1
Physics and Applications of "Slow" Light
Dan Gauthier
Duke University, Department of Physics, Fitzpatrick Center for Photonics
and Communication Systems
Collaborators:
Michael Stenner, Heejeong Jeong, Andrew Dawes (Duke Physics)
Mark Neifeld (U. of Arizona, ECE, Optical Sciences Center)
Robert Boyd (U. of Rochester, Institute of Optics)
John Howell (U. of Rochester, Physics)
Alexander Gaeta (Cornell, Applied Physics)
Alan Willner (USC, ECE)
Dan Blumenthal (UCSB, ECE)
Fitzpatrick Center Summer School, July 27, 2004
Funding from the U.S. National Science Foundation
2
Outline
• Information and optical pulses
• Optical networks: The Problem
• Possible solution: "Slow" and "Fast" light
• Review of pulse propagation in dispersive media
• Optical pulse propagation in a resonant systems
• Slow light via EIT
• Fast Light via Raman Scattering
• Our Experiments
• Fiber-Based Slow Light
3
Information and Optical Pulses:
Basic Review
4
Digital Information
• computers only work with numbers - vast majority use
binary
• need standards for converting "information" to a binary
representation
Text:
ASCII (American Standard Code for Information Exchange)
developed years ago for teletype communication
1 byte (8 bits) needed for "standard" alphabet
each character assigned a number
e.g.: A = 41 (decimal) = 00101001 (binary)
a = 97 = 01100001
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Digital Information: Images
image is divided into
pixels
each pixel is assigned a number using a standard
e.g.: 8-bit color: one byte per color, three colors
Red, Green, Blue
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Using Light to Transmit Digital Information
Encode bits on a beam of light
... 01100001...
laser
modulator
various modulation formats!
e.g., amplitude, phase, frequency
to optical
fiber
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Modern Optical Telecommunication Systems:
NRZ common for <= 10 Gbit/s
http://www.picosecond.com/objects/AN-12.pdf
NRZ data
1
0
1
1
0
clock
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Modern Optical Telecommunication Systems:
RZ common for > 10 Gbits/s
http://www.picosecond.com/objects/AN-12.pdf
1
0
1
1
0
RZ data
clock
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Why Optics?
Fast Data Rates!
can transmit data at high rates over optical fibers in comparison
to copper wires (low loss, low distortion of pulses)
important breakthrough: use multiple wavelengths per fiber
each wavelength is an independent channel
(DWDM - Dense Wavelength Division Multiplexing