High-order harmonics with fully tunable polarization by attosecond synchronization of electron recollisions,, Ofer Kfir, Zvi Diskin, Pavel Sidorenko and Oren Cohen Department of Physics and Optical Engineering, Ort Braude College, Israel Solid State Institute and Physics Department, Technion, Israel A. Fleischer et al. Nature Photonics 8 543 (04). O. Kfir et al. Nature Photonics 9 99 (05). A. Fleischer et al. arxiv: 40.657 (04). A. Fleischer et al. Optics and Photonics News, Special Issue: Optics in 04. /9
High Harmonic Generation (HHG) Coherent (laser-like) Synthesis of high energy photons (kev) from low energy (ev) ones. Ω = n ω, n=...,7,9,,...,504 Table-top alternative to Free-Electron Lasers http://en.wikipedia.org/wiki/free_electron_laser Stanford LCLS (Linac Coherent Light Source ) /9 December 5, 0 Ort Braude
High Harmonic Generation (HHG) 3-step model i Ψ r, t = + V0 r eεcos ωt Ψ r, t t m HHG Larmor law: E, 0, m ( ) ( ) ( ) ( ) ( t) Ψ( r t) V ( r) Ψ( r t) ~670as Ω I p (3) Recombination () Free Evolution () Ionizaion in E ~00as P. B. Corkum PRL 7 994 (993). HHG T 3T π E ( t) = a( t) a t + a( t T) a t +... T = ω ( ) a t recombination light burst (attosecond chirp curve) Time domain: XUV radiation emitted as a train of ~00 attosecond pulses (as=0-8 sec). Frequency domain: a comb of odd-integer harmonics of. ω Ω / ω = n ± ω Ω / ω=,3,5,7,,... December 5, 0 Ort Braude Ω= 7 ω 3/9
Attosecond Camera Imaging ultrafast dynamics requires an ultrafast camera! 887 960 A. Fleischer et al. PRL 08 3003 (0). 990: FemtoChemistry 0 Attosecond Science December 5, 0 Ort Braude 4/9
High Harmonic Generation (HHG) Coherent (laser-like) Synthesis of high energy photons (kev) from low energy (ev) ones. 3-step model: (3) Recombination Ω () Free Evolution Ω = n ω, n=...,7,9,,...,504 Control over: Temporal characteristics of recollision. Spectral characteristics of recollision. I p () Ionizaion in E P. B. Corkum PRL 7 994 (993). Has been the subject of extensive study over the past 0 years. } Trajectory (atto-chirp curve) manipulation Spatial characteristics of the high-harmonic beam. o Polarization? December 5, 0 Ort Braude 5/9
Polarization states of High harmonics Linear (ε~0) Isotropic media (atoms, randomly -oriented molecules) in linear driver A. McPherson et al. JOSA B 4 595 (987); P. B. Corkum PRL 7 994 (993). Elliptical (ε<0.4) Atoms in elliptical driver F. A. Weihe et al. PRA 5 R3433 (995). V. V. Strelkov et al. PRL 07, 04390 (0). Diatomic molecules in linear driver X. Zhou et al. PRL 0 07390 (009). Y. Mairesse et al. PRL 04 360 (00). Low efficiency (few %). Poor Control. M. Möller et al. PRA 86 040 (0). - ion - electron driver electric field (Lissajous curve) e z e y e x e z e -x e y Circular (ε=) Reflective quarter-waveplate B. Vodungbo et al. Opt. Exp. 9 4346 (0). Transmission<5% 6/9
Polarization states of High harmonics? Circular (ε=) Metal Nano-antennas in a circular driver A. Husakou et al. Opt. Exp. 9 5346 (0). Optical rotation quasi phase matching in a gas-filled waveguide L. Z. Liu et al. Opt. Lett. 37 45 (0). Asymmetric diatomic molecules in circular driver K. J. Yuan et al. PRA 84 0340 (0). Harmonic polarization control by seeding A. Fleischer et al. Opt. Lett. 38 3 (03). s Complete Control. Atom Efficiency <0%. ε Molecules with rotational symmetry in circular driver: O. Alon et al. PRL 80 3743 (998). ω Ω = ±ω s + nω ω Ω / ω = 6n ± ω circ same ε Atoms in counter-rotating bichromatic circular drivers: Eichmann, H. et al., PRA 5, R344 (995) S. Long et al. PRA 5 6 (995). D. B. Milošević et al. PRA 6 063403 (000). Ω / ω = 3n ± circ ( ω,ω ) Selection rules observed Harmonic ellipticity not measured. 7/9
HHG with counter-rotating circularly-polarized bichromatic fields: circular harmonics = β = 45 45 0 0 ( ω, ω ) Ω/ ω 3n Correct selection rules Ω / ω = 3n ± High Efficiency (comparable to linear bichromatic scheme). 8/9
