This article examines fatigue crack nucleation and propagation in laser deposited TC18 titanium alloy. The Widmanstatten structure was obtained by double-annealing treatment,. High-cycle fatigue (HCF) tests were con...This article examines fatigue crack nucleation and propagation in laser deposited TC18 titanium alloy. The Widmanstatten structure was obtained by double-annealing treatment,. High-cycle fatigue (HCF) tests were conducted at room temperature with the stress ratio of 0.1 and the notch concentration factor Kt = 1. Fatigue cracks initiated preferentially at micropores, which had great effect on the HCF properties. The effect decreased with the decrease of pore size and the increase of distance from the pore location to the specimen surface. The crack initiation region was characterized by the cleavage facets of a lamella and the tearing of β matrix. The soft a precipitated-free zone formed along grain boundaries accelerated the crack propagation. Subsurface observation indicated that the crack preferred to propagate along the grain boundary α or border of a lamella or vertical to a lamella.展开更多
In this paper, the generalized nonlinear Schrodinger equation (GNLSE) is solved by an adaptive split-step Fourier method (ASSFM). It is found that ASSFM must be used to solve GNLSE to ensure precision when the sol...In this paper, the generalized nonlinear Schrodinger equation (GNLSE) is solved by an adaptive split-step Fourier method (ASSFM). It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre (PCF) parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.展开更多
The octahedral spherical hohlraums have natural superiority in maintaining high radiation symmetry during the entire capsule implosion process in indirect drive inertial confinement fusion.While,in contrast to the cyl...The octahedral spherical hohlraums have natural superiority in maintaining high radiation symmetry during the entire capsule implosion process in indirect drive inertial confinement fusion.While,in contrast to the cylindrical hohlraums,the narrow space between the laser beams and the spherical hohlraum wall is usually commented.In this Letter,we address this crucial issue and report our experimental work conducted on the SGIII-prototype laser facility which unambiguously demonstrates that a simple design of cylindrical laser entrance hole(LEH)can dramatically improve the laser propagation inside the spherical hohlraums.In addition,the laser beam deflection in the hohlraum is observed for the first time in the experiments.Our 2-dimensional simulation results also verify qualitatively the advantages of the spherical hohlraums with cylindrical LEHs.Our results imply the prospect of adopting the cylindrical LEHs in future spherical ignition hohlraum design.展开更多
An exact, general solution for laser beams propagating in longitudinally inhomogeneous plasmas is obtained in the form of the diffraction integral. The Gaussian beam and the Hermite-Gaussian beam are taken for example...An exact, general solution for laser beams propagating in longitudinally inhomogeneous plasmas is obtained in the form of the diffraction integral. The Gaussian beam and the Hermite-Gaussian beam are taken for example. In the case of an increasing plasma density along the propagation distance, natural diffraction of the Gaussian beam is retarded. This retardance has a less effect on the central part of the Hermite-Gaussian beam while a considerable rise of the power in bucket (PIB) occurs in the surrounding part of the beam.展开更多
The propagation performance of high-power partially coherent fibre laser beams in a real environment is inves- tigated and the theoretical model of a high-power fibre laser propagating in a real environment is establi...The propagation performance of high-power partially coherent fibre laser beams in a real environment is inves- tigated and the theoretical model of a high-power fibre laser propagating in a real environment is established. The influence of a collimating system and thermal blooming is considered together with atmospheric turbulence and me- chanical jitter. The laser energy concentration of partially coherent beams in the far field is calculated and analysed based on the theoretical model. It is shown that the propagation performance of partially coherent beams depends on the collimating system, atmospheric turbulence, mechanical jitter and thermal blooming. The propagation performance of partially coherent beams and fully coherent beams is studied and the results show that partially coherent beams are less sensitive to the influence of thermal blooming, which results in that the energy degeneration for partially coherent beams is only 50% of that for fully coherent beams. Both partially coherent beams and fully coherent beams become less sensitive to thermal blooming when the average structural constant of the refraction index fluctuations increases to 1.7×10^-14 m^-2/3. The investigation presents a reference for applications of a high-power fibre laser system.展开更多
