摘要
强激光与原子分子相互作用中产生的一系列非线性现象越来越受到了人们的关注。如今强场物理快速发展，已经不再是一个只存在于实验室或者计算机模拟里面的“空中楼阁”，在很多与人们生活息息相关的领域都发挥了至关重要的作用：医学领域和生物工程方面的全息立体成像技术、利用超紫外射线在半导体器件上的光刻技术、生命科学里面的电子探针X射线显微分析乃至人工激光诱导核聚变等等。在这些领域中都能找到强场物理的影子，可以说“旧时王谢堂前燕，飞入寻常百姓家”。但是受限于超紫外光源的成本、计算模拟的资源开销，很多问题还没有得到解决。作者理论研究了强场物理中的三个热点问题，为这几个问题的解决提供了新的方案和思路。这三部分的具体内容包括：
第一，我们基于Lewenstein理论计算了氮气分子的高次谐波谱。我们通过在x轴添加弱的线性激光改进了传统的“极化门”方案。通过调节脉宽等激光场参数成功地将阿秒脉冲的强度提高了两倍，同时阿秒脉冲的持续时间缩短到了105阿秒。时频分析的结果表明，改进的方案提高了氮气分子的电离几率从而提高了谐波的效率。此外我们发现当分子轴与激光场的夹角越小谐波的效率越高。
第二，我们研究了激光场作用下原子束缚态跃迁产生的载波相位效应。通过求解三维含时薛定谔方程得到了原子束缚态在激光场结束之后的布居数。我们发现即使激光脉冲持续时间达到了几十个光周期，原子束缚态的布居数仍然能够展示出明显的载波相位效应。利用含时微绕理论我们发现双光子跃迁可以分解成两个振幅相同、携带相位信息不同的跃迁子路径。这两个跃迁子路径之间的干涉造成了长脉冲下的载波相位效应。另外我们利用相邻高里德堡态之间能级差小这一性质，得到了低频场的载波相位效应。我们的结果为实验物理学家提供了一个探测激光脉冲的绝对相位效应的新方案。
第三，基于B样条函数和球坐标系我们开发了一套求解He原子与激光场作用的三维含时薛定谔方程的方法。作者详细介绍了在球坐标中如何把含时薛定谔方程转化为一组耦合微分方程组，通过求解这个微分方程组得到He原子在激光场作用后的波函数。通过对比其他文献中的He原子基态能级和激光场结束之后的电离几率，验证了程序的精确性。另外我们分别计算了不同初态电离几率同脉宽的变化曲线，我们发现尽管这两个态的能级非常相似，但是初态在1s2p态的初态在1s2s态的情况电离几率要大两倍左右。为了节省计算时间，我们成功地将程序改写为适用于GPU计算的并行程序，使得计算速度照比CPU提高了近一百五十倍。
Nonlinear phenomena in the interaction between strong field and atom or moleculehave attracted lots of attention. Recently, the strong field has developed fast. Thestrong field plays an important role in many areas, holographic imaging and stereoimaging in medicine and bioengineering, electron microprobe X-ray micro-analysis inbiological science, laser fusion, and so on. However, lots of problems in strong fieldremain unsolved, limited by the costs of the XUV laser source and the speed of CPU.Three hot topics of strong field were studied theoretically in this thesis. We providednew schemes and ideas to solve the problems. This thesis is divided into three parts:
First, we present a new scheme to control the harmonic generation process fromaN2molecule with a modulated polarization gating. The polarization gating ismodulated by a weaker linearly polarized pulse. We shorten the attosecond pulseduration by31attoseconds, and enhance the efficiency by one time. Moreover, weinvestigate the dependence of (HHG) on orientation ofN2molecule and find theHHG intensity is enhanced when the angle between the axis of the molecule and theapplied electric field decreases.
Second, we provide a path to investigate the carrier envelope phase (CEP) effectin atomic bound-bound transitions. An obvious CEP effect on a two-photonthree-level transition can be observed for a long laser pulse which contains severaltens of optical cycles. The CEP effect originates from the interference between thesum-frequency and the difference-frequency within the two-photon transition. Andthis interference is independent of the pulse duration. Therefore the CEP effect canstay robust even for a long laser pulse. Besides, we theoretically investigate the CEPeffect in a bound-bound transition of an atom in a low-frequency long laser pulseusing the characteristic of small energy difference between two high Rydberg states.We find that the population changes dramatically with the CEP of the low-frequency pulse. This CEP effect is attributed to the interference between the positive-frequencyand negative-frequency components in one-photon transition. These results mayprovide a new method to measure the CEP value of a long laser pulse with lowfrequency.
