非線形逆トムソン散乱によるガンマ線渦の発生

Yoshitaka Taira1, Masahiro Katoh2

1: National Institute of Advanced Industrial Science and Technology (AIST)2: Institute for Molecular Science (IMS)

The 15th Annual Meeting of PASJ, WEOM04, 8/8/2018

-π

π

-π

π 0

1

0

1

Optical vortices forming helical wavefrontsPhase Spatial distributionWavefront

Carrying ℓħ orbital angular momentum (OAM) Representative optical vortex: Laguerre Gaussian mode

Topological charge

( )φiE exp∝

ℓ= 0

ℓ= 1

Y. Taira, Generation of gamma-rays carrying orbital angular momentum by inverse Compton scattering 11

Poynting vector and total AM

L. Allen et al., Phys. Rev. A 45 (1992) 8185.L. Allen et al., Prog. Opt. 39 (1999) 291.

++

+∝×= z

R kzzz eeeBES φρ ρ

ρ

22

Spin AM + OAM = ± ħ +ℓħ or ℓħ

spread of the beam

Circularly polarized optical vortex

Linearly polarized optical vortex

Spiral Poynting vector gives OAM

k: wave number of LG lightρ: distance from the z-axis

z

Poynting vector of Laguerre Gaussian mode

Total angular momentum

2

Ω

/ zHk(

µ√)

W

∆m–2 –1 0 1 2

mph=–24

3

2

1

0

Transfer of OAM using optical vortex lasers

C. T. Schmiegelow et al., Nat. Comm. 7 (2016) 12998.

To a micro particle To a valence electron

Quadruple transition at 729 nm of 40Ca+ ion.

SAM = ―1OAM = ―1

Rabi

freq

uenc

y

+1/2mJ =–1/2

+3/2 +5/2+1/2–1/2–3/2mJ =–5/2

729

nm

4S 1/2

3D5/2

∆m =―2

+1―10

+2

AM = 0

Tim

e

OAM + SAMOAM φ 2 µm

N. B. Simpson et al., Opt. Lett. 22 (1997) 52.3

Purpose

1 m

10 cm

1 cm

1 mm

100 µm

10 µm

1 µm

100 nm

10 nm

100 pm

1 nm

Wavelength

103

102

101

100

10-1

10-2

10-3

10-4

10-5

Energy (eV) 104

105 6

10

710

810

X-raysUltraviolet

VisibleInfra-redMicrowaves

10 pm

1 pm

100 fm

10 fm

LaserMicro/THz wave

Developed vortex beams

Generation of gamma-ray vortices (more than sub-MeV energy) and development of their application.

Unexplored region

Except for the electromagnetic wave

300 kV electron Cold neutron

Gamma-ray vortex

UV X-ray

4

0 30 60 90 120 150 1800

0.02

0.04

0.06

0.08

θ [deg]

dσtw

/ dΩ

[b/s

r]

θp = 0o

θp = 30o

θp = 60o

θp = 90o

(b)

Applications of gamma-ray vortices

Other potential application

Compton scattering

Insight into the proton structureProton spin puzzle: Only 30% of the proton spin is carried by the quark spin.

If OAM of gamma-rays affects to OAM of quark or gluon, it becomes novel probe of the proton spin.

Excitation of nucleus, Generation of positron vortices, Astrophysics, etc.

GeV gamma-ray

J. A. Sherwin, Phys. Rev. A 96 062120 (2017).

θp: Momentum ratio between transverse and longitudinal component

They may be applied to solid state physics by being expanded to magnetic Compton scattering.

Cross section (E0 = 500 keV)

5

Plane wave

Charge, m = 4

OAM = m × nn=0n=―1 n=+1 n=+2

n=―2

Generation of optical vortices

J. Courtial et al., Opt. Comm. 159 (1999) 13.M. W. Beijersbergen et al., Opt. Comm. 112 (1994) 321.

B. J. McMorran et al., Science 331 (2011) 192.

Cylindrical lens

Spiral phase plate

Fork grating

6

Optical vortices from free electrons

2nd harmonics(1ħ OAM)

1 spiral interference fringe(Helical + Spherical)

99 eV photonsJ. Bahrdt et al., PRL 111 034801 (2013).M. Katoh et al., Sci. Rep. 7 6130 (2017).

S. Sasaki et al., PRL. 100 124801 (2008).M. Katoh et al., PRL. 118 094801 (2017).

An electron moving on a circular trajectory emits optical vortices

This was demonstrated in ultraviolet and soft X-ray regions.

Electric field emitted by a helical undulator

nth higher harmonics carry (n―1)ħ OAM

( ) exp 1C i n φ +∝ −E e

Electron

7

Gamma-ray vortices via NITSNonlinear inverse Thomson scattering (NITS)

Electron

Circularly polarized laser

Y. Taira et al., Sci. Rep. 7 5018 (2017).Y. Taira et al., The Astrophysical Journal 860 45 (2018).

Gamma-ray vortex

γ0: Lorentz factor of an electron

a0: Laser strength parameter EL: Energy of laser photon

Gamma-ray energyElectron trajectory inside a laser

nth higher harmonics carry (n―1)ħ OAM

1018 W/cm2 reaches a0 ≃ 1−2 −1 0 1 2 −20 0

20−20

0

20

z (µ m)

x (µ m)

y (µ m)

2020

41 2

Ln EEaγγ

=+

8

-3 0 3γ 0 sin θ cosφ

-3

0

3

γ 0 si

nθ

sin

φ

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

-3 0 3γ 0 sin θ cosφ

-3

0

3

γ 0 si

nθ

sin

φ

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

-3 0 3γ 0 sin θ cosφ

-3

0

3

γ 0 si

nθ

sin

φ

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

Spatial distributions of NITS gamma-raysn = 1 n = 2

OAM = 1ħOAM = 0

OAM = 2ħ

n = 3 Only higher harmonic gamma-rays show annular intensity distribution, which is consistent with the characteristics of an optical vortex.

