NRL Plasma Physics Division

Electro­Optic
and
THz
Diagnostics Daniel
Gordon, Michael
Helle*,
Dmitri
Kaganovich,
Antonio
Ting Naval
Research
Laboratory,
Plasma
Physics
Division,
Washington
DC *Georgetown
University,
Washington,
DC

2010 Advanced Accelerator Concepts Workshop, Annapolis, MD, June 13-19 Supported by Department of Energy and Office of Naval Research

Outline

• Background • Three
Dimensional
Effects • Short
Bunches • Conclusions

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THz
Techniques
for
Bunch
 Diagnostics

• Electro‐optic
sampling
is
a
well
established
 technique
for
measuring
THz
waveforms

• Short
electron
bunches
produce
THz
Hields ‐ Radiatively
through,
e.g.,
CTR ‐ Self
Hields • Electro‐optic
sampling
of
THz
Hields
due
to
short
 bunches
gives
information
about
the
bunch

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Electro­Optic
Effect DC electric field induces birefringence

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EO
Bunch
Diagnostic

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Electro­Optic
Decoding
of
THz
Fields v

y

u x

Upon input, laser is x-polarized. THz field is y-polarized. principle axes (u,v) are at 45°.

laser polarization Upon output, Eu and Ev are shifted in phase by ω Γ = (nu − nv )L c Phase shift gives THz field through nu − nv ∝ ET

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Balanced
Diode
Technique optical probe

EO-crystal

λ/4

Woll. Prism

Balanced PD

THz Wave

The differential signal on the diodes gives THz field |Ex | − |Ey | ∝ Γ 2

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2

Scanning a delay line produces the THz waveform.

Cross
Correlation
Technique EO crystal Woll. Prism

optical probe

THz Wave

signal gate

Dump

θ

SHG Crystal

Image of SHG crystal gives THz Intensity via ∆x sin θ ∆t = c

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|Ey |2 ∝ Γ2

Camera

EO
Response
of
Gallium­Phosphide Thin crystal has flatter response:

#G!Ω"$r!Ω"#

1.0

L=50 µm L=100 µm

0.8 0.6

L=200 µm

0.4 0.2 0.0

0

5 10 15 Frequency !THz"

20

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Characterization
of
Photoinjector
 Bunches
at
FLASH*
(DESY)

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e deflecting cavity diagnostic

linac

To cross correlator chirped optical probe

ZnTe or GaP

Analyzer

• Resolution of 40 fs achieved • Benchmarked against deflecting cavity method * G. Berden et al., Phys. Rev. Lett. 93, 114802 (2004), G. Berden et al., Phys. Rev. Lett. 99, 164801 (2007)

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Characterization
of
Bunches from
LWFA*
(LBL) CTR at plasma-vacuum interface

e

To other diagnostics

Plasma

THz Wave

optical probe

ZnTe or GaP

Analyzer

Camera, Spectrometer, etc.

Established 50 fs maximum bunch length * J. van Tilborg et al., Phys. Rev. Lett. 96, 014801 (2006), J. van Tilborg et al., Opt. Lett. 33, 1186 (2008)

Characterization
of
Bunches From
LWFA*
(RAL)

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Al Foil

e

To other diagnostics

Plasma

THz Wave

To cross correlator

optical probe ZnTe

Analyzer

• Inferred bunch duration < 38 fs * A.D. Debus et al., Phys. Rev. Lett. 104, 084802 (2010)

Simulation
Model: Extension
of
TurboWAVE

• 3D
PIC
combined
with
nonlinear
optics
model • Massively
Parallel • Arbitrary
crystal
orientations
and
parameters • Fully
explicit
Hields
and
material
polarization • All
orders
of
dispersion,
optical
+
THz • All
second
order
effects
(electro‐optic
effect,
 sum
generation,
difference
generation,
etc.)

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Nonlinear
Lorentz
Model Model dielectric as population of anharmonic oscillators: q 2 r¨i + νij r˙j + (Ω )ij rj + aijk rj rk = Ei m Typically use two oscillators: one in the UV, one in the THz. Form polarization and compute effective current density and charge density for use in PIC algorithm: P=

! s

qs ns fs · rs

(f is an oscillator strength, typically the identity matrix)

ρeff = ρ − ∇ · P Jeff

∂P =J+ ∂t

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Simulations
of
3D
Bunch
Fields in
a
Crystal

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• Pass bunch over crystal • Examine field in crystal • Speed of light frame • PML boundaries

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3D
Bunch
Fields
in
GaP
Crystal Crystal Dimensions