Finally, we develop a program to solve the time dependent Schrodinger equation（TDSE） based on the B-spline and spherical coordinate. We demonstrate how totransform the two electrons TDSE into a coupled differential equations. Using thegraph method we get the transition matrix. We apply the Adams method to solve thesedifferential equations. We compare our results with the literatures related to this workby computing the energy level of He and ionization rate. Then, we calculate theionization yield as a function of the full width at half-maximum (FWHM) durationwith different initial states, finding the ionization yield originated from the initial state1s2p is higher than the initial state1s2s. We successfully convert the programinto Graphic Processing Unit (GPU) parallel code, for saving the time. The computingspeed of GPU is nearly150times faster than CPU.
引文
[1] MAIMAN T H. Stimulated optical radiation in ruby,[J].Nature,1960,187,493.
[2] PROTOPAPAS M, KEITEL C H AND KNIGHT P L.Atomic physics withsuper-high intensity lasers [J].Rep. Prog. Phys.,1997,60:389.
[3] AGOSTINI P, DIMAURO L F. The physics of attosecond light pulses [J]. Rep.Prog. Phys.,2004,67:813–855.
[4] TOMLINSON R G, Multiphoton ionization and the breakdown of noble gases,[J].Phys. Rev. Lett.1965,14,489.
[5] VORONOV G S and DELONE N B, Many-photon Ionization of the XenonAto by Ruby Laser Radiation,[J].Sov. Phys.-1966, JETP23,54.
[6] AGOSTINI P, BARJOT G, BONNAL J, MAINFRAY G, MANUS C andMORELLEC J, Multiphoton ionization of hydrogen and rare gases,[J].IEEE J.1968,4,667.
[7] FRANKEN P A, HILL A E, PETERS C W, and Weinreich G, Generation ofoptical harmonics,[J].Phys. Rev. Lett.1961,7,118.
[8] MAKER P D and TERHUNE R W, Study of optical effects due to an inducedpolarization third order in the electric field strength,[J]. Phys. Rev.1965,137,A801.
[9] WARD J F and NEW G H C, Optical third harmonic generation in gases by afocused laser beam,[J].Phys. Rev.1969,185, R14.
[10] STRICKLAND D, and MOUROU G, Compression of amplified chirped opticalpulses,[J].Opt. Commun.1985,55,447.
[11] AGOSTINI P, FABRE F, MAINFRAY G, PETITE G, RAHMAN N K.Free-free transitions following six-photon ionization of Xenon atoms.[J]. Phys.Rev. Lett.,1979,42,1127-1130.
[12] AMMOSOV M V, DELONE N B, KRAINOV V P. Tunnel ionization ofcomplex atoms and of atomic ions in an alternating electromagnetic field [J].Sov. Phys. JETP,1986,64:1191-1194.
[13] SHORE B W, and KNIGHT P L, Investigations of above-threshold ionizationusing subpicosecond laser pulses,[J]. J. Phys. B1987,24,325.
[14] MCPHERSON A, GIBSON G, JARA H, JOHANN U, LUK T S, MCLNTYRE IA, BOYER K and RHODES C K, Studies of multiphoton production ofvacuumultraviolet radiation in the rare gases,[J]. J. Opt. Soc. Am. B1987,4,595.
[15] REISS H R. Effect of an intense electromagnetic field on a weakly bound system[J]. Physical Review A,1980,22:1786-1813.
[16] REISS H R. Spectrum of atomic electrons ionized by an intense field [J]. J. Phys.B,1987,20(3): L79-L83.
[17] BLAGA C I, CATOIRE F, COLOSIMO P, PAULUS G G, MULLER H G,AGOSTINI P, DIMAURO L F. Strong-field photoionization revisited [J].Nature,2009,5:335-338.
[18] QUAN W, LIN Z, WU M, KANG H, LIU H, LIU X, CHEN J, LIU J, HE X T,CHEN S G, XIONG H, GUO L, XU H, FU Y, CHENG Y, XU Z Z. Classicalaspects in above-threshold ionization with a midinfrared strong laser field [J].Physical Review Letters,2009,103(9):093001.
[19] L’HUILLIER A, LOMPRé L A, MAINFRAY G AND MANUS C. Multiplycharged ions induced by multiphoton absorption in rare gases at0.53um[J].Phys. Rev. A,1983,27:2503.ALEKSAKHIN I S, ZAPESOCHNYI I P ANDSURAN V V.Double multiphoton ionization of strontium atom [J]. JETP Lett.,1977,26:14-16.
[20] FITTINGHOFF D N, BOLTON P R, CHANG B AND KULANDER K C.Observation of nonsequential double ionization of helium with optical tunneling[J]. Phys. Rev. Lett.,1992,69:2642.
[21] KONDO K, SAGISAKA A, TAMIDA T, NABEKAWA Y AND WATANABES.Wavelength dependence of nonsequential double ionization in He [J].Phys.Rev. A,1993,48: R2531.