Considering the atmospheric extinction and turbulence effects,we investigate the propagation performances of supercontinuum laser sources in atmospheric turbulence statistically by using the numerical simulation metho...Considering the atmospheric extinction and turbulence effects,we investigate the propagation performances of supercontinuum laser sources in atmospheric turbulence statistically by using the numerical simulation method,and the differences in propagation properties between the super-continuum(SC)laser and its pump laser are also analyzed.It is found that the propagation characteristics of super-continuum laser are almost similar to those of the pump laser.The degradation of source coherence degree may cause the relative beam spreading and scintillation indexes to decrease at different propagation distances or different turbulence strengths.The root-mean-square value of beam wandering is insensitive to the variation of source correlation length,and less aperture averaging occurs when the laser source becomes less coherent.Additionally,from the point of view of beam wandering,the SC laser has no advantage over the pump laser.Although the pump laser can bring about a bigger aperture average,the SC laser has a lower scintillation which may be due to the multiple wavelength homogenization effects on intensity fluctuations.This would be the most important virtue of the SC laser that can be utilized to improve the performance of laser engineering.展开更多
By containing ponderomotive self-channeling,the propagation behavior of an intense laser beam and the physical conditions are obtained theoretically in a radial power-law plasma channel.It is found that ponderomotive ...By containing ponderomotive self-channeling,the propagation behavior of an intense laser beam and the physical conditions are obtained theoretically in a radial power-law plasma channel.It is found that ponderomotive self-channeling results in the emergence of a solitary wave and catastrophic focusing,which apparently decreases the region for stable propagation in a parameter space of laser power and the ratio of the initial laser spot radius to the channel radius(RLC).Direct numerical simulation confirms the theory of constant propagation,periodic defocusing and focusing oscillations in the parameter space,and reveals a radial instability which prevents the formation of bright and dark solitary waves.The corresponding unstable critical curve is added in the parameter space numerically and the induced unstable region above the unstable critical curve covers that of catastrophic focusing,which shrinks the stable region for laser beams.For the expected constant propagation,the results reveal the need for a low RLC.Further study illustrates that the channel power-law exponent has an obvious effect on the final stable region and laser propagation,for example increasing this exponent can enlarge the stable region significantly,which is beneficial for guiding of the laser and increases the lowest RLC for constant propagation.Our results also show that the initial laser amplitude has an apparent influence on the propagation behavior.展开更多
The nonlinear propagation of an intense Laguerre-Gaussian(LG)laser pulse in a parabolic preformed plasma channel is analyzed by means of the variational method.The evolution equation of the spot size is derived includ...The nonlinear propagation of an intense Laguerre-Gaussian(LG)laser pulse in a parabolic preformed plasma channel is analyzed by means of the variational method.The evolution equation of the spot size is derived including the effects of relativistic self-focusing,preformed channel focusing,and ponderomotive self-channeling.The parametric conditions of the LG laser pulse and plasma channel for propagating with constant spot size,periodically focusing and defocusing oscillation,catastrophic focusing,and solitary waves are obtained.Compared with the laser pulse with fundamental Gaussian(FG)mode,it is found that the effect of vacuum diffraction is reduced by half and the effects of relativistic and wakefield focusing are decreased by a quarter due to the hollow transverse intensity profile of the LG laser pulse,while the effect of channel focusing is the same order of magnitude with that of the FG laser pulse.Thus,the matched condition for the intense LG laser pulse with constant spot size is released obviously,while the parameters of the laser and plasma for the existence of solitary waves nearly coincide with those of the FG laser pulse.展开更多
Laser cooling of heavy ion beams is the most promising method to realize crystalline beams at storage rings[1].In order to perform the laser cooling experiment of C3+ at the CSRe[2], we tested the laser propagation an...Laser cooling of heavy ion beams is the most promising method to realize crystalline beams at storage rings[1].In order to perform the laser cooling experiment of C3+ at the CSRe[2], we tested the laser propagation and controlby using the He-Ne laser at the straight part (about 25 m long) before the experiment. The experimental resultsindicated that the laser was collimated and stable, and the laser intensity was strong enough after a long distancepropagation at the CSRe which satis ed the requirement of laser cooling of heavy ion beams.展开更多
