强场作用下氦离子高次谐波发射及孤立阿秒脉冲的产生
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摘要
本论文在单电子近似下,利用二阶分裂算符方法数值求解了激光场与He~+离子相互作用的含时Schr(o|¨)dinger方程。深入细致地研究了在组合激光场作用下的一维模型He~+离子的高次谐波发射及孤立阿秒脉冲的产生,提出了三种既能增强谐波转换效率又能产生超宽远紫外连续谱以及获得脉宽较短孤立阿秒脉冲的有效方案,并分析了谐波增强、超宽远紫外连续谱形成及孤立阿秒脉冲产生的物理机理。
本论文研究工作主要由以下三部分组成:
第一部分,理论研究了模型He~+离子在双色场作用下的高次谐波发射。数值结果表明:在初态为基态和第一激发态的等权相干叠加态时,不仅实现了谐波截止的有效扩展,而且谐波的发射效率得到了大幅度地提高。另外,高次谐波平台显示一个超宽的远紫外连续谱,对一些级次的连续谐波进行叠加,就会直接产生一个宽度为47 as的超强孤立阿秒脉冲,与单色基频脉冲作用于基态He~+离子获得的阿秒脉冲相比,强度提高了5个量级以上。此外,通过半经典三步模型和小波时频分析方法,我们分析了结果,给出了物理解释。
第二部分,提出一种直接得到脉宽超短单个阿秒脉冲的有效方案。利用一个双色激光与一个超短xuv阿秒脉冲的组合场作用于模型He~+离子,通过选取两个不同的相对时间延迟,不但得到了效率较高的谐波发射,而且实现了单一量子轨道的控制,并且高能区的谐波谱显示出超宽远紫外连续特性。特别是在实现长量子轨道控制以后,对超宽连续谱上的一段进行滤波就可以直接得到宽度为39 as的超短孤立阿秒脉冲。然而,值得一提的是,在该方案中,xuv脉冲附加到合成的双色场能够大幅度提高连续谐波的转换效率,这对产生一个超强的孤立阿秒脉冲是非常有利的,对此我们做了分析,并给出了详细的物理解释。
第三部分,提出一种产生强100 as以下的单个阿秒脉冲的有效方法。利用在中红外激光脉冲上附加一个xuv脉冲作为驱动源,研究了模型He~+离子的高次谐波发射。通过调节两个脉冲之间的相对时间延迟,实现了单一量子轨道的有效选取,并且产生谐波转化效率较高的超连续谱。特别是通过抑制电子的短轨道而加强电子的长轨道对谐波的贡献,得到了脉宽为81 as的单个阿秒脉冲。此外,在两种相对时间延迟情况下,对超宽连续谱上不同频率范围但具有相同带宽的谐波谱进行叠加,得到了中心波长可调谐的、脉宽低于100 as的单个阿秒脉冲。
When matter such as atoms or molecules is subject to a high-intense laser pulse, the electronic response is highly nonlinear. As a result of this, a coherent wave whose frequency is an integral multiple of that of the incident laser field is radiated, which is known as high-order harmonic generation (HHG). Since the HHG covers the spectral range from the infrared to xuv and even to soft x-rays regions, it is fast becoming a candidate for breaking through femtosecond limit and realizing attosecond pulse generation. Currently, the HHG is the most promising way to generate attosecond (as) pulses in experiment. Almost all harmonic spectra experimently and theoretically show a common characteristic: the harmonic intensities decrease rapidly for the few low orders, then the intensities keep almost constant for many orders to form a broad plateau, and finally the intensity drops sharply at the highest harmonic orders, which is named the cutoff. The physical picture of the HHG process can be well understood by the semiclassical three-step model and the fully quantum theory. According to the three-step model, the electron first tunnels through the effective barrier formed by the atomic potential and the laser field, then it oscillates almost freely in the laser field and gains additional kinetic energy, and finally when the laser field reverses its direction, it may recombine with the parent ion and emit a harmonic photon with energy up to I_p+3.17U_p, where I_p is the atomic ionization potential and U_p is the ponderomotive energy. The above process is repeated every half an optical cycle of the driving laser field, which leads to the generaton of an attosecond pulse train with a periodicity of half an optical cycle. However, the generation of a single attosecond pulse can play a very important role in practical application, because it enables the researches of the ultrafast sciences to enter into a drastically new regime, where it is possible for people to trace the movement of the electrons and observe the electronic relaxation processes inside atoms and molecules, etc. Hence, how to produce an isolated attosecond pulse has attracted a lot of attention. The classical and quantum theory have shown that there are two dominant quantum paths to each harmonic emission, one path with earlier ionization time but later emission time is called the long path and the other path with later ionization time but earlier emission time is called the short path. In the classical picture of the HHG, for the harmonics in the plateau, since each harmonic originates from two different electronic paths with different emission times in each half optical cycle of the fundamental laser, the plateau harmonics are not emitted at the same time, thereby, the superposition of several harmonics results in an irregular as pulse train (APT) including the two bursts in every half optical cycle. For the harmonics in the cutoff region, since the emission times of the long and short paths are almost the same, the cutoff harmonics are emitted in phase, therefore, the superposition of several
harmonics results in the generation of an isolated as pulse in every one optical cycle. Though an isolated and clean as pulse can be created by filtering several continuous harmonics in the cutoff, it is very difficult to obtain an isolated as pulse with a duration shorter than 100 as due to the limitation of the continuous spectrum width. In order to obtain a single as pulse with much shorter pulse duration, the bandwidth of much broader supercontinuous harmonics is acquired strongly. Recently, a lot of schemes have been theoretically proposed to broaden the bandwidth and reduce the pulse duration. For the single-atom response, the control of quantum path is an efficient method to generate an isolated as pulse. Its main idea is by means of waveform control of laser pulse to further control the quantum paths of the electrons, thus the continuous harmonics are mainly attributed to the contribution of one dominating electron path. Once a single quantum path is selected, in terms of the harmonic synthesis technique, an isolated as pulse is producted by superposing some properly selected harmonics in the supercontinuum.
In this thesis, based on the single-active electron approximation, we numerically solve the 1D time-dependent Schr?dinger equation (TDSE) for interacting the intense laser with He~+ ion with the help of the two-order splitting-operator fast-Fourier transform technique. By the numerical approach, we investigate the high-order harmonic emission and an isolated as pulse generation from He~+ ion in the combined laser field and put forward three kinds of methods of not only enhancing the harmonics conversion efficiency and generating an ultrabroad extreme ultraviolet (xuv) supercontinuum, but also obtaining an isolated as pulse with short pulse duration. We also analyse the results and give some reasonable explanation. The main work of this thesis is composed of three parts:
In the first part, we theoretically investigate that the high-order harmonic generation when a helium ion is subject to a two-color laser field. It is shown that when the initial state is prepared as a coherent superposition of the ground and the first excited states, not only the conversion efficiency of the harmonics is enhanced significantly and an ultrabroad xuv supercontinuum is generated, but also the cutoff energy is extended effectively. In our simulation, we find that the contribution from the long path can be suppressed, wherease the contribution from the short path can be enhanced. Then by superposing some properly selected harmonic orders, an intense isolated 47 as pulse is generated successfully. Compared with the case of the ground state in a one-color field, the intensity of this isolated as pulse is 5 orders of magnitude higher. It is noteworthy that the two-color scheme presents several unique characteristics. First, when the relative phaseφbetween two laser pulses changes from 0 to 0.45π, we can still obtain an isolated sub-50 as pulse by superposing proper continuous harmonics. Second, the duration of the 2400 nm laser pulse in this scheme has little effect on our simulation results (e.g., from 10 to 64 fs). Third, the population of the first excited state is not stringent; a little more or less population than 0.5 will not result in obvious changes of the HHG and as pulses generation. The fascinating characteristics above make one more easily manipulate our scheme in practical experimental implementations. What is more important, this scheme overcomes a limitation of generating a broad frequence bandwidth and can produce an ultrabroad xuv supercontinuum, which is in favour of the generation of a short and intense isolated as pulse.