[22] WALKER B, SHEEHY B, DIMAURO L F, AGOSTINI P, SCHAFER K J ANDKULANDER K C. Precision measurement of strong field double ionization ofhelium [J].Phys. Rev. Lett.,1994,73:1227.
[23] MCPHERSON A, GIBSON G, JARA H, JOHANN U, LUK T S, MCINTYRE IA, BOYER K,RHODES C K.Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases [J].J. Opt. Soc. Am. B,1987,4:595.
[24] FERRAY M, L’HUILLIER A., LI X F, LOMPRE L A, MAINFRAY G. ANDMANUS C. Multiple-harmonic conversion of1064nm radiation in raregases [J], J. Phys. B,1988,21:31-35.
[25] GOULIELMAKIS E, SCHULTZE M, HOFSTETTER M, et al. Single-cyclenonlinear optics [J]. Science,2008,320:1614-1617.
[26] GIBSON E A, PAUL A, WAGNER NICK, Tobey R, GAUDIOSI D, BACKUS S,CHRISTOV I P, AQUILA A., GULLIKSON E M, ATTWOOD D T, MURNANE M M,KAPTEYN H C.Coherent soft x-ray generation in the water window withquasi-phase matching [J]. Science,2003,302:95-98.
[27] PIAZZA A D, MULLER C, HATSAGORTSAN K. Z. AND KEITEL C H,[J].Rev. Mod.Phys.,2012,84:1177.
[28] MOUROU G AND TAJIMA T.Large-scale laser facilities may also provide theultimate source of ultrashort laser pulses [J]. Science,2011,331:41-42.
[29] KRAUSZ F AND IVANOV M. Attosecond physics [J].Rev. Mod. Phys.,2009,81:163.
[30] CHANG ZENGHU.Single attosecond pulse and xuv supercontinuum in thehigh-order harmonic plateau [J]. Phys. Rev. A,2004,70:043802.
[31] SHON N H, SUDA A, MIDORIKAWA K. Attosecond pulse generation in Hegas with few-cycle KrF driver pulses [J], Japanese Journal Of Applied Physics,1999,38:6298-6301.
[32] GOULIELMAKIS E, SCHULTZE M, HOFSTETTER M, et al. Single-cyclenonlinear optics [J]. Science,2008,320:1614-1617.
[33] TARANUKHIN V D, High-order harmonic generation by atoms in a two-colorlaser field: Phase control of recombination radiation spectrum and duration [J],Journal of Experimental and Theoretical Physics,2004,98:678-686.
[34] YOSHITOMI D, KOBAYASHI Y, TAKADA H, et al.100-attosecond timingjitter between two-color mode-locked lasers by active-passive hybrid sy nc hronization [J], Optics Letters,2005,30:1048-1410.
[35] ZENG Z Z, CHENG Y, SONG X H, et al. Generation of an extreme ultravioletsuperconuum in a two-color laser fields [J]. Phys. Rev. Lett.,2007,98:203901.
[36] PFEIFER T, GALLMANN L, ABEL M J, et al. Single attosecond pulsegeneration in the multicycle-driver regime by adding a weak second-harmonicfield [J]. Opt. Lett.,2006,31:975-977.
[37] CORKUM P B, BURNETT N H, AND IVANOV M Y. Subfemtosecond pulses[J], Optics Letters,1994,19:1870-1982.
[38] SANSONE G, BENEDETTI E, CALEGARI F, et al. Isolated single-cycleattosecond pulses [J]. Science,2006,314:443-446.
[39] WANG HE. From Few-Cycle Femtosecond Pulse To Single AttosecondPulsecontrolling And Tracking Electron Dynamics With AttosecondPrecision,[D]. Kansas: Kansas State University,2005.
[40] CHANG Z H. Chirp of the single attosecond pulse generated by a polarizationgating [J]. Phys. Rev. A,2005,71:023813.
[41] CHANG Z H. Controlling attosecond pulse generation with a double opticalgating [J]. Phys. Rev. A,2007,76:051403.
[42] MASHIKO H, GILBERTSON S, LI C, et al. Double optical gating of high orderharmonic generation with carrier-envelope phase stabilized laser [J]. Phys. Rev.Lett.,2008,100:103906.
[43] ZHANG Q B, LU P X, LAN P F, et al. Multi-cycle laser-driven broadbandsupercontinuum with a modulated polarization gating [J]. Optics Express,2008,16:9795-9803.
[44] VAN DER ZWAN E V, LEIN M. Molecular imaging using high-order harmonicgeneration and above-threshold ionization[J]. Physical Review Letters,2012,108:043004.
[45] ZHAI Z, CHEN J, YAN Z C, FU P M AND WANG B B. Direct probing ofelectronic density distribution of a rydberg state by high-order harmonicgeneration in a few-cycle laser pulse [J]. Phys. Rev. A,2010,82:043422.
