High order harmonic generation and applications

High order harmonic generation and applications E. CONSTANT Centre Laser Intenses et Applications H39 H69 ELI & Hilase Summer School 2016 1 21 26 August 2016

Introduction Laser are unique light sources: they are a key to confine spatially the light and achieve very high photon flux. Short pulses offer the possibility to follow dynamics by taking snapshot of an excited system and follow its evolution (stroboscopy or pump probe) if the pulse is shorter than the dynamic time scale. Ultrashort pulse fs as are a key to follow ultrafast dynamics Short laser pulses also offer the possibility to confine light energy both in space and time and very high intensities are accessible. I (W/m 2 ) = 2 E (J) / (t pw 2 ) Focusing such intense laser on matter can strongly perturb it. This interaction can lead to several non linear processes : multiphoton excitation, ionization, photon emission, etc 2

A brief history of the high order harmonic field - Laser are over 50 years old: Th. Maiman (1960, ruby laser) - Femtosecond pulses and Ti:sapph laser years 1980 (P. Moulton, Opt. News 8, 9 1982). - Amplification of femtosecond Ti:Sapph laser: years 1990 (CPA by D. Strickland and G. Mourou, Opt. Comm. 56, p219 1985) - HHG in gases discovered in 1987 (Mc Pherson et al, JOSA B 4, 595 1987, M. Ferray et al, J. Phys. B 21, L31 1988) a broadband coherent ultrashort XUV source. - Physics of HHG understood (P.B. Corkum, PRL 71, p1994 1993) and proposition of isolated attosecond pulses production (P.B. Corkum, Opt. Lett. 19, 1840 1994) - 2000: Attosecond XUV pulses observed in the groups of P. Agostini (train of attosecond pulses P. M. Paul et al., Science 292, 1689 (2001)) and F. Krausz (isolated atto second pulses, Drescher et al, Science 291, 1923 2001) - Measurements, applications, HHG & rapid evolution of the lasers 3

Outline of the presentation Introduction and brief history Generation of high order harmonics in gases - Experimental setup and measured HHG characteristics - Underlying physics of HHG: single atom response and macroscopic emission. - Control of the harmonic pulse duration for attosecond XUV pulse production - Characterization of XUV harmonic pulses. Applications of harmonic generation HHG as an ultrashort XUV source HHG characteristics as a signature of the emitting medium 4

Generation of high order harmonics: typical setup Focusing of an ultrashort intense laser beam on a gaseous target under vacuum Characterization of the emitted photons. laser Iris Lens Gas (jet, cell, capillary) Grating miror Slit trap detector M. Ferray et al, J. Phys. B 21, L31 (1988) Mc Pherson et al, JOSA B 4, 595 (1987) XUV beam co-propagating with the fundamental beam 5

Spectral characteristics - Observation of XUV radiation with frequencies multiple to the fundamental frequency + odd harmonics only: w q = (2n+1) w 0 - Decrease in efficiency for low order harmonics and afterward constant efficiency over a broad frequency range (plateau) - No significant emission after a cutoff frequency. Cutoff law : ħw q = I p + 3.2 U p. U p =q 2 E 2 /4 mw 2 U p =9 ev @ 10 14 W/cm 2 & 800nm I p : ionization potential of the atom 6

Influence of the generating gas I p = 12.13 ev I = 7x10 13 Wcm -2 I p = 13.99 ev I = 1x10 14 Wcm -2 I p = 15.76 ev I = 2x10 14 Wcm -2 From J.F. Hergott, PhD Manuscript I p = 21.56 ev I = 4x10 14 Wcm -2 The gas species influences strongly the width of the plateau and the HHG efficiency 7

Influence of the laser intensity I 0 < I sat ħw c = I p + 3.2 U p (I 0 ) I 0 > I sat ħw c = I p + 3.2 U p (I sat ) The XUV signal depends strongly on I until I sat is reached Wahlström et al., PRA 48, 4709 (1993) 8

Impact of the pulse duration Harmonics generated in Neon for short and long pulses E. Priori et al. PRA 6, 063801 (2000) At high intensity, the plateau width increases when the pulse duration, t, decreases 9

