Advanced Radiation Application E high-order harmonic generation & attosecond science
High-harmonic generation 高次高調波発生 No.
高調波発生 (Harmonic generation) 結晶 ガス等(crystal, gas) Linear optical effect 線形光学効果 弱い光 ω ω Material response is linear in light intensity 物質の応答が 入射光強度に比例 非線形光学効果 強い光 ω Nonlinear optical effect Nonlinear material response 物質の応答が 入射光強度に非線形に依存 ω,3ω,5ω, 波長変換 (frequency conversion) D = ε E + P P = ε [ χ E + χ E + χ E + ] (1) () (3) 3 非線形分極 (nonlinear) 線形分極 linear polarization 3ω ３次高調波(3rd harmonic) 5ω ５次高調波(5th harmonic) 反転対称な媒質では χ () = for a medium with inversion symmetry D E = µ t No. 3
摂動論的高調波発生 (perturbative harmonic generation) 3rd harmonic ３次高調波 Ionization 電離 5th harmonic ５次高調波 Ionization 電離 仮想準位 Virtual level ω Virtual level 仮想準位 ω ω ω 3 ω Ground state 基底状態 ω ω 5 ω ω ω Ground state 基底状態 次数が高くなるほど 発生効率は減少 Harmonic order Efficiency No. 4
高次高調波発生 High-harmonic generation (HHG) discovered in 1987 Intense laser pulse gas jet harmonics of high orders Highly nonlinear optical process in which the frequency of laser light is converted into its integer multiples. Harmonics of very high orders are generated.!! 新しい極端紫外 軟エックス線光源として注目される New extreme ultraviolet (XUV) and soft X-ray source No. 5
How high orders? Harmonic spectrum 高調波スペクトル Wahlström et al., Phys. Rev. A 48, 479 (1993) 41111-3 Takahashi et al. Takahashi et al., Appl. Phys. Lett. 93, 41111 (8) Harmonic intensity (arb. unit) 15 W/cm 1-1 - -3-4 -5-6 -7-8 FIG. 4.!Color online" Experimentally obtained harmonic spectra in Ar. Red and blue profile depict the spectra with # =.8!m pump and # = 1.4!m pump, respectively. Both HH spectra are normalized to the peak intensity. The laser focused intensity is adjusted to generate HH under a neutral condition for both wavelengths. The inset shows a measured two dimensional harmonic spectrum image driven by 1.4!m pump. 8 nm, 1.6 14 W/cm Only odd orders 奇数次のみ Simulation 3 Harmonic order 4 5 8 31= 6 was raised up to 6 mj, a maximal output energy exceeding 7 mj was achieved at the signal wavelength near 1.4!m. Temporal characterization of amplified OPA pulses was performed using a single-shot autocorrelation!ac" technique. A typical AC trace is shown in the inset of Fig.. a Gaussian pulse shape, the pulse width of 1.4!m nmassuming pulse was evaluated to be 4 fs in full width at half maximum!fwhm", the energy of which corresponds to the red filled circles in Fig. 3. The solid red line depicts the Fourier- matching cond propagation ax the Ar harmon cutoff energy w spectrum drive magnitudes low measured HH significant cuto the.8!m dr field generate higher energy This photon en predicted valu In conclu sources based monic beams. pulse width w 1.4!m. Total #45% conver HH spectrum extension exce file is almost p is attractive no the kiloelectro ergy scaling o 1 M. 6 Hentschel, R No. T. Brabec, P. Co ture!london" 4
