Selection of SiC for the electro-optic
measurement of short electron bunches
K.S. Sullivan & N.I. Agladze
Short electron bunches are needed for dense collisions in
particle accelerators.
How to measure the shape of a short electron bunch?
Use the cross-correlation between coherent THz produced
by the bunch together with narrow-band incoherent
visible/UV radiation.
Electro-optic crystals
• Material-specific
properties
• Electro-optic effect on
polarized light
http://dev.fiber-sensors.com/wp-content/uploads/2010/08/electro-optic_example-01.png
Cross-correlation of coherent and incoherent
radiation in EO medium
THz coherent pulse
Incoherent pulse
t1
• Cross-correlation
• Non-collinear
propagation enables a
delay dependence
CRYSTAL
t2
Advantages
I
0
DETECTOR
x
1. Single shot capability
2. Resolution determined by
the EO crystal dispersion
Cross-correlation: principle experiment
Source
Zinc Telluride (ZnTe)
• High electro-optic coefficient
• Useful frequency range limited by low vibrational mode
(190 cm-1 compared to GaP’s 366 or SiC’s 794)
• Dispersion due to TO resonance
http://refractiveindex.info/figures/figures_RI/n_CRYSTALS_ZnTe_HO.png
Silicon Carbide (SiC)
• Comparable electro-optic coefficient to ZnTe
• Higher TO resonance permits larger frequency range
Polytype Choice
Cubic SiC
• Pure
• Expensive
Hexagonal SiC
• Subject to free carriers
• Readily available
http://japantechniche.com/wp-content/uploads/2009/12/sdk-sic-mosfet.jpg
6H Considerations
• Free carriers or doping
• Metallic behavior
• Electro-optic coefficient’s
angular dependence
http://metallurgyfordummies.com/wp-content/uploads/2011/04/doping-semiconductor.jpg
6H Transmission
• Increase in transmission
toward Brewster angle
• Lacks metallic free carriers
• Unexpected feature at
~110 wavenumbers
6H Absorption Coefficient
• Use transmission relation
to plot absorption
coefficient, α
• Ideally zero
• Notable frequency
dependence
• Unknown feature possibly
due to fold-back or material
defects
Focus on 3C
• Unlike 6H, 3C does not
require calculation of an
angle to maximize the
electro-optic coefficient
• Cubic/Zinc-blende
structure similar to ZnTe
and GaP
• Necessary to calculate
electro-optic response
http://upload.wikimedia.org/wikipedia/commons/4/4f/SiC3Cstructure.jpg
Electro-optic Response
• Transmission coefficient based on refractive index
• Integral uses frequency, thickness, phase velocity
of THz radiation, and group velocity at optical
frequency
• Shape of resulting function comes primarily from
the mismatch between phase and group velocity
Dielectric Model
Because of the electro-optic response function’s reliance on
phase and group velocities, we need a model of the dielectric
function from the UV to the THz.
Comparative Responses
• GaP shown at optical group
velocity at 8352 cm-1
• ZnTe at 12500 cm-1
• SiC at 37495 cm-1
• Cut-off frequency set at 4
THz
Electro-optic Performance
• Previous approach masks
full electro-optic properties
• Transmission, crystal
thickness, and electro-optic
coefficient all important
• Figure of merit proportional
to the polarization rotation
produced by the THz field
r (10-12
m/V)
d
(microns)
Figure of
merit (r×d)
GaP
1
1800
1800
ZnTe
4
185
740
SiC
2.7
4950
13365
Alternate Comparison
• Material group velocity
maintained by choosing
the optimal visible/UV
frequency
• Figure of merit held at
500 for each material
• Note SiC covers a larger
range
Results and Further Research
• 6H unsuited for measurement of bunch length
• 3C seems promising due to a larger broad-band
capability than both ZnTe and GaP
• Idealized electro-optic response analysis of SiC shows
significant improvement over similar crystals at optimal
optical frequencies
Acknowledgements
Al Sievers and Nick Agladze
CLASSE
National Science Foundation