Impact of the fundamental pulse wavelength K. Midorikawa Jpn. J. Appl Phys 50, 090001 (2011) Fundamental centered at 800 nm, E max ~ 55 ev (h35) with Ar. Fundamental centered at 1400 nm, E max ~ 100 ev (h99). For a given atom, it is possible to generate shorter XUV wavelength by using a fundamental with longer wavelength. Strong impact of the central wavelength 10

Impact of the polarisation of the fundamental pulse e = 0 Linear polarisation E(t) = E 0 (cos(wt) x + e sin(wt) y) HHG is very sensitive to the ellipticity, e, of the fundamental pulse. The efficiency is usually maximum for linear polarisation. 11

Typical efficiencies of HHG in gases Efficiency = energy in an harmonic pulse/ fundamental pulse energy At 800 nm: Xe, Kr 2-5x10-5 (q max ~ 21) Argon ~ 10-5 (q max ~ 35). Néon ~ 10-7 (q max ~ 81) Hélium ~ 10-8 (q max ~ 301). High average power XUV source (High rep rate laser or HHG in cavities). J. Boullet et al Opt. Lett. 34, 1489 (2009), J.Rothhardt New Jour. Phys. 16, 033022 (2014) Harmonic pulse with µj energy can be obtained with high energy fundamental lasers. J.F. Hergott, PRA 66 021801R (2002), E. Takahashi PRA 66, 021802 (2002). XUV intensities compatible with the observation of XUV induced non linear transitions. P. Tzallas et al, Nature 426, 267 (2003), E. Takahashi et al, Nature Com. 4, 2691 (2013) 12

Spatial coherence of the XUV beam Interference pattern at l = 60.8 nm (13 th harmonic) Michelson interferometer XUV interferometer without XUV beam splitter Beam splitters 50% - 50% Time delay Lens f = 500mm Aperture Gas jet Spherical grating f = 500 mm Beam laser l = 790 nm E = 6-10 mj @ 100 fs Image plane 0 order CCD camera MCP detector M. Bellini et al., Phys. Rev. Lett. 81, 297 (1998) 13

14 Spatial coherence of the XUV beam Coherence observation with Young slit (HHG in gas filled capillary) T. Popmintchev, Nat. Photonics 4, 822 (2010) r l Spectrally resolved far field structures due to spatial coherence A. Dubrouil et al. Nat. Com. 5 4637 (2014)

The physics underlying HHG in gases. 15

The three step semi classical model (strong field, low frequency) P. B. Corkum, PRL 71, 1994 (1993) 1: Ionisation 2: Oscillation 3: Radiative recombinaison emission of an XUV photon This coherent periodic process leads to HHG 16

Quantum electron wavepacket P.B. Corkum and F. Krausz, Nature physics 3, 381 (2007) Dipole due to the coherent superposition of two parts of a single wavepacket (free and bound) : the phase of the radiation is imposed by the laser: coherent emission. 17

2 nd step: classical motion and electron trajectory With m dv/dt = qe, E(t) = E 0 (t) cos (w 0 t +j) and initial conditions (x 0 =0, V 0 =0), we know the electron trajectory. It strongly depends on the ionization time t i. Some trajectories can bring the electron back to the initial position (0<wt i < p/2 [p]) x (t) = -(qe 0 /mw 2 ) [cos(wt) cos(wt 0 ) + w (t - t i ) sin(wt i )] oscillation drift 18

Classical motion: electron velocity An electron released (x=0, V=0) at t i in a field E(t) E(t) = E 0 (t) cos (w 0 t +j) acquires a velocity : V(t) = q/m w 0 {E 0 (t) sin (w 0 t + j) - E 0 (t 0 ) sin (w 0 t i + j) } This defines the kinetic energy, E c, at recollision (x=0) and the photon energy: hn xuv = I p + E c U p = q 2 E 2 / 4mw 2 This energy has a maximum of 3.17 U p and explains the cutoff law hn max = I p + 3.2 Up 19