In the second part, we theoretically present an efficient method to generate an isolated short as pulse in the combination of a synthesized two-color field and an xuv as pulse. We also show that the selection of a specific quantum path can be realized by using an xuv pulse with different central energy at a proper time. Concretely, by adding a 0.5-fs, 62.3-nm xuv pulse to the synthesized two-color field atω_0τ_(delay)=-0.9π, the harmonic intensity is effectively enhanced and an ultrabroad xuv supercontinuum can be formed compared with the two-color case. In addition, the short path is selected to effectively contribute to the HHG, then an isolated 40 as pulse is generated directly by filtering out harmonics from 265th to 325th. Furthermore, by adding a 0.5-fs, 29.6-nm xuv pulse to the synthesized two-color field atω_0τ_(delay)=-1.22π, both the enhancement of the HHG and the generattion of a broadband continuous harmonic spectrum can be observed, and the long path is selected, then an isolated 39 as pulse is obtained straightforwardly by superposing harmonics from 265th to 325th. Specifically, in our two schemes, the enhancement of the harmonics in the supercontinuum region is much more efficient. Since the xuv pulse holds the high photon energy and the extremely short pulse duration, the production time and property of the electron wave packet (EWP) can be operated. As a result, the ionization yields of the electrons with a specific quantum path can be increased, i.e., one of two quantum paths (long and short) is selected to effectively contribute to the HHG. It should be emphasized that, in our schemes, increasing the duration of the 1200 nm laser pulse up to 64 fs or keeping the wavelength of the subharmonic laser pulse in the region of 1160-1240 nm, we find that the results have little change. In our numerical simulation, we select the laser parameters achievable in the current laboratory. Therefore, the schemes presented here are feasible for an experimental demonstration in the near future. The importance we think is that our schemes can overcome the limitation of the low efficiency in the HHG emission and produce an ultrabroad xuv supercontinuum spectrum, which benefits to the generation of an intense short as pulse.
In the third part, we theoretically present an efficient method to generate an intense isolated as pulse. When a 0.9 fs, 29.6 nm xuv pulse is added to a 12.5 fs, 2000 nm mid-IR laser pulse at a different time delay, not only the enhancement of the HHG and the formation of an ultrabroad supercontinuum are observed, but also the selection of a single quantum path is achieved and an isolated sub-100 as pulse is obtained. By superposing the different harmonic ranges in continuum region, isolated sub-100 as pulses with extremely short and tunable central wavelengths can be generated, which may play an important role in controlling and studying the core-level dynamics inside atoms. In our schemes, the 2000 nm laser pulse can effectively extend the harmonic cutoff and generate energetic harmonics photons due to theλ2 scaling of Up; on the other hand, the conversion efficiency of the HHG is low, specially for the continuous harmonics in the cutoff region, this is owing to the increase of the spreading of the wave packets. However, the 29.6 nm xuv pulse holds the high photon energy and the extremely short pulse duration, it can promote electronic transition from the ground state to the second excited state for a He~+ system, thus the second excited state has a large electron population. Combining the advantages of both the long wavelength laser pulse and the xuv pulse, the ionization yields of the electrons corresponding to a single quantum path which contribute to the continuous harmonics can be significantly increased, then the efficiency of the continuous harmonics is higher. As a result, an intense isolated as pulse can be produced. Considering the practical application of this scheme, we take the laser parameters achievable in the current laboratory, which makes it feasible for one to carry out our scheme in practical experimental implementations.
本论文研究工作主要由以下三部分组成:
第一部分,理论研究了模型He~+离子在双色场作用下的高次谐波发射。数值结果表明:在初态为基态和第一激发态的等权相干叠加态时,不仅实现了谐波截止的有效扩展,而且谐波的发射效率得到了大幅度地提高。另外,高次谐波平台显示一个超宽的远紫外连续谱,对一些级次的连续谐波进行叠加,就会直接产生一个宽度为47 as的超强孤立阿秒脉冲,与单色基频脉冲作用于基态He~+离子获得的阿秒脉冲相比,强度提高了5个量级以上。此外,通过半经典三步模型和小波时频分析方法,我们分析了结果,给出了物理解释。
第二部分,提出一种直接得到脉宽超短单个阿秒脉冲的有效方案。利用一个双色激光与一个超短xuv阿秒脉冲的组合场作用于模型He~+离子,通过选取两个不同的相对时间延迟,不但得到了效率较高的谐波发射,而且实现了单一量子轨道的控制,并且高能区的谐波谱显示出超宽远紫外连续特性。特别是在实现长量子轨道控制以后,对超宽连续谱上的一段进行滤波就可以直接得到宽度为39 as的超短孤立阿秒脉冲。然而,值得一提的是,在该方案中,xuv脉冲附加到合成的双色场能够大幅度提高连续谐波的转换效率,这对产生一个超强的孤立阿秒脉冲是非常有利的,对此我们做了分析,并给出了详细的物理解释。
第三部分,提出一种产生强100 as以下的单个阿秒脉冲的有效方法。利用在中红外激光脉冲上附加一个xuv脉冲作为驱动源,研究了模型He~+离子的高次谐波发射。通过调节两个脉冲之间的相对时间延迟,实现了单一量子轨道的有效选取,并且产生谐波转化效率较高的超连续谱。特别是通过抑制电子的短轨道而加强电子的长轨道对谐波的贡献,得到了脉宽为81 as的单个阿秒脉冲。此外,在两种相对时间延迟情况下,对超宽连续谱上不同频率范围但具有相同带宽的谐波谱进行叠加,得到了中心波长可调谐的、脉宽低于100 as的单个阿秒脉冲。
When matter such as atoms or molecules is subject to a high-intense laser pulse, the electronic response is highly nonlinear. As a result of this, a coherent wave whose frequency is an integral multiple of that of the incident laser field is radiated, which is known as high-order harmonic generation (HHG). Since the HHG covers the spectral range from the infrared to xuv and even to soft x-rays regions, it is fast becoming a candidate for breaking through femtosecond limit and realizing attosecond pulse generation. Currently, the HHG is the most promising way to generate attosecond (as) pulses in experiment. Almost all harmonic spectra experimently and theoretically show a common characteristic: the harmonic intensities decrease rapidly for the few low orders, then the intensities keep almost constant for many orders to form a broad plateau, and finally the intensity drops sharply at the highest harmonic orders, which is named the cutoff. The physical picture of the HHG process can be well understood by the semiclassical three-step model and the fully quantum theory. According to the three-step model, the electron first tunnels through the effective barrier formed by the atomic potential and the laser field, then it oscillates almost freely in the laser field and gains additional kinetic energy, and finally when the laser field reverses its direction, it may recombine with the parent ion and emit a harmonic photon with energy up to I_p+3.17U_p, where I_p is the atomic ionization potential and U_p is the ponderomotive energy. The above process is repeated every half an optical cycle of the driving laser field, which leads to the generaton of an attosecond pulse train with a periodicity of half an optical cycle. However, the generation of a single attosecond pulse can play a very important role in practical application, because it enables the researches of the ultrafast sciences to enter into a drastically new regime, where it is possible for people to trace the movement of the electrons and observe the electronic relaxation processes inside atoms and molecules, etc. Hence, how to produce an isolated attosecond pulse has attracted a lot of attention. The classical and quantum theory have shown that there are two dominant quantum paths to each harmonic emission, one path with earlier ionization time but later emission time is called the long path and the other path with later ionization time but earlier emission time is called the short path. In the classical picture of the HHG, for the harmonics in the plateau, since each harmonic originates from two different electronic paths with different emission times in each half optical cycle of the fundamental laser, the plateau harmonics are not emitted at the same time, thereby, the superposition of several harmonics results in an irregular as pulse train (APT) including the two bursts in every half optical cycle. For the harmonics in the cutoff region, since the emission times of the long and short paths are almost the same, the cutoff harmonics are emitted in phase, therefore, the superposition of several
harmonics results in the generation of an isolated as pulse in every one optical cycle. Though an isolated and clean as pulse can be created by filtering several continuous harmonics in the cutoff, it is very difficult to obtain an isolated as pulse with a duration shorter than 100 as due to the limitation of the continuous spectrum width. In order to obtain a single as pulse with much shorter pulse duration, the bandwidth of much broader supercontinuous harmonics is acquired strongly. Recently, a lot of schemes have been theoretically proposed to broaden the bandwidth and reduce the pulse duration. For the single-atom response, the control of quantum path is an efficient method to generate an isolated as pulse. Its main idea is by means of waveform control of laser pulse to further control the quantum paths of the electrons, thus the continuous harmonics are mainly attributed to the contribution of one dominating electron path. Once a single quantum path is selected, in terms of the harmonic synthesis technique, an isolated as pulse is producted by superposing some properly selected harmonics in the supercontinuum.
In this thesis, based on the single-active electron approximation, we numerically solve the 1D time-dependent Schr?dinger equation (TDSE) for interacting the intense laser with He~+ ion with the help of the two-order splitting-operator fast-Fourier transform technique. By the numerical approach, we investigate the high-order harmonic emission and an isolated as pulse generation from He~+ ion in the combined laser field and put forward three kinds of methods of not only enhancing the harmonics conversion efficiency and generating an ultrabroad extreme ultraviolet (xuv) supercontinuum, but also obtaining an isolated as pulse with short pulse duration. We also analyse the results and give some reasonable explanation. The main work of this thesis is composed of three parts:
In the first part, we theoretically investigate that the high-order harmonic generation when a helium ion is subject to a two-color laser field. It is shown that when the initial state is prepared as a coherent superposition of the ground and the first excited states, not only the conversion efficiency of the harmonics is enhanced significantly and an ultrabroad xuv supercontinuum is generated, but also the cutoff energy is extended effectively. In our simulation, we find that the contribution from the long path can be suppressed, wherease the contribution from the short path can be enhanced. Then by superposing some properly selected harmonic orders, an intense isolated 47 as pulse is generated successfully. Compared with the case of the ground state in a one-color field, the intensity of this isolated as pulse is 5 orders of magnitude higher. It is noteworthy that the two-color scheme presents several unique characteristics. First, when the relative phaseφbetween two laser pulses changes from 0 to 0.45π, we can still obtain an isolated sub-50 as pulse by superposing proper continuous harmonics. Second, the duration of the 2400 nm laser pulse in this scheme has little effect on our simulation results (e.g., from 10 to 64 fs). Third, the population of the first excited state is not stringent; a little more or less population than 0.5 will not result in obvious changes of the HHG and as pulses generation. The fascinating characteristics above make one more easily manipulate our scheme in practical experimental implementations. What is more important, this scheme overcomes a limitation of generating a broad frequence bandwidth and can produce an ultrabroad xuv supercontinuum, which is in favour of the generation of a short and intense isolated as pulse.
