The molecular orientation created by laser fields is important for steering chemical reactions. In this paper, we propose a theoretical scheme to manipulate field-free molecular orientation by using an intense super-G...The molecular orientation created by laser fields is important for steering chemical reactions. In this paper, we propose a theoretical scheme to manipulate field-free molecular orientation by using an intense super-Gaussian laser pulse and a time-delayed terahertz half-cycle pulse(THz HCP). It is shown that the degree of field-free orientation can be doubled by the combined pulse with respect to the super-Gaussian pulse or THz HCP alone. Moreover, different laser intensities, carrier envelop phases, shape parameters, and time delays have great influence on the positive and negative orientations, with other conditions unchanged. Furthermore, it is indicated that the maximum degree and direction of molecular orientation can be precisely controlled by half of the duration of the super-Gaussian pulse. Finally, by adjusting the laser parameters of the super-Gaussian laser pulse and THz HCP, the optimal results of negative orientation and corresponding rotational populations are obtained at different temperatures of the molecular system.展开更多
SnS∶Ag thin films were deposited on ITO glasses by pulse electro-deposition. By studying the effect of duty cycle on the properties of SnS∶Ag thin films, the optimum off-time(toff) is obtained to be 5 s, namely, the...SnS∶Ag thin films were deposited on ITO glasses by pulse electro-deposition. By studying the effect of duty cycle on the properties of SnS∶Ag thin films, the optimum off-time(toff) is obtained to be 5 s, namely, the optimal duty cycle is about 67%. The primary phase of SnS∶Ag films deposited on optimum parameters condition is SnS compound with good crystallization, and the films prefer to grow towards (111) plane. The films are dense, smooth and uniform with good microstructure, and the grains in the films are densely packed together, and their direct bandgap is about 1.40 eV. In addition, the bandgap of the films first rises and then drops with the increase of the duty cycle.展开更多
We theoretically investigate the characteristics of terahertz(THz) radiation from monolayer graphene exposed to normal incident few-cycle laser pulses, by numerically solving the extended semiconductor Bloch equations...We theoretically investigate the characteristics of terahertz(THz) radiation from monolayer graphene exposed to normal incident few-cycle laser pulses, by numerically solving the extended semiconductor Bloch equations. Our simulations show that the THz spectra in low frequency regions are highly dependent on the carrier envelope phase(CEP) of driving laser pulses. Using an optimal CEP of few-cycle laser pulses, we can obtain broadband strong THz waves, due to the symmetry breaking of the laser-graphene system. Our results also show that the strength of the THz spectra depend on both the intensity and central wavelength of the laser pulses. The intensity dependence of the THz wave can be described by the excitation rate of graphene, while wavelength dependence can be traced back to the band velocity and the population of graphene. We find that a near single-cycle THz pulse can be obtained from graphene driven by a mid-infrared laser pulse.展开更多
Within the framework of plane-wave angular spectrum analysis of the electromagnetic field structure, a solution valid for tightly focused radially polarized few-cycle laser pulses propagating in vacuum is presented. T...Within the framework of plane-wave angular spectrum analysis of the electromagnetic field structure, a solution valid for tightly focused radially polarized few-cycle laser pulses propagating in vacuum is presented. The resulting field distribution is significantly different from that based on the paraxial approximation for pulses with either small or large beam diameters. We compare the electron accelerations obtained with the two solutions and find that the energy gain obtained with our new solution is usually much larger than that with the paraxial approximation solution.展开更多
二很少周期脉搏导致的 D <SUB>2</SUB> 的动态排列被基于一个僵硬转子模型数字地解决时间依赖者 Schrodinger 方程调查。只要在二之间的时间延期搏动, D <SUB>2</SUB>的排列能被二很少周期脉搏与由单个很少周...二很少周期脉搏导致的 D <SUB>2</SUB> 的动态排列被基于一个僵硬转子模型数字地解决时间依赖者 Schrodinger 方程调查。只要在二之间的时间延期搏动, D <SUB>2</SUB>的排列能被二很少周期脉搏与由单个很少周期脉搏可完成的水平相比提高的结果表演适当地被选择,并且二激光的脉搏持续时间在 D <SUB>2</SUB>分子的排列过程起一个重要作用。展开更多
A Fourier analysis method is used to accurately determine not only the absolute phase but also the tempuralpulse phase of an isolated few-cycle (chirped) laser pulse. This method is independent of the pulse shape an...A Fourier analysis method is used to accurately determine not only the absolute phase but also the tempuralpulse phase of an isolated few-cycle (chirped) laser pulse. This method is independent of the pulse shape and can fully characterize the light wave even though only a few samples per optical cycle are available. It pavas the way for investigating the absolute phase-dependent extreme nonlinear optics, and the evolutions of the absolute phase and the temporal-pulse phase of few-cycle laser pulses.展开更多
