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

Avner Fleischer1,2, Ofer Kfir1, Zvi Diskin1, Pavel Sidorenko1 and Oren Cohen1

1Solid State Institute and Physics Department, Technion, Israel2Department of Physics and Optical Engineering, Ort Braude College, Israel

December 3rd 2013, CHILI Avner Fleischer

1/15

High-Harmonic Generation with Fully Controlled Polarization:

Examination of the Role of Spin Angular Momentum in Extreme Non-Linear

Optics

• Energy conservation:

• Spin conservation:

2 main messages :•Full control over the polarization of high-harmonics by controlling

the direction, strength and timings of attosecond recollisions.

•Energy-spin is not conserved!

21,

2/15

1 2

1 21 2

1 2

, 1

n n

n n

- ion

- electron

driver electric

field(Lissajous

curve)


Circular (ε=1) • Reflective quarter-waveplate B. Vodungbo et al. Opt. Exp. 19 4346 (2011).

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).

ex

ezey

Elliptical (ε<0.4) • Atoms in elliptical driver F. A. Weihe et al. PRA 51 R3433 (1995). V. V. Strelkov et al. PRL 107, 043902 (2011).• Diatomic molecules in linear driver X. Zhou et al. PRL 102 073902 (2009). Y. Mairesse et al. PRL 104 213601 (2010).

•Poor Control. •Low efficiency (few %).

3/15

ex

ez ey

•Transmission<4%

M. Möller et al. PRA 86 011401 (2012).


Polarization states of High harmonics : state of the art Circularly-polarized HHs• Metal Nano-antennas in a circular driver A. Husakou et 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%.

s 2s k

Atom same

4/15

• Molecules with rotational symmetry in circular driver: “Intra-molecular recollision” O. Alon et al. PRL 80 3743 (1998). / 6 1

/ =5,7,11,13,...circ

circ

k


• A scheme: Eichmann, H. et al., PRA 51, R3414 (1995) S. Long et al. PRA 52 2262 (1995). D. B. Milošević et al. PRA 61 063403 (2000).

2,

/ =3k 1

/ =1,2, 3

circ

circ

,4,5, 6 ,7,8, 9 ,...

5,

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Dynamical-Symmetry Resemblance

Molecules with C6 rotational symmetry

in circular driver:

Atoms in

Counter-rotating bichromatic circular driver

/ 6 1

/ =5,7,11,13,...circ

circ

k

• Selection rules observed• Harmonic elipticity not measured.December 3rd 2013, CHILI Avner Fleischer

/ 3k • Selection rules in different gases:

HHG with counter-rotating circularly-polarized bichromatic fields:circular harmonics

40fs, 2mJ

• High Efficiency (comparable to linear bichromatic scheme).

2,

6/15

0

0

45

45


Circular Harmonics

• Measured ellipticity

• Time domain: sub-cycle synchronization of 3 recollisions

19 0.95

0 01 1 1

0 01 1

3k 1 3k 1

3k 1 3k 1

2cos 120 cos 2403 3

20 sin 120 sin 2403 3

1, 1

1, 1

x

y

T Ta t a t a t a t

T Ta t a t a t

hh

measured fit

7/15December 3rd 2013, CHILI Avner Fleischer

• Opposite helicity for consecutive harmonics • First downstream experiment of magnetism using our source

X-ray Magnetic Circular Dichroism • XMCD of ferromagnet transition metals at the M-edge (~60eV) :

8/15

2,

• Absorption spectra for Cobalt :

O. Kfir et al. , in collaboration with Kapteyn-Murnane group in JILA


5,1.9

9/15

• Changing Changing the sub-cycle synchronization of the 3 recollisions (timings, directions, strengths) changing the polarization state of the high harmonics.

HHG with counter-rotating elliptical-circular bichromatic fields:


• Resolved harmonic channels (identifying the integers n1, n2).• For instance

• Changing breaking the C2.95v symmetry new harmonics appear (and disappear) selection rules for bichromatic HHG

1 2 1 221 , 2 1n n n n k

A. Fleischer et al. PRA 74 053806 (2006).

10/15

Rich Spectra- Resolved Channels

0

is scanned

45

2.95 , 3,...1/ k

Experimental Spectra

Numerical Spectra

channel 7,6 = 18.7 since 7 1+6 1.95=18.7H December 3rd 2013, CHILI Avner Fleischer

• Changing by as little as 80 modifies the polarization of all 8 presented harmonics from circular (ε=1) to linear (ε=0).

Experimental and numerical Spectra and ellipticity·helicity

11/15

Controlling HHG Polarization

numerical ellipticity·helicity


HHG as a “photon exchange” process: the role of the spin• Energy conservation:

• Spin conservation:

• Harsh constraint:

1 2

1 2

1 1 2 2

221, 1

,

1

n n

n n

n n

n n

• Many features, but not all, stem from and comply with spin conservation. For instance, the existence region for harmonic channels (n1+1,n1):

12/15

7,6

7 6

0 0

,

7 6

1 7sin 2 6 1

22.

sin 2

8 6 .2

1

7

• What about harmonic channels (n1-1,n1)?

0

6,7 1 6sin 2 7 1

45 only

• In sharp contrast to experiment and numerics!December 3rd 2013, CHILI Avner Fleischer

Going back to the numerics• ellipticity

• Polarization-ellipse orientation

13/15• Are the 2 channels (n1+1,n1), (n1-1,n1) correlated?December 3rd 2013, CHILI Avner Fleischer

HHG photon-pairing• NL correction to spin conservation:

1 2 1 2

1 2

1 2

1 2

1 2

,1

, ,1 2

22,

,

2sin 2

1

n n n n

nn n

n n

n

n n

hn n

• Conservation law hold true for harmonic pairs:

14/15

1 2 2 1

1 2 2 1 1

1 2 1 2

1

,

2

,

, 2 1 2,

1.95

n n n n

n n n n

n n n n

n n n n

1 21 2

1 21

1 2

2

,,

,,, 0

n nn n

n

n nn n

nN

N


Summary

15/15

• 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?


11/11June 12th 2013, CLEO Avner Fleischer





Documents

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