Download presentation

Presentation is loading. Please wait.

Published byGabriella Whiteaker Modified over 2 years ago

1
High-order Harmonic Generation (HHG) in gases by Benoît MAHIEU 1

2
Introduction Will of science to achieve lower scales – Space: nanometric characterization – Time: attosecond phenomena (electronic vibrations) Period of the first Bohr orbit : 150.10 -18 s λ = c/ν 2

3
Introduction LASER: a powerful tool – Coherence in space and time – Pulsed LASERs: high power into a short duration (pulse) Two goals for LASERs: – Reach UV-X wavelengths (1-100nm) – Generate shorter pulses (10 -18 s) Electric field time Continuous Pulses 3

4
Outline -> How does the HHG allow to achieve shorter space and time scales? 1.Link time / frequency 2.Achieve shorter LASER pulse duration 3.HHG characteristics & semi-classical model 4.Production of attosecond pulses 4

5
Part 1 Link time / frequency t / ν (or ω = 2πν) 5

6
LASER pulses Electric field E(t) Intensity I(t) = E²(t) Gaussian envelop: I(t) = I 0.exp( -t² / Δt² ) ‹t›: time of the mean value I(t) Δt: width of standard deviation Δt = pulse duration 6

7
Spectral composition of a LASER pulse F OURIER TRANSFORM Pulse = sum of different spectral components 7

8
Effects of the spectral composition Fourier decomposition of a signal: Electric field of a LASER pulse: More spectral components => Shorter pulse Spectral components not in phase (« chirp ») => Longer pulse 8

9
Phase of the spectral components TimeFrequency Fourier transform chirp + no chirp chirp - No chirp: minimum pulse duration Phase of the ω component Phase of each ω Moment of arrival of each ω Electric field in function of time All the ω in phase 9

10
Fourier limit Link between the pulse duration and its spectral width Fourier limit: Δω ∙ Δt ≥ ½ For a perfect Gaussian: Δω ∙ Δt = ½ Δt: pulse duration Δω: spectral width Fourier transform t I(t) t ω I(ω) ω t I(t) ω I(ω) 1 2 3 10

11
Part 1 conclusion Link time / frequency A LASER pulse is made of many wavelengths inside a spectral width Δω Its duration Δt is not « free »: Δω ∙ Δt ≥ ½ Δω ∙ Δt = ½: Gaussian envelop – pulse « limited by Fourier transform » If the spectral components ω are not in phase, the pulse is lengthened: there is a chirp Shorter pulse -> wider bandwidth + no chirp 11

12
Part 2 Achieve shorter LASER pulse duration 12

13
Need to shorten wavelength Problem: pulse length limited by optical period – Solution: reach shorter wavelengths Problem: few LASERs below 200nm – Solution: generate harmonic wavelengths of a LASER beam? 13

14
Classical harmonic generation In some materials, with a high LASER intensity Problems: – low-order harmonic generation (λ/2 or λ/3) – crystal: not below 200nm – other solutions not so efficient 2 photons E=hν1 photon E=h2ν λ 0 = 800nm fundamental wavelength λ 0 /2 = 400nm harmonic wavelength 14

15
Dispersion / Harmonic generation Difference between: – Dispersion: separation of the spectral components of a wave – Harmonic generation: creation of a multiple of the fundamental frequency I(ω) ω ω ω0ω0 2ω02ω0 ω 2 nd HG (Harmonic Generation) 15

16
Part 2 conclusion Achieve shorter LASER pulse duration Pulse duration is limited by optical period => Reach lower optical periods ie UV-X LASERs Technological barrier below 200nm Low-order harmonic generation: not sufficient One of the best solutions: High-order Harmonic Generation (HHG) in particular in gases gas jet/cell λ0λ0 λ 0 /n 16

17
Part 3 HHG characteristics & Semi-classical model 17

18
Harmonic generation in gases Grating Gas jet LASER source fundamental wavelength λ 0 Harmonic order nNumber of photons LASER output harmonic wavelengths λ 0 /n Classical HG Low efficiency Multiphotonic ionization of the gas: n ∙ hν 0 -> h(nν 0 ) => Low orders (New & Ward, 1967) 18

19
Increasing of LASER intensity Pulse length Intensity Years 10 9 10 13 10 15 10 19 W/cm² Energy : ε = 1J Short pulse : Δt 10 18 W/cm² Focused on a small area : S = 100μm² HHG 1fs 100fs 100ps 100ns 19671988 λ ~ 800nm 19

20
High-order Harmonic Generation (HHG) in gases Grating Gas jet LASER source fundamental wavelength λ 0 Harmonic order nNumber of photons LASER output harmonic wavelengths λ 0 /n How to explain? up to harmonic order 300!! quite high output intensity Interest : UV-X ultrashort-pulsed LASER source « plateau » « cutoff » (Saclay & Chicago, 1988) 20

21
Semi-classical model in 3 steps 3Recombination to fundamental state t ~ 2 h =I p +E k Acceleration in the electric LASER field t = 3 /2 2 Tunnel ionization t ~ /2 E laser K. Kulander et al. SILAP (1993) P.B. Corkum PRL 71, 1994 (1993) t = 0 Ip 1 EkEk Energy of the emitted photon = Ionization potential of the gas (Ip) + Kinetic energy won by the electron (Ek) Periodicity T 0 /2 harmonics are separated by 2 0 --- - - - - Electron of a gas atom Fundamental state 21