Plateau プラトー - remarkable feature of high-harmonic generation plateau cutoff 15 W/cm Harmonic intensity (arb. unit) Wahlström et al., Phys. Rev. A 48, 479 (1993) 1-1 - -3-4 -5-6 -7-8 8 nm, 1.6 14 W/cm plateau cutoff Simulation 3 Harmonic order 4 5 プラトー(plateau) Efficiency does NOT decrease with increasing harmonic order. 次数が上がっても強度が落ちない カットオフ(cutoff) Maximum energy of harmonic photons e E 14 Ec Ip + 3Up Up (ev) = = 9.3 I(W/cm ) (µm) 4m ponderomotive energy 摂動論的には解釈できない(non-perturbative) No. 7
高次高調波発生のメカニズム Mechanism of HHG 摂動論的高調波 perturbative 電離 ionization 高次高調波 非摂動論的 HHG(non-perturbative) Laser field レーザー電場 recombination virtual state 仮想準位 再結合 発光 photon emission (HHG) ω ω ω 3 ω ground state 基底状態 electron 電子 トンネル 電離 tunneling ionization 電場中の古典 的運動 Semiclassical electron motion 3-step model Paul B. Corkum, Phys. Rev. Lett. 71, 1994 (1993) No. 8
高次高調波発生の３ステップモデル 3-step model of HHG Paul B. Corkum, Phys. Rev. Lett. 71, 1994 (1993) Ionization at ωt = φ E [(cos φ cos φ ) + (φ φ ) sin φ ] z= ω Ekin = Up (sin φ sin φ ) Recombination at φ = φret (φ ), which satisfies z = Laser field E(t) = E cos ωt レーザー電場 recombination Phase of recombination (phi_r) 35 3 再結合 発光 photon emission (HHG) 5 15 electron 電子 5 5 Phase of electron release (phi) 15 トンネル 電離 tunneling ionization 電場中の古典 的運動 Semiclassical electron motion No. 9
高次高調波発生の３ステップモデル 3-step model of HHG Field (in E) 1 field recombination ionization -1 3 There is the maximum kinetic energy which is classically allowed. Ec = Ip + 3.17Up 1 9 18 long short short long Electron kinetic energy (in Up) Simple explanation of the cutoff law カットオフ則のシンプルな説明 7 36 Phase (degrees) There are two pairs of ionization and recombination times which contribute to the same harmonic energy. Short and long trajectories No.
Even up to 1.6 kev, > 5 orders almost x-ray! Popmintchev et al., Science 336, 187 (1) a new type of laser- based radiation source レーザーをベースにした新しいタイプの放射線源 No. 11
re I ωl and I ωl,);# <+=4#>, 4+;# #?-+/3)', 3' /"%## 3$#',3)', +' ()$1-/# )./+3'# *% /"# %+3+/3)' )* /"#,/%)'&65%3;#' +/)$3( 31)#, -,3'& +of &#'#%+5 /+ #%%)%K, Advanced Radiation Application (Kenichi ISHIKAWA) for internal use only (Univ. Tokyo) Both PROOF and FROG-CRAB assume only 3@+/3)' )* /"#?-+'/-$that /%#+/$#'/ )* %#*: 8A:!"#,#,3$-+/3)', 63# /"# ;3,3.# y, ωl, and twice + BCD5+, 75%+6 1-,# '#+% /"# 1%)1+&+/3)' +=3, 3' /"# *+% E# 43/"3' #=1#%3$#' + B5#F,1#(/%+ %+'&# '#+% GD #F H*- 3'# 3' I3&: JKL +(()$1+'3#.6 /"# (+%%3#% photoelectrons emitted in a small angle in the streaking delay between + *#4,$+,+/#3/# 1-,#,:!"# +11#+%+'(# )*,+/#3/#,,#1+%+/#.6,#()' 1%# What happens if the fundamental laser!! MN *%)$ /"# (#'/%+ 1-,# #+, /) +,1#(/%+ $)-+/3)' 43/" + )* /"# 4+; photoelectron 1#%3) )* /43(# /"# +,#% 1")/)' #'#%&6L +, %#;#+#.6 /"# (+(-+/# +$13/-#,1#(/%-$ H*- 3'#K 3' /"# 3',#/ )* I3&: J:!"# #1/" )* /"3, 3'& /"# #; $)-+/3)' 1%);3#, +,#',3/3;# $#+,-%# )*,+/#3/# ()'/#'/:!"# +//),#()' information of pulse is very short? では 超短パルスレーザ $#+,-%#,1#(/%-$ )* /"# "+%$)'3( 75%+6 1-,# %#O#(/#.6 )-% *#45(6(# <)MP3 $-/3+6#% H)//# 3'# 3' /"# 3',#/ )* I3&: JK,#/, +,+*# -11#% "3&"5"+%$ ncoded in I ωl, 3T# Hentschel et al. (1) H$)%# ーによる高次高調波はどんな感じ )/"#% /"+' se are guessed *%+(/3)' )* 8 6 86 4 9 Energy (ev) 94 τx = 53 as 6 4 Time (fs) 4 6 Laser electric field (arbitrary units) X-ray intensity (arbitrary units) D %'3"- 5 P'($3('%#+.'