Y. Taira et al., Sci. Rep. 7 5018 (2017).9

NITS using RF accelerated electronsSLAC BNL M. Babzien et al., PRL 96 054802 (2006).C. Bula et al., PRL 76 3116 (1996).

with 0.01 mm Ag foil

Spatial distributions of linearly polarized X-rays

10

DC

C yar-X

CCDCCD

Delay stage fLWFA=1m, F/13 1.4mmfcol =0.8m, F/25

2.4m

LaserInput 1.5J

Collisionposition 20µm Al

10µm Al +250µm Kapton

Electronspectrometer

0.3J

1.2J

300µm conicaldeLaval nozzle

0 10 20 30Electron beam peak energy [MeV]

X-r

ay b

eam

pea

k en

ergy

[keV

]

40 500

10

20

30

40

50

20 35 50electron energy [MeV]

Number ofelectrons in the beamscattered X−Ray photons/msr

4

8

6

a0 = 0.0

a0 = 0.83

NITS using laser wakefield accelerated e-Ludwig-Maximilians-Universität München

AIST

U of Nebraska-Lincoln

Rutherford Appleton Laboratory

K. Khrennikov et al., PRL 114 195003 (2015).

E. Miura et al., APEX 7 046701 (2014).

W. Yan et al., Nat. Phot. 11 514 (2017).

G. Sarri et al., PRL 113 224801 (2014).J. M. Cole et al., PRX 8 011020 (2018).

11

-10 0 10X (mm)

-10

0

10

Y (m

m)

0

1

Second harmonic X-rays at BNL (a0=0.6)

Y. Sakai et al., PRSTAB 18 060702 (2015).

This will be a X-ray vortex.

Measurement of a herical wavefront.

Next step

γ = 128

λ0 = 10.6 µm, pulse energy = 2 J,2ω0 = 100 µm, pulse width = 5 ps (FWHM)

Calculation (Y. Taira) Measurement (BNL)

E = 13 keV (λ = 0.095 nm)

Electron

Circularly polarized laser

X-ray vortex (13 keV)

OAM = 1ħ

12

Experimental plans at KPSI and UVSOR-IIIKPSI of QST

UVSOR-III

Microtron + J-KAREN-P PW laser (800 nm)

90-degree collision

0.4 MeV gamma-ray vortices.Nγ = 103 ~ 105 photons/sec

Measurement of annular distribution and helical wavefront.Study of Compton scattering.

Measurement of annular distribution.Study of Compton scattering and nuclear excitation.

Purpose:

10 MeV gamma-ray vortices.Nγ ~ 800 photons/sec

γ0 = 300a0 < 3

γ0 = 1470a0 ~ 0.6

Ti:Sa laser

Electron bunchPurpose:

13

Measurement of γ-ray vortex is challenging

Explore measurement methods of γ-ray vortices

Energy (eV)

Wavelength

104 105 610 710 810 910

10 pm 1 pm 100 fm 10 fm 1 fm

Diffraction

InterferenceCompton scattering

Nuclear excitation

Pair production

Interaction with

hadrons

~10 keV

0.1~10 MeV 1 MeV <

1 MeV ~ 30 MeV 1 GeV <

14

Diffraction method

0

1

-50 0 50X (µ m)

-50 0 50X (µ m)

-50

0

50

Y (µ

m)

Triangle aperture

Electron

Triangle aperture20 µm

Imaging detectorMagnet

Circularly polarized laser X-ray vortex Diffracted X-ray

ℓ= 1 ℓ= 2 A triangle aperture can be used to measure the helical wavefronts.

R&D is carried out at SPring-8.

2nd harmonicsCalculated diffraction pattern (5keV)

3rd harmonics

15

AcknowledgmentThis work was supported by JSPS Overseas Research Fellowships and JSPS KAKENHI Grant Number 18H03477.Dipangkar Dutta (Mississippi State University).Joseph Grames, Shukui Zhang, Dave Gaskell, Matthew Poelker, Geoffrey Krafft, Andrew Hutton (Jefferson Lab).Benjamin McMorran (University of Oregon).Masahiro Katoh (IMS). Yoshiki Kohmura (RIKEN).Takehito Hayakawa, Masaki Kando, Nobuhiko Nakanii (QST).Yusuke Sakai (UCLA).Group member of Radiation Imaging Measurement Group at AIST.Andrei Afanasev (George Washington University).Daniel Seipt (Helmholtz Institut Jena).Valeriy Serbo (Novosibirsk State University).

16

Summary

Measurement of gamma-ray vortices is a big issue.

In the low energy region, diffraction and interference methods must work.

Compton scattering may work around MeV energy region.

Thank you for your attention!

Gamma-ray vortices can be generated by nonlinear inverse Thomson scattering.

n-th higher harmonic gamma-rays carry (n―1)ħ OAM.

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