[46] SALIERES P, MAQUET A, HAESSLER S, CAILLAT J, et al.Imaging orbitalswith attosecond and angstrom resolutions:toward attochemistry?.Rep. Prog.Phys.,2012,75:062401.
[47] HAESSLER S, CAILLAT J AND SALIERES P.Self-probing of molecules withhigh harmonic generation [J].J. Phys. B,2011,44:203001.
[48] NIIKURA H, W RNER H J, VILLENEUVE D M AND CORKUM P B.Packet usingshaped recollision trajectories[J].Phys.Rev.Lett.,2011,107:093004.
[49] CORKUM P B, Plasma perspective on strong field multiphoton ionization,[J].Phys. Rev. Lett.1993,71,1994.
[50] CORKUM P B, BURNETT N H, and IVANOV M Y, Subfemtosecond pulses,[J].Opt. Lett.1994,19,1870.
[51] LEWENSTEIN M, BALCOU P, IVANOV M Y, L’HUILLIER A, andCORKUM P B, Theory of high-harmonic generation by low-frequency laserfields,[J].Phys. Rev. A1994,49,2117.
[52] WINTERFELDT C, SPIELMANN C, GERBER G. Colloquium: optimalcontrol of high-harmonic generation[J].Rev.Mod.Phys.,2008,80:117-140.
[53] WALKER B, SHEEHY B, DIMAURO L F, AGOSTINI P, SCHAFER K J,KULANDER K C,Precision measurement of strong field double ionization ofhelium[J]. Phys Rev A.1994,73:1227
[54] FITTINGHOFF D N, BOLTON P R, CHANG B, KULANDER K C.Observation of nonsequential double ionization of helium with optical tunneling[J]. Phys Rev Lett.1992,69:2642
[55] WALKER B, MEVEL E, YANG B R, BREGER P, CHAMBARET J P,ANTONETTI A, DIMAURO L F, AGOSTINI P. Double ionization in theperturbative and tunneling regimes [J]. Phys Rev A.1993,48:R894
[56] LAROCHELLE S F J, TALEBPOUR A, CHIN S L. Coulomb effect inmultiphoton ionization of rare-gas atoms [J]. J Phys B.1998,31:1215–1224
[57] MOSHAMMER R, FEUERSTEIN B, SCHMITT W, DORN A, SCHR¨OTER CD, ULLRICH J, ROTTKE H, TRUMP C, WITTMANN M, KORN G,HOFFMANN K, SANDNER W. Momentum Distributions of Nen+Ions Createdby an Intense Ultrashort Laser Pulse [J]. Phys Rev Lett.2000,84:447–450
[58] WEBER T, WECKENBROCK M, STAUDTE A, SPIELBERGER L,JAGUTZKI O, MERGEL V, AFANEH F, URBASCH G, VOLLMER M,GIESSEN H, DORNER R. Sequential and nonsequential contributions to doubleionization in strong laser fields [J]. J Phys B.2000,33:L127–L133。
[59] BRABEC T and KRAUSZ F Intense few-cycle laser fields: Frontiers ofnonlinear optics.[J].Rev. Mod. Phys.2000,72545
[60] POSTHUMUS J H The dynamics of small molecules in intense laser fields,[J].Rep. Prog. Phys.2004,67623
[61] CORKUM P B Plasma perspective on strong-field multiphoton ionization,[J].Phys. Rev. Lett.1993,711994
[62] ZHOU X. X., TONG X. M., ZHAO Z. X., and LIN C. D. Alignmentdependence of high-order harmonic generation from N2and O2molecules inintense laser fields,[J]. Phys. Rev. A,2005,72033412
[63] ZHU X, ZHANG Q, HONG W, LAN P, and LU P Two-center interference inhigh-order harmonic generation from heteronuclear diatomic molecules，[J]. Opt.Express,2011,19436
[64] PEI L and GUO C Nonsequential double ionization of triatomic molecules instrong laser fields，[J]. Phys. Rev. A,2010,82021401(R)
[65] ITATANI J, LEVESQUE J., ZEIDLER D., NIIKURA H., PEPIN H., KIEFFERJ. C., CORKUM P. B. and VILLENEUVE D. M. Tomograhpic imaging ofmolecular orbitals，[J]. Nature,2004,423867
[66] KRAUSZ F and IVANOV M Attosecond physics Rev. Mod. Phys.2009,81163
[67] HENTSCHEL M., KIENBERGER R., SPIELMANN C., REIDER G. A.,MILOSEVIC N., BRABEC T., CORKUM P., HEINZMANN U., DRESCHERM. and KRAUSZ F. Attosecond metrology，[J]. Nature,2001,414509
[68] SANSONE G., BENEDETTI E., CALEGARI F., VOZZI C., AVALDI L.,FLAMMINI R., POLETTO L., VILLORESI, P. ALTUCCI C., VELOTTA R.,STAGIRA S., De SILVESTRI S. and NISOLI M. Isolated single-cycleattosecond pulses，[J].Science,2006,314443
[69] HONG W, WEI P, ZHANG Q, WANG S and LU P Mid-infrared modulatedpolarization gating for ultra-broadband supercontinuum generation,[J].Opt.Express,2010,1811308
[70] CHANG Z Chirp of the single attosecond pulse generated by a polarizationgating,[J]. Phys. Rev.A,2005,71023813
[71] CHANG Z Single attosecond pulse and xuv supercontinuum in the high-orderharmonic plateau,[J].Phys. Rev. A,2004,70043802
[72] DU H and HU B Broadband supercontinuum generation method combiningmid-infrared chirped-pulse modulation and generalized polarization gating,[J].Opt. Express,2010,1825958
[73] LAN P., LU P., LI Q., LI F., HONG W. and ZHANG Q. Macroscopic effects forquantum control of broadband isolated attosecond pulse generation with atwo-color field,[J]. Phys. Rev. A,2009,79043413.
