Instability Limits to “Fast” Light
Pulse Propagation
Michael D. Stenner
and
Daniel J. Gauthier
Duke University Department of Physics
Funded by NSF
New Anomalous Dispersion Technique
anomalous
dispersion
absorption coefficient (α)
refractive index (n-1)
A new method for creating anomalous dispersion
was recently proposed and implemented.
0
-4
-2
0
frequency
2
4
We are interested in studying this system in the
high gain limit.
Steinberg and Chiao (1994), Wang (2000)
Creation of Bichromatic Raman Gain
ω+
ω-
39
K vapor cell
∆ω
ω-
ω+
ω-
ω+
∆g
Large ground state coherence results in extremely
large optical amplification!
Wang et al. used red-detuned Raman pumps in
cesium.
Wang (2000), Harris (1997)
Nonlinear Optical Processes in the Driven
Vapor: Raman Stokes/anti-Stokes
Raman anti-Stokes
∆ω
ω−
ω+
∆g
generates: ( ω+ + ∆ g )
−
Raman Stokes/anti-Stokes coupling
generates: ( ω+ +- ∆ g )
−
Bloembergen (1967)
Nonlinear Optical Processes in the Driven
Vapor: Induced Modulation Instability
Induced Modulation Instability
generates: ( ω+ -+ n ∆ ω)
-
with the Raman processes:
(ω
+
+
-
∆ g -+ n ∆ ω)
Harris PRA (2002) and references therein,
Hasegawa (1980), Millot (2001)
Experimental Setup
ω+
39
Output power (mW)
ω−
5
4
3
2
1
0
0
Bichromatic
K
Monochromatic
10
20
30
40
50
Single-beam input power (mW)
60
• Threshold (0.1% conversion) occurs
at αL ≈ −10
• We easily see 10% conversion!
• Using bichromatic light dramatically reduces
the threshold!
Optical Spectrum of the Generated Light
Power (arb units)
fine peaks at ∆ω
∆g
pump frequency
-1
0
1
Frequency (GHz)
2
Stokes/anti-Stokes
coupling
( ω+ +- ∆ g )
−
Induced Modulation
Instability
( ω+ +- ∆ g +- n ∆ ω )
−
Raman anti-Stokes
( ω+ + ∆ g )
−
Electronic Power Spectrum
Detector power (dBm)
• Look at electronic spectrum of detector output
• Finer resolution in frequency and power
0
-20
-40
-60
-80
0
∆g
2∆g
500
1000
3∆g
4∆g
1500
2000
2500
-40
-60
-80
400
∆ω
420
RBW = 1 MHz
440
460
480
Frequency (MHz)
500
• Spectrum extends over several GHz
• Harris and Sokolov predict comb of δ functions
• 20 dB above noise for > 1 GHz, not discrete
peaks
Harris and Sokolov (1998)
Temporal Evolution of the
Intensity (arb units)
Generated Light
0
20
40
60
80
100
500 ps
10
15
20
Time (ns)
25
30
• Large structure at 40 ns → 25 MHz = ∆ω
• Small structure at 1 ns → 1 GHz ≈ 2∆g
• At the limit of the analog bandwidth of the
oscilloscope!
• May be chaotic – not enough vertical resolution to analyze!
Conclusions
• The induced modulation instablility severely restricts this “fast” light approach
• Generates broad (> 3 GHz) continuous spectrum from pure bichromatic (25 MHz) light
• Potentially chaotic behavior
• Slower analog to ultrafast pulse generation techniques of Harris
• Same processes (Raman amplification and Induced Modulation Instability) used in modern
fiber telecommunications research