1. July 26, 2006 8:30 AM OSA Slow and Fast Light Topical Meeting Backwards Pulse Propagation with a Negative Group Velocity in Erbium Doped Fiber George Gehring 1, Aaron Schweinsberg 1, Christopher Barsi 2, Natalie Kostinski 3, Robert Boyd 1 1. University of Rochester, Rochester, NY 14627 USA 2. Manhattan College, New York, NY 10471, USA 3. University of Michigan, Ann Arbor, MI 48109, USA

2. July 26, 2006 8:30 AMOSA Slow and Fast Light Topical Meeting 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 n g = n + ! d n d ! v g = c = n g d n = d !

3. July 26, 2006 8:30 AMOSA Slow and Fast Light Topical Meeting Negative Group Velocity Inside the material, the peak is expected to travel backwards, linking output and input This raises some questions –Why doesn’t this violate causality? –How is energy conserved? –In what direction is energy flowing? –Does this ‘backwards-traveling’ peak really exist?

4. July 26, 2006 8:30 AMOSA Slow and Fast Light Topical Meeting Instructional Video M. Ware, S. Glasgow, and J. Peatross, Optics Express 9, 519-532 (2001)

5. July 26, 2006 8:30 AMOSA Slow and Fast Light Topical Meeting 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.

6. July 26, 2006 8:30 AMOSA Slow and Fast Light Topical Meeting Why EDOF? Erbium doped optical fiber exhibits gain or loss dependant on optical pumping power at 980 nm T 1 ≈ 10 ms Fiber geometry is favorable –Tight confinement –Large interaction lengths Schweinsberg, Lepeshkin, Bigelow, Boyd and Jarabo, Europhys. Lett., 73 (2), 218 (2006).

7. July 26, 2006 8:30 AMOSA Slow and Fast Light Topical Meeting Experimental Setup Setup for testing direction of energy flow 128 mW 0.5 mW

8. July 26, 2006 8:30 AMOSA Slow and Fast Light Topical Meeting Experimental Setup Setup for temporal resolution experiments

9. July 26, 2006 8:30 AMOSA Slow and Fast Light Topical Meeting 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).

10. July 26, 2006 8:30 AMOSA Slow and Fast Light Topical Meeting Video Creation These traces are then arranged spatially and played back simultaneously

11. July 26, 2006 8:30 AMOSA Slow and Fast Light Topical Meeting 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

12. July 26, 2006 8:30 AMOSA Slow and Fast Light Topical Meeting Video

13. July 26, 2006 8:30 AMOSA Slow and Fast Light Topical Meeting 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 n g ≈ -4000 (v g ≈ -75 km/s)

14. July 26, 2006 8:30 AMOSA Slow and Fast Light Topical Meeting Video – Gain Removed

15. July 26, 2006 8:30 AMOSA Slow and Fast Light Topical Meeting 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

16. July 26, 2006 8:30 AMOSA Slow and Fast Light Topical Meeting Acknowledgements Nonlinear Optics Group http://www.optics.rochester.edu/~boyd/ Financial support from –DARPA/DSO Slow Light program –NSF