Classical motion: attosecond emission (cutoff) The cutoff photons follow hn c = I p +3.2 U p And are emitted during: dt << T 0 HHG + spectral filtering = attosecond pulse emission (both for plateau and cutoff) T 0 = 2.66 fs @ 800 nm short long Pseudoperiodicity of T 0 /2: train of attosecond pulses + Time of emission linked to the IR field phase (crucial for measure & applications) dt < fs 20

Experimental observation of the attosecond structure Atomic ionization with IR + XUV Photo e - detection w 0 E P. M. Paul et al., Science 292, 1689 (2001) V. Véniard et al., Phys. Rev. A 54, 721 (1996) Sideband: some photoelectrons of specific energy are created by the simultaneous absorption of an XUV and the absorption (j q +j 0 ) or stimulated emission (j q+2 -j 0 ) of an IR photon S q+1 =A + B cos(2w O t + j q - j q+2 + Dj at ) w 0 w q w q+2 0 Photoelectron spectrum The amplitude of the sideband q+1 depends on the harmonic phase and on t, the delay between XUV and IR (oscillations) The position of these oscillations depends on the phase difference between two consecutive harmonics. Oscillations? Only if phase linked harmonics. Measuring j q -j q+2 is a way to reconstruct the temporal profile 21

Experimental observation of the attosecond structure Atomic ionisation with IR + XUV w 0 w 0 E j 13 - j 11 sideband j 15 - j 13 w q w q+2 0 j 17 - j 15 Photoelectron spectrum j 19 - j 17 Spectral filtering : H11 à H19 Reconstruction of the attosecond train with a single phase per harmonic + harmonic amplitude 250 as FWHM T 0 /2N 22 P. M. Paul et al., Science 292, 1689 (2001)

Large delay range scans for full reconstruction Loriot et al, J. Phys. 635, 012006 (2015) With high stability scans, it is possible to reconstruct the complete temporal profile by using several reconstruction approaches: Frog-crab, PCGPA, Proof, Ptychography etc. Y. Mairesse et al, PRA 71, 011401 (2005) M. Chini et al, Opt. Expr. 18 13006 (2010) M. Lucchini et al, Opt. expr. 23 29502 (2015) 23

Ionisation step Probabilistic (ADK formula) : periodicity Only possible if some neutral atoms remain. This implies I I sat Xenon (I p = 12.13 ev) I max ~ 8 10 13 W/cm 2 q max = 17 Krypton (I p = 13.99 ev) I max ~ 1.5 10 14 W/cm 2 q max = 27 Argon (I p = 15.75 ev) I max ~ 2.5 10 14 W/cm 2 q max = 41 Néon (I p = 21.56 ev) I max ~ 8.6 10 14 W/cm 2 q max = 119 Hélium (I p = 24.58 ev) I max ~ 1.5 10 15 W/cm 2 q max = 201 The plateau width increases with I p, for short pulses t and for long fundamental wavelength. 24

Recombination step Depends on the electron wavefunctions (bound and free) overlap. Maximum efficiency in linear polarisation (straight/curved motion). Maximum efficiency in the plateau with short fundamental wavelength (wave function transverse spreading). 25

Physics of HHG This simplified 3 steps model allows quantitative understanding but deeper understanding and quantitative predictions are also possible via quantum simulations with several levels of complexity (SFA model, TDSE, etc ) For references see for instance : M. Lewenstein et al, Phys. Rev. A 49, 2117(1994). P. Agostini and L. F. Di Mauro, Rep. Prog. Phys. 67, 813 (2004). F. Krausz and Misha Ivanov, Review of Modern Physics 81, 163 (2009). So far only the single atom response was considered but collective effects are also very important. 26

Macroscopic emission In the gas medium, many atoms are excited by the fundamental laser. Each atom can emit XUV light with a defined phase (coherent). The output XUV field is the summ of the emission of all the emitters. A coherent signal usually varies as the square of the density of emitters (P 2 ). This is only true if P does not change the propagation and generation conditions. Gas medium Propagation Maximum signal if all the harmonics are in phase at the exit of the medium k qk kq Dk L p D 0 K - Generalized phase matching Ph. Balcou et al. PRA 55, 3204 (1997) K grad(i) 27

