Avner Fleischer 1,2 , Ofer Kfir 1 , Zvi Diskin 1 , Pavel Sidorenko 1 and Oren Cohen 1

1. High-Harmonic Generation with Fully Controlled Polarization: Examination of the Role of Spin Angular Momentum in Extreme Non-Linear Optics AvnerFleischer1,2, OferKfir1, ZviDiskin1, PavelSidorenko1and Oren Cohen1 1Solid State Institute and Physics Department, Technion, Israel 2Department of Physics and Optical Engineering, Ort Braude College, Israel 1/15 December 3rd 2013, CHILI Avner Fleischer

2. 2 main messages : • Full control over the polarization of high-harmonics by controlling • the direction, strength and timings of attosecondrecollisions. • Energy-spin is not conserved! - ion - electron driver electric field (Lissajous curve) • Energy conservation: • Spin conservation: 2/15 December 3rd 2013, CHILI Avner Fleischer

3. ez Polarization states of High harmonics • Linear (ε~0) • Atoms, randomly-oriented molecules in linear driver A. McPherson et al. JOSA B 4 595 (1987); P. B. Corkum PRL 71 1994 (1993). ey ex ez ey • Elliptical (ε<0.4) • Atoms in elliptical driver • F. A. Weiheet al. PRA 51 R3433 (1995). • V. V. Strelkovet al. PRL 107, 043902 (2011). • Diatomic molecules in linear • driver • X. Zhou et al. PRL 102 073902 (2009). • Y. Mairesseet al. PRL 104 213601 (2010). ex M. Mölleret al. PRA 86 011401 (2012). • Poor Control. • Low efficiency (few %). • Circular (ε=1) • Reflective quarter-waveplate • B. Vodungboet al. Opt. Exp. 19 4346 (2011). • Transmission<4% 3/15 December 3rd 2013, CHILI Avner Fleischer

4. Polarization states of High harmonics : state of the art • Circularly-polarized HHs • Metal Nano-antennas in a circular driver A. Husakouet al. Opt. Exp. 19 25346 (2011). • Optical rotation quasi phase matching in a gas-filled waveguide L. Z. Liu et al. Opt. Lett. 37 2415 (2012). • Asymmetric diatomic molecules in circular driver K. J. Yuan et al. PRA 84 023410 (2011). • Harmonic polarization control by seeding • A. Fleischer et al. Opt. Lett. 38 223 (2013). • Complete Control. • Efficiency <10%. Atom • Molecules with rotational symmetry • in circular driver: • “Intra-molecular recollision” • O. Alon et al. PRL 80 3743 (1998). 4/15 December 3rd 2013, CHILI Avner Fleischer

5. Dynamical-Symmetry Resemblance  Atoms in Counter-rotating bichromatic circular driver Molecules with C6 rotational symmetry in circular driver: H12 H15 H18 H21 • A scheme: • Eichmann, H. et al., PRA 51, R3414 (1995) • S. Long et al. PRA 52 2262 (1995). • D. B. Miloševićet al. PRA 61 063403 (2000). • Selection rules observed • Harmonic elipticity not measured. 5/15 December 3rd 2013, CHILI Avner Fleischer

6. HHG with counter-rotating circularly-polarized bichromatic fields: circular harmonics ez 40fs, 2mJ ey H20 ex H19 H21 H18 H22 H17 • Selection rules in different gases: H23 Harmonic Order H24 Linear-linear Circular-circular 6/15 • High Efficiency (comparable to linear bichromatic scheme). December 3rd 2013, CHILI Avner Fleischer

7. Circular Harmonics ez • Measured ellipticity ey ex measured fit • Time domain: sub-cycle synchronization of 3 recollisions 7/15 December 3rd 2013, CHILI Avner Fleischer

8. X-ray Magnetic Circular Dichroism ez • XMCD of ferromagnet transition metals at the M-edge (~60eV) : ey ex • Absorption spectra for Cobalt : O. Kfiret al. , in collaboration with Kapteyn-Murnane group in JILA • Opposite helicity for consecutive harmonics • First downstream experiment of magnetism using our source 8/15 December 3rd 2013, CHILI Avner Fleischer

9. HHG with counter-rotating elliptical-circular bichromatic fields: • Changing   Changing the sub-cycle synchronization of the 3 recollisions (timings, directions, strengths)  changing the polarization state of the high harmonics. 9/15 December 3rd 2013, CHILI Avner Fleischer

10. Rich Spectra- Resolved Channels Experimental Spectra Numerical Spectra ez ey ex • Changing   breaking the C2.95v symmetry  new harmonics appear (and disappear)  selection rules for bichromaticHHG (b)- Log scale of (a) A. Fleischer et al. PRA 74 053806 (2006). • Resolved harmonic channels (identifying the integers n1, n2). • For instance 10/15 December 3rd 2013, CHILI Avner Fleischer

11. Controlling HHG Polarization ez numerical ellipticity·helicity Experimental and numerical Spectra and ellipticity·helicity ey (7,6) (6,7) ex (b)- Log scale of (a) • Changing  by as little as 80 modifies the polarization of all 8 presented harmonics from circular (ε=1) to linear (ε=0). 11/15 December 3rd 2013, CHILI Avner Fleischer

12. HHG as a “photon exchange” process: the role of the spin • Energy conservation: • Spin conservation: • Harsh constraint: ez ey • Many features, but not all, stem from and comply with spin conservation. For instance, the existence region for harmonic channels (n1+1,n1): ex • What about harmonic channels (n1-1,n1)? 12/15 • In sharp contrast to experiment and numerics! December 3rd 2013, CHILI Avner Fleischer

13. Going back to the numerics • ellipticity • Polarization-ellipse orientation ez ey ex • Are the 2 channels (n1+1,n1), (n1-1,n1) correlated? 13/15 December 3rd 2013, CHILI Avner Fleischer

14. HHG photon-pairing • NL correction to spin conservation: ez ey ex • Conservation law hold true for harmonic pairs: 14/15 December 3rd 2013, CHILI Avner Fleischer

15. Summary • Full control over polarization of HHG by attosecond & angle control over the 2D recollisions • Resolve (n1,n2) channels using single-atom physics • Role of spin angular momentum in extreme NLO • Conservation of spin angular momentum: • - Qualitative agreement with experimental & numerical results • - Quantitative disagreement with experimental & numerical results •  missing component. Correlated harmonics? 15/15 December 3rd 2013, CHILI Avner Fleischer

16. 11/11 June 12th 2013, CLEO Avner Fleischer

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20. 11/11 June 12th 2013, CLEO Avner Fleischer