In the second part, we theoretically present an efficient method to generate an isolated short as pulse in the combination of a synthesized two-color field and an xuv as pulse. We also show that the selection of a specific quantum path can be realized by using an xuv pulse with different central energy at a proper time. Concretely, by adding a 0.5-fs, 62.3-nm xuv pulse to the synthesized two-color field atω_0τ_(delay)=-0.9π, the harmonic intensity is effectively enhanced and an ultrabroad xuv supercontinuum can be formed compared with the two-color case. In addition, the short path is selected to effectively contribute to the HHG, then an isolated 40 as pulse is generated directly by filtering out harmonics from 265th to 325th. Furthermore, by adding a 0.5-fs, 29.6-nm xuv pulse to the synthesized two-color field atω_0τ_(delay)=-1.22π, both the enhancement of the HHG and the generattion of a broadband continuous harmonic spectrum can be observed, and the long path is selected, then an isolated 39 as pulse is obtained straightforwardly by superposing harmonics from 265th to 325th. Specifically, in our two schemes, the enhancement of the harmonics in the supercontinuum region is much more efficient. Since the xuv pulse holds the high photon energy and the extremely short pulse duration, the production time and property of the electron wave packet (EWP) can be operated. As a result, the ionization yields of the electrons with a specific quantum path can be increased, i.e., one of two quantum paths (long and short) is selected to effectively contribute to the HHG. It should be emphasized that, in our schemes, increasing the duration of the 1200 nm laser pulse up to 64 fs or keeping the wavelength of the subharmonic laser pulse in the region of 1160-1240 nm, we find that the results have little change. In our numerical simulation, we select the laser parameters achievable in the current laboratory. Therefore, the schemes presented here are feasible for an experimental demonstration in the near future. The importance we think is that our schemes can overcome the limitation of the low efficiency in the HHG emission and produce an ultrabroad xuv supercontinuum spectrum, which benefits to the generation of an intense short as pulse.
In the third part, we theoretically present an efficient method to generate an intense isolated as pulse. When a 0.9 fs, 29.6 nm xuv pulse is added to a 12.5 fs, 2000 nm mid-IR laser pulse at a different time delay, not only the enhancement of the HHG and the formation of an ultrabroad supercontinuum are observed, but also the selection of a single quantum path is achieved and an isolated sub-100 as pulse is obtained. By superposing the different harmonic ranges in continuum region, isolated sub-100 as pulses with extremely short and tunable central wavelengths can be generated, which may play an important role in controlling and studying the core-level dynamics inside atoms. In our schemes, the 2000 nm laser pulse can effectively extend the harmonic cutoff and generate energetic harmonics photons due to theλ2 scaling of Up; on the other hand, the conversion efficiency of the HHG is low, specially for the continuous harmonics in the cutoff region, this is owing to the increase of the spreading of the wave packets. However, the 29.6 nm xuv pulse holds the high photon energy and the extremely short pulse duration, it can promote electronic transition from the ground state to the second excited state for a He~+ system, thus the second excited state has a large electron population. Combining the advantages of both the long wavelength laser pulse and the xuv pulse, the ionization yields of the electrons corresponding to a single quantum path which contribute to the continuous harmonics can be significantly increased, then the efficiency of the continuous harmonics is higher. As a result, an intense isolated as pulse can be produced. Considering the practical application of this scheme, we take the laser parameters achievable in the current laboratory, which makes it feasible for one to carry out our scheme in practical experimental implementations.
引文
[1] LOMPRéL A, MAINFRAY G, MANUS C, THEBAULT J. Multiphoton ionization of rare gases by a tunable-wavelength 30-psec laser pulse at 1.06μm [J]. Phys. Rev. A, 1977, 15: 1604-1012.
[2] KULANDER K C. Multiphoton ionization of hydrogen: a time-dependent theory [J]. Phys. Rev. A, 1987, 35: 445-447.
[3] PERRY M D, LANDEN O L, SZ?KE A, CAMPBELL E M. Multiphoton ionization of the noble gases by an intense 1014 W/cm2 dye laser [J]. Phys. Rev. A, 1988, 37: 747-760.
[4] PROTOPAPAS M, KEITEL C H, KNIGHT P L. Atomic physics with super-high intensity lasers [J]. Rep. Prog. Phys., 1997, 60: 389-486.
[5] YERGEAU F, PETITE G, AGOSTINI P. Above-threshold ionisation without space charge [J]. J. Phys. B, 1986, 19: L663-L669.
[6] CORKUM P B, BURNET N H, BRUNEL F. Above-threshold ionization in the long-wavelength limit [J]. Phys. Rev. Lett., 1989, 62: 1259-1262.
[7] MILO?EVI? D B, PAULUS G G, BAUER D, BECKER W. Above-threshold ionization by few-cycle pulses [J]. J. Phys. B, 2006, 39: R203-R262.
[8] AUGST S, STRICKLAND D, MEYERHOFER D D, et al. Tunneling ionization of noble gases in a high-intensity laser field [J]. Phys. Rev. Lett., 1989, 63: 2212-2215.
[9] GIBSON G, LUK T S, RHODES C K. Tunneling ionization in the multiphoton regime [J]. Phys. Rev. A, 1990, 41: 5049-5052.
[10] BREWCZYK M, RZA?EWSKI K. Over-the-barrier ionization of multielectron atoms by intense vuv free-electron laser [J]. J. Phys. B, 1999, 32: L1-L4.
[11] EBERLY J H, SU Q, JAVANAINEN J. High-order harmonic production in multiphoton ionization [J]. J. Opt. Soc. Am. B, 1989, 6: 1289-1298.
[12] MAINFRAY G, MANUS C. Multiphoton ionization of atoms [J]. Rep. Prog. Phys., 1991, 54: 1333-1372.
[13]陈秀娥.超短脉冲激光器原理及应用[M].北京:科学出版社, 1991.
[14] AGOSTINI P, DIMAURO L F. The physics of attosecond light pulses [J]. Rep. Prog. Phys., 2004, 67: 813–855.
[15] FERRAY M, LOMPRéL A, GOBERT O, et al. Multiterawatt picosecond Nd-glass laser system at 1053 nm [J]. Opt. Commun., 1990, 75: 278-282.
[16] KELDYSH L V. Ionization in the field of a strong electromagnetic wave [J]. Sov. Phys. JETP, 1965, 20: 1307-1314.
[17] CHU S I, COOPER J. Threshold shift and above-threshold multiphoton ionization of atomic hydrogen in intense laser fields [J]. Phys. Rev. A, 1985, 32: 2769-2775.
[18] FABRE F, PETITE G, AGOSTINI P, CLEMENT M. Multiphoton above-threshold ionisation of xenon at 0.53 and 1.06 pm [J]. J. Phys. B, 1982, 15: 1353-1369.
[19] PETITE G, FABRE F, AGOSTINI P. Nonresonant multiphoton ionization of cesium in strong fields: angular distributions and above-threshold ionization [J]. Phys. Rev. A, 1984, 29: 2677-2689.
[20] AGOSTINI P, FABRE F, MAINFRAY G, et al. Free-free transition following six-photo ionization of xenon atoms [J]. Phys. Rev. Lett., 1979, 42: 1127-1130.
[21] GONTIER Y, TRAHIN M. Energetic electron generation by multiphoton absorption [J]. J. Phys. B, 1980, 13: 4383-4390.
[22] AMMOSOV M V, DELONE N B, KRAINOV V P. Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field [J]. Sov. Phys. JETP, 1986, 64: 1191-1194.
[23] RASHID S. Approximate solution of the hydrogenlike atoms in intense laser radiation [J]. Phys. Rev. A, 1989, 40: 4242-4244.
[24] SHORE B W, KNIGHT P L. Enhancement of high optical harmonics by excess-photon ionization [J]. J. Phys. B, 1987, 20: 413-423.
[25] MCPHERSON A, GIBSON G, JARA H, et al. Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases [J]. J. Opt. Soc. Am B, 1987, 4: 595-601.