Truncation manipulation is a simple but effective way to improve the intensity distribution properties of the phase-locked Gaussian beam array at the receiving plane. In this paper, the analytical expression for the p...Truncation manipulation is a simple but effective way to improve the intensity distribution properties of the phase-locked Gaussian beam array at the receiving plane. In this paper, the analytical expression for the propagation of the phase-locked truncated Gaussian beam array in a turbulent atmosphere is obtained based on the extended Huygens--Fresnel principle. Power in the diffraction-limited bucket is introduced as the beam quality factor to evaluate the influence of different truncation parameters. The dependence of optimal truncation ratio on the number of beamlets, the intensity of turbulence, propagation distance and laser wavelength is calculated and discussed. It is revealed that the optimal truncation ratio is larger for the laser array that contains more lasers, and the optimal truncation ratio will shift to a larger value with an increase in propagation distance and decrease in intensity of atmosphere turbulence. The optimal truncation ratio is independent of laser wavelength.展开更多
Based on the Collins integral formula, the analytic expressions of propagation of the coherent and the incoherent off-axis Hermite-cosh-Gaussian (HChG) beam combinations with rectangular symmetry passing through a p...Based on the Collins integral formula, the analytic expressions of propagation of the coherent and the incoherent off-axis Hermite-cosh-Gaussian (HChG) beam combinations with rectangular symmetry passing through a paraxial first-order optical system are derived, and corresponding numerical examples are given and analysed. The resulting beam quality is discussed in terms of power in the bucket (PIB). The study suggests that the resulting beam cannot keep the initial intensity shape during the propagation and the beam quality for coherent mode is not always better than that for incoherent mode. Reviewing the numerical simulations of Gaussian, Hermite-Gaussian (HG) and cosh- Gaussian (ChG) beam combinations indicates that the Hermite polynomial exerts a chief influence on the irradiance profile of composite beam and far field power concentration.展开更多
The laser beam used to establish a communication channel between satellite and ground segments has a small divergence angle and a tiny spot on the Earth's surface,which may lead to the fail of the system.So it'...The laser beam used to establish a communication channel between satellite and ground segments has a small divergence angle and a tiny spot on the Earth's surface,which may lead to the fail of the system.So it's important to study the deflection of laser beam by the Earth's atmosphere and find a way to calibrate this error.Both theoretical analysis and real data processing method are used to obtain the mathematical model for divergence angle of laser communication beam and its correction function.Then the model has been applied to the data,which was used to describe the atmosphere state by traditional ground segments to obtain the critical elevation angle.According to the results of calculation,our conclusion will be that the correction should be done when the critical elevation happens.展开更多
The effect of diffraction on the geometry of initially plane acoustic transients propagating in liquids is studied.Theoretical considerations concern the transition from plane to spherical waves upon passing the borde...The effect of diffraction on the geometry of initially plane acoustic transients propagating in liquids is studied.Theoretical considerations concern the transition from plane to spherical waves upon passing the border between near and far wave zone.Experiments with CO_(2)-laser-generated acoustic waves in absorbing liquids are discussed.The wavefront curvatures and lateral extensions at different propagating distances in n-heptane are analyzed by high-speed shadowgraphy and measurements with a piezoelectric transducer.Good agreement between theory and experiment is obtained.展开更多
An essential dispersion relation,which can describe the dynamic properties of stimulated Raman scattering instability as a laser beam propagates through plasmas,is derived analytically.The development of growth mode,a...An essential dispersion relation,which can describe the dynamic properties of stimulated Raman scattering instability as a laser beam propagates through plasmas,is derived analytically.The development of growth mode,angle distribution,and temperature dependence of the instabilities are presented by solving this dispersion relation numerically.A significant dynamic characteristic has been revealed that the temperature increasing of the electron would result in redshift of scattered spectrum at high laser intensities.Furthermore,a novel modulational instability with double-peak temporal structure appears in a limited density region because of the coupling of scattered upshift and downshift waves.展开更多
