Upload
hope-beasley
View
223
Download
1
Tags:
Embed Size (px)
Citation preview
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
http://dev.fiber-sensors.com/wp-content/uploads/2010/08/electro-optic_example-01.png
• Material-specific properties
• Electro-optic effect on polarized light
1. Single shot capability2. Resolution determined by
the EO crystal dispersion
I
x
0
Cross-correlation of coherent and incoherent radiation in EO medium
THz coherent pulse Incoherent pulse
• Cross-correlation• Non-collinear
propagation enables a delay dependence
t1
t2
Advantages
CRYSTAL
DETECTOR
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
http://japantechniche.com/wp-content/uploads/2009/12/sdk-sic-mosfet.jpg
Cubic SiC Hexagonal SiC
• Pure• Expensive
• Subject to free carriers• Readily available
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