[26] FERRAY M, L’HUILLIER A, LI X F, et al. Multiple-harmonic conversion of 1064 nm radiation in rare gases [J]. J. Phys. B, 1988, 21 : L31-L35.
[27] LI X F, L’HUILLIER A, FERRAY L A, et al. Multiple-harmonic generation in rare gases at high laser intensity [J]. Phys. Rev. A, 1989, 39: 5751-5761.
[28] L’HUILLIER A, BALCOU P. High-order harmonic generation in rare gases with a 1-ps 1053-nm laser [J]. Phys. Rev. Lett., 1993, 70: 774-777.
[29] SARUKURA N, HATA K, ADACHI T, NODOMI R. Coherent soft x-ray generation by the harmonics of an ultrahigh-power KrF laser [J]. Phys. Rev. A, 1991, 43: 1669-1672.
[30] MIYAZAKI K, SAKAI H. High-order harmonic generation in rare gases with intense subpicosecond dye laser pulses [J]. J. Phys. B, 1992, 25: L83-L89.
[31] BALCOU P, CORNAGGIA C, GOMES A S L, et al. Optimizing high-order harmonic generation in strong fields [J]. J. Phys. B, 1992, 25: 4467-4485.
[32] MACKLIN J J, KMETEC J D, GORDON III C L. High-order harmonic generation using intense femtosecond pulses [J]. Phys. Rev. A, 1993, 70: 766-769.
[33] PERRY M D, CRANE J K. High-order harmonic emission from mixed fields [J]. Phys. Rev. A, 1993, 48: R4051-R4054.
[34] WATANABE S, KONDO K, NABEKAWA Y, et al. Two-color phase control in tunneling ionization and harmonic generation by a strong laser field and its third harmonic [J]. Phys. Rev. Lett., 1994, 73: 2692–2695.
[35] MIYAZAKI K, TAKADA H. High-order harmonic generation in the tunneling regime [J]. Phys. Rev. A, 1995, 52: 3007-3021.
[36] DITMIRE T, CRANE J K, NGUYEN H, et al. Energy-yield and conversion-efficiency measurements of high-order harmonic radiation [J]. Phys. Rev. A, 1995, 51: R902-R905.
[37] PEATROSS J, MEYERHOFER D D. Intensity-dependent atomic-phase effects in high-order harmonic generation [J]. Phys. Rev. A, 1995, 52: 3976-3987.
[38] PRESTON S G, SANPERA A, ZEPF M, et al. High-order harmonics of 248.6-nm KrF laser from helium and neon ions [J]. Phys. Rev. A, 1996, 53: R31-R34.
[39] ZHOU J, PEATROSS J, MURNANE M M, KAPTEYN H C. Enhanced high-harmonic generation using 25 fs laser pulses [J]. Phys. Rev. Lett., 1996, 76: 752-755.
[40] CHANG Z H, RUNDQUIST A, WANG H W, et al. Generation of coherent soft x rays at 2.7 nm using high harmonics [J]. Phys. Rev. Lett., 1997, 79: 2967-2970.
[41] SCHNüRER M, SPIELMANN C, WOBRAUSCHEK P, et al. Coherent 0.5-keV x-ray emission from helium driven by a sub-10-fs laser [J]. Phys. Rev. Lett., 1998, 80: 3236-3239.
[42] RUNDQUIST A, DURFEE III C G, CHANG Z H, et al. Phase-matched generation of coherent soft x-rays [J]. Science, 1998, 280: 1412-1415.
[43] LANGE H R, CHIRON A, RIPOCHE J F, et al. High-order generation and quasiphase matching in xenon using self-guided femtosecond pulses [J]. Phys.Rev.Lett., 1998, 81: 1611-1613.
[44] NORREYS P A, ZEPF M, MOUSTAIZIS S, et al. Efficient extreme uv harmonics generated from picosecond laser pulse interactions with solid targets [J]. Phys, Rev. Lett., 1996, 76: 1832-1835.
[45] GIBSON E A, PAUL A, WAGNER N, TOBEY R, et al. Coherent soft x-ray generation in the water window with quasi-phase matching [J]. Science, 2003, 302: 95-98.
[46] SERES J, YAKOVLEV V S, SERES E, et al. Coherent superposition of laser-driven soft-x-ray harmonics from successive sources [J]. Nat. Phys., 2007, 11: 878-883.
[47] CORKUM P B. Plasma perspective on strong-field multiphoto ionization [J]. Phys. Rev. Lett., 1993, 71: 1994-1997.
[48] WINTERFELDT C, SPIELMANN C, GERBER G. Colloquium: optimal control of high-harmonic generation [J]. Rev. Mod. Phys., 2008, 80: 117-140.
[49] KULANDER K C, SHORE B W. Calculations of multiple-harmonic conversion of 1064-nm radiation in Xe [J]. Phys. Rev. Lett., 1989, 62: 524-526.
[50] KRAUSE J L, SCHAFER K J, KULANDER K C. High-order harmonic generation from atoms and ions in the high intensity regime [J]. Phys. Rev. Lett., 1992, 68: 3535-3538.
[51] LEWENSTEIN M, BALCOU P, IVANOV M Y, et al. Theory of high-harmonic generation by low-frequency laser fields [J]. Phy. Rev. A, 1994, 49: 2117-2132.
[52] ANTOINE P, L’HUILLIER A, LEWENSTEIN M. Attosecond pulse trains using high-order harmonics [J]. Phys. Rev. Lett., 1996, 77: 1234-1237.
[53] CHRISTOV I P, MURNANE M M, KAPTEYN H C. High-harmonic generation of attosecond pulses in the single-cycle regime [J]. Phys. Rev. Lett., 1997, 78: 1251-1254.
[54] PAUL P M, TOMA E S, BREGER P, et al. Observation of a train of attosecond pulses from high harmonic generation [J]. Science, 2001, 292: 1689-1692.
[55] GOULIELMAKIS E, SCHULTZE M, HOFSTETTER M, et al. Single-cycle nonlinear optics[J]. Science, 2008, 320: 1614-1617.
[56] DRESCHER M, HENTSCHEL M, KIENBERGER R, et al. X-ray pulses approaching the attosecond frontier [J]. Science, 2001, 291: 1923-1927.
[57] MAIRESSE Y, DE BOHAN A, FRASINSKI L J, et al. Attosecond synchronization of high-harmonic soft x-rays [J]. Science, 2003, 302: 1540-1543.
[58] SPIELMANN C, BURNETT N H, SARTANIA S, et al. Generation of coherent x-rays in the water window using 5-femtosecond laser pulses [J]. Science, 1997, 278: 661-664.
[59] LEE K, CHA Y H, SHIN M S, et al. Relativistic nonlinear thomson scattering as attosecond x-ray source [J]. Phys. Rev. E, 2003, 67: 026502.
[60] SOKOLOV A V, WALKER D R, YAVUZ D D, et al. Raman generation by phased and antiphased molecular states [J]. Phys. Rev. Lett., 2000, 85: 562-565.
[61] HENTSCHEL M, KIENBERGER R, SPIELMANN C, et al. Attosecond metrology [J]. Nature, 2001, 414: 509-513.
[62] CORKUM P B, BURNETT N H, IVANOV M Y. Subfemtosecond pulses [J]. Opt. Lett., 1994, 19: 1870-1872.
[63] SANSONE G, BENEDETTI E, CALEGARI F, et al. Isolated single-cycle attosecond pulses [J]. Science, 2006,314: 443-446.
[64] CAVALIERIL A L, GOULIELMAKIS E, HORVATH B, et al. Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua [J]. New J. Phys., 2007, 9: 242.
[65] PFEIFER T, GALLMANN L, ABEL M J, et al. Single attosecond pulse generation in the multicycle-driver regime by adding a weak second-harmonic field [J]. Opt. Lett., 2006, 31: 975-977.
[66] ZENG Z Z, CHENG Y, SONG X H, et al. Generation of an extreme ultraviolet superconuum in a two-color laser fields [J]. Phys. Rev. Lett., 2007, 98: 203901.
[67] ZHAI Z, LIU X S, Extension of the high-order harmonics and an isolated sub-100 as pulse generation in a two-colour laser field [J]. J. Phys. B, 2008, 41: 25602.
[68] ZHAI Z, Yu R F, LIU X S, Yang Y J. Enhancement of high-order harmonic emission and intense sub-50-as pulse generation [J]. Phys. Rev. A, 2008, 78: 041402(R).
[69] HONG W Y, LI Y H, LU P X, et al. Control of quantum paths in the multicycle regime and efficient broadband attosecond pulse generation [J]. J. Opt. Soc. Am. B, 2008, 25: 1684-1689.
[70] LI P C, ZHOU X X, WANG G L, ZHAO Z X. Isolated sub-30-as pulse generation of an He+ ion by an intense few-cycle chirped laser and its high-order harmonic pulses [J]. Phys. Rev. A, 2009, 80: 05382.