&<E#(+8 1#'&<'Q* %#7"-&'( *1%#1*%; "&-E(# -. ' -.%<@<&'; "3(#4 5,# @<&'; "3(# * "&-+3$#+ *1 ' G<77<(-16 IDD<7>'& 1#-1 6' =-(37# >; ' B<.8 BCD< 17 6'3*'1 ('#& "3(# )*%, '1-1<'Q* "#'J *1%#1*%; -. L " FDF H $7!I4 R-& %,# #(#$%&*$ E#(+ -. %,# ('#& "3(#8 %9# :! #Q"9!# IS%IT :$-9&D# U!: )*%,! O D 9$-*1# "3(#:8 ),#&# %T * %,# "3(# +3&'%*-18 &D * %,# '163('& $'&&*#&.&#?3#1$; '1+! * %,# V'>-(3%#W ",'#4 5,# +',#+ (*1#,-) %,# -1<'Q* #(#$%&*$ E#(+ -. %,# ('#& "3(# (#'=*16 %,# *1%#&'$%*-1 *-14 5,# $'($3('%#+ @<&'; &'+*'%*-1 * #(#$%#+ )*%,*1 ' C<#M "#$%&'( &'16# 1#'& LD #M4 N1#%8 $'($3('%#+ 9.3(( (*1#: '1+ 7#'3&#+ 9+-%%#+ (*1#: @<&'; "3(# "#$%&37 #(#$%#+ >; %,# X-S!* &#Y#$%-&8,-)*16 %,'% '>-3% LDZ -. %,# %-%'( Y3#1$# * )*%,*1 ' C<#M &'16# '&-31+ LD #M4 Zhao et al. (1) Light emission takes place only once. )*+!"#$%&' (%' V3/" 3/, %+6 1-,# #;)-/3)' ) 3',/+'/+'#) ;3,3.# 3&",3'-,)3+!"# )/, 3' $+''#%L %#!9BD '$ / "+;# /) %#$ )'# &#'#%+ (+(-+/# 75%+6,)-%!"# $#+ +%&#% /"+' /3;#6 /"# 1 /"+/ /"# ). 1 Macmillan Magazine -18 sec) pulse Attosecond Fig. 3. (Color online) Characterization of a 67 as( XUV pulse. 光の放出は１回だけ (a) Streaked photoelectron spectrogram obtained experimenアト秒パルス tally. (b) Filtered I ω trace (left) from the spectrogram in L /3)' /) /"# %3;#% 1-3$1%);# /" $#'/,: No. 1 (a) and the retrieved I ωl trace (right). (c) Photoelectron spec-
Electronic dynamics Pulse duration (fs) Molecular vibration Molecular rotation From femtosecond to attosecond -15 sec -18 sec 5 4 3 1-6 -4 - -1 Single cycle at 8 nm - 196 197 198 199 Year (by J. Itatani) c= dt No. 13
Attosecond Science アト秒科学 No. 14
femtosecond, attosecond ミリ m -3 マイクロ μ -6 ナノ n -9 ピコ p -1 フェムト f -15 アト a -18 Light propagates during 3 fs 3 8 (m/s) 3 15 (s) = 9 6 (m) = 9 µm 15 No.
Why so short pulses? necessary shutter speed snapping ultrafast motion 16 for No.
Electrons moving around the nucleus Orbital period of the electron inside an atom Electron Nucleus π = π T = ω! e 1 mω r = 4π# r 4π# mr3 18 = 15 s = 15 as e Need for attosecond shutter No. 17
Dynamics of the Auger effect オージェ効果のダイナミクス A method to analyze ultrafast processes with a laser field. No. 18
Auger effect Ejection of a core electron オージェ効果 Photoelectron 光電子 Augerオージェ電子 electron 光電子 Photoelectron 内殻電子が電離 光電効果 Instantaneous Core-excited ion 内殻励起状態のイオン ~ a few fs Ejection of a valence electron 特性Ｘ線を放出するかわり に軌道電子を放出 Observation of the ejection of Auger electrons Ionizing X rays < a few fs Attosecond pulse No. 19
How to measure the electron ejection time? Pump イオン化を引き起 こす 高調波(HHG) Probe 電子の放出時刻を 測る レーザー光 laser No.
How to measure the electron ejection time? 高調波とレーザー光を遅 延時間を持たせて照射 Irradiate an atom with an attosecond pulse and laser pulse with delay No. 1
How to measure the electron ejection time? E(t) = E (t) cos(ωt + φ) dv dp =m = ee(t) dt dt ionization at t = tr で電離 Initial momentum 初速度 運動量! p = m(h ωx Ip ) p = p + p! " ee (t) sin(ωtr +φ) = 4mUp (tr ) sin(ωtr +φ) p = e E(t)dt = ea(tr ) ω tr 検出器での運動量 Momentum at the detector 検出器での運動エネルギー Kinetic energy at the detector p p = W + W W + m! 8W Up (tr ) sin(ωtr + φ) No.
