0.05).CONCLUSION:This study sheds light on choroidal changes in postoperative corneal crosslinking for keratoconus.While it suggests the procedure’s relative safety for submacular choroid,more extensive research is necessary to confirm these findings and their clinical significance.

Automated evaluation of parapapillary choroidal microvasculature in crowded optic discs:a controlled,optical coherence tomography angiography study

AIM:To compare superficial and deep vascular properties of optic discs between crowded discs and controls using optical coherence tomography angiography(OCT-A).METHODS:Thirty patients with crowded discs,and 47 control subjects were enrolled in the study.One eye of each individual was included and OCT-A scans of optic discs were obtained in a 4.5×4.5 mm^(2) rectangular area.Radial peripapillary capillary(RPC)density,peripapillary retinal nerve fiber layer(pRNFL)thickness,cup volume,rim area,disc area,cup-to-disc(c/d)area ratio,and vertical c/d ratio were obtained automatically using device software.Automated parapapillary choroidal microvasculature(PPCMv)density was calculated using MATLAB software.When the vertical c/d ratio of the optic disc was absent or small cup,it was considered as a crowded disc.RESULTS:The mean signal strength index of OCT-A images was similar between the crowded discs and control eyes(P=0.740).There was no difference in pRNFL between the two groups(P=0.102).There were no differences in RPC density in whole image(P=0.826)and peripapillary region(P=0.923),but inside disc RPC density was higher in crowded optic discs(P=0.003).The PPCMv density in the inner-hemisuperior region was also lower in crowded discs(P=0.026).The pRNFL thickness was positively correlated with peripapillary RPC density(r=0.498,P<0.001).The inside disc RPC density was negatively correlated with c/d area ratio(r=-0.341,P=0.002).CONCLUSION:The higher inside disc RPC density and lower inner-hemisuperior PPCMv density are found in eyes with crowded optic discs.

Evaluation of retinal and choroidal thickness changes in overweight and obese adults without ocular symptoms by swept-source optical coherence tomography

AIM:To evaluate the relationship of overweight and obesity with retinal and choroidal thickness in adults without ocular symptoms by swept-source optical coherence tomography(SS-OCT).METHODS:According to the body mass index(BMI)results,the adults enrolled in the cross-sectional study were divided into the normal group(18.50≤BMI<25.00 kg/m^(2)),the overweight group(25.00≤BMI<30.00 kg/m^(2)),and the obesity group(BMI≥30.00 kg/m^(2)).The one-way ANOVA and the Chi-square test were used for comparisons.Pearson’s correlation analysis was used to evaluate the relationships between the measured variables.RESULTS:This research covered the left eyes of 3 groups of 434 age-and sex-matched subjects each:normal,overweight,and obesity.The mean BMI was 22.20±1.67,26.82±1.38,and 32.21±2.35 kg/m^(2) in normal,overweight and obesity groups,respectively.The choroid was significantly thinner in both the overweight and obesity groups compared to the normal group(P<0.05 for all),while the retinal thickness of the three groups did not differ significantly.Pearson’s correlation analysis showed that BMI was significantly negatively correlated with choroidal thickness,but no significant correlation was observed between BMI and retinal thickness.CONCLUSION:Choroidal thickness is decreased in people with overweight or obesity.Research on changes in choroidal thickness contributes to the understanding of the mechanisms of certain ocular disorders in overweight and obese adults.

Predictive visual field outcomes after optic chiasm decompressive surgery by retinal vessels parameters using optical coherence tomography angiography

AIM:To evaluate the predictive value of superficial retinal capillary plexus(SRCP)and radial peripapillary capillary(RPC)for visual field recovery after optic cross decompression and compare them with peripapillary nerve fiber layer(pRNFL)and ganglion cell complex(GCC).METHODS:This prospective longitudinal observational study included patients with chiasmal compression due to sellar region mass scheduled for decompressive surgery.Generalized estimating equations were used to compare retinal vessel density and retinal layer thickness preand post-operatively and with healthy controls.Logistic regression models were used to assess the relationship between preoperative GCC,pRNFL,SRCP,and RPC parameters and visual field recovery after surgery.RESULTS:The study included 43 eyes of 24 patients and 48 eyes of 24 healthy controls.Preoperative RPC and SRCP vessel density and pRNFL and GCC thickness were lower than healthy controls and higher than postoperative values.The best predictive GCC and pRNFL models were based on the superior GCC[area under the curve(AUC)=0.866]and the tempo-inferior pRNFL(AUC=0.824),and the best predictive SRCP and RPC models were based on the nasal SRCP(AUC=0.718)and tempo-inferior RPC(AUC=0.825).There was no statistical difference in the predictive value of the superior GCC,tempo-inferior pRNFL,and tempo-inferior RPC(all P>0.05).CONCLUSION:Compression of the optic chiasm by tumors in the saddle area can reduce retinal thickness and blood perfusion.This reduction persists despite the recovery of the visual field after decompression surgery.GCC,pRNFL,and RPC can be used as sensitive predictors of visual field recovery after decompression surgery.