[71] YAO J P, LI Y, ZENG B, et al. Generation of an xuv supercontinuum by optimization of the angle between polarization planes of two linearly polarized pulses in a multicycle two-color laser field [J]. Phys. Rev. A, 2010, 82: 023826.
[72] CHEN J G, ZENG S L, YANG Y J. Generation of isolated sub-50-as pulses by quantum path control in the multicycle regime [J]. Phys. Rev. A, 2010, 82: 043401.
[73] CHEN J G, YANG Y J, ZENG S L, LIANG H Q. Generation of intense isolated sub-40-as pulses from a coherent superposition state by quantum path control in the multicycle regime [J]. Phys. Rev. A, 2011, 83: 023401.
[74] SCHAFER K J, GAARDE M B, HEINRICH A. Strong field quantum path control using attosecond pulse trains [J]. Phys. Rev. Lett., 2004, 92: 023003.
[75] BANDRAUK A D, NGUYEN H S. Attosecond control of ionization and high-order harmonic generation in molecules [J]. Phys. Rev. A, 2002, 66: 031401(R).
[76] BANDRAUK A D, CHELKOWSKI S, NGUYEN H S. Controlling continuum harmonic generation with attosecond pulses [J]. Appl. Phys. B, 2003, 77: 337–342.
[77] LAN P F, LU P X, CAO W, WANG X L. Efficient generation of an isolated single-cycle attosecond pulse [J]. Phys. Rev. A, 2007, 76: 043808.
[78] ZHAO S F, ZHOU X X, LI P C, CHEN Z J. Isolated short attosecond pulse produced by using an intense few-cycle shaped laser and an ultraviolet attosecond pulse [J]. Phys. Rev. A, 2008, 78: 063404.
[79] OD?AK S, MILO?EVI? D B. Attosecond pulse generation by a coplanar circular and static field combination [J]. Phys. Lett. A, 2006, 355: 368-372.
[80] HONG W Y, LU P X, CAO W, et al. Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field [J]. J. Phys. B, 2007, 40: 2321–2331.
[81] HONG W Y, LU P X, LAN P F, et al. Broadband xuv supercontinuum generation via controlling quantum paths by a low-frequency field [J]. Phys. Rev. A, 2008, 77: 033410.
[82] HONG W Y, LU P X, LAN P F, et al. Few-cycle attosecond pulses with stabilized- carrier-envelope phase in the presence of a strong terahertz field [J]. Opt. Express, 2009, 17: 5139-5146.
[83] XIANG Y, NIU Y P, GONG S Q. Control of the high-order harmonics cutoff through the combination of a chirped laser and static electric field [J]. Phys. Rev. A, 2009, 79: 053419.
[84] CAO W, LU P X, LAN P F, et al. Control of quantum paths in high-order harmonic generation via aω+3ωbichromatic laser field [J]. J. Phy. B, 2007, 40: 869-875.
[85] YU Y L, SONG X H, FU Y X, et al. Theoretical investigation of single attosecond pulse generation in an orthogonally polarized two-color laser field [J]. Opt. Express, 2008, 16: 686-694.
[86] KIM C M, KIM I J, NAM C H. Generation of a strong attosecond pulse train with an orthogonally polarized two-color laser field [J]. Phys. Rev. A, 2005, 72: 033817.
[87] KIM C M, NAM C H. Selection of an electron path of high-order harmonic generation in two-colour femtosecond laser field [J]. J. Phys. B, 2006, 39: 3199-3209.
[88] HONG W Y, LU P X, LAN P F, et al. Method to generate directly a broadband isolated attosecond pulse with stable pulse duration and high signal-to-noise ratio [J]. Phys. Rev. A, 2009, 78: 063407.
[89] YU Y L, XU J J, FU Y X, et al. Single attosecond pulse generation from aligned molecules using two-color polarization gating [J]. Phys. Rev. A, 2009, 80: 053423.
[90] ANTOINE P, MILO?EVI? D B, L’HUILLIER A, et al. Generation of attosecond pulses in macroscopic media [J]. Phys. Rev. A, 1997, 56: 4960-4969.
[91] LóPEZ-MARTENS R, VARJúK, JOHNSSON P, et al. Amplitude and phase control of attosecond light pulses [J]. Phys. Rev. Lett., 2005, 94: 033001.
[92] LU R F, HE H X, GUO Y H, HAN K L. Theoretical study of single attosecond pulse generation with a three-colour laser field [J]. J. Phys. B, 2009, 42: 225601.
[93] ORLANDO G, CORSO P P, FIORDILINO E, PERSICO F. A three-colour scheme to generate isolated attosecond pulses [J]. J. Phys. B, 2010, 43: 025602.
[94] SHAN B, CHANG Z H. Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field [J]. Phys. Rev. A, 2001, 65: 011804(R).
[95] COLOSIMO P, DOUMY G, BLAGA C I, et al. Scaling strong-field interactions towards the classical limit [J]. Nat. Phys., 2008, 4: 386-389.
[96] XU H, XIONG H, ZENG Z N, et al. Fine interference fringes formed in high-order harmonic spectra generated by infrared driving laser pulses [J]. Phys. Rev. A, 2008, 78: 033841.
[97] HONG W Y, ZHANG Q B, YANG Z Y, LU P X. Electron dynamic control for the quantum path in the midinfrared regime using a weak near-infrared pulse [J]. Phys. Rev. A, 2009, 80: 053407.
[98] LEIN M. Mechanisms of ultrahigh-order harmonic generation [J]. Phys. Rev. A, 2005, 72: 053816.
[99] LAN P F, LU P X, CAO W, et al. Phase-locked high-order-harmonic and sub-100-as pulse generation from stretched molecules [J]. Phys. Rev. A, 2006, 74: 063411.
[100] FIGUEIRA DE MORISSON FARIA C. High-order harmonic generation in diatomic molecules: a quantum-orbit analysis of the interference patterns [J]. Phys. Rev. A, 2007, 76: 043407.
[101] ZHENG Y H, ZENG Z N, ZOU P, et al. Dynamic chirp control and pulse compression for attosecond high-order harmonic emission [J]. Phys. Rev. Lett., 2009, 103: 043904.
[102] FENG X M, GILBERTSON S, MASHIKO H, et al. Generation of isolated attosecond pulses with 20 to 28 femtosecond lasers [J]. Phys. Rev. Lett., 2009, 103: 183901.
[103] SU Q, EBERLY J H, JAVANAINEN J. Dynamics of atomic ionization suppression and electron localization in an intense high-frequency radiation field [J]. Phys. Rev. Lett., 1990, 64: 862-865.
[104] MERCOURIS T, KOMNINOS Y, DIONISSOPOULOU S, NICOLAIDES C A. Computation of strong-field multiphoton processes in polyelectronic atoms: state-specific method and applications to H and Li- [J]. Phys. Rev. A, 1994, 50: 4109-4121.
[105] CHU S I. Recent developments in semiclassical floquet theories for intense-field multiphoton processes [J]. Adv. At. Mol. Phys., 1985, 21: 197-253.
[106] ZHOU X X, LIN C D. Linear-least-squares fitting method for the solution of thetime-dependent Schr?dinger equation: applications to atoms in intense laser fields [J]. Phys. Rev. A, 2000, 61: 053411.
[107] FEIT M D, FLECK J A, et al. Solution of the schr?dinger equation by a spectral method [J]. J. Comput. Phys., 1982, 47: 412-433.
[108] GAVRILA M. Atomic stabilization in superintense laser fields [J]. J. Phys. B, 2002, 35: R147-R193.
[109] SU Q, EBERLY J H. Model atom for multiphoton physics [J]. Phys. Rev. A, 1991, 44: 5997-6008.
[110] RAE S C, CHEN X, BURNETT K. Saturation of harmonic generation in one- and three-dimensional atoms [J]. Phys. Rev. A, 1994, 50: 1946-1949.
[111]彭玉华.小波变换与工程应用[M].北京:科学出版社, 1999.
[112] ANTOINE P, PIRAUX B. Time profile of harmonics generated by a single atom in a strong electromagnetic field [J]. Phys. Rev. A, 1995, 51: R1750-R1753.
[113] BAITU?KA A, UDEM T, UIBERACKER M, et al. Attosecond control of electronic processes by intensity light fields, Nature, 2003, 421: 611-615.
[114] ZHANG L, ZENG Z N, SONG X H, et al. Single sub-100 attosecond pulse generation in a two-colour time-gating laser field [J]. J. Phy. B, 2008, 41: 115601.
[115] LAN P F, LU P X, CAO W, et al. Isolated sub-100-as pulse generation via controlling electron dynamics [J]. Phys. Rev. A, 2007, 76: 011402(R).
[116] BURNETT K, REED V C, COOPER J, KNIGHT P L. Calculation of the background emitted during high-harmonic generation [J]. Phys. Rev. A, 1992, 45: 3347-3349.