The asymmetric photoionization of atoms irradiated by intense, few-cycle laser pulses is studied numerically. The results show that the pulse intensity affects the asymmetric photoionization in three aspects. First, a...The asymmetric photoionization of atoms irradiated by intense, few-cycle laser pulses is studied numerically. The results show that the pulse intensity affects the asymmetric photoionization in three aspects. First, at higher intensities, the asymmetry becomes distinctive for few-cycle pulses of longer durations. Second, as the laser intensity increases, the maximal asymmetry first decreases then increases after it has reached a minimal value. Last, the value of the carrier-envelope phase corresponding to the maximal asymmetry varies with the pulse intensity. This study reveals that the increasing of pulse intensity is helpful for observing the asymmetric photoionization.展开更多
We numerically study the pulse compression approaches based on atomic or molecular gases in a hollow-core fiber.From the perspective of self-phase modulation(SPM), we give the extensive study of the SPM influence on...We numerically study the pulse compression approaches based on atomic or molecular gases in a hollow-core fiber.From the perspective of self-phase modulation(SPM), we give the extensive study of the SPM influence on a probe pulse with molecular phase modulation(MPM) effect. By comparing the two compression methods, we summarize their advantages and drawbacks to obtain the few-cycle pulses with micro- or millijoule energies. It is also shown that the double pump-probe approach can be used as a tunable dual-color source by adjusting the time delay between pump and probe pulses to proper values.展开更多
In the present paper we conduct a theoretical study of the thermal accumulation effect of a typical bipolar transistor caused by high power pulsed microwaves(HPMs),and investigate the thermal accumulation effect as ...In the present paper we conduct a theoretical study of the thermal accumulation effect of a typical bipolar transistor caused by high power pulsed microwaves(HPMs),and investigate the thermal accumulation effect as a function of pulse repetition frequency(PRF) and duty cycle.A study of the damage mechanism of the device is carried out from the variation analysis of the distribution of the electric field and the current density.The result shows that the accumulation temperature increases with PRF increasing and the threshold for the transistor is about 2 kHz.The response of the peak temperature induced by the injected single pulses indicates that the falling time is much longer than the rising time.Adopting the fitting method,the relationship between the peak temperature and the time during the rising edge and that between the peak temperature and the time during the falling edge are obtained.Moreover,the accumulation temperature decreases with duty cycle increasing for a certain mean power.展开更多
In this article, we present a time-dependent model that enables us to describe the dynamic behavior of pulsed DC reactive sputtering and predict the film compositions of VOx prepared by this process. In this modeling,...In this article, we present a time-dependent model that enables us to describe the dynamic behavior of pulsed DC reactive sputtering and predict the film compositions of VOx prepared by this process. In this modeling, the average current J is replaced by a new parameter of Jeff. Meanwhile, the four species states of V, V2O3, VO2, and V2O5 in the vanadium oxide films are taken into consideration. Based on this work, the influences of the oxygen gas supply and the pulsed power parameters including the duty cycle and frequency on film compositions are discussed. The model suggests that the time to reach process equilibrium may vary substantially depending on these parameters. It is also indicated that the compositions of VOx films are quite sensitive to both the reactive gas supply and the duty cycle when the power supply works in pulse mode. The 'steady-state' balance values obtained by these simulations show excellent agreement with the experimental data, which indicates that the experimentally obtained dynamic behavior of the film composition can be explained by this time-dependent modeling for pulsed DC reactive sputtering process. Moreover, the computer simulation results indicate that the curves will essentially yield oscillations around the average value of the film compositions with lower pulse frequency.展开更多
