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

t

1 Incoherent pulse

CRYSTAL

• Cross-correlation • Non-collinear propagation enables a delay dependence

t

2

I

0

DETECTOR



Advantages



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

Cubic SiC

• Pure • Expensive Polytype Choice

Hexagonal SiC

• Subject to free carriers • Readily available http://japantechniche.com/wp-content/uploads/2009/12/sdk-sic-mosfet.jpg

6H Considerations http://metallurgyfordummies.com/wp-content/uploads/2011/04/doping-semiconductor.jpg

• Free carriers or doping • Metallic behavior • Electro-optic coefficient’s angular dependence

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 GaP ZnTe SiC r (10 -12 m/V) 1 4 2.7

d (microns) 1800 Figure of merit (r ×d) 1800 185 4950 740 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