Synthesis of multi-color laser pulses has been developed as a promising way to improve low conversion efficiency of high-order harmonic generation(HHG). Here we systematically study the effect of laser focus in a two-...Synthesis of multi-color laser pulses has been developed as a promising way to improve low conversion efficiency of high-order harmonic generation(HHG). Here we systematically study the effect of laser focus in a two-color waveform on generation of macroscopic HHG in soft x-rays. We find that the dependence of HHG yields on laser focus at low or high gas pressure is sensitive to the characteristics of single-atom harmonic response, in which “short”-or “long”-trajectory emissions can be selectively controlled by changing the waveform of two-color synthesized laser pulse. We uncover the phase-matching mechanism of HHG in the gas medium by examining the propagation of the two-color waveform and the evolution of time-frequency emissions of high-harmonic field. We further reveal that the nonlinear effects, such as geometric phase, atomic dispersion, and plasma defocusing, are responsible for modification of two-color waveform upon propagation. This work can be used to find better macroscopic conditions for generating soft x-ray HHG by employing two-color optimized waveforms.展开更多
基金financially supported by the Cheung Kong Scholars Innovative Research Team Program of Ministry of Education, China (No. IRT0805)the State Key Basic Research Program of China (No. 2011CB606305)
文摘This article examines fatigue crack nucleation and propagation in laser deposited TC18 titanium alloy. The Widmanstatten structure was obtained by double-annealing treatment,. High-cycle fatigue (HCF) tests were conducted at room temperature with the stress ratio of 0.1 and the notch concentration factor Kt = 1. Fatigue cracks initiated preferentially at micropores, which had great effect on the HCF properties. The effect decreased with the decrease of pore size and the increase of distance from the pore location to the specimen surface. The crack initiation region was characterized by the cleavage facets of a lamella and the tearing of β matrix. The soft a precipitated-free zone formed along grain boundaries accelerated the crack propagation. Subsurface observation indicated that the crack preferred to propagate along the grain boundary α or border of a lamella or vertical to a lamella.
文摘In this paper, the generalized nonlinear Schrodinger equation (GNLSE) is solved by an adaptive split-step Fourier method (ASSFM). It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre (PCF) parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.
基金supported by the Development Foundation of CAEP(2013A0102002)the National Natural Science Foundation of China(Grant Nos.11405011 and 11475033).
文摘The octahedral spherical hohlraums have natural superiority in maintaining high radiation symmetry during the entire capsule implosion process in indirect drive inertial confinement fusion.While,in contrast to the cylindrical hohlraums,the narrow space between the laser beams and the spherical hohlraum wall is usually commented.In this Letter,we address this crucial issue and report our experimental work conducted on the SGIII-prototype laser facility which unambiguously demonstrates that a simple design of cylindrical laser entrance hole(LEH)can dramatically improve the laser propagation inside the spherical hohlraums.In addition,the laser beam deflection in the hohlraum is observed for the first time in the experiments.Our 2-dimensional simulation results also verify qualitatively the advantages of the spherical hohlraums with cylindrical LEHs.Our results imply the prospect of adopting the cylindrical LEHs in future spherical ignition hohlraum design.
基金Project supported by the National Natural Science Foundation of China (Grant No 19874020) and the Natural Science Foundation of Hunan Province, China (Grant No 05JJ30004).
文摘An exact, general solution for laser beams propagating in longitudinally inhomogeneous plasmas is obtained in the form of the diffraction integral. The Gaussian beam and the Hermite-Gaussian beam are taken for example. In the case of an increasing plasma density along the propagation distance, natural diffraction of the Gaussian beam is retarded. This retardance has a less effect on the central part of the Hermite-Gaussian beam while a considerable rise of the power in bucket (PIB) occurs in the surrounding part of the beam.
文摘The propagation performance of high-power partially coherent fibre laser beams in a real environment is inves- tigated and the theoretical model of a high-power fibre laser propagating in a real environment is established. The influence of a collimating system and thermal blooming is considered together with atmospheric turbulence and me- chanical jitter. The laser energy concentration of partially coherent beams in the far field is calculated and analysed based on the theoretical model. It is shown that the propagation performance of partially coherent beams depends on the collimating system, atmospheric turbulence, mechanical jitter and thermal blooming. The propagation performance of partially coherent beams and fully coherent beams is studied and the results show that partially coherent beams are less sensitive to the influence of thermal blooming, which results in that the energy degeneration for partially coherent beams is only 50% of that for fully coherent beams. Both partially coherent beams and fully coherent beams become less sensitive to thermal blooming when the average structural constant of the refraction index fluctuations increases to 1.7×10^-14 m^-2/3. The investigation presents a reference for applications of a high-power fibre laser system.