Harmonic signal (arb. units) Impact of phase matching on HHG Durfee et al. PRL 83, 2187 (2002) Phase matching in long media (capillary) controlled by pressure On axis PM ~quasi 1D situation 10000 1000 100 H27 10 1 0 1 2 3 4 5 6 7 8 Cell length (mm) Maker Fringes S. Kazamias et al, PRL 90 193901 (2003) When the signal is maximum phase matching effects are not apparent The impact of phase matching on HHG strongly depends on the specific conditions (medium length, harmonic order, time dependent and 3D). 28

Re-absorption of the harmonics The XUV radiations are strongly absorbed by matter and if the emitting medium is too long, they will not exit it: T = exp(-z/l abs ). Ex l = 42 nm (q = 19 @ 800 nm) propagating in 10 mbar of Argon (r = 2.69 10 17 at/cm 3 ), s ~ 25 Mbarn (1Mbarn = 10-18 cm 2 ) leads to L abs = 1 / s r = 1.48 mm It is therefore necessary to consider both phase matching and re absorption of the harmonics that can reduce the effective medium length. Dk L p 29

Output photon flux (arb. units) Macroscopic efficiency E. Constant et al. PRL 82 1668 (1999) 1,0 0,5 No absorption Infinite L coh L >> L coh abs L = 10 L coh abs L = 5 L coh abs Macroscopic response close to optimum for L med > 3 L abs L coh > 5 L abs L = L coh abs 0,0 0 2 4 6 8 10 12 14 Medium length (L units) L med Lmed z Nout r Aq exp( ) exp( idkz) dz 2 L 0 abs The total signal depends on both the microscopic and macroscopic response. The shape of the beam can also be influenced by spatial coherence. abs 2 30

Control of the XUV pulse duration: from femtosecond to attosecond pulses HHG depends on many parameters and the periodicity of HHG leads to the emission of a train of attosecond pulses after spectral selection. Isolated as pulse can also be emitted if the periodicity is rapidly broken that is possible by modulating a critical parameter in HHG. Intensity gating : confinement by ultrafast variation of the fundamental intensity (few cycle pulses and cutoff selection). Polarisation gating : confinement by polarisation modulation. Ionization gating: microscopic confinement by depletion of the medium. Transient phase matching: Macroscopic confinement induced via ionization. Attosecond light house: confinement by modulation of the pulse wavefront direction combined with spatial post-selection. 31

Emission of as pulse via intensity gating Spectral selection: cutoff Ultrashort fundamental pulse : 5 fs Laser -10-5 0 5 10 t (fs) EUV XUV Isolated attosecond pulse after spectral selection of the cutoff photons. 32

Impact of the carrier envelop phase f = p/2 2 as pulses f = 0 single as pulse Strong cep influence on the emission of isolated attosecond pulses in the cutoff Baltuska et al. Nature 421, 611 (2003) Kienberger et al, Nature 427, 817 (2004) 33

Confinement by polarization gating Fundamental pulse Harmonic pulse Temporal domain P.B. Corkum, Opt Lett. 19, 1870 (1994) V. T. Platonenko and V. V. Strelkov, JOSA B 16, 435 (1999) O. Tcherbakoff et al., Phys. Rev. A 68, 043804 (2003) M. Kovacev et al., EPJD 26, 79 (2003) Z. Chang et al Josab 27 B16 (2010) GDOG Spectral domain 34

XUV signal (arb. Units) Polarization induced confinement in Neon I. J. Sola et al, Nature Physics 2, 319 (2006) d= 6.2 fs, t = 5 fs, d t g = 0.64 fs Theory: 215 as (85 as without chirp) CEP dependent emission of 1 or 0 attosecond pulses 0,5 0,4 0,3 0,2 Confined XUV emission in Neon (31788) (d = 5.04 fs, t = 5 fs, = 45 ) d= 5 fs, t = 5 fs, CEP dependent emission of 1 or 2 attosecond pulses 0,1 0,0 30 40 50 60 70 Harmonic order Strong impact of the carrier envelop phase for isolated pulse generation 35