[117] WANG B B, CHENG T W, LI X F, FU P M. Pulse-duration dependence of high-order harmonic generation with coherent superposition state [J]. Phys. Rev. A, 2005, 72: 063412.
[118] CAO W, LU P X, LAN P F, et al. Efficient isolated attosecond pulse generation from a multi-cycle two-color laser field [J]. Opt. Express, 2007, 15: 530-535.
[119] MILO?EVI? D B, BECKER W. Attosecond pulse trains with unusual nonlinear polarization [J]. Phys. Rev. A, 2000, 62: 011403(R).
[120] MILO?EVI? D B, OD?AK S. Attosecond pulse generation by a coplanar circular and static field combination [J]. Phys. Lett. A, 2006, 355: 368-372.
[121] SALIèRES P, L’HUILLIER A, LEWENSTEIN M. Coherence control of high-order harmonics [J]. Phys. Rev. Lett., 1995, 74: 3776-3779.
[122] BIEGERT J, HEINRICH A, HAURI C P, et al. Enhancement of high-order harmonic emission using attosecond pulse trains [J]. Laser Phys., 2005, 15: 899-902.
[123] HONG W Y, LU P X, LI Q G, ZHANG Q B. Broadband water window supercontinu-um generation with a tailored mid-IR pulse in neutral medial [J]. Opt. Lett., 2009, 34: 2102-2104.
[124] TATE J, AUGUSTE T, MULLER H, et al. Scaling of wave-packet dynamics in an intense midinfrared field [J]. Phys. Rev. Lett., 2007, 98: 013901.
[125] ISHIKAWA K. Photoemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses [J]. Phys. Rev. Lett., 2003, 91: 043002.
[126] KIENBERGER R, GOULIELMAKIS E, UIBERACKER M, et al. Atomic transient recorder [J]. Nature, 2004, 427: 817-821.
[127] TZALLAS P, SKANTZAKIS E, KALPOUZOS C, et al. Generation of intense continuum extreme-ultraviolet radiation by many-cycle laser fields [J]. Nat. phys., 2007, 3: 846-850.
[128] MASHIKO H, GILBERTSON S, Li C et al. Double pptical gating of high-order harmonic generation with carrier-envelope phase stabilized lasers [J]. Phys. Rev. Lett., 2008, 100: 103906.
[2] KULANDER K C. Multiphoton ionization of hydrogen: a time-dependent theory [J]. Phys. Rev. A, 1987, 35: 445-447.
[3] PERRY M D, LANDEN O L, SZ?KE A, CAMPBELL E M. Multiphoton ionization of the noble gases by an intense 1014 W/cm2 dye laser [J]. Phys. Rev. A, 1988, 37: 747-760.
[4] PROTOPAPAS M, KEITEL C H, KNIGHT P L. Atomic physics with super-high intensity lasers [J]. Rep. Prog. Phys., 1997, 60: 389-486.
[5] YERGEAU F, PETITE G, AGOSTINI P. Above-threshold ionisation without space charge [J]. J. Phys. B, 1986, 19: L663-L669.
[6] CORKUM P B, BURNET N H, BRUNEL F. Above-threshold ionization in the long-wavelength limit [J]. Phys. Rev. Lett., 1989, 62: 1259-1262.
[7] MILO?EVI? D B, PAULUS G G, BAUER D, BECKER W. Above-threshold ionization by few-cycle pulses [J]. J. Phys. B, 2006, 39: R203-R262.
[8] AUGST S, STRICKLAND D, MEYERHOFER D D, et al. Tunneling ionization of noble gases in a high-intensity laser field [J]. Phys. Rev. Lett., 1989, 63: 2212-2215.
[9] GIBSON G, LUK T S, RHODES C K. Tunneling ionization in the multiphoton regime [J]. Phys. Rev. A, 1990, 41: 5049-5052.
[10] BREWCZYK M, RZA?EWSKI K. Over-the-barrier ionization of multielectron atoms by intense vuv free-electron laser [J]. J. Phys. B, 1999, 32: L1-L4.
[11] EBERLY J H, SU Q, JAVANAINEN J. High-order harmonic production in multiphoton ionization [J]. J. Opt. Soc. Am. B, 1989, 6: 1289-1298.
[12] MAINFRAY G, MANUS C. Multiphoton ionization of atoms [J]. Rep. Prog. Phys., 1991, 54: 1333-1372.
[13]陈秀娥.超短脉冲激光器原理及应用[M].北京:科学出版社, 1991.
[14] AGOSTINI P, DIMAURO L F. The physics of attosecond light pulses [J]. Rep. Prog. Phys., 2004, 67: 813–855.
[15] FERRAY M, LOMPRéL A, GOBERT O, et al. Multiterawatt picosecond Nd-glass laser system at 1053 nm [J]. Opt. Commun., 1990, 75: 278-282.
[16] KELDYSH L V. Ionization in the field of a strong electromagnetic wave [J]. Sov. Phys. JETP, 1965, 20: 1307-1314.
[17] CHU S I, COOPER J. Threshold shift and above-threshold multiphoton ionization of atomic hydrogen in intense laser fields [J]. Phys. Rev. A, 1985, 32: 2769-2775.
[18] FABRE F, PETITE G, AGOSTINI P, CLEMENT M. Multiphoton above-threshold ionisation of xenon at 0.53 and 1.06 pm [J]. J. Phys. B, 1982, 15: 1353-1369.
[19] PETITE G, FABRE F, AGOSTINI P. Nonresonant multiphoton ionization of cesium in strong fields: angular distributions and above-threshold ionization [J]. Phys. Rev. A, 1984, 29: 2677-2689.
[20] AGOSTINI P, FABRE F, MAINFRAY G, et al. Free-free transition following six-photo ionization of xenon atoms [J]. Phys. Rev. Lett., 1979, 42: 1127-1130.
[21] GONTIER Y, TRAHIN M. Energetic electron generation by multiphoton absorption [J]. J. Phys. B, 1980, 13: 4383-4390.
[22] AMMOSOV M V, DELONE N B, KRAINOV V P. Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field [J]. Sov. Phys. JETP, 1986, 64: 1191-1194.
[23] RASHID S. Approximate solution of the hydrogenlike atoms in intense laser radiation [J]. Phys. Rev. A, 1989, 40: 4242-4244.
[24] SHORE B W, KNIGHT P L. Enhancement of high optical harmonics by excess-photon ionization [J]. J. Phys. B, 1987, 20: 413-423.
[25] MCPHERSON A, GIBSON G, JARA H, et al. Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases [J]. J. Opt. Soc. Am B, 1987, 4: 595-601.
[26] FERRAY M, L’HUILLIER A, LI X F, et al. Multiple-harmonic conversion of 1064 nm radiation in rare gases [J]. J. Phys. B, 1988, 21 : L31-L35.
[27] LI X F, L’HUILLIER A, FERRAY L A, et al. Multiple-harmonic generation in rare gases at high laser intensity [J]. Phys. Rev. A, 1989, 39: 5751-5761.
[28] L’HUILLIER A, BALCOU P. High-order harmonic generation in rare gases with a 1-ps 1053-nm laser [J]. Phys. Rev. Lett., 1993, 70: 774-777.
[29] SARUKURA N, HATA K, ADACHI T, NODOMI R. Coherent soft x-ray generation by the harmonics of an ultrahigh-power KrF laser [J]. Phys. Rev. A, 1991, 43: 1669-1672.
[30] MIYAZAKI K, SAKAI H. High-order harmonic generation in rare gases with intense subpicosecond dye laser pulses [J]. J. Phys. B, 1992, 25: L83-L89.
[31] BALCOU P, CORNAGGIA C, GOMES A S L, et al. Optimizing high-order harmonic generation in strong fields [J]. J. Phys. B, 1992, 25: 4467-4485.
[32] MACKLIN J J, KMETEC J D, GORDON III C L. High-order harmonic generation using intense femtosecond pulses [J]. Phys. Rev. A, 1993, 70: 766-769.
[33] PERRY M D, CRANE J K. High-order harmonic emission from mixed fields [J]. Phys. Rev. A, 1993, 48: R4051-R4054.
[34] WATANABE S, KONDO K, NABEKAWA Y, et al. Two-color phase control in tunneling ionization and harmonic generation by a strong laser field and its third harmonic [J]. Phys. Rev. Lett., 1994, 73: 2692–2695.
[35] MIYAZAKI K, TAKADA H. High-order harmonic generation in the tunneling regime [J]. Phys. Rev. A, 1995, 52: 3007-3021.
[36] DITMIRE T, CRANE J K, NGUYEN H, et al. Energy-yield and conversion-efficiency measurements of high-order harmonic radiation [J]. Phys. Rev. A, 1995, 51: R902-R905.
[37] PEATROSS J, MEYERHOFER D D. Intensity-dependent atomic-phase effects in high-order harmonic generation [J]. Phys. Rev. A, 1995, 52: 3976-3987.
