Electro-optic Effect made simple?

David A. ReisFOCUS Center and Department of Physics, University. of Michigan

FOCUS

Motivation

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

Susceptibility and Electro-optic effect

Induced Birefringence

n0

Enx

ny

n~3, r41~4pm/V

CW modulation & probeEffective length depends on phase

matching

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

Impulse response (idealized)

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

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Assume ~800nm pulse,

ZnTe: Phase matched just below and in Restrahlen band GaP: Phase matched only in Restrahlen band

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Dispersion in Pockels’ Coefficient

(Faust & Henry, PRL 17(25), 1265, 1966

C < 0 meansIonic and Electroniccontribution of susceptibility have oppositesigns for < TO

real part = 0 slightlybelow TO

C = -0.07

Impulse Response with dispersion

Finite (Gaussian) Bandwidth

Fresnel Reflections and Fabry-Perot effects

…… …The reflected and transmitted waves:

2

What are we actually measuring?

(multi reflections, cavity modesetc.

spatial variation...)

e-

c

c c

c/n

c/n

Electric field of an ultra-relativistic electron bunch

c c

c/n

QuickTime™ and aYUV420 codec decompressor

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A. Cavalieri, et al. SPPS Collab.

Wakefields

Time [ps]-3.3 0. 3.3 6.7 10. 13.3 16.7 20.0 23.3 26.7

Time [ps]

Cherenkov Radiation

-3.3 0. 3.3 6.7 10. 13.3 16.7 20.0 23.3 26.7

Time Series of Single Shot EO Measurements(balnaced detection) shows two directions of THz propagation

1mm ZnTe, circ. pol. probe

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

SPPS Collaboration

UC Berkeley DESY

Roger W. Falcone Jochen Schneider Aaron Lindenberg Thomas Tschentscher Donnacha Lowney Horst Schulte-Schrepping Andrew MacPhee

APS Argonne Nat’l Lab BioCARS

Dennis Mills Keith Moffat Reinhard Pahl

MSD Argonne National Lab ESRF

Paul Fuoss Francesco Sette Brian Stephenson Olivier Hignette Juana Rudati U. of Michigan SLAC

David Reis Paul Emma Philip H. Bucksbaum Patrick Krejcik Adrian Cavalieri Holger Schlarb Soo Lee John Arthur David Fritz Sean Brennan Matthew F. DeCamp Roman Tatchyn

Jerome Hastings Kelly Gaffney NSLS Copenhagen University D. Peter Siddons Jens Als-Nielsen Chi-Chang Kao

Uppsala University

Janos Hajdu Lund University David van der Spoel Jörgen Larsson Richard W. Lee Ola Synnergren Henry Chapman Tue Hansen Carl Calleman Magnus Bergh Chalmers University of Technology

Gosta Huldt Richard Neutze

Acknowledgement: Cherenkov Radiation: R. Merlin, U.M.