How to measure the electron ejection time? 検出器での運動エネルギー! W W + 8W Up (tr ) sin(ωtr + φ) Electron kinetic energy Ejection time 光電子のエネルギーと 遅延時間の関係 No. 3
Life time of the Auger decay 8 fs Auger effect 光電子 オージェ電子 Auger electron 光電子 Probe Laser 75 nm Photoelectron Pump HHG soft x rays 13 nm フェムト秒程度の超高速過程が見える Ultrafast process fs No. 4
Delay in photoemission 光電効果には何アト秒かかるか No. 5
When Does Photoemission Begin? The photoelectric effect is usually considered instantaneous. e Ne Ne+ ts p Ne s Short light pulse Ne Ne+ tp e No. 6
rent experimental parameters, the small devia- time for allowing us to track the history of measure only re that modeled via the CVA give rise to a -as discrepancy in the relative delay. Accepting this small discrepancy, manyelectron models were applied to investigate the effects of electron correlation. As a first attempt, the multiconfigurational Hartree-Fock method was used to evaluate transition matrix elements from the ground state of Ne to states where the electron wave asymptotically propagated along the direction of the streaking NIR electric field. These calls for precise knowledge of the delay between the XUV pulse and an outgoing electron wave packet (henceforth, absolute delay). This can only be inferred from theory. For multielectron systems, such as Ne, physical description of the discrepancies revealed by this work proved to be a challenge. The sensitive experimental test to which time-dependent manyelectron models can now be subjected will benefit their development. lute delays relies tested time-dep Presently, only tw provide this deg photoionization cause of low S/N complex system of the photoelect streaking will atomic photoion sensitive tests, w ually improving predictions. Thes understanding of and will make t atomic chronosco Advanced Radiation Application (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo) photoemission c tions between the electron s exact motion and microscopic phenomena accurately (Fig. 1A) The s electron appears to come out 1 attoseconds earlier than the p electron! References a 1.. 3. 4. 5. 6. 7. 8. 9.. 11. Fig. 3. The relative delay between photoemission from the p and s subshells of Ne atoms, induced by Schultze et al.,sub -as, Science 38, 1658 () near -ev XUV pulses. The depicted delays are extracted from measured attosecond streaking spectrograms by fitting a spectrogram, within the strong-field approximation, with parameterized NIR and XUV fields. Our optimization procedure matches the first derivatives along the time delay dimension of the measured and reconstructed spectrograms, thereby eliminating the influence of unstreaked background electrons [for details on the fitting algorithm, see (9)]. From the analysis of a set of spectrograms, the measured delays and associated retrieval uncertainties are plotted against the amplitude of the vector potential applied in the attosecond streak camera. Spectrograms measured in the presence of a satellite attosecond pulse were found to exhibit a less accurate retrieval of the delay value. When a subset of data (red diamonds) that represents scans with less than 3% satellite pulse content was evaluated, a mean delay value of 1 as with a standard deviation of ~5 as was found. The green circles represent the result of analyzing spectrograms recorded with an XUV pulse with narrower bandwidth in order to exclude the potential influence of shakeup states contributing to the electron kinetic energy spectrum. 1. 13. 14. 15. 16. 17. 18. 19.. 1. H. Hertz, Annal W. Hallwachs, A A. Einstein, Ann E. P. Wigner, Ph C. A. A. de Carv 83 (). A. F. Starace, in (Springer, Berlin S. T. Manson, R M. Y. Ivanov, J. (7). A. Baltuška et a R. Kienberger e M. Nisoli, G. Sa (9). G. Sansone et a M. Schultze et a E. Goulielmakis M. Hentschel et A. Borisov, D. S Echenique, Che A. L. Cavalieri e A. K. Kazansky, 17741 (9) C. Lemell, B. So A 79, 691 ( J. C. Baggesen, 436; and er U. Becker, D. A Photoionization (Plenum, New Y A. Rudenko et a J. Mauritsson et 7 No.. 3.
