Oren Cohen Solid State Institute and Physics Department, Technion, - PowerPoint PPT Presentation

Spin angular momentum in extreme nonlinear optics: Controlling the polarization of high-order harmonics Oren Cohen Solid State Institute and Physics Department, Technion, Israel QCN kick of meeting

Extreme Nonlinear Optics Group @ Technion PI: Oren Cohen Research fellow: Dr. Avner Fleischer PhD students: Pavel Sidorenko, Ofer Kfir & Oren Lahav MSc students: Tzvi Diskin, Zohar Avnat & Tsachi Batkilin Metrology of laser pulses Atmospheric plasma filamentation Ultrashort intense Sound wave Spatio-temporal solitons: Light bullets laser pulse Our Vision: Induce photonic structures in Linear propagation air from remote Nonlinear propagation: 3D solitons Frequency up-conversion to extreme UV and X-rays Develop ultrafast nano-imaging techniques & applications Vision: - enhance the process efficiency - control the EUV & X-rays properties

Spin angular momentum in extreme nonlinear optics Avner Fleischer, Ofer Kfir, Tzvi Diskin, Pavel Sidorenko and Oren Cohen Energy conservation        n n NL Medium HHG 1 1 2 2        2 n n 1 1 2 HHG   Spin conservation 1 Experiment: mixing of waves with controlled polarizations

Spin angular momentum in extreme nonlinear optics Avner Fleischer, Ofer Kfir, Tzvi Diskin, Pavel Sidorenko and Oren Cohen Energy conservation        n n NL Medium HHG 1 1 2 2        2 n n 1 1 2 HHG   Spin conservation 1 Experiment: mixing of waves with controlled polarizations Main achievements Spin angular momentum in XNLO • Full control over polarization of high-order harmonics using • a simple knob, without compromising efficiency. Missing quanta for conservation of angular momentum • don’t always coexist •

Spin angular momentum in extreme nonlinear optics Avner Fleischer, Ofer Kfir, Tzvi Diskin, Pavel Sidorenko and Oren Cohen Energy conservation        n n NL Medium HHG 1 1 2 2         2 + n n HHG 1 1 2   Spin conservation 1 Experiment: mixing of waves with controlled polarizations Main achievements Spin angular momentum in XNLO • Full control over polarization of high-order harmonics using • a simple knob, without compromising efficiency. Missing component for conservation of angular momentum • don’t always coexist •

Outline 6  Introduction to extreme nonlinear optics  High harmonic generation: - Polarization  Controlling the polarization of HHG  Spin angular momentum conservation NL Medium

High Harmonic Generation 7  Intense femtosecond pulse interacts with a gas generates high harmonics. I~10 14 W/cm 2 Extreme UV & x-rays A. McPherson et al ., JOSA B 4, 595 (1987) M. Ferray et al., J. of Phys. 21, L31 (1988). Kulander, K. C., et al . Laser Physics 3 , 359 (1993) P . B. Corkum, PRL 71 , 1994 (1993) 1 3 5 7 9 ⋯ M. Lewenstein et al., PRA 49, 2117 (1994) Frequency

Sources of Extreme UV & X-rays 8 HHG-based Sources ℏ𝜕 ~10 keV LCLS-SLAC  Imaging resolution ( ∝ 𝜇 )  Chemical sensitivity HHG → Femto and Atto-second pulses → Improved Coherency BESSY Synchotron

Ellipticity Effect 9  High harmonic radiation commonly composed of odd harmonics , with linear polarization 𝜁 ≈ 0 .  Ellipticity diminishes HHG efficiency  maximal measured HHG ellipticity 𝜁 < 0.4 Weihe, F.A., et al ., PRA 51 , R3433 (1995) Zhou, X., et al ., PRL 102 , 073902 (2009) Atom 𝑦 𝑧 ⊙ 𝑢 Driving Electric field Möller, M., et al . PRA 86 , 011401 (2012)  𝜁 = 

Circularly & Elliptically Polarized HHG 10 Circularly polarized HHG Using an extreme- UV “wave - plate” Long, S., et al ., PRA 52 , 2262 (1995) Transmission<4% Vodungbo, B., et al ., Opt. Exp. 19 , 4346 (2011) Milošević , D. B., et al ., PRA 61 , 063403 (2000) Down Stream “wave - plate” Alon, O., et al ., PRL 80 , 3743 (1998) Nobusada, K., and Yabana, K., PRA 75 , 032518 (2007) Yuan, K. J., et al ., PRA 84 , 023410 (2011) Lewis, Z. L., et al ., OL 37 , 2415 (2012) Husakou, A., Opt. Exp. 19 , 25346 (2011) Yuan & Bandrauk, PRL 110 023003 (2013) Elliptically polarized HHG Weihe, F. A., et al ., PRA 51 , R3433 (1995) Strelkov, V. V. et al ., PRL 107 , 043902 (2011) k  Z  Zhou, X., et al ., PRL 102 , 073902 (2009)      k  s 2 Atom Yuan, K. J. and Bandrauk., A. D.,PRA 83 , 063422 (2011) s same   Fleischer, A., et al. , OL 38 , 223 (2013) 

