Transcript Electro-optic Effect made simple?

FOCU S
Electro-optic Effect made simple?
David A. Reis
FOCUS Center and Department of Physics, University. of Michigan
Motivation
understand limitations on using
electro-optic sampling for bunch
duration and timing information.
Susceptibility and Electro-optic effect
Induced Birefringence
ny
nn0 x
E
n~3, r41~4pm/V
CW modulation & probe
Effective 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(W)
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
Assume ~800nm pulse,
ZnTe: Phase matched just below and in Restrahlen band
GaP: Phase matched only in Restrahlen band
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Dispersion in Pockels’ Coefficient
(Faust & Henry, PRL 17(25), 1265, 1966
C = -0.07
C < 0 means
Ionic and Electronic
contribution of
susceptibility have opposite
signs for w < wTO
real part = 0 slightly
below wTO
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 modes
etc.
spatial variation...)
Electric field of an ultra-relativistic electron bunch
e=1
c/n
c/n
qc
c
e-
c
c
qc
e=1
c/n
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
A. Cavalieri, et al. SPPS Collab.
Time Series of Single Shot EO Measurements
(balnaced detection) shows two directions of THz propagation
1mm ZnTe, circ. pol. probe
Wakefields
-3.3
0.
3.3
6.7
10.
Time [ps]
13.3
16.7
20.0
23.3
26.7
16.7
20.0
23.3
26.7
Cherenkov Radiation
-3.3
0.
3.3
6.7
10.
13.3
Time [ps]
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
UC Berkeley
Roger W. Falcone
Aaron Lindenberg
Donnacha Lowney
Andrew MacPhee
APS Argonne Nat’l Lab
Dennis Mills
DESY
Jochen Schneider
Thomas Tschentscher
Horst Schulte-Schrepping
BioCARS
Keith Moffat
Reinhard Pahl
MSD Argonne National Lab
ESRF
Paul Fuoss
Brian Stephenson
Juana Rudati
SPPS Collaboration
U. of Michigan
David Reis
Philip H. Bucksbaum
Adrian Cavalieri
Soo Lee
David Fritz
Matthew F. DeCamp
NSLS
D. Peter Siddons
Chi-Chang Kao
Francesco Sette
Olivier Hignette
SLAC
Paul Emma
Patrick Krejcik
Holger Schlarb
John Arthur
Sean Brennan
Roman Tatchyn
Jerome Hastings
Kelly Gaffney
Copenhagen University
Jens Als-Nielsen
Uppsala University
Acknowledgement: Cherenkov Radiation:
R. Merlin, U.M.
Janos Hajdu
David van der Spoel
Richard W. Lee
Henry Chapman
Carl Calleman
Magnus Bergh
Gosta Huldt
Lund University
Jörgen Larsson
Ola Synnergren
Tue Hansen
Chalmers University of Technology
Richard Neutze