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

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)Optical vortices forming helical wavefronts
Wavefront
Topologicalcharge

Phase

Spatial distribution
π1-ππ0ℓ= 01ℓ= 1-π0E ∝ exp (iφ ) Carrying ℓħ orbital angular momentum (OAM)
Representative optical vortex: Laguerre Gaussian mode
Y. Taira, Generation of gamma-rays carrying orbital angular momentum by inverse Compton scattering

1Poynting vector and total AM
Poynting vector of Laguerre Gaussian mode ρz k: wave number of LG light
S = E×B ∝  2e +eφ + e z  ρ: distance from the z-axis
2 ρkρ z + zR
spread of the beamSpiral Poynting vector gives OAM
z

Total angular momentum
Spin AM + OAM = ± ħ +ℓħ or ℓħCircularly polarized
optical vortex

Linearly polarized
optical vortex
L. Allen et al., Phys. Rev. A 45 (1992) 8185.
L. Allen et al., Prog. Opt. 39 (1999) 291.
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Transfer of OAM using optical vortex lasers
To a micro particle
AM = 0OAM

To a valence electron

OAM + SAM

φ 2 µmQuadruple transition at729 nm of 40Ca+ ion.

N. B. Simpson et al., Opt. Lett. 22 (1997) 52.

Ω (kHz / √µW)

Rabi frequencym J =–1/2

3D 5/24S 1/2+1/24m ph =–23

SAM = ―1
OAM = ―1210+5/2

nm―1 0∆m =―2+3/2+1 +2729

Time–1/2 +1/2–3/2m J =–5/2–2 –10 1∆m2C. T. Schmiegelow et al., Nat. Comm. 7 (2016) 12998.
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Purpose
Generation of gamma-ray vortices (more than sub-MeVenergy) and development of their application.
Unexplored
regionDeveloped vortex beams
Energy (eV)

1010678X-ray

1010 510 4

Ultraviolet

3Visible

Infra-red

101

10 2

100-1

Laser UVMicrowaves

Gamma-rayvortexX-rays

10 fm

100 fm

1 pm

10 pm

100 pm

1 nm

10 nm

100 nm

1 µm

10 µm

100 µm

1 mm

1 cm

10 cm

1m

Wavelength

1010-310 -21010 -4

10 -5

Micro/THz wave

Except for the electromagnetic wave

300 kV electron

Cold neutron
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Applications of gamma-ray vortices
Compton scattering
0.08oθp = 0dσtw / dΩ [b/sr]

Cross section (E0 = 500 keV)(b)

θ = 30o0.06p

θp: Momentum ratio between transverse andlongitudinal component

θ = 60opo

θ = 90
p

0.04

0.02

00306090
θ [deg]J. A. Sherwin, Phys. Rev. A 96 062120 (2017).

120150180

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

Insight into the proton structure
Proton spin puzzle: Only 30% of the proton spinis carried by the quark spin.
GeV gamma-rayIf OAM of gamma-rays affects to OAM of quark orgluon, it becomes novel probe of the proton spin.

Other potential application
Excitation of nucleus, Generation of positron vortices, Astrophysics, etc.
5Generation of optical vortices
Cylindrical lens

Fork grating
Plane wave
Charge, m = 4

Spiral phase platen=―2n=―1n=0 n=+1 n=+2OAM = m × n

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.
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Optical vortices from free electronsAn electron moving on a circular trajectory emits optical vortices
Electric field emitted by a helicalundulator

ElectronE ∝ C exp {i ( n − 1) φ } e +S. Sasaki et al., PRL. 100 124801 (2008).
M. Katoh et al., PRL. 118 094801 (2017).

nth higher harmonics carry (n―1)ħ OAM

This was demonstrated in ultraviolet and soft X-ray regions.
2nd harmonics(1ħ OAM)

1 spiral interference fringe(Helical + Spherical)
99 eV photons

J. Bahrdt et al., PRL 111 034801 (2013).
M. Katoh et al., Sci. Rep. 7 6130 (2017).
7Gamma-ray vortices via NITS
Nonlinear inverse Thomson scattering (NITS)
Gamma-ray vortex
Electron

Circularly polarized laser
Electron trajectory inside a laser
20y (µ m) 0−2020−2 −10 1z (µ m)2−200 x (µ m)nth higher harmonics
carry (n―1)ħ OAM