基金Project supported by the Director Fund of Advanced Laser Technology Laboratory of Anhui Province,China(Grant No.20191002).
文摘Considering the atmospheric extinction and turbulence effects,we investigate the propagation performances of supercontinuum laser sources in atmospheric turbulence statistically by using the numerical simulation method,and the differences in propagation properties between the super-continuum(SC)laser and its pump laser are also analyzed.It is found that the propagation characteristics of super-continuum laser are almost similar to those of the pump laser.The degradation of source coherence degree may cause the relative beam spreading and scintillation indexes to decrease at different propagation distances or different turbulence strengths.The root-mean-square value of beam wandering is insensitive to the variation of source correlation length,and less aperture averaging occurs when the laser source becomes less coherent.Additionally,from the point of view of beam wandering,the SC laser has no advantage over the pump laser.Although the pump laser can bring about a bigger aperture average,the SC laser has a lower scintillation which may be due to the multiple wavelength homogenization effects on intensity fluctuations.This would be the most important virtue of the SC laser that can be utilized to improve the performance of laser engineering.
基金supported by National Natural Science Foundation of China(Nos.11765017,11865014,12047574,11847304,11764039,12165018)by the Scientific Research Project of Gansu Higher Education(No.2019B-034).
文摘By containing ponderomotive self-channeling,the propagation behavior of an intense laser beam and the physical conditions are obtained theoretically in a radial power-law plasma channel.It is found that ponderomotive self-channeling results in the emergence of a solitary wave and catastrophic focusing,which apparently decreases the region for stable propagation in a parameter space of laser power and the ratio of the initial laser spot radius to the channel radius(RLC).Direct numerical simulation confirms the theory of constant propagation,periodic defocusing and focusing oscillations in the parameter space,and reveals a radial instability which prevents the formation of bright and dark solitary waves.The corresponding unstable critical curve is added in the parameter space numerically and the induced unstable region above the unstable critical curve covers that of catastrophic focusing,which shrinks the stable region for laser beams.For the expected constant propagation,the results reveal the need for a low RLC.Further study illustrates that the channel power-law exponent has an obvious effect on the final stable region and laser propagation,for example increasing this exponent can enlarge the stable region significantly,which is beneficial for guiding of the laser and increases the lowest RLC for constant propagation.Our results also show that the initial laser amplitude has an apparent influence on the propagation behavior.
基金the National Natural Science Foundation of China(Grant Nos.61665006 and 61865011)the Natural Science Foundation of Jiangxi Province of China(Grant Nos.20171ACB21018,20161BAB212041,and 20162BCB23012).
文摘The nonlinear propagation of an intense Laguerre-Gaussian(LG)laser pulse in a parabolic preformed plasma channel is analyzed by means of the variational method.The evolution equation of the spot size is derived including the effects of relativistic self-focusing,preformed channel focusing,and ponderomotive self-channeling.The parametric conditions of the LG laser pulse and plasma channel for propagating with constant spot size,periodically focusing and defocusing oscillation,catastrophic focusing,and solitary waves are obtained.Compared with the laser pulse with fundamental Gaussian(FG)mode,it is found that the effect of vacuum diffraction is reduced by half and the effects of relativistic and wakefield focusing are decreased by a quarter due to the hollow transverse intensity profile of the LG laser pulse,while the effect of channel focusing is the same order of magnitude with that of the FG laser pulse.Thus,the matched condition for the intense LG laser pulse with constant spot size is released obviously,while the parameters of the laser and plasma for the existence of solitary waves nearly coincide with those of the FG laser pulse.
文摘Laser cooling of heavy ion beams is the most promising method to realize crystalline beams at storage rings[1].In order to perform the laser cooling experiment of C3+ at the CSRe[2], we tested the laser propagation and controlby using the He-Ne laser at the straight part (about 25 m long) before the experiment. The experimental resultsindicated that the laser was collimated and stable, and the laser intensity was strong enough after a long distancepropagation at the CSRe which satis ed the requirement of laser cooling of heavy ion beams.