Delay in photoemission Neon atom measured by attosecond streaking Ne Ne + e t s Ne s p from s (inner shell) from p (outer shell) delay 1 as Short light pulse short light pulse Ne t p Ne + e how long does it take? photon absorption What%is%happening? Dynamic multielectron correlation? electron emission e relative delay betweenphotoemissionfromthep Schultze al., Science and s subshells 38, of1658 Ne atom () stationary-state correlation Mechanism Eisenbud-Wigner-Smith delay Coulomb-laser coupling laser-induced state distortion unknown mechanisms... laser effect 8 1/
Time- dependent ab- initio simulation of inner- shell photoionization of an excited He atom (e.g., 1sp) XUV pulse 9 1/
Method: Time- dependent Schrödinger equation (TDSE) i " "t #(r 1,r,t) = [ H atom + ( z 1 + z )E(t)]#(r 1,r,t) H atom = " 1 # r 1 " 1 # r " r 1 " r + 1 r 1 1 r 1 = ' & #= # # 4" r < #+1 & Y $ #q (ˆ r 1 )Y #q (ˆ r ) # +1 r > q=%# P L "(r 1,r,t) = l1 l (r 1,r,t) $ $ # L l1 l r 1 r ( r ˆ 1,ˆ r ) L l 1,l " L l1 l (ˆ r 1,ˆ r ) = $ l 1 ml # m L Y (ˆ r ) l1 m 1 Y (ˆ r ) l,#m Discretization of m P l1 l L (r,r,t) on (r,r ) 1 1 grid Coupled spherical harmonics $ r 1 " j 1 # 1 ' & % ( )*r r " $ j # 1 ' & % )*r P L L ( l1 l (r 1,r,t) " P l1 l j 1 j (t) Ishikawa et al., Phys. Rev. A 7, 1347 (5), Phys. Rev. Lett. 8, 333 (1), Phys. Rev. Lett. 8, 931 (1) 3 1/
inner-shell photoionization of an excited helium atom XUV pulse 3D TDSE 1D TDSE Ĥ = i=1 ˆp i r i + 1 r 1 r Ĥ = i=1 ˆp i z i + a + a = b =.8a.u. 1 (z 1 z ) + b temporal evolution of the ionic state 1. remove the bound states of the neutral below the first ionization threshold. remove doubly excited (autoionizing) states 3. project on each ionic state 31 1/
3D simulation Photoionization of 1sp 1 P He temporal evolution of the ionic state two distinct time scales 7.9 ev, 5 cycles, 1 W/cm 3.x -6.5 XUV pulse p shake- up. 3p 1.5 1. 3d knock- up.5. 4 6 s 4f 8 the pulse ends Sukiasyan, Ishikawa, Ivanov, Phys. Rev. A 86, 3343 (1) 3 1/
1D simulation Similar dynamics is seen for 1D simulations from the 1st excited atom from the nd excited atom 8. -4 odd-number states populated by knock-up 3 (b) 3 (c) even-number states populated by knock-up 1. -3 4 4. -4 only even-number states can be populated by photoabsorption 4 3 4 Time, a.u. 1 5 5. -4 only odd-number states can be populated by photoabsorption 3 5 1 3 4 Time, a.u. Sukiasyan, Ishikawa, Ivanov, Phys. Rev. A 86, 3343 (1) 33 1/
6. -5 4. -5. -5 1. -3 4 5. -4 1D from the nd excited atom 7 (a) 3 4 5 Time, a.u. (c) 3 5 1 3 4 Time, a.u. 8 9 knock-up lasts longer for higher ionic channels. 3.x -6 Population.5. 1.5 1..5. Shake-up Knock-up XUV pulse 34 4 p 3p Time (as) 6 reflects the larger radii of the higher excited states 3d s 4f 8 XUV pulse 3D knock- up Sukiasyan, Ishikawa, Ivanov, Phys. Rev. A 86, 3343 (1) 1/
Time-dependent transition matrix element by the e-e interaction i(z 1,z,t) 1/ (z 1 z ) + b j(z 1,z,t).5..15 7-8 8-9 (b) 1D attosecond cascades.1.5 6-8 8-3 4 5 Time, a.u. increasing delays reflect the larger radii of the excited states involved Sukiasyan, Ishikawa, Ivanov, Phys. Rev. A 86, 3343 (1) 35 1/
summary knock-up in attosecond photoionization of an excited helium atom Post-ionization interaction of the outgoing core electron with the outer spectator electron Neon atom Short light pulse Ne s p short light pulse photon absorption Ne Ne t s t p Ne + from s (inner shell) from p (outer shell) how long does it take? What%is%happening? Dynamic multielectron correlation e Ne + electron emission e Sukiasyan, Ishikawa, Ivanov, Phys. Rev. A 86, 3343 (1) 36 1/