[74] MASHIKO H., GILBERTSON S., Li C., KHAN S. D., SHAKYA M. M.,MOON E. and CHANG Z. Double optical gating of high-order harmonicgeneration with carrier-envelope phase stabilized lasers,[J]. Phys. Rev. Lett.2008,100103906
[75] ODZAK S. and MILOSEVIC D. B., Interference effects in high-order harmonicgeneration by homonuclear diatomic molecules,[J]. Phys. Rev. A,2009,79023414
[76] JIA X Y, LI W D, LIU J and CHEN J Alignment-dependent nonsequentialdouble ionization of N2in intense laser fields,[J].Phys. Rev. A,2009,80053405
[77] YU Y, XU J, FU Y, XIONG H, XU H, YAO J, ZENG B, CHU W, CHEN J,CHENG Y and XU Z Single attosecond pulse generation from aligned moleculesusing two-color polarization gating,[J].Phys. Rev. A,2009,80053423
[78] LENWENSTEIN M, BALCOU P, IVANOV M Y, L’HUILLIER A andCORKUM P B Theory of high harmonic generation by low-frequency laserfields,[J].Phys. Rev. A,1994,492117
[79] MILOSEVIC D. B. Strong-field approximation for ionization of a diatomicmolecule by a strong laser field,[J].Phys. Rev. A,2006,74,063404
[80] FARIA C, Laser-induced nonsequential double ionization in diatomic molecules:oneand two-centre rescattering scenarios,[J]. J. Phys. B,2009,42105602
[81] CHIRILA C. C. and LEIN M. Strong-field approximation for harmonicgeneration in diatomic molecules，[J]. Phys. Rev. A,2006,73023410
[82] HETZHEIM H., FARIA C and BECKER W Interference effects inabovethreshold ionization from diatomic molecules:Determining the internuclearseparation，[J].Phys. Rev. A.2007,76023418
[83] ISERLES A., NORSETT S.P. and OLVER S. Highly oscillatory quadrature:the story so far，[J]. Numerical Mathematics and Advanced Applications Part1,2006,97-118.
[84] TONG X. M., ZHAO Z. X. and LIN C. D. Theory of molecular tunnelingionization，[J].Phys. Rev. A,2002,66,033402.
[85] HONG W., ZHANG Q., YANG Z. and LU P. Electron dynamic control for thequantum path in the midinfrared regime using a weak near-infrared pulse，[J].Phys. Rev. A,2009,80053407.
[86] ANTOINE P., LHUILLIER A. and LEWENSTEIN M. Attosecond pulse trainsusing high-order harmonics，[J].Phys. Rev. Lett.1996,771234.
[87] KAMTA G. L. and BANDRAUK A. D. Phase Dependence of EnhancedIonization in Asymmetric Molecules，[J].Phys. Rev. Lett.2005,94203003
[88] SHAN B., GHIMIRE S. and CHANG Z. Effect of orbital symmetry onhigh-order harmonic generation from molecules，[J].Phys. Rev. A.2004,69021404(R)
[89] de BOHAN A., ANTOINE P., MILOSEVIC D. B., and PIRAUX B.,Phase-Dependent Harmonic Emission with Ultrashort Laser Pulses，[J].Phys.Rev.Lett.1998,81,1837.
[90] APOLONSKI A, POPPE A, TEMPEA G, SPIELMANN C, UDEM T,HOLZWARTH R, HANSCH TW, and KRAUSZ F, Controlling the PhaseEvolution of Few-Cycle Light，[J]. Pulses Phys. Rev. Lett.2000,85,740.
[91] PAULUS G G, LINDNER F, WALTHER, H, BALTUSKA A,GOULIELMAKIS E, LEZIUS M, and KRAUSZ F, Measurement of the Phaseof Few-Cycle Laser Pulses，[J]. Phys. Rev. Lett.2003,91,253004.