An improved constant volume cycle (CVC) model is developed to analyze the nozzle effects on the thrust and specific impulse of pulse detonation rocket engine (PDRE). Theoretically, this model shows that the thrust...An improved constant volume cycle (CVC) model is developed to analyze the nozzle effects on the thrust and specific impulse of pulse detonation rocket engine (PDRE). Theoretically, this model shows that the thrust coefficient/specific impulse of PDRE is a function of the nozzle contraction/expansion ratio and the operating frequency. The relationship between the nozzle contraction ratio and the operation frequency is obtained by introducing the duty ratio, by which the key problem in the theoretical design can be solved. Therefore, the performance of PDRE can be accessed to guide the preliminary shape design of nozzle conveniently and quickly. The higher the operating frequency of PDRE is, the smaller the nozzle contraction ratio should be. Besides, the lower the ambient pressure is, the larger the expansion ratio of the nozzle should be. When the ambient pressure is 1.013 × 105 Pa, the optimal expansion ratio will be less than 2.26. When the ambient pressure is reduced to vacuum, the extremum of the optimal thrust coefficient is 2.236 9, and the extremum of the specific impulse is 321.01 s. The results of the improved model are verified by numerical simulation.展开更多
The problem of optimal periodic pulse jamming design for a quadrature phase shift keying(QPSK)communication system is investigated.First a closed-form bit-error-rate(BER)of QPSK system under the jamming of pulse s...The problem of optimal periodic pulse jamming design for a quadrature phase shift keying(QPSK)communication system is investigated.First a closed-form bit-error-rate(BER)of QPSK system under the jamming of pulse signal is derived.Then the asymptotic performance of the derived BER is analyzed as the signal-to-noise ratio(SNR)grows to infinity.In order to maximize the BER of the QPSK system,the optimal parameters of periodic pulse jamming signal,including the duty cycle and signal-tojamming power ratio(SJR),are found out.Numerical results are presented to verify our analytical results and the optimality of our design.展开更多
An exact analytic expression for an ultrashort hollow-Airy wave packet is presented beyond the slowly varying envelope approximation. The hollow-Airy wave packet combines the hollow-Gaussian beam in the spatial domain...An exact analytic expression for an ultrashort hollow-Airy wave packet is presented beyond the slowly varying envelope approximation. The hollow-Airy wave packet combines the hollow-Gaussian beam in the spatial domain and the Airy pulse in the temporal domain. The spatiotemporal propagation dynamics of the ultrashort hollow- Airy pulse are analyzed by the numerical simulations. During the propagation in free space, the spatial intensity profile evolves from hollow-Gaussian to Gaussian shape; the temporal intensity profile retains Airy shape over several Rayleigh ranges. The acceleration property of the ultrashort Airy pulse is also demonstrated.展开更多
By means of the numerical solution of time-dependent Schr6dinger equation, we verify a scaling law of photoionization in ultrashort pulses. We find that for a given carrier-envelope phase and duration of the pulse, id...By means of the numerical solution of time-dependent Schr6dinger equation, we verify a scaling law of photoionization in ultrashort pulses. We find that for a given carrier-envelope phase and duration of the pulse, identical photoionizations are obtained provided that when the central frequency of the pulse is enlarged by k times, the atomic binding potential is enlarged by k times, and the laser intensity is enlarged by ka times. The scaling law allows us to reach a significant control over direction of photoemission and offers exciting prospects of reaching similar physical processes in different interacting systems which constitutes a novel kind of coherent control.展开更多
We have experimentally demonstrated pulses 0.4 mJ in duration smaller than 12 fs with an excellent spatial beam profile by self-guided propagation in argon. The original 52 fs pulses from the chirped pulsed amplificat...We have experimentally demonstrated pulses 0.4 mJ in duration smaller than 12 fs with an excellent spatial beam profile by self-guided propagation in argon. The original 52 fs pulses from the chirped pulsed amplification laser system are first precompressed to 32 fs by inserting an acoustic optical programmable dispersive filter instrument into the laser system for spectrum reshaping and dispersion compensation, and the pulse spectrum is subsequently broadened by filamentation in an argon cell. By using chirped mirrors for post-dispersion compensation, the pulses are successfully compressed to smaller than 12 fs.展开更多