Gamma-ray energy
4nγ 02 ELEγ =1 + a02 2
γ0: Lorentz factor of an electron
EL: Energy of laser photon
a0: Laser strength parameter
1018 W/cm2 reaches a0 ≃ 1
Y. Taira et al., Sci. Rep. 7 5018 (2017).
Y. Taira et al., The Astrophysical Journal 860 45 (2018).
8Spatial distributions of NITS gamma-rays
n=10OAM = 0-3-33γ 0 sin θ sin φ

1.1
10.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.100γ 0 sin θ cos φ

0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
00OAM = 2ħ-3-30γ 0 sin θ cos φ

0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

n=20OAM = 1ħ-3-33

n=33γ 0 sin θ sin φγ 0 sin θ sin φ30γ 0 sin θ cos φ3Only higher harmonic gamma-rays
show annular intensity distribution,
which is consistent with thecharacteristics of an optical vortex.

3Y. Taira et al., Sci. Rep. 7 5018 (2017).
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NITS using RF accelerated electrons
SLAC

C. Bula et al., PRL 76 3116 (1996).

BNL

M. Babzien et al., PRL 96 054802 (2006).

Spatial distributions of linearly polarized X-rays

with 0.01 mm Ag foil

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NITS using laser wakefield accelerated eLudwig-Maximilians-Universität München
300µm conicaldeLaval nozzle

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

Collision
position

0.3J

ElectronspectrometerfLWFA=1m, F/13

Delay stage
50

X-ray beam peak energy [keV]

CCDDCC

1.4mm
fcol =0.8m, F/25

2.4m

AIST

Number ofelectrons in the beam
scattered X−Ray photons/msr

4010µm Al +250µm Kapton

20µm AlX-ra y C C D

1.2J

Laser
Input 1.5J

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

8630

U of Nebraska-Lincoln

42035
electron energy [MeV]50

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

20a0 = 0.0

100Rutherford Appleton Laboratorya0 = 0.83010203040

Electron beam peak energy [MeV]50G. Sarri et al., PRL 113 224801 (2014).
J. M. Cole et al., PRX 8 011020 (2018).
11Second harmonic X-rays at BNL (a0=0.6)
Electron

X-ray vortex (13 keV)

Circularly
polarized laser

γ = 128λ0 = 10.6 µm, pulse energy = 2 J,
2ω0 = 100 µm, pulse width = 5 ps (FWHM)

Calculation (Y. Taira)Y (mm)

1010-100-100X (mm)10OAM = 1ħMeasurement (BNL)This will be a X-rayvortex.
Next step
Measurement of aherical wavefront.
E = 13 keV (λ = 0.095 nm)
Y. Sakai et al., PRSTAB 18 060702 (2015).
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Experimental plans at KPSI and UVSOR-III
KPSI of QST

Microtron + J-KAREN-P PW laser (800 nm)
γ0 = 300
a0 < 3

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

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

UVSOR-III

90-degree collision
γ0 = 1470
a0 ~ 0.6
Electron bunch

Ti:Sa laser

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

Purpose:Measurement of annular distribution.
Study of Compton scattering and nuclear excitation.
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Measurement of γ-ray vortex is challenging
Energy (eV)104Wavelength

1051010 pm

61 pm

107100 fm

10810 fm

1 MeV ~ 30 MeV

InterferenceDiffraction

1 fm

Interaction
withhadrons

Compton scattering
0.1~10 MeV

91 GeV <Nuclear excitation~10 keV

101 MeV <Pair production

Explore measurement methods of γ-ray vortices

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Diffraction method
Triangle aperture
MagnetTriangle
aperture
20 µm

Circularly polarized laser X-ray vortex

Diffracted X-ray

ElectronImaging
detector

Calculated diffraction pattern (5keV)

Y (µ m)50

2nd harmonicsℓ= 1

3rd harmonicsℓ= 20-50-500X (µ m)50-500X (µ m)50

1 A triangle aperture can beused to measure thehelical wavefronts.

0R&D is carried out at
SPring-8.

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Acknowledgment
This 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).
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Summary
Gamma-ray vortices can be generated by nonlinear inverse
Thomson scattering.
n-th higher harmonic gamma-rays carry (n―1)ħ OAM.

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!
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