[38] PRESTON S G, SANPERA A, ZEPF M, et al. High-order harmonics of 248.6-nm KrF laser from helium and neon ions [J]. Phys. Rev. A, 1996, 53: R31-R34.
[39] ZHOU J, PEATROSS J, MURNANE M M, KAPTEYN H C. Enhanced high-harmonic generation using 25 fs laser pulses [J]. Phys. Rev. Lett., 1996, 76: 752-755.
[40] CHANG Z H, RUNDQUIST A, WANG H W, et al. Generation of coherent soft x rays at 2.7 nm using high harmonics [J]. Phys. Rev. Lett., 1997, 79: 2967-2970.
[41] SCHNüRER M, SPIELMANN C, WOBRAUSCHEK P, et al. Coherent 0.5-keV x-ray emission from helium driven by a sub-10-fs laser [J]. Phys. Rev. Lett., 1998, 80: 3236-3239.
[42] RUNDQUIST A, DURFEE III C G, CHANG Z H, et al. Phase-matched generation of coherent soft x-rays [J]. Science, 1998, 280: 1412-1415.
[43] LANGE H R, CHIRON A, RIPOCHE J F, et al. High-order generation and quasiphase matching in xenon using self-guided femtosecond pulses [J]. Phys.Rev.Lett., 1998, 81: 1611-1613.
[44] NORREYS P A, ZEPF M, MOUSTAIZIS S, et al. Efficient extreme uv harmonics generated from picosecond laser pulse interactions with solid targets [J]. Phys, Rev. Lett., 1996, 76: 1832-1835.
[45] GIBSON E A, PAUL A, WAGNER N, TOBEY R, et al. Coherent soft x-ray generation in the water window with quasi-phase matching [J]. Science, 2003, 302: 95-98.
[46] SERES J, YAKOVLEV V S, SERES E, et al. Coherent superposition of laser-driven soft-x-ray harmonics from successive sources [J]. Nat. Phys., 2007, 11: 878-883.
[47] CORKUM P B. Plasma perspective on strong-field multiphoto ionization [J]. Phys. Rev. Lett., 1993, 71: 1994-1997.
[48] WINTERFELDT C, SPIELMANN C, GERBER G. Colloquium: optimal control of high-harmonic generation [J]. Rev. Mod. Phys., 2008, 80: 117-140.
[49] KULANDER K C, SHORE B W. Calculations of multiple-harmonic conversion of 1064-nm radiation in Xe [J]. Phys. Rev. Lett., 1989, 62: 524-526.
[50] KRAUSE J L, SCHAFER K J, KULANDER K C. High-order harmonic generation from atoms and ions in the high intensity regime [J]. Phys. Rev. Lett., 1992, 68: 3535-3538.
[51] LEWENSTEIN M, BALCOU P, IVANOV M Y, et al. Theory of high-harmonic generation by low-frequency laser fields [J]. Phy. Rev. A, 1994, 49: 2117-2132.
[52] ANTOINE P, L’HUILLIER A, LEWENSTEIN M. Attosecond pulse trains using high-order harmonics [J]. Phys. Rev. Lett., 1996, 77: 1234-1237.
[53] CHRISTOV I P, MURNANE M M, KAPTEYN H C. High-harmonic generation of attosecond pulses in the single-cycle regime [J]. Phys. Rev. Lett., 1997, 78: 1251-1254.
[54] PAUL P M, TOMA E S, BREGER P, et al. Observation of a train of attosecond pulses from high harmonic generation [J]. Science, 2001, 292: 1689-1692.
[55] GOULIELMAKIS E, SCHULTZE M, HOFSTETTER M, et al. Single-cycle nonlinear optics[J]. Science, 2008, 320: 1614-1617.
[56] DRESCHER M, HENTSCHEL M, KIENBERGER R, et al. X-ray pulses approaching the attosecond frontier [J]. Science, 2001, 291: 1923-1927.
[57] MAIRESSE Y, DE BOHAN A, FRASINSKI L J, et al. Attosecond synchronization of high-harmonic soft x-rays [J]. Science, 2003, 302: 1540-1543.
[58] SPIELMANN C, BURNETT N H, SARTANIA S, et al. Generation of coherent x-rays in the water window using 5-femtosecond laser pulses [J]. Science, 1997, 278: 661-664.
[59] LEE K, CHA Y H, SHIN M S, et al. Relativistic nonlinear thomson scattering as attosecond x-ray source [J]. Phys. Rev. E, 2003, 67: 026502.
[60] SOKOLOV A V, WALKER D R, YAVUZ D D, et al. Raman generation by phased and antiphased molecular states [J]. Phys. Rev. Lett., 2000, 85: 562-565.
[61] HENTSCHEL M, KIENBERGER R, SPIELMANN C, et al. Attosecond metrology [J]. Nature, 2001, 414: 509-513.
[62] CORKUM P B, BURNETT N H, IVANOV M Y. Subfemtosecond pulses [J]. Opt. Lett., 1994, 19: 1870-1872.
[63] SANSONE G, BENEDETTI E, CALEGARI F, et al. Isolated single-cycle attosecond pulses [J]. Science, 2006,314: 443-446.
[64] CAVALIERIL A L, GOULIELMAKIS E, HORVATH B, et al. Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua [J]. New J. Phys., 2007, 9: 242.
[65] PFEIFER T, GALLMANN L, ABEL M J, et al. Single attosecond pulse generation in the multicycle-driver regime by adding a weak second-harmonic field [J]. Opt. Lett., 2006, 31: 975-977.
[66] ZENG Z Z, CHENG Y, SONG X H, et al. Generation of an extreme ultraviolet superconuum in a two-color laser fields [J]. Phys. Rev. Lett., 2007, 98: 203901.
[67] ZHAI Z, LIU X S, Extension of the high-order harmonics and an isolated sub-100 as pulse generation in a two-colour laser field [J]. J. Phys. B, 2008, 41: 25602.
[68] ZHAI Z, Yu R F, LIU X S, Yang Y J. Enhancement of high-order harmonic emission and intense sub-50-as pulse generation [J]. Phys. Rev. A, 2008, 78: 041402(R).
[69] HONG W Y, LI Y H, LU P X, et al. Control of quantum paths in the multicycle regime and efficient broadband attosecond pulse generation [J]. J. Opt. Soc. Am. B, 2008, 25: 1684-1689.
[70] LI P C, ZHOU X X, WANG G L, ZHAO Z X. Isolated sub-30-as pulse generation of an He+ ion by an intense few-cycle chirped laser and its high-order harmonic pulses [J]. Phys. Rev. A, 2009, 80: 05382.
[71] YAO J P, LI Y, ZENG B, et al. Generation of an xuv supercontinuum by optimization of the angle between polarization planes of two linearly polarized pulses in a multicycle two-color laser field [J]. Phys. Rev. A, 2010, 82: 023826.
[72] CHEN J G, ZENG S L, YANG Y J. Generation of isolated sub-50-as pulses by quantum path control in the multicycle regime [J]. Phys. Rev. A, 2010, 82: 043401.
[73] CHEN J G, YANG Y J, ZENG S L, LIANG H Q. Generation of intense isolated sub-40-as pulses from a coherent superposition state by quantum path control in the multicycle regime [J]. Phys. Rev. A, 2011, 83: 023401.
[74] SCHAFER K J, GAARDE M B, HEINRICH A. Strong field quantum path control using attosecond pulse trains [J]. Phys. Rev. Lett., 2004, 92: 023003.
[75] BANDRAUK A D, NGUYEN H S. Attosecond control of ionization and high-order harmonic generation in molecules [J]. Phys. Rev. A, 2002, 66: 031401(R).
[76] BANDRAUK A D, CHELKOWSKI S, NGUYEN H S. Controlling continuum harmonic generation with attosecond pulses [J]. Appl. Phys. B, 2003, 77: 337–342.
[77] LAN P F, LU P X, CAO W, WANG X L. Efficient generation of an isolated single-cycle attosecond pulse [J]. Phys. Rev. A, 2007, 76: 043808.
[78] ZHAO S F, ZHOU X X, LI P C, CHEN Z J. Isolated short attosecond pulse produced by using an intense few-cycle shaped laser and an ultraviolet attosecond pulse [J]. Phys. Rev. A, 2008, 78: 063404.
[79] OD?AK S, MILO?EVI? D B. Attosecond pulse generation by a coplanar circular and static field combination [J]. Phys. Lett. A, 2006, 355: 368-372.
[80] HONG W Y, LU P X, CAO W, et al. Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field [J]. J. Phys. B, 2007, 40: 2321–2331.
[81] HONG W Y, LU P X, LAN P F, et al. Broadband xuv supercontinuum generation via controlling quantum paths by a low-frequency field [J]. Phys. Rev. A, 2008, 77: 033410.