We theoretically investigate the high-order harmonic generation from the hydrogen atom driven by the laser pulses with the durations less than the optical cycle. It is found that the switching term of the laser field ...We theoretically investigate the high-order harmonic generation from the hydrogen atom driven by the laser pulses with the durations less than the optical cycle. It is found that the switching term of the laser field may have an obvious influence on the cutoff, intensity or plateau structure of the high-order harmonic spectrum. Generally speaking, the switching term can shorten the cutoff of the high-order harmonic spectrum for a relatively longer pulse and extend the cutoff for a relatively shorter pulse.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674198 and 11874241)the Taishan Scholar Project of Shandong Province,China
文摘The molecular orientation created by laser fields is important for steering chemical reactions. In this paper, we propose a theoretical scheme to manipulate field-free molecular orientation by using an intense super-Gaussian laser pulse and a time-delayed terahertz half-cycle pulse(THz HCP). It is shown that the degree of field-free orientation can be doubled by the combined pulse with respect to the super-Gaussian pulse or THz HCP alone. Moreover, different laser intensities, carrier envelop phases, shape parameters, and time delays have great influence on the positive and negative orientations, with other conditions unchanged. Furthermore, it is indicated that the maximum degree and direction of molecular orientation can be precisely controlled by half of the duration of the super-Gaussian pulse. Finally, by adjusting the laser parameters of the super-Gaussian laser pulse and THz HCP, the optimal results of negative orientation and corresponding rotational populations are obtained at different temperatures of the molecular system.
基金National Nature Sciences Funding of China(61076063)Key Project of Fujian Provincial Department of Science &Technology(2008I0019)Fujian Provincial Natural Science Foundation of China(2009J01285)
文摘SnS∶Ag thin films were deposited on ITO glasses by pulse electro-deposition. By studying the effect of duty cycle on the properties of SnS∶Ag thin films, the optimum off-time(toff) is obtained to be 5 s, namely, the optimal duty cycle is about 67%. The primary phase of SnS∶Ag films deposited on optimum parameters condition is SnS compound with good crystallization, and the films prefer to grow towards (111) plane. The films are dense, smooth and uniform with good microstructure, and the grains in the films are densely packed together, and their direct bandgap is about 1.40 eV. In addition, the bandgap of the films first rises and then drops with the increase of the duty cycle.
基金Supported by the National Natural Science Foundation of China (Grant Nos.11764038,11864037,11765018,and 91850209)。
文摘We theoretically investigate the characteristics of terahertz(THz) radiation from monolayer graphene exposed to normal incident few-cycle laser pulses, by numerically solving the extended semiconductor Bloch equations. Our simulations show that the THz spectra in low frequency regions are highly dependent on the carrier envelope phase(CEP) of driving laser pulses. Using an optimal CEP of few-cycle laser pulses, we can obtain broadband strong THz waves, due to the symmetry breaking of the laser-graphene system. Our results also show that the strength of the THz spectra depend on both the intensity and central wavelength of the laser pulses. The intensity dependence of the THz wave can be described by the excitation rate of graphene, while wavelength dependence can be traced back to the band velocity and the population of graphene. We find that a near single-cycle THz pulse can be obtained from graphene driven by a mid-infrared laser pulse.
基金supported by the National Natural Science Foundation of China (Grant Nos.10734130,10935002,and 11075105)the National Basic Research Program of China (Grant No.2009GB105002)
文摘Within the framework of plane-wave angular spectrum analysis of the electromagnetic field structure, a solution valid for tightly focused radially polarized few-cycle laser pulses propagating in vacuum is presented. The resulting field distribution is significantly different from that based on the paraxial approximation for pulses with either small or large beam diameters. We compare the electron accelerations obtained with the two solutions and find that the energy gain obtained with our new solution is usually much larger than that with the paraxial approximation solution.
文摘二很少周期脉搏导致的 D <SUB>2</SUB> 的动态排列被基于一个僵硬转子模型数字地解决时间依赖者 Schrodinger 方程调查。只要在二之间的时间延期搏动, D <SUB>2</SUB>的排列能被二很少周期脉搏与由单个很少周期脉搏可完成的水平相比提高的结果表演适当地被选择,并且二激光的脉搏持续时间在 D <SUB>2</SUB>分子的排列过程起一个重要作用。
基金Project supported by the National Natural Science Foundation of China (Grant No 60478002), and the Basic Research Key Foundation of Shanghai (Grant Nos 04JC14036 and 05DJ14003).