[92] FORTIER T M, ROOS P A, JONES D J, CUNDIFF S T, BHAT R D R, andSIPE J E, Carrier-Envelope Phase-Controlled Quantum Interference of InjectedPhotocurrents in Semiconductors,[J].Phys. Rev. Lett.2004,92,147403.
[93] MILOSEVIC D B, PAULUS G G, BAUER D, and BECKER W,Above-threshold ionization by few-cycle pulses,[J].J. Phys. B,2006,39, R203.
[94] BECKER W, LIU X, HO P, and EBERLY J H, Theories of photoelectroncorrelation in laser-driven multiple atomic ionization,[J].Rev. Mod. Phys.2012,84,1011.
[95] RATHJE T, JOHNSON N G, MOLLER M, SU MANN F, ADOLPH D,KUBEL M, KIENBERGER R, KLING M F, PAULUS G G, andSAYLER A M,Review of attosecond resolved measurement and control via carrier–envelopephase tagging with above-threshold ionization,[J].J. Phys.2012,B45,074003.
[96] TABE T, ONO N, TONG X M, and TOSHIMA N, Laser information encoded inatomic asymmetrical ionization in few-cycle laser fields,[J].Phys. Rev. A,2011,84,023409.
[97] HENTSCHEL M, KIENBERGER R, SPIELMANN C, REIDER G A,MILOSEVIC N, BRABEC T, CORKUM P, HEINZMANN U, DRESCHER M,and KRAUSZ F, Attosecond metrology,[J].Nature,2001,414,509.
[98] DRESCHER M, HENTSCHEL M, KIENBERGER R, TEMPEA G,SPIELMANN C, RE IDER A G, CORKUM P B, and KRAUSZ F, X-ray PulsesApproaching theAttosecond Frontier,[J]. Science,2001,291,1923.
[99] BERGUES B, KUBEL M, JOHNSON N G, FISCHER B, CAMUS N,BETSCHK J, HERRWERTH O, SENFTLEBEN A, SAYLER A M, RATHJE T,PFEIFER T, BEN-ITZHAK I, JONES R R, PAULUS G G, KRAUSZ F,MOSHAMMER R, ULLRICH J, and KLING M F, Attosecond tracing ofcorrelated electron-emission in non-sequential double ionization,[J].Nat. Comm.2012,3,813.
[100] XIE X H, DOBLHOFF-DIER K, ROITHER S, SCHOFFLER M S,KARTASHOV D, XU H L, RATHJE T, PAULUS G G, BALTUSKA A,GRAFE S, and KITZLER M, Attosecond-Recollision-Controlled SelectiveFragmentation of Polyatomic Molecules,[J].Phys. Rev. Lett.2012,109,243001.
[101] SANSONE G, VOZZI C, STAGIRA S, PASCOLINI M, POLETTO L,VILLORESI P, TONDELLO G, De SILVESTRI S, and NISOLI M, Observationof Carrier-Envelope Phase Phenomena in the Multi-Optical-Cycle Regime,[J].Phys.Rev. Lett.2004,92,113904.
[102] JHA P K, ROSTOVTSEV Y V, Li H, SAUTENKOV V A, and SCULLY M O,Experimental observation of carrier-envelope-phase effects by multicycle pulses,[J].Phys. Rev. A,2011,83,033404.
[103] MILOSEVIC D B, PAULUS G G, and BECHER W, Phase-Dependent Effectsof a Few-Cycle Laser Pulse,[J]. Phys. Rev. Lett.2002,89,153001.
[104] PAULUS G G, GRASBON F, WALTHER H, VILLORESI P, NISOLI M,STAGIRA S, PRIORI E, and De SILVESTRI S, Absolute-phase phenomena inphotoionization with few-cycle laser pulses,[J].Nature,2001,414,182.
[105] WANG B, T. CHENG, Li X, FU P, CHEN S, and LIU J, Pulse-durationdependence of high-order harmonic generation with coherent superposition state,[J].Phys. Rev. A,2005,72,063412.
[106] LI H, CHEN J, JIANG H, FU P, LIU J, GONG Q, Z.-C. YAN, and B. WANG,Carrier-envelope phase dependence of non-sequential double ionization infew-cycle pulses,[J].Opt. Express,2008,16,20562.
[107] TONG X M, HINO K, and TOSHIMA N, Phase-dependent atomic ionization infew-cycle intense laser fields,[J].Phys. Rev. A,2006,74,031405.
[108] WANG B, CHEN J, LIU J, YAN Z C, and FU P, Attosecond-pulse-controlledhigh-order harmonic generation in ultrashort laser fields,[J].Phys. Rev. A,2008,78,023413.
[109] Kelly H P,[J]. Phys. Rev.,1963,131,684.
