1. 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.

2. 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

3. 1.Single shot capability 2.Resolution determined by the EO crystal dispersion Cross-correlation of coherent and incoherent radiation in EO medium THz coherent pulseIncoherent pulse Cross-correlation Non-collinear propagation enables a delay dependence Advantages CRYSTAL DETECTOR

4. Cross-correlation: principle experiment Source

5. 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

6. Silicon Carbide (SiC) Comparable electro-optic coefficient to ZnTe Higher TO resonance permits larger frequency range

7. Polytype Choice http://japantechniche.com/wp-content/uploads/2009/12/sdk-sic-mosfet.jpg Cubic SiCHexagonal SiC Pure Expensive Subject to free carriers Readily available

8. 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

9. 6H Transmission Increase in transmission toward Brewster angle Lacks metallic free carriers Unexpected feature at ~110 wavenumbers

10. 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

11. 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

12. 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

13. 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.

14. 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

15. 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) GaP11800 ZnTe4185740 SiC2.7495013365

16. 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

17. 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

18. Acknowledgements Al Sievers and Nick Agladze CLASSE National Science Foundation