Electro-optic Effect made simple?

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Electro-optic Effect made simple?

• David A. Reis
• FOCUS Center and Department of Physics,
  University. of Michigan

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Motivation

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

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Susceptibility and Electro-optic effect
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Induced Birefringence
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CW modulation probeEffective length depends on
phase matching
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Short Probe PulseGroup 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_wn_g

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Impulse response (idealized)
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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)
• LO206 cm-1 (6.2 THz)
• 3 cm-1

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Assume 800nm pulse, ZnTe Phase matched just
below and in Restrahlen band GaP Phase matched
only in Restrahlen band
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Dispersion in Pockels Coefficient
(Faust Henry, PRL 17(25), 1265, 1966
C -0.07
C lt 0 means Ionic and Electronic contribution of
susceptibility have opposite signs for w lt
wTO real part 0 slightly below wTO
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Impulse Response with dispersion
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Finite (Gaussian) Bandwidth
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Fresnel Reflections and Fabry-Perot effects
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The reflected and transmitted waves
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(No Transcript)
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What are we actually measuring?(multi
reflections, cavity modesetc.spatial
variation...)
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Electric field of an ultra-relativistic electron
bunch
e 1
e 1
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A. Cavalieri, et al. SPPS Collab.
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Time Series of Single Shot EO Measurements (balnac
ed detection) shows two directions of THz
propagation
1mm ZnTe, circ. pol. probe
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Issues...

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

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