1. Electro-optic Effect made simple? David A. Reis FOCUS Center and Department of Physics, University. of Michigan

2. Motivation understand limitations on using electro-optic sampling for bunch duration and timing information.

3. Susceptibility and Electro-optic effect

4. Induced Birefringence n0n0 E nxnx nyny n~3, r 41 ~4pm/V

5. CW modulation & probe Effective length depends on phase matching

6. Short Probe Pulse: Group velocity mismatch picture assume short pulse travelling w/ v_g ignore GVD on both pulse width & phase matching assume AR coated phase matching approximately n_w=n_g

7. Impulse response (idealized)

8. Low frequency dispersion in n(  ) phonon-polariton for zinc-blende materials such as ZnTe and GaP ZnTe: TO= 177 cm -1 (5.3 THz) LO=206 cm -1 (6.2 THz)  = 3 cm -1

9. Assume ~800nm pulse, ZnTe: Phase matched just below and in Restrahlen band GaP: Phase matched only in Restrahlen band

10. Dispersion in Pockels’ Coefficient (Faust & Henry, PRL 17(25), 1265, 1966 C < 0 means Ionic and Electronic contribution of susceptibility have opposite signs for  <  TO real part = 0 slightly below  TO C = -0.07

11. Impulse Response with dispersion

12. Finite (Gaussian) Bandwidth

13. Fresnel Reflections and Fabry-Perot effects …… … The reflected and transmitted waves: 2

15. What are we actually measuring? (multi reflections, cavity modes etc. spatial variation...)

16. e- c cc c c/n Electric field of an ultra-relativistic electron bunch cc c c/n 

17. A. Cavalieri, et al. SPPS Collab.

18. Time Series of Single Shot EO Measurements (balnaced detection) shows two directions of THz propagation 1mm ZnTe, circ. pol. probe

19. Issues... limit in resolution: laser pulse duration, crystal thickness & mismatch. fidelity limited by FP, dispersion, nonlinearities in measurement and ultimately Kerr @ high fields. What fields are you measuring? Not discussed is experimental arrangement to measure Gamma(t), assume well designed

20. SPPS Collaboration Acknowledgement: Cherenkov Radiation: R. Merlin, U.M.