文摘A Fourier analysis method is used to accurately determine not only the absolute phase but also the tempuralpulse phase of an isolated few-cycle (chirped) laser pulse. This method is independent of the pulse shape and can fully characterize the light wave even though only a few samples per optical cycle are available. It pavas the way for investigating the absolute phase-dependent extreme nonlinear optics, and the evolutions of the absolute phase and the temporal-pulse phase of few-cycle laser pulses.
基金supported by the National Natural Science Foundation of China (Grant Nos 60408008 and 10774153)the Natural Science Key Foundation of Shanghai (Grant No 04JC14036)+1 种基金the National Basic Research Program of China (Grant No 2006CD806000)the Rising Star Program of Shanghai,China (Grant No 08QH1402400)
文摘The asymmetric photoionization of atoms irradiated by intense, few-cycle laser pulses is studied numerically. The results show that the pulse intensity affects the asymmetric photoionization in three aspects. First, at higher intensities, the asymmetry becomes distinctive for few-cycle pulses of longer durations. Second, as the laser intensity increases, the maximal asymmetry first decreases then increases after it has reached a minimal value. Last, the value of the carrier-envelope phase corresponding to the maximal asymmetry varies with the pulse intensity. This study reveals that the increasing of pulse intensity is helpful for observing the asymmetric photoionization.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11204328,61221064,61078037,11127901,11134010,and 61205208)the National Basic Research Program of China(Grant No.2011CB808101)the Natural Science Foundation of Shanghai,China(Grant No.13ZR1414800)
文摘We numerically study the pulse compression approaches based on atomic or molecular gases in a hollow-core fiber.From the perspective of self-phase modulation(SPM), we give the extensive study of the SPM influence on a probe pulse with molecular phase modulation(MPM) effect. By comparing the two compression methods, we summarize their advantages and drawbacks to obtain the few-cycle pulses with micro- or millijoule energies. It is also shown that the double pump-probe approach can be used as a tunable dual-color source by adjusting the time delay between pump and probe pulses to proper values.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60776034)
文摘In the present paper we conduct a theoretical study of the thermal accumulation effect of a typical bipolar transistor caused by high power pulsed microwaves(HPMs),and investigate the thermal accumulation effect as a function of pulse repetition frequency(PRF) and duty cycle.A study of the damage mechanism of the device is carried out from the variation analysis of the distribution of the electric field and the current density.The result shows that the accumulation temperature increases with PRF increasing and the threshold for the transistor is about 2 kHz.The response of the peak temperature induced by the injected single pulses indicates that the falling time is much longer than the rising time.Adopting the fitting method,the relationship between the peak temperature and the time during the rising edge and that between the peak temperature and the time during the falling edge are obtained.Moreover,the accumulation temperature decreases with duty cycle increasing for a certain mean power.
基金Project partially supported by the National Natural Science Foundation of China(Grant Nos.61071032,61377063,and 61235006)
文摘In this article, we present a time-dependent model that enables us to describe the dynamic behavior of pulsed DC reactive sputtering and predict the film compositions of VOx prepared by this process. In this modeling, the average current J is replaced by a new parameter of Jeff. Meanwhile, the four species states of V, V2O3, VO2, and V2O5 in the vanadium oxide films are taken into consideration. Based on this work, the influences of the oxygen gas supply and the pulsed power parameters including the duty cycle and frequency on film compositions are discussed. The model suggests that the time to reach process equilibrium may vary substantially depending on these parameters. It is also indicated that the compositions of VOx films are quite sensitive to both the reactive gas supply and the duty cycle when the power supply works in pulse mode. The 'steady-state' balance values obtained by these simulations show excellent agreement with the experimental data, which indicates that the experimentally obtained dynamic behavior of the film composition can be explained by this time-dependent modeling for pulsed DC reactive sputtering process. Moreover, the computer simulation results indicate that the curves will essentially yield oscillations around the average value of the film compositions with lower pulse frequency.