[110] ZHAI Z, PENG D, ZHAO X, GUO F, YANG Y, FU P, CHEN J, YAN Z C,and WANG B, Carrier-envelope-phase effect on laser-driven bound-boundtransitions in the high-frequency region,[J]. Phys. Rev. A,2012,86,043432.
[111] NAKAJIMA T and WATANABE S, Effects of the Carrier-Envelope Phase inthe Multiphoton Ionization Regime,[J].Phys. Rev. Lett.2006,96,213001.
[112] CORKUM P B. Plasma perspective on strong field multiphoton ionization[J].Phys Rev Lett.1993,71:1994–1997
[113] SCHAFER K J, YANG B, DIMAURO L F, KULANDER K C. Abovethreshold ionization beyond the high harmonic cutoff”[J]. Phys Rev Lett.1993,70:1599–1602
[114] YANG B, SCHAFER K J, WALKER B, KULANDER K C, AGOSTINI P,DIMAURO L F. Intensitydependent scattering rings in high orderabove-threshold ionization [J]. Phys Rev Lett.1993,71:3770–3773
[115] SHI T Y, LIN C D. Double Photoionization and Transfer Ionization of He:Shakeoff Theory Revisite [J]. Phys Rev Lett.2002,89:163202
[116] LITVINYUK I V, LEGARE F, DOOLEY P W, VILLENEUVE D M,CORKUM P B, ZANGHELLINI J, PEGARKOV A, FABIAN C, BRABEC T.Shakeup Excitation during Optical Tunnel Ionization [J].Phys Rev Lett.2005,94:033003
[117] EICHMANN U, DORR M, H. MAEDA, BECKER W, SANDNER W.Collective Multielectron Tunneling Ionization in Strong Fields [J]. Phys Rev Lett.2000,84:3550–3553
[118] WEBER T, GIESSEN H, WECKENBROCK M, URBASCH G, STAUDTE A,SPIELBERGER L, JAGUTZKI O, MERGEL V, VOLLMER M, DORNER R.Correlated electron emission in multiphoton double ionization [J]. Nature.2000,405:658
[119] STAUDTE A, RUIZ C, SCHOFFLER M, ZEIDLER S D, WEBER T,MECKEL M, VILLENEUVE D M, CORKUM P B, BECKER A, DORNER R.Binary and Recoil Collisions in Strong Field Double Ionization of Helium [J].Phys Rev Lett.2007,99:263002
[120] RUDENKO A, de JESUS V L B, ERGLER T, ZROST K, FEUERSTEIN B,SCHR¨OTER C D, MOSHAMMER R, ULLRICH J. Correlated Two-ElectronMomentum Spectra for Strong-Field Nonsequential Double Ionization of He at800nm [J]. Phys Rev Lett.2007,99:263003
[121] FARIA, LIU X, SANPERA A, LEWENSTEIN M. Classical andquantummechanical treatments of nonsequential double ionization withfew-cycle laser pulses [J]. Phys Rev A.2004,70:043406
[122]. HO PHAY J, EBERLY J H. Classical Effects of Laser Pulse Duration onStrong-Field Double Ionization [J]. Phys Rev Lett.2005,95:193002
[123] ZHOU Y, LIAO Q, LU P. Mechanism for high-energy electrons innonsequential double ionization below the recollision-excitation threshold [J].Phys Rev A.2009,80:023412
[124] KANG H, QUAN W, WANG Y, LIN Z, WU M, LIU H, LIU X, WANG B B,LIU J, GU Y Q, JIA X Y, J LIU, CHEN J, CHENG Y. Structure Effects inAngle-Resolved High-Order Above-Threshold Ionization of Molecules [J]. PhysRev Lett.2010,104:203001
[125] Ho J, EBERLY J H. Classical Effects of Laser Pulse Duration on Strong-FieldDouble Ionization [J]. Phys Rev Lett.2005,95:193002
[126] YE D F, LIU X, LIU J. Classical Trajectory Diagnosis of a Fingerlike Pattern inthe Correlated Electron Momentum Distribution in Strong Field DoubleIonization of Helium [J]. Phys Rev Lett.2008,101:233003
[127] J. CHEN, J. FAN, Y. LI, S. P. YANG. Semiclassical theory of molecularnonsequential double ionization[J]. Phys Rev A.2007,76:013418
[128] HAO X, LI W, LIU J, Chen J. Effect of the electron initial longitudinal velocityon the nonsequential double-ionization process [J]. Phys Rev A.2011,83:053422
[129] WANG X, EBERLY J H. Effects of Elliptical Polarization on Strong-FieldShort-Pulse Double Ionization[J]. Phys Rev Lett.2009,103:103007
[130] WANG X, EBERLY J H. Elliptical Polarization and Probability of DoubleIonization [J]. Phys Rev Lett.2010,105:083001
[131] HAO, WANG, JIA, LI, LIU, Chen. Nonsequential double ionizationof Ne in an elliptically polarized intense laser field [J]. Phys Rev A.2009,80:023408