Retinal capillary plexus in Parkinson’s disease using optical coherence tomography angiography

AIM:To evaluate the alterations of the retinal microvasculature and foveal avascular zone in patients with Parkinson’s disease(PD)using optical coherence tomography angiography(OCT-A).METHODS:A retrospective study of PD patients examined in the Ophthalmology Department of the General Hospital of Athens,“Georgios Gennimatas”from March 2021 to March 2022 was conducted.Totally 44 patients with PD were included and 18 healthy controls were examined,hence a total of 124 eyes were enrolled in the study.The foveal and parafoveal superficial and deep capillary plexus vascular density(fSCP-VD,fDCP-VD,pSCP-VD,pDCP-CD)and foveal avascular zone(FAZ)were quantified with OCTA.Optical coherence tomography(OCT)was used to measure macular thickness.Our statistical analysis was conducted by using a mixed effect linear regression model.RESULTS:After adjustment for age and gender,the mean parafoveal superficial capillary plexus vascular density(pSCP-VD)and mean parafoveal deep capillary plexus vascular density(pDCP-VD)were significantly decreased in individuals with PD(P<0.001 in both)by-2.35(95%CI-3.3,-1.45)and-7.5(95%CI-10.4,-4.6)respectively.fSCP-VD and fDCP-VD didn’t approach statistical significance.The FAZ area and perimeter were significantly decreased(P<0.001 in both)by-0.1 mm^(2)(95%CI-0.13,-0.07)and-0.49 mm^(2)(95%CI-0.66,-0.32)respectively.Circularity didn’t approach statistical significance.Central retinal thickness(CRT)was significantly decreased in individuals with PD(P<0.001)by-23.1μm(95%CI-30.2,-16)and temporal retinal thickness(TRT)was decreased(P=0.025)by-11μm(95%CI-22,-1.5)while nasal retinal thickness(NRT)only approached statistical significance(P=0.066).CONCLUSION:The mean pSCP-VD,pDCP-VD,CRT and TRT are significantly decreased and FAZ is altered in individuals with PD.These findings can be potentially used as biomarkers for the diagnosis and evaluation of early PD.

Three-dimensional choroidal vascularity index and choroidal thickness in fellow eyes of acute and chronic primary angle-closure using swept-source optical coherence tomography

AIM:To compare the three-dimensional choroidal vascularity index(CVI)and choroidal thickness between fellow eyes of acute primary angle-closure(F-APAC)and chronic primary angle-closure glaucoma(F-CPACG)and the eyes of normal controls.METHODS:This study included 37 patients with unilateral APAC,37 with asymmetric CPACG without prior treatment,and 36 healthy participants.Using swept-source optical coherence tomography(SS-OCT),the macular and peripapillary choroidal thickness and three-dimensional CVI were measured and compared globally and sectorally.Pearson’s correlation analysis and multivariate regression models were used to evaluate choroidal thickness or CVI with related factors.RESULTS:The mean subfoveal CVIs were 0.35±0.10,0.33±0.09,and 0.29±0.04,and the mean subfoveal choroidal thickness were 315.62±52.92,306.22±59.29,and 262.69±45.55μm in the F-APAC,F-CPACG,and normal groups,respectively.All macular sectors showed significantly higher CVIs and choroidal thickness in the F-APAC and F-CPACG eyes than in the normal eyes(P<0.05),while there were no significant differences between the F-APAC and F-CPACG eyes.In the peripapillary region,the mean overall CVIs were 0.21±0.08,0.20±0.08,and 0.19±0.05,and the mean overall choroidal thickness were 180.45±54.18,174.82±50.67,and 176.18±37.94μm in the F-APAC,F-CPACG,and normal groups,respectively.There were no significant differences between any of the two groups in all peripapillary sectors.Younger age,shorter axial length,and the F-APAC or F-CPACG diagnosis were significantly associated with higher subfoveal CVI and thicker subfoveal choroidal thickness(P<0.05).CONCLUSION:The fellow eyes of unilateral APAC or asymmetric CPACG have higher macular CVI and choroidal thickness than those of the normal controls.Neither CVI nor choroidal thickness can distinguish between eyes predisposed to APAC or CPACG.A thicker choroid with a higher vascular volume may play a role in the pathogenesis of primary angle-closure glaucoma.

High-Order Soliton Solutions and Hybrid Behavior for the (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations

In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.