Circularly & Elliptically Polarized HHG 11 Circularly polarized HHG Long, S., et al ., PRA 52 , 2262 (1995) Pioneering experiment by Eichmann, H. et al ., PRA 51 , R3414 (1995) Milošević , D. B., et al ., PRA 61 , 063403 (2000) Alon, O., et al ., PRL 80 , 3743 (1998) Nobusada, K., and Yabana, K., PRA 75 , 032518 (2007) Yuan, K. J., et al ., PRA 84 , 023410 (2011) Lewis, Z. L., et al ., OL 37 , 2415 (2012) Husakou, A., Opt. Exp. 19 , 25346 (2011) Yuan & Bandrauk, PRL 110 023003 (2013) Elliptically polarized HHG Weihe, F. A., et al ., PRA 51 , R3433 (1995) Strelkov, V. V. et al ., PRL 107 , 043902 (2011) Zhou, X., et al ., PRL 102 , 073902 (2009) Yuan, K. J. and Bandrauk., A. D.,PRA 83 , 063422 (2011) Fleischer, A., et al ., OL 38 , 223 (2013)

Counter-Rotating Bi-Chromatic Driver 12 𝜇 = 800 𝑜𝑛 , left helicity 𝜇 = 400 𝑜𝑛 , right helicity 𝑦 ⊙ 𝑧 𝑨 𝐹 𝐼𝐼 𝑢 + 𝑈 = 𝑆 120 𝑝 𝐹 𝐼𝐼 𝑢 𝜇 = 400 𝑜𝑛 𝜇 = 800 𝑜𝑛 3 Right Left 𝑦 𝐹 400 𝑢 + 𝐹 800 𝑢 𝑧 Long, S. et al ., PRA 52 2262 (1995).

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

Comparable efficiency to HHG by lineally polarized driver 14 HH signal for 1.2W red & 0.67W blue H20 Linear-linear H19 Circular-circular H21 H18 H22 H17 H23 H24 Harmonic Order    / 3 k 1        n n 2 HHG 1 1 2 1        n n 2 No solutions with HHG 1 1 2      / 3 k Spin conservation 1 HHG 1  n n 2 =odd integer 1

Comparable efficiency to HHG by lineally polarized driver 15 HH signal for 1.2W red & 0.67W blue H20 Linear-linear H19 Circular-circular H21 H18 H22 H17 H23 H24 Harmonic Order             7 6 2 6 7 2 19 H 1 1 20 H 1 1                6 (1) 7 ( 1) 1 7 (1) 6 ( 1) 1 20 H 19 H

Circularly-polarized HHG Measured circularity •    0.95 19   theo 1 measured fit 19 Sub-cycle synchronization of 3 recollisions •        T   2 T          0 0 a t a t cos 120 a  t  cos 240 a  t   x 1 1 1      3 3         T   2 T        0 0 a t 0 sin 120 a t sin 240 a t      y 1 1      3 3    1  3k 1

High harmonic generation with counter-rotating elliptically-polarized bi-chromatic fields I  1.95 0 I  2 0 Changing  ,  . •

Rich spectra – Resolved channels Experimental Numerical Spectra Spectra        n n HHG 1 1 2 2

Rich spectra – spin angular momentum Experimental Numerical   Spin conservation 1 Spectra Spectra     f ( ) n n HHG 1 2 19H: (7 , 6) f(α) = 1 → σ HHG = +1 f(α) = 5/7 → σ 𝐼𝐼𝐻 = −1 20H: 6,7 f(α) = 1 → σ 𝐼𝐼𝐻 = −1        n n 1 1 2 2 HHG

Rich spectra – spin angular momentum Experimental Numerical Numerical Experimental Spectra Spectra Spectra Spectra        n n     HHG 1 1 2 2 n g ( ) n     HHG 1 2     f ( ) n n , f ( ) , g ( ) 1 HHG 1 2

Controlling HHG ellipticity Numerical Numerical spectra ellipticity * helicity Experimental intensity and ellipticity   Changing  by as little as 8 0 modifies the polarization of H19 from circular ( ε =1) to linear ( ε =0). •

Discrepancy in conservation of spin angular momentum Energy        • n n 1.95   1 2 n , n conser conserva vation: tion: 1 2 Spin •          conservation: n n , 1   1 1 2 2 n , n 1 2        6 7 1.95 H 19.65          6 7 1 H 19.65 1    0 1 45    1    0  1, 1 45         1 1 H 19.65 H 19.65 H19.65 19.65 should r should remain cir emain circular cularly-polariz polarized ed • regar gardless dless of of the the value of value of  . . Experiment and Experiment and numerics numerics indica indicate t te the opposit he opposite! •