基金supported by the National Natural Science Foundation of China(No.11472167)
文摘An improved constant volume cycle (CVC) model is developed to analyze the nozzle effects on the thrust and specific impulse of pulse detonation rocket engine (PDRE). Theoretically, this model shows that the thrust coefficient/specific impulse of PDRE is a function of the nozzle contraction/expansion ratio and the operating frequency. The relationship between the nozzle contraction ratio and the operation frequency is obtained by introducing the duty ratio, by which the key problem in the theoretical design can be solved. Therefore, the performance of PDRE can be accessed to guide the preliminary shape design of nozzle conveniently and quickly. The higher the operating frequency of PDRE is, the smaller the nozzle contraction ratio should be. Besides, the lower the ambient pressure is, the larger the expansion ratio of the nozzle should be. When the ambient pressure is 1.013 × 105 Pa, the optimal expansion ratio will be less than 2.26. When the ambient pressure is reduced to vacuum, the extremum of the optimal thrust coefficient is 2.236 9, and the extremum of the specific impulse is 321.01 s. The results of the improved model are verified by numerical simulation.
基金Supported by the National Natural Science Foundation of China(61271258)
文摘The problem of optimal periodic pulse jamming design for a quadrature phase shift keying(QPSK)communication system is investigated.First a closed-form bit-error-rate(BER)of QPSK system under the jamming of pulse signal is derived.Then the asymptotic performance of the derived BER is analyzed as the signal-to-noise ratio(SNR)grows to infinity.In order to maximize the BER of the QPSK system,the optimal parameters of periodic pulse jamming signal,including the duty cycle and signal-tojamming power ratio(SJR),are found out.Numerical results are presented to verify our analytical results and the optimality of our design.
基金Supported by the National Natural Science Foundation of China under Grant Nos 61475139 and 11174249the National HighTechnology Research and Development of China under Grant No 2011AA060504the Fundamental Research Funds for the Central Universities under Grant No 2014FZA3002
文摘An exact analytic expression for an ultrashort hollow-Airy wave packet is presented beyond the slowly varying envelope approximation. The hollow-Airy wave packet combines the hollow-Gaussian beam in the spatial domain and the Airy pulse in the temporal domain. The spatiotemporal propagation dynamics of the ultrashort hollow- Airy pulse are analyzed by the numerical simulations. During the propagation in free space, the spatial intensity profile evolves from hollow-Gaussian to Gaussian shape; the temporal intensity profile retains Airy shape over several Rayleigh ranges. The acceleration property of the ultrashort Airy pulse is also demonstrated.
基金Supported by the National Science Foundation of China under Grant No 60408008, the Natural Science Key Foundation of Shanghai under Grant No 04JC14036, and the Shanghai Rising-Star Programme.
文摘By means of the numerical solution of time-dependent Schr6dinger equation, we verify a scaling law of photoionization in ultrashort pulses. We find that for a given carrier-envelope phase and duration of the pulse, identical photoionizations are obtained provided that when the central frequency of the pulse is enlarged by k times, the atomic binding potential is enlarged by k times, and the laser intensity is enlarged by ka times. The scaling law allows us to reach a significant control over direction of photoemission and offers exciting prospects of reaching similar physical processes in different interacting systems which constitutes a novel kind of coherent control.
基金Supported by the National Natural Science Foundation of China under Grant No 60578049, and the Major Basic Research Project of Shanghai Commission of Science and Technology under Grant No 04dz14001.
文摘We have experimentally demonstrated pulses 0.4 mJ in duration smaller than 12 fs with an excellent spatial beam profile by self-guided propagation in argon. The original 52 fs pulses from the chirped pulsed amplification laser system are first precompressed to 32 fs by inserting an acoustic optical programmable dispersive filter instrument into the laser system for spectrum reshaping and dispersion compensation, and the pulse spectrum is subsequently broadened by filamentation in an argon cell. By using chirped mirrors for post-dispersion compensation, the pulses are successfully compressed to smaller than 12 fs.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10734080,11074263,60978013,60921004,and 10874194)the Doctor Fund of Henan Polytechnic University (Grant No. B2011-076)
文摘We theoretically investigate the high-order harmonic generation from the hydrogen atom driven by the laser pulses with the durations less than the optical cycle. It is found that the switching term of the laser field may have an obvious influence on the cutoff, intensity or plateau structure of the high-order harmonic spectrum. Generally speaking, the switching term can shorten the cutoff of the high-order harmonic spectrum for a relatively longer pulse and extend the cutoff for a relatively shorter pulse.