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

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

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

Acknowledgements

Al Sievers and Nick Agladze

CLASSE

National Science Foundation