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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
are needed to see this picture.
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.
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