Circular Harmonics H9 polarization scan: measured fit ε 9 = 0.95 A. Fleischer et al. Nature Photonics 8 543 (04). Time domain model: sub-cycle synchronization of 3 recollisions 0 T 0 T ax ( t) = a( t) + cos( 0 ) a t + cos( 40 ) a t 3 3 0 T 0 T ay ( t) = 0 + sin ( 0 ) a t + sin ( 40 ) a t 3 3 Ω / ω = 3n ± circ ε =, h =+ 3n+ 3n+ ε3n =, h3n = ellipticity helicity 9/9
X-ray Magnetic Circular Dichroism (XMCD) XMCD of ferromagnet transition metals at the M-edge (~60eV) : ( ω,ω ) Absorption spectra of magnetized Cobalt: up down I I XMCD = I up down + I β = tanh ( XMCD) kωd Im n = β ± β [ ] Δβ-Magneto-Optical dichroic absorption coefficient. O. Kfir et al. Nature Photonics 9 99 (05). Opposite helicity for consecutive harmonics. First downstream experiment of magnetism using our source. 0/9
HHG with counter-rotating elliptical-circular bichromatic fields: Breaking the symmetry: Changing the sub-cycle synchronization of the 3 recollisions (timings, directions, strengths) changing the polarization state of the high harmonics. ( ω,.95ω ) 0 α = β = 45 Ω / ω = 3n ± / ω.95n Ω = ± /9
HHG channels α is scanned β = 45 0 ( ω,.95ω ) Experimental Spectra Numerical Spectra (3D-TDSE) Changing α away from 45 0 breaking the C.95v symmetry new harmonics appear (and disappear) selection rules for any bichromatic HHG scheme Ω = nω + nω, n+ n = k Ω / ω =.95n ±, ± 3,... A. Fleischer et al. PRA 74 053806 (006). A. Fleischer et al. Nature Photonics 8 543 (04). Resolved harmonic channels (identifying the integers n, n ). For instance channel ( 7, 6 ) =7 +6.95= H8.7 With i.e., channels not resolved. ( ) ( ) ( ω, ω) 7,6 =,4 = H9 /9
HHG with tunable polarization Experimental and numerical Spectra and ellipticity helicity numerical ellipticity helicity Changing α by as little as 8 0 modifies harmonic polarization from circular (ε=) to linear (ε=0) without compromising efficiency! 3/9
HHG as a photon exchange process: the role of the spin Energy conservation: Spin conservation: Harsh constraint: Ω = n ω + n ω ( n, n ) ( n n ) In sharp contrast to experiment and numerics! σ, σ = n σ + n σ Many features, but not all, stem from and comply with spin conservation. For instance, the existence region for harmonic channel (7,6): σ σ ( ) = 7 sin 7,6 ( α ) + 6 ( ) 7sin 6 ( ) ( α 76, ). 8 α 6 7. 0 0 What about harmonic channel (6,7)? σ 6sin 7 6,7 ( ) ( α ) α = 0 45 only 4/9
Going back to the numerics ellipticity helicity ε h Polarization-ellipse orientation φ Are the channels (n +,n), (n -,n) correlated? 5/9
Possible solution: HHG photon-pairing σ ( n,n ) = n σ + n σ + δ ( n,n ) Non linear correction to spin conservation: δ ( n,n ) = δ ( n, n ) N ( n,n )δ ( n,n ) ( n, n ) N ( n,n ) ( h ε )( n, n ) ε ( n, n ) + n sin ( α ) + n 0 Conservation law don t hold true for single harmonic but do for harmonic pairs: Ω n + n ω + n + n.95ω ( n, n ) + Ω( n, n ) = ( ) ( ) σ ( n,n ) + σ ( n,n ) = ( n + n ) σ + ( n + n ) σ 6/9
Polarization fan harmonics: Coalescence of the channels A scheme: e.g., ( ω,.95ω ) Ω = 9 ω + 8 ω = H 4.6, σ = Ω ( 9,8) ( 6,5) = 8 ω + 9 ω = H 5.55, σ = + ( 8,9) ( 5, 6) ω What happens when? Ω Ω H7, σ =? ( 9,8) ( 8,9) ( 9,8) ω α = 45 β = 45 A. Fleischer et al. arxiv: 40.657 (04). 0 0 7/9
Summary and future directions: Problem: Ellipticity comes at the expense of efficiency. - ion - electron driver electric field (Lissajous curve) Problem Solution ( ω ω ), Solution: Bright high-harmonics with fully-controlled polarization by controlling the direction, strength and timings of attosecond head-on recollisions in a D plane. Role of spin angular momentum in HHG: Energy-spin not conserved! Energy conservation: Ω = n ω + n ω, n + n = k σ n σ + n σ, σ Spin conservation: missing component. Correlated harmonics? 8/9
Future directions: Attosecond pulses with circular and elliptical polarizations. Study of Chirality: geometrical and magnetic. Ultrafast magnetism: high spatiotemporal imaging of magnetic domains. Thank you! S. Eisebitt et al. Nature 43 885 (004) (by synchrotron) 9/9