22
The cutoff law Kinetic energy gained by the electron F(t) = qE 0 ∙ cos(ω 0 t)&F(t) = m ∙ a(t) a(t) = (qE 0 /m) ∙ cos(ω 0 t) v(t) = (qE 0 /ω 0 m) ∙ [sin(ω 0 t)-sin(ω 0 t i )] t i : ionization time => v(t i )=0 E k (t) = (½)mv²(t) ∝ I ∙ λ 0 ² Maximum harmonic order hν max = Ip + E k max hν ∝ Ip + I ∙ λ 0 ² Harmonic order grows with: – Ionization potential of the gas – Intensity of the input LASER beam – Square of the wavelength of the input LASER beam!! Harmonic order nNumber of photons « plateau » « cutoff » hν max = Ip + E k max The cutoff law is proved by the semi-classical model 22

23
Electron trajectory Positive chirp of output LASER beam on attosecond timescale: the atto-chirp Emission time (t e ) x Time (T L ) 0 1 Harmonic order 15 17 19 21 0 Electron position Different harmonic orders different trajectories different emission times t e Long traj. Short traj. If short traj. selected (spatial filter on axis) Kazamias and Balcou, PRA 69, 063416 (2004) Chirp > 0Chirp < 0 Mairesse et al. Science 302, 1540 (2003) x(t i )=0 v(t i )=0 23

24
Part 3 conclusion HHG characteristics Input LASER beam: I~10 14 -10 15 W/cm² ; λ=λ 0 ; linear polarization Jet of rare gas: ionization potential Ip Output LASER beam: train of odd harmonics λ 0 /n, up to order n~300 ; hν max ∝ Ip + I.λ 0 ² Semi-classical model: – Understand the process: Tunnel ionization of one atom of the gas Acceleration of the emitted electron in the electric field of the LASER -> gain of Ek ∝ I∙λ 0 ² Recombination of the electron with the atom -> photoemission E=Ip + Ek – Explain the properties of the output beam -> prediction of an atto-chirp gas jet/cell λ0λ0 λ 0 /n Number of photons E=hν Order of the harmonic Plateau Cutoff hν max = Ip+Ek max 24

25
Part 4 Production of attosecond pulses 25

26
Temporal structure of one harmonic Input LASER beam – Δt ~ femtosecond – λ 0 ~ 800nm One harmonic of the output LASER beam – Δt ~ femtosecond – λ 0 /n ~ some nanometers (UV or X wavelength) -> Selection of one harmonic – Characterization of processes at UV-X scale and fs duration Intensity Time Harmonic order 26

27
« Sum » of harmonics without chirp: an ideal case Central wavelength: λ=λ 0 /n -> λ 0 = 800nm ; order n~150 ; λ~5nm Bandwidth: Δλ -> 25 harmonics i.e. Δλ~2nm Fourier limit for a Gaussian: Δω ∙ Δt = ½ Δω/ω = Δλ/λ ; ω = c/λ Δω = c ∙ Δλ ∙ (n/λ 0 )² Δt = (λ 0 /n)² ∙ (1/cΔλ ) Δt ~ 10 ∙ 10 -18 s -> 10 attosecond pulses! If all harmonics in phase: generation of pulses with Δt ~ T 0 /2N T 0 /2N T 0 /2 Intensity Time ~ 10 fs E(t) Time 27

28
Chirp of the train of harmonics Problem: confirmation of the chirp predicted by the theory During the duration of the process (~10fs): – Generation of a distorted signal – No attosecond structure of the sum of harmonics T 0 /2N T 0 /2 Intensity Time ~ 10 fs Emission times measured in Neon at λ 0 =800nm ; I=4 10 14 W/cm 2 28

29
H35-43 H45-53 H55-63 Y. Mairesse et al. Science 302, 1540 (2003) Δt=150 as (Δt TF =50 as) 23 harmonics + H25-33 (5) Optimum spectral bandwith: Δt=130 as (Δt TF =120 as) 11 harmonics 150 as 130 as Mairesse et al, 302, 1540 Science (2003)Mairesse et al, Science 302, 1540 (2003) (Measurement in Neon) Solution: select only few harmonics 29

30
Part 4 conclusion Production of attosecond pulses Shorter pulse -> wider bandwidth (Δω.Δt = ½) + no chirp i.e. many harmonics in phase Generation of 10as pulses by addition of all the harmonics? Problem: chirp i.e. harmonics are delayed => pulse is lengthened Solution: Selection of some successive harmonics => Generation of ~100as pulses 30

31
General Conclusion High-order Harmonic Generation in gases One solution for two aims: – Achieve UV-X LASER wavelengths – Generate attosecond LASER pulses Characteristics – High coherence -> interferometric applications – High intensity -> study of non-linear processes – Ultrashort pulses: Femtosecond: one harmonic Attosecond: selection of successive harmonics with small chirp In the future: improve the generation of attosecond pulses 31

32
Thank you for your attention! Questions? Thanks to: Pascal Salières (CEA Saclay) Manuel Joffre (Ecole Polytechnique) Yann Mairesse (CELIA Bordeaux) David Garzella (CEA Saclay ) 32

Similar presentations

Presentation is loading. Please wait....

OK

Femtosecond lasers István Robel

Femtosecond lasers István Robel

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on indian classical music Ppt on review writing groups Ppt on importance of friction in our daily life Ppt on simple distillation and fractional distillation Ppt on do's and don'ts of group discussion games A ppt on albert einstein Ppt on viruses and anti viruses software Ppt on personality development for teachers Ppt on means of communication in olden days Ppt on power system stability course