Caracterisation of isolated attosecond pulses Intensity gate ~ 80 as, @ 80 ev MPQ Germany E. Goulielmakis et al, science 320 1614 (2008) Polarisation gate ~130 as, @36 ev G.Sansone et al Science 314, 443 (2006) Characterisation of the attosecond pulses by the streak camera technique: ionization of atoms by the XUV in presence of a rapidly evolving field 36

Attosecond streak camera E. Constant et al, Phys. Rev. A 56, 3870 (1997) J. Itatani et al. Phys. Rev. Lett. 88, 173903 (2002) Ionization by XUV only: detection of photoelectrons with velocityv 1 V 1 V 2 (t i ) MCP Ionization by XUV + intense laser field dv m dt qe velocity V(t) = V 1 + V 2 (t i ) V(t) = V 1 + V 2 sin (w 0 (t-t i )) + cte And after the pulse V = V 1 - V 2 sin (w 0 t i ) V 1 V tot (t i ) V tot (t i ) V 2 (t i ) MCP For an XUV pulse shorter than T 0 /2, the photoelectron energy distribution can give access to the temporal profile of the XUV pulse. 37

Applications of XUV harmonics Two main types of applications Harmonic as an XUV source to probe or excite a system (compact, coherent, ultrashort etc). Harmonics generated directly in a system under study. 38

Time resolved auger relaxation in Krypton Drescher et al, Nature 419, 803 (2002) 39

Electron spectra 40

Auger electrons created in Kr with 900 as pulses: Measured Auger life time 7.9 fs 41

Experimental setup for IR-XUV pump probe experiment. 42

Direct characterization of a few cycle IR pulse E. Goulielmakis et al. Science 305, 1267 (2004) 43

First direct characterization of a monocycle IR pulse E. Goulielmakis et al. Science 305, 1267 (2004) 44

Time resolved photoemission in solids (Tungsten) 45

Delays in photo emission Cavalieri et al., Nature 449 1029 (2007) Depending on their initial states, the photoelectrons seem to exit the solid at different times. Here experiments on Tungsten crystal (XUV 300 as 95 ev + 5 fs 750 nm). Similar delays were obsered in atoms and these observations initiated lot of discussions and theoretical works. 46

Direct harmonic generation in the system under study: an ultrashort probe sensitive to the medium structure XUV 47

Laser induced rotation of N 2 Laser S-pol H21 pol Mairesse et al. New Jour. Phys. 10 025028 (2008) H21 H19 H21 pol Laser P-pol HHG in molecules pre aligned by a short pulse shows the rotational dynamics of the molecules 48

Tomographic reconstruction of molecular orbitals J. Itatani et al Nature 432, 867 (2004) 49

Tomographic reconstruction of molecular orbitals J. Itatani et al Nature 432, 867 (2004) This approach is a way to access to the shape of the wavefunction and even the changes of sign inside a wavefunction 50

Ultrafast dynamics in NO 2 molecules Excitation around 400 nm + HHG in molecules: Access to stretching, bending, dynamics around conical intersection and dissociation. Pble: with ultrashort pulsed excitation only a small fraction of the molecules are excited 51

Ultrafast dynamics in excited NO 2 molecules Excitation grating technique : Y. Mairesse et al, PRL 100, 143903 (2008) 52

Spatialy resolved spectra 800 nm only 800 nm + 400 nm At t = 0. 800 nm + 400 nm t > 0. Diffraction due to structured excitation depends on excited molecules. 53

Long time of evolution: dissociation of NO 2 E exc < Seuil l= 407 nm bound E exc > Seuil l= 397 nm Dissociates 54

Short evolution time H.J. Woerner et al, Science 334, 208 (2011). Signatures of ultrafast dynamics around the conical intersection 55

Conclusion It is possible to generate high order harmonics in gases on a day to day basis. The underlying physics is well understood and some of it can be explained via simple models. Possible to control the XUV emission and even to confine it to attosecond duration. New approaches for HH generation, control and measurement are still appearing. Applications of these pulses are now blooming. 56