Polarization of the fastest flashes of light Oren

Polarization of the fastest flashes of light Oren Cohen Extreme nonlinear optics group Dr. Avner Fleischer, Ofer Kfir, Tzvi Diskin, Pavel Sidorenko

What are the (controlled) fastest flashes? Why do we care?

Stroboscopic photography Millisecond flash Controlled microsecond flash Bullet Piercing an Apple, 1964 (H. E. Edgerton).

The Birth of Ultrafast Technology Bet: Do all four hooves of a galloping horse ever simultaneously leave the ground? Leland Stanford Eadweard Muybridge The “Galloping Horse” Controversy Palo Alto, CA 1872 Time Resolution: 1/60 th of a second http: //www. artcyclopedia. com/artists/muybridge_eadweard. html

1887 1960 1990: Femto. Chemistry December 25, 2012 Ort Braude Avner Fleischer

Ultra-short laser pulses 2. 7 fs 800 nm 30 nm Attosecond pulses are produced through high-harmonic generation

What is high harmonic generation (HHG)? How it produces attosecond pulses?

Second-Harmonic Generation Ruby laser 347 nm Lens 694 nm Prism Quartz crystal Log intensity Photographic plate P. A. Franken et al, PRL 7, 118 (1961) Epump<<Eatomic Frequency

High-harmonic generation Soft X-ray beam I~1014 - 1016 W/cm 2 Typically λ=800 nm Log(Intensity) Epump~Eatomic Plateau Photon energy Cut-off energy Mc. Pherson et al. , JOSA B 4, 595 (1987) Ferray et al. , J. Phys. B 21, L 31 (1988)

High harmonic generation & attosecond pulses 1 0 Electron jiggles in the driving oscillating electric field. Recollision emission of attosecond burst of radiation Multiple re-collisions train of attosecond pulses & comb of high harmonics. Linear polarization A train of linearly polarized attosecond pulses Atom Spectrum Oscillating Electric field Mc. Pherson et al. , JOSA B 4, 595 (1987) Ferray et al. , J. of Phys. 21, L 31 (1988).

High harmonic generation (HHG) a unique light source Control - Coherence (laser-like) - Spectrum – broad / single harmonic - Spatial profile - Temporal Attosecond science - Polarization: our group A. Fleischer et al. , Nature Photonics 8, 543 (2014). O. Kfir et al. , Nature Photonics 9, 99 (2015).

Polarization h= +1 Helicity: h= ± 1

Quarter-wave plates: visible vs extreme UV Visible - Control polarization - Lossless Extreme UV Extreme-UV “wave-plate” - Lossy - Limited spectral regions - Sensitive - No applications Vodungbo et al. , Opt. Exp. 19, 4346 (2011)

Why control polarization?

Why was it difficult to control the polarization of high-order harmonics and attosecond pulses?

Ellipticity effect in HHG 16 Ellipticity diminishes HHG efficiency Ellipticity of HHG field <0. 4 Atom Möller, M. , et al. PRA 86, 011401 (2012)

Our method to produce circularly polarized high harmonics

Counter-rotating bi-chromatic drivers 18 Long et al. , PRA 52 2262 (1995). Bi-chromatic field 800 nm + 400 nm

Circularly polarized harmonics Atom t Spectrum HHG order

High harmonic generation with counter-rotating circularly polarized bi-chromatic fields

Comparable efficiency to HHG by lineally polarized driver H 20 H 19 Linear-linear Circular-circular H 21 H 22 H 23 H 24 Harmonic Order • Measured circularity measured fit H 18 H 17

Bright circularly-polarized HHG at Co M-edge

X-ray Magnetic Circular Dichroism (XMCD) • XMCD of ferromagnet transition metals at the M-edge (~60 e. V) : • Absorption spectra of magnetized Cobalt: Δβ-Magneto-Optical dichroic absorption coefficient. • • O. Kfir et al. Nature Photonics 9 99 (2015). Opposite helicity for consecutive harmonics. First downstream experiment of magnetism using our source.

What about circularly polarized attosecond pulses? H 20 H 19 H 23 H 24 H 17 H 22 H 21 H 18 Harmonic Order We somehow need to suppress the harmonics with right/left helicity. We do it through phase matching.

Need phase matching to generate bright x-rays beams Bright x-ray beam Pump laser x-ray beam Nonlinear medium Phase (momentum) matching Phase matching - the emission from all atoms interfere constructively!

Harmonic field Phase mismatch Phase matched Non phase matched z LC=π/Δk Armstrong et al. , PR 127, 1918 (1962)

Helicity-dependent phase matching If are phase matched, the are not

Time domain - chiral attosecond pulses Fourier transform of the 80% measured harmonic spectrum corresponds to train of pulses with duration down to 170 as attoseconds and elliptical polarization. 60% 60% Different degree of circular 60% polarization of the pulses may stress the peak contrast in chiral experiments HHG order Time [fs]

Summary • Full control over polarization of HHG • First experiments using circularly-polarized HHG • Conservation of spin angular momentum in HHG • Phase matching of circularly polarized harmonics • Towards circularly polarized attosecond pulses A. Fleischer et al. , Nature Photonics 8, 543 (2014). O. Kfir et al. , Nature Photonics 9, 99 (2015). • Next? • Circularly polarized attosecond pulses • High spatiotemporal imaging of magnetic domains • Chiral molecules • Circulating electronic motion in molecules