[82] HONG W Y, LU P X, LAN P F, et al. Few-cycle attosecond pulses with stabilized- carrier-envelope phase in the presence of a strong terahertz field [J]. Opt. Express, 2009, 17: 5139-5146.
[83] XIANG Y, NIU Y P, GONG S Q. Control of the high-order harmonics cutoff through the combination of a chirped laser and static electric field [J]. Phys. Rev. A, 2009, 79: 053419.
[84] CAO W, LU P X, LAN P F, et al. Control of quantum paths in high-order harmonic generation via aω+3ωbichromatic laser field [J]. J. Phy. B, 2007, 40: 869-875.
[85] YU Y L, SONG X H, FU Y X, et al. Theoretical investigation of single attosecond pulse generation in an orthogonally polarized two-color laser field [J]. Opt. Express, 2008, 16: 686-694.
[86] KIM C M, KIM I J, NAM C H. Generation of a strong attosecond pulse train with an orthogonally polarized two-color laser field [J]. Phys. Rev. A, 2005, 72: 033817.
[87] KIM C M, NAM C H. Selection of an electron path of high-order harmonic generation in two-colour femtosecond laser field [J]. J. Phys. B, 2006, 39: 3199-3209.
[88] HONG W Y, LU P X, LAN P F, et al. Method to generate directly a broadband isolated attosecond pulse with stable pulse duration and high signal-to-noise ratio [J]. Phys. Rev. A, 2009, 78: 063407.
[89] YU Y L, XU J J, FU Y X, et al. Single attosecond pulse generation from aligned molecules using two-color polarization gating [J]. Phys. Rev. A, 2009, 80: 053423.
[90] ANTOINE P, MILO?EVI? D B, L’HUILLIER A, et al. Generation of attosecond pulses in macroscopic media [J]. Phys. Rev. A, 1997, 56: 4960-4969.
[91] LóPEZ-MARTENS R, VARJúK, JOHNSSON P, et al. Amplitude and phase control of attosecond light pulses [J]. Phys. Rev. Lett., 2005, 94: 033001.
[92] LU R F, HE H X, GUO Y H, HAN K L. Theoretical study of single attosecond pulse generation with a three-colour laser field [J]. J. Phys. B, 2009, 42: 225601.
[93] ORLANDO G, CORSO P P, FIORDILINO E, PERSICO F. A three-colour scheme to generate isolated attosecond pulses [J]. J. Phys. B, 2010, 43: 025602.
[94] SHAN B, CHANG Z H. Dramatic extension of the high-order harmonic cutoff by using a long-wavelength driving field [J]. Phys. Rev. A, 2001, 65: 011804(R).
[95] COLOSIMO P, DOUMY G, BLAGA C I, et al. Scaling strong-field interactions towards the classical limit [J]. Nat. Phys., 2008, 4: 386-389.
[96] XU H, XIONG H, ZENG Z N, et al. Fine interference fringes formed in high-order harmonic spectra generated by infrared driving laser pulses [J]. Phys. Rev. A, 2008, 78: 033841.
[97] HONG W Y, ZHANG Q B, YANG Z Y, LU P X. Electron dynamic control for the quantum path in the midinfrared regime using a weak near-infrared pulse [J]. Phys. Rev. A, 2009, 80: 053407.
[98] LEIN M. Mechanisms of ultrahigh-order harmonic generation [J]. Phys. Rev. A, 2005, 72: 053816.
[99] LAN P F, LU P X, CAO W, et al. Phase-locked high-order-harmonic and sub-100-as pulse generation from stretched molecules [J]. Phys. Rev. A, 2006, 74: 063411.
[100] FIGUEIRA DE MORISSON FARIA C. High-order harmonic generation in diatomic molecules: a quantum-orbit analysis of the interference patterns [J]. Phys. Rev. A, 2007, 76: 043407.
[101] ZHENG Y H, ZENG Z N, ZOU P, et al. Dynamic chirp control and pulse compression for attosecond high-order harmonic emission [J]. Phys. Rev. Lett., 2009, 103: 043904.
[102] FENG X M, GILBERTSON S, MASHIKO H, et al. Generation of isolated attosecond pulses with 20 to 28 femtosecond lasers [J]. Phys. Rev. Lett., 2009, 103: 183901.
[103] SU Q, EBERLY J H, JAVANAINEN J. Dynamics of atomic ionization suppression and electron localization in an intense high-frequency radiation field [J]. Phys. Rev. Lett., 1990, 64: 862-865.
[104] MERCOURIS T, KOMNINOS Y, DIONISSOPOULOU S, NICOLAIDES C A. Computation of strong-field multiphoton processes in polyelectronic atoms: state-specific method and applications to H and Li- [J]. Phys. Rev. A, 1994, 50: 4109-4121.
[105] CHU S I. Recent developments in semiclassical floquet theories for intense-field multiphoton processes [J]. Adv. At. Mol. Phys., 1985, 21: 197-253.
[106] ZHOU X X, LIN C D. Linear-least-squares fitting method for the solution of thetime-dependent Schr?dinger equation: applications to atoms in intense laser fields [J]. Phys. Rev. A, 2000, 61: 053411.
[107] FEIT M D, FLECK J A, et al. Solution of the schr?dinger equation by a spectral method [J]. J. Comput. Phys., 1982, 47: 412-433.
[108] GAVRILA M. Atomic stabilization in superintense laser fields [J]. J. Phys. B, 2002, 35: R147-R193.
[109] SU Q, EBERLY J H. Model atom for multiphoton physics [J]. Phys. Rev. A, 1991, 44: 5997-6008.
[110] RAE S C, CHEN X, BURNETT K. Saturation of harmonic generation in one- and three-dimensional atoms [J]. Phys. Rev. A, 1994, 50: 1946-1949.
[111]彭玉华.小波变换与工程应用[M].北京:科学出版社, 1999.
[112] ANTOINE P, PIRAUX B. Time profile of harmonics generated by a single atom in a strong electromagnetic field [J]. Phys. Rev. A, 1995, 51: R1750-R1753.
[113] BAITU?KA A, UDEM T, UIBERACKER M, et al. Attosecond control of electronic processes by intensity light fields, Nature, 2003, 421: 611-615.
[114] ZHANG L, ZENG Z N, SONG X H, et al. Single sub-100 attosecond pulse generation in a two-colour time-gating laser field [J]. J. Phy. B, 2008, 41: 115601.
[115] LAN P F, LU P X, CAO W, et al. Isolated sub-100-as pulse generation via controlling electron dynamics [J]. Phys. Rev. A, 2007, 76: 011402(R).
[116] BURNETT K, REED V C, COOPER J, KNIGHT P L. Calculation of the background emitted during high-harmonic generation [J]. Phys. Rev. A, 1992, 45: 3347-3349.
[117] WANG B B, CHENG T W, LI X F, FU P M. Pulse-duration dependence of high-order harmonic generation with coherent superposition state [J]. Phys. Rev. A, 2005, 72: 063412.
[118] CAO W, LU P X, LAN P F, et al. Efficient isolated attosecond pulse generation from a multi-cycle two-color laser field [J]. Opt. Express, 2007, 15: 530-535.
[119] MILO?EVI? D B, BECKER W. Attosecond pulse trains with unusual nonlinear polarization [J]. Phys. Rev. A, 2000, 62: 011403(R).
[120] MILO?EVI? D B, OD?AK S. Attosecond pulse generation by a coplanar circular and static field combination [J]. Phys. Lett. A, 2006, 355: 368-372.
[121] SALIèRES P, L’HUILLIER A, LEWENSTEIN M. Coherence control of high-order harmonics [J]. Phys. Rev. Lett., 1995, 74: 3776-3779.
[122] BIEGERT J, HEINRICH A, HAURI C P, et al. Enhancement of high-order harmonic emission using attosecond pulse trains [J]. Laser Phys., 2005, 15: 899-902.
[123] HONG W Y, LU P X, LI Q G, ZHANG Q B. Broadband water window supercontinu-um generation with a tailored mid-IR pulse in neutral medial [J]. Opt. Lett., 2009, 34: 2102-2104.
[124] TATE J, AUGUSTE T, MULLER H, et al. Scaling of wave-packet dynamics in an intense midinfrared field [J]. Phys. Rev. Lett., 2007, 98: 013901.
[125] ISHIKAWA K. Photoemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses [J]. Phys. Rev. Lett., 2003, 91: 043002.
[126] KIENBERGER R, GOULIELMAKIS E, UIBERACKER M, et al. Atomic transient recorder [J]. Nature, 2004, 427: 817-821.
[127] TZALLAS P, SKANTZAKIS E, KALPOUZOS C, et al. Generation of intense continuum extreme-ultraviolet radiation by many-cycle laser fields [J]. Nat. phys., 2007, 3: 846-850.
[128] MASHIKO H, GILBERTSON S, Li C et al. Double pptical gating of high-order harmonic generation with carrier-envelope phase stabilized lasers [J]. Phys. Rev. Lett., 2008, 100: 103906.