300 x 180 x 170 µm3

Bunch Size

8.4 µm radius, 80 fs long

Bunch Energy

250 MeV

x=0

Ey - Transverse Cut 15

z - ct = -158 µm

10 Electric Field (kV/cm)

Ey - Longitudinal Cut

5

0

-5

-10

-15

Animation
of
3D
Bunch
Fields Crystal Dimensions

300 x 180 x 170 µm3

Bunch Size

8.4 µm radius, 80 fs long

Bunch Energy

250 MeV

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Cherenkov
Wake
from
Dielectric
Surface* Consider coherent radiation emitted by 109 electrons at 250 MeV propagating parallel to the surface of a dielectric at a distance d:

Radiated Energy !erg"s#rad"

10!10 d = 0.1 mm

!12

10

d = 1 mm

10!14 d = 10 mm

!16

10

10!18 0.1

0.5 1.0 5.0 10.0 Frequency !THz"

50.0

There is an azimuthal dependence which is strongly peaked along normal to surface

* V.E. Pafomov, Zh. eksp. teor. fiz. 32 (3), 610 (1957)

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1D
vs.
3D
Models

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Waveforms offset for clarity

1D
Simulations
of
EO
Decoding 800 nm, 500 fs optical probe*

Vac.

Crystal

Vac.

To cross correlator x-pol.

THz Half-Wave

y-pol.

y-pol.

50 µm

signal intensity envelope

peak ~ 500 kV/cm

* wavelength not to scale

Boundaries absorb all radiation coming from inside simulation box

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Cross
Correlation
with
50
fs
Gate

70 60 50 40 30 20 10 0 1.0

60 fs Bunch* 30 Intensity !AU"

Intensity !AU"

120 fs Bunch*

1.2 1.3 Time !ps"

1.1

1.4

1.5

R = 0.022 !

R=!

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2 |E (ω)| dω y opt

2 dω |E (ω)| x opt

|Ey (t) ∗ G(t)|2

25 20

I(t)2

15 10 5 0 1.0

1.1

1.2 1.3 Time !ps"

1.4

1.5

R = 0.009

*pulse width defined by FWHM of I(t)

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Cross
Correlation
:
15
fs
Bunch

|Ey (t) ∗ G(t)|

Intensity !AU"

2.0

I(t)2

1.5

|Ey (t)|

2

1.0

0.5

0.0 1.0

1.1

1.2 1.3 Time !ps"

1.4

1.5

Even with delta-function gate (black curve), the bunch cannot be resolved. Red curve uses 50 fs gate.

2

Overall
Output
Spectra from
15
fs
Bunch y-polarization

Scattered THz

100

104 Spectral Intensity !AU"

Spectral Intensity !AU"

x-polarization

0.1 10!4

Phonon Resonance

!7

10

10!10

1

5

10

50 100 Frequency !THz"

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500 1000

Phonon Resonance

100

Scattered Light

1

0.01 10!4

1

5

10

50 100 Frequency !THz"

500 1000

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Detail
of
Optical
Spectra from
15
fs
Bunch Initial polarization (x)

Scattered polarization (y) 10 Spectral Intensity !AU"

Spectral Intensity !AU"

70 000 60 000

0.8 µm

50 000 40 000 30 000 20 000 10 000 0 350

360

Frequency !THz" 370

380

8 6 4 2 0

390

350

360

Frequency !THz" 370

spectral modulation due to etalon effect

!

R=!

|Ey (ω)| dω 2

opt

opt

|Ex

(ω)|2 dω

= 0.00075

380

390

Gabor
Transform
of
Optical
Pulse from
15
fs
Bunch

100X

Can be done experimentally via X-FROG

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X­FROG
Diagnostic Signal Gate

1 THz Modulation

BBO Crystal

3 THz Modulation

(Experimental Data)

Lens

Imaging Spectrometer 10 THz Modulation

Synthesis
of
THz
Pulses 0.7 THz Oscillator

Stretcher

Regen

G1 M1

1.0 THz L1 M2

Slits λ/2 GaSe

Amplifier

G2

Compressor

2.0 THz Bolometer F1

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Experimental
and
Simulated Phase
Matching
Curves
at
1.0
THz

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Conclusion

• Phonon
resonance
limits
time
resolution
of
 standard
EO
diagnostics
to
about
50
fs.

• 3D
simulation
model
developed ‐ Modeling
shows
superposition
of
CTR
and
 Cherenkov
wakes
in
EO
crystal

‐

Reduced
1D
models
work
if
probe
pulse
is
 spatially
separated
from
Cherenkov
wakes

• EO
Response
above
phonon
resonance
may
lead
 to
observable
frequency
shift

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