基金supported by the Innovation Foundation for Postgraduate of Hunan Province
文摘Truncation manipulation is a simple but effective way to improve the intensity distribution properties of the phase-locked Gaussian beam array at the receiving plane. In this paper, the analytical expression for the propagation of the phase-locked truncated Gaussian beam array in a turbulent atmosphere is obtained based on the extended Huygens--Fresnel principle. Power in the diffraction-limited bucket is introduced as the beam quality factor to evaluate the influence of different truncation parameters. The dependence of optimal truncation ratio on the number of beamlets, the intensity of turbulence, propagation distance and laser wavelength is calculated and discussed. It is revealed that the optimal truncation ratio is larger for the laser array that contains more lasers, and the optimal truncation ratio will shift to a larger value with an increase in propagation distance and decrease in intensity of atmosphere turbulence. The optimal truncation ratio is independent of laser wavelength.
文摘Based on the Collins integral formula, the analytic expressions of propagation of the coherent and the incoherent off-axis Hermite-cosh-Gaussian (HChG) beam combinations with rectangular symmetry passing through a paraxial first-order optical system are derived, and corresponding numerical examples are given and analysed. The resulting beam quality is discussed in terms of power in the bucket (PIB). The study suggests that the resulting beam cannot keep the initial intensity shape during the propagation and the beam quality for coherent mode is not always better than that for incoherent mode. Reviewing the numerical simulations of Gaussian, Hermite-Gaussian (HG) and cosh- Gaussian (ChG) beam combinations indicates that the Hermite polynomial exerts a chief influence on the irradiance profile of composite beam and far field power concentration.
基金Supported by the Strategic Priority Research Program of Chinese Academy of Sciences(XDA04080201)。
文摘The laser beam used to establish a communication channel between satellite and ground segments has a small divergence angle and a tiny spot on the Earth's surface,which may lead to the fail of the system.So it's important to study the deflection of laser beam by the Earth's atmosphere and find a way to calibrate this error.Both theoretical analysis and real data processing method are used to obtain the mathematical model for divergence angle of laser communication beam and its correction function.Then the model has been applied to the data,which was used to describe the atmosphere state by traditional ground segments to obtain the critical elevation angle.According to the results of calculation,our conclusion will be that the correction should be done when the critical elevation happens.
文摘The effect of diffraction on the geometry of initially plane acoustic transients propagating in liquids is studied.Theoretical considerations concern the transition from plane to spherical waves upon passing the border between near and far wave zone.Experiments with CO_(2)-laser-generated acoustic waves in absorbing liquids are discussed.The wavefront curvatures and lateral extensions at different propagating distances in n-heptane are analyzed by high-speed shadowgraphy and measurements with a piezoelectric transducer.Good agreement between theory and experiment is obtained.
文摘An essential dispersion relation,which can describe the dynamic properties of stimulated Raman scattering instability as a laser beam propagates through plasmas,is derived analytically.The development of growth mode,angle distribution,and temperature dependence of the instabilities are presented by solving this dispersion relation numerically.A significant dynamic characteristic has been revealed that the temperature increasing of the electron would result in redshift of scattered spectrum at high laser intensities.Furthermore,a novel modulational instability with double-peak temporal structure appears in a limited density region because of the coupling of scattered upshift and downshift waves.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.91950102,12274230,and 11834004)the Funding of Nanjing University of Science and Technology (Grant No.TSXK2022D005)。
文摘Synthesis of multi-color laser pulses has been developed as a promising way to improve low conversion efficiency of high-order harmonic generation(HHG). Here we systematically study the effect of laser focus in a two-color waveform on generation of macroscopic HHG in soft x-rays. We find that the dependence of HHG yields on laser focus at low or high gas pressure is sensitive to the characteristics of single-atom harmonic response, in which “short”-or “long”-trajectory emissions can be selectively controlled by changing the waveform of two-color synthesized laser pulse. We uncover the phase-matching mechanism of HHG in the gas medium by examining the propagation of the two-color waveform and the evolution of time-frequency emissions of high-harmonic field. We further reveal that the nonlinear effects, such as geometric phase, atomic dispersion, and plasma defocusing, are responsible for modification of two-color waveform upon propagation. This work can be used to find better macroscopic conditions for generating soft x-ray HHG by employing two-color optimized waveforms.