Backwards Pulse Propagation with a Negative Group Velocity in Erbium Doped Fiber

1
Backwards Pulse Propagation with a Negative Group
Velocity in Erbium Doped Fiber

• George Gehring1, Aaron Schweinsberg1,
  Christopher Barsi2, Natalie Kostinski3, Robert
  Boyd1

1. University of Rochester, Rochester, NY 14627
USA2. Manhattan College, New York, NY 10471,
USA3. University of Michigan, Ann Arbor, MI
48109, USA
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Slow and Fast Light

• In dispersive media, pulses propagate at the
  group velocity
• If is made sufficiently negative, then the
  group velocity becomes negative
• Pulse is advanced in time
• Peak of the output pulse exits the material
  before the peak of the input pulse enters

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Negative Group Velocity

• Inside the material, the peak is expected to
  travel backwards, linking output and input
• This raises some questions
• Why doesnt this violate causality?
• How is energy conserved?
• In what direction is energy flowing?
• Does this backwards-traveling peak really exist?

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Instructional Video
M. Ware, S. Glasgow, and J. Peatross, Optics
Express 9, 519-532 (2001)
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Coherent Population Oscillations

• Coherent Population Oscillations (CPO) utilized
  to create narrow spectral hole in an absorption
  or gain feature
• The excited state population oscillates at the
  beat frequency between pump and probe fields

Hillman, Boyd, Krasinski and Stroud, Jr.,Optics
Communications 45, No. 6, 416 (1983).
Coherent Population Oscillation effect in a ruby
crystal.
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Why EDOF?

• Erbium doped optical fiber exhibits gain or loss
  dependant on optical pumping power at 980 nm
• T1 10 ms
• Fiber geometry is favorable
• Tight confinement
• Large interaction lengths

Schweinsberg, Lepeshkin, Bigelow, Boyd and
Jarabo, Europhys. Lett., 73 (2), 218 (2006).
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Experimental Setup
0.5 mW
128 mW
Strong
Very Weak

• Setup for testing direction of energy flow

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Experimental Setup

• Setup for temporal resolution experiments

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Example Data Trace

• Traces taken for lengths of fiber between 0-9 m
• The fiber is physically cut in 25 cm intervals
  between each data trace

G. M. Gehring, A. Schweinsberg, R. W. Boyd, et
al. Science 312, 895 (2006).
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Video Creation

• These traces are then arranged spatially and
  played back simultaneously

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Video Frames

• Arrows emphasize peak positions inside and
  outside the material
• Peak inside the material travels backward, but
  not with a constant velocity
• This is a result of distortion caused by
  non-uniformity of the gain curve, primarily due
  to gain saturation

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Video
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Video Frames

• Effects of gain removed
• Peak position is clearly seen to travel from
  right to left inside the material
• Peak moves at the same speed inside and outside
  the matieral
• ng -4000 (vg -75 km/s)

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Video Gain Removed
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Summary

• EDOF and CPO utilized to study pulse propagation
  effects in a medium with a negative group
  velocity
• For a pulse propagating through a medium with a
  negative group velocity
• Pulse peak moves backwards in the material
• Energy transport is always in the forward
  direction

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Acknowledgements

• Nonlinear Optics Group
  http//www.optics.rochester.edu/boyd/
• Financial support from
• DARPA/DSO Slow Light program
• NSF