Advanced Radiation Engineering 放射線応用工学E Kenichi Ishikawa (石川顕一) http://ishiken.free.fr/english/lecture.html
[email protected]
高次高調波発生と アト秒科学 high-order harmonic generation & attosecond science
Advanced Radiation Application (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo)
High-harmonic generation 高次高調波発生
10/23 No. 2
Advanced Radiation Application (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo)
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 = ε0 E + P
€
P = ε0 [ χ E + χ E + χ E +] (1)
€ €
(2)
2
(3)
3
非線形分極 (nonlinear) 線形分極 linear polarization
反転対称な媒質では、 χ
(2)
for a medium with inversion symmetry
∂ 2D ∇ × ∇ × E = −µ 0 2 ∂t €
€3ω：３次高調波(3rd harmonic) 5ω：５次高調波(5th harmonic)
€ =0 €
10/23 No. 3
Advanced Radiation Application (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo)
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 €
3ω
€ € Ground state 基底状態 €
ω ω
5ω
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 ↓ 10/23 No. 4
Advanced Radiation Application (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo)
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 10/23 No. 5
Advanced Radiation Application (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo)
How high orders?
Harmonic spectrum 高調波スペクトル Wahlström et al., Phys. Rev. A 48, 4709 (1993)
041111-3
Takahashi et al.
Takahashi et al., Appl. Phys. Lett. 93, 041111 (2008)
Harmonic intensity (arb. unit)
1015 W/cm2
10
2
10
1
10
0
10
-1
10
-2
10
-3
10
-4
10
-5
10
-6
10
-7
10
-8
FIG. 4. !Color online" Experimentally obtained harmonic spectra in Ar. Red and blue profile depict the spectra with #0 = 0.8 !m pump and #0 = 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.
800 nm, 1.6×1014 W/cm2
Only odd orders 奇数次のみ
Simulation 0
10
20 30 Harmonic order
40
50
800÷31= 26
matching propagatio the Ar har cutoff ene spectrum magnitude measured significant the 0.8 !m field gene higher ene This photo predicted In co sources ba monic be pulse wid 1.4 !m. T #45% co HH spectr extension file is alm is attractiv the kiloele ergy scalin
was raised up to 26 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. 2. a Gaussian pulse shape, the pulse width of 1.4 !m nmAssuming pulse was evaluated to be 40 fs in full width at half maxi1 M. 6 Hentsc mum !FWHM", the energy of which corresponds to 10/23 No. the red T. Brabec, filled circles in Fig. 3. The solid red line depicts the Fourier-
ture !Lond
Advanced Radiation Application (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo)
Plateau（プラトー）- remarkable feature of high-harmonic generation plateau cutoff
1015 W/cm2
Harmonic intensity (arb. unit)
Wahlström et al., Phys. Rev. A 48, 4709 (1993) 10
2
10
1
10
0
10
-1
10
-2
10
-3
10
-4
10
-5
10
-6
10
-7
10
-8
800 nm, 1.6×1014 W/cm2
plateau cutoff
Simulation 0
10
20 30 Harmonic order
40
50
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 e2 E02 2 2 14 Ec Ip + 3Up Up (eV) = = 9.3 10 I(W/cm ) (µm) 2 4m ponderomotive energy
• 摂動論的には解釈できない(non-perturbative) 10/23 No. 7
Advanced Radiation Application (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo)
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 €
3ω 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)
10/23 No. 8
Advanced Radiation Application (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo)
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
ωt0 = φ0
E0 [(cos φ − cos φ0 ) + (φ − φ0 ) sin φ0 ] z= ω2 Ekin = 2Up (sin φ − sin φ0 )2 Recombination at φ = φret (φ0 ) , which satisfies z = 0 Laser field E(t) = E0 cos ωt レーザー電場 recombination
Phase of recombination (phi_r)
350 300 250
再結合→ 発光 photon emission (HHG)
200 150 100
electron 電子
50 0 0
50
100
Phase of electron release (phi0)
150
トンネル 電離 tunneling ionization
電場中の古典 的運動
Semiclassical electron motion 10/23 No. 9
Advanced Radiation Application (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo)
高次高調波発生の３ステップモデル 3-step model of HHG
Field (in E0)
1
field
0
recombination
ionization
-1
3
There is the maximum kinetic energy which is classically allowed. Ec = Ip + 3.17Up
1 0 0
90
180
long
short
short
2 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
270
360
Phase (degrees)
There are two pairs of ionization and recombination times which contribute to the same harmonic energy.
Short and long trajectories 10/23 No. 10
Advanced Radiation Application (Kenichi ISHIKAWA) for internal use only (Univ. of Tokyo)
Even up to 1.6 keV, > 5000 orders almost x-ray!
Popmintchev et al., Science 336, 1287 (2012)
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 10/23 No. 11
the retrieved pulse duration was 88 as. I ωL and I 2ωL ,)2;#0 , 4+;# #?-+/3)', 3' /"%## 03$#',3)', +'0 ()$1-/#0 )./+ /"# %+03+/3)' )* /"# ,/%)'&2650%3;#' +/)$3( 031)2#, -,3'& +of &#'#%+25 /+2 # Advanced Radiation Application (Kenichi ISHIKAWA) for internal use only (Univ. Tokyo) Both PROOF and FROG-CRAB assume that only 3@+/3)' )* /"# ?-+'/-$ /%#+/$#'/ )* %#*: 8A: !"#,# ,3$-2+/3)', 63#20 /"# ; ωL , and twice + BCD5+, 75%+6 1-2,# '#+% /"# 1%)1+&+/3)' +=3, 3' /"# *+% E#20 43/"3' #=1# + B5#F ,1#(/%+2 %+'&# '#+%streaking GD #F H*-22 23'# 3' I3&: JKL +(()$1+'3#0 .6 /"# ( photoelectrons emitted in a small angle in the lay between + *#4 ,$+22 ,+/#223/# 1-2,#,: !"# +11#+%+'(# )* ,+/#223/#, ,#1+%+/#0 .6 ,#() What happens if the fundamental laser !! MN *%)$ /"# (#'/%+2 1-2,# 2#+0, /) + ,1#(/%+2 $)0-2+/3)' 43/" + )* /" hotoelectron 1#%3)0 )* /43(# /"# 2+,#% 1")/)' #'#%&6L +, %#;#+2#0 .6 /"# (+2(-2+/#0 +$1 ,1#(/%-$ H*-22 23'#K 3' /"# 3',#/ )* I3&: J: !"# 0#1/" )* /"3, 3'& $)0-2+/3)' 1%);30#, + ,#',3/3;# $#+,-%# )* ,+/#223/# ()'/#'/: !"# +//), ormation of pulse is very short? では、超短パルスレーザ $#+,-%#0 ,1#(/%-$ )* /"# "+%$)'3( 75%+6 1-2,# %#O#(/#0 .6 )-% *#45