[132] LI Y, CHEN J, YANG S P, LIU J. Alignment effect in nonsequential doubleionization of diatomic molecules in strong laser fields [J]. Phys Rev A.2007,76:023401
[133] CHEN J, LIU J, FU B, ZHENG W M. Interpretation of momentum distributionof recoil ions from laser-induced nonsequential double ionization bysemiclassical rescattering model [J]. Phys Rev A.2000,63:011404
[134] PARKER J S, DOHERTY B J S, TAYLOR K T, SCHULTZ K D, BLAGA C I,DIMAURO L F. High-Energy Cutoff in the Spectrum of Strong-FieldNonsequential Double Ionization [J]. Phys Rev Lett.2006,96:133001
[135] LEIN M, GROSS E K U, ENGEL V. Intense-Field Double Ionization ofHelium: Identifying the Mechanism [J]. Phys Rev Lett.2000,85:4707–4710
[136] ECKHARDT B, SACHA K. Classical threshold behaviour in a(1+1)-dimensional model for double ionization in strong fields [J]. J Phys B.2006,39:3865–3871
[137] ZHANG Z, PENG Liang-You, XU Ming-Hui, ANTHONY F. STARACE, ToruMORISHITA, and QIHUANG GONG, Two-photon double ionization of helium:Evolution of the joint angular distribution with photon energy and two-electronenergy sharing, Phys. Rev. A,2011.84,043409.
[138] ZHANG Z, PENG, GONG, and MORISHITA T, Momentum space analysis ofmultiphoton double ionization of helium by intense attosecond xuv pulses,Optics Express2010,18,8976.
[139] PARKER J S, MOORE L R, MEHARG K J, DUNDAS D, TAYLOR K T.Double-electron above threshold ionization of helium[J]. J Phys B.2001,34:L69
[140] FOUMOUO E, KAMTA G L, EDAH G, PIRAUX B. Theory of multiphotonsingle and double ionization of two-electron atomic systems driven byshort-wavelength electric fields: An ab initio treatment [J]. Phys Rev A.2006,74:063409
[141] PIRAUX B, BAUER J, LAULAN S, BACHAU H. Probing electron-electroncorrelation with attosecond pulses[J]. Eur Phys J D.2003,26:7–13
[142] HASBANI R, CORMIER E and BACHAU H, Resonant and non-resonantionization of helium by XUV ultrashort and intense laser pulses [J]. J. Phys. B:At. Mol. Opt. Phys.2000,332101.
[143] http://www.pcpop.com/doc/0/521/521832_all.shtml
[144] http://www.cnblogs.com/chunshan/archive/2011/07/18/2110076.html
[145] http://news.watchstor.com/industry-141011_1.htm
[146] PALACIOS A., RESCIGNO T. N., MCCURDY C. W.. Time-dependenttreatment of two-photon resonant single and double ionization of helium byultrashort laser pulses [J]. Phys Rev A.2009,79:033402
[147] De BOOR C，A practical guide to Splines.(Springer, New York,1978)
[148] JOHNSON W R, BLUNDELL S A and SAPIRSTEIN J，Finite basis sets for theDirac equation constructed from B splines,[J] Phys. Rev. A,1988,37,307.
[149] CHANG T N， Energy levels and the oscillator strengths of the Be atomdetermined by a configuration-interaction calculation with a infinite basis setfrom B splines,[J] Phys. Rev. A,198939,4946.
[150] CHANG T N，Combined perturbation and conˉguration-interaction calculationfor theˉne-structure level splittings of the states of helium,[J] Phys. Rev. A,1989,39,6129
[151] SHI T Y, BAO C G and LI B W，Energy Spectra of the Confined AtomsObtained by Using B-Splines,[J] Commun. Theor. Phys.,2001,35,195
[152] ZHANG Y X, LIU Q, SHI T Y, The Hydrogen Molecular Ion in Strong FieldsUsing the B-Spline Method, CHIN. PHYS. LETT.2013,Vol.30, No.4,043101
[153] HU S L, ZHAO Z X, SHI T Y, Alignment-Dependent Ionization of CO2in theIntense Laser Fields: Single-Active-Electron Approach,[J] CHIN. PHYS. LETT.2013, Vol.30, No.10,103103.
[154] Li-Yan Tang, Yong-Bo Tang, Ting-Yun Shi, and J. Mitroy, Solution of theDirac Coulomb equation for helium-like ions in the Poet-Temkin model,[J] TheJournal of Chemical Physics,2013,139,134112.
[155] Hu S L and Shi T Y, Vibrational transition spectra of H+2in a strong magneticfield, Chin. Phys. B,2013, Vol.22, No.9,093101