Superluminal light propagation

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Superluminal light propagation Presented
by Shlomo Sklarz
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Outline of talk 1) Light propagation Group
velocity- basic concepts. 2) Effects of
dispersion on group velocity. 3) Experimental
realization. 4) Conformation with relativity and
causality.
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Fundamentals

• Electromagnetic Wave Equation
• Fourier decomposition

Frequency components
Wave packet
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Dispersive media

• In dispersive mediaPolarization occurs in
  linear response to field
• Dispersion relation
• Dispersion frequency components experience
  different refractive index values.

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Phase velocity vs. Group velocity
Contribution only where phase is slowly varying
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Group Velocity

• We assume for simplicity no absorption or gain.
  (n is real)
• When n is linear in ?, a pulse propagates without
  distortion.
• Various regimes1) In vacuum 2) Normal
  dispersion3)Anomalous dispersion4)
  Negative group velocity

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Negative Group velocity

• Pulse exits medium before(!) entering.
• Within an anomalous dispersion medium longer wave
  lengths appear shorter.
• Medium facilitates rephasing.

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Wang Experiment L.J. Wang et al. Nature 406
(2000) p277
Cesium Gas Cell
Probe pulse
0.2ns 6cm
3.7?s 1.1km
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Results

• No pulse shape distortion.
• Negative velocity of -c/310.
• Peak travels 20m (62ns) out of cell before
  incoming pulse enters.

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Problem How do these results conform with our
common notions of relativity and causality?
?
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Solution Sharp distinction between
A. Sommerfeld L. Brillouin (1914) wave
propagation and group velocity

• Signal velocity
• Motion of sharp signal front.Physical meaning.
• Sharp fronts imply contribution from all
  frequency components.
• No physical medium can achieve anomalous
  dispersion over all frequencies.

• Group velocity
• Motion of pulse peak.Geometrical meaning.
• Gaussian peaks - infinite tails.
• Leading front carries information about coming
  pulse.
• Medium amplifies leading wing to reconstruct
  following pulse

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No true superlminal signal motion Leading front
of pulse is amplified at expense of tail to
achieve advancement of peak center.
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So where is the trick?
Sharp wave front discontinuity travels at
vc. Packet peak is shifted forwards, and so
travels at vgtc.
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• Conclusions
• Dispersive media can alter the group velocity of
  a light pulse
• The Group velocity can be lower, equal to, or
  higher than the speed of light and even negative.
• These effects have been realized experimentally.
• This is not at odds with relativity since
  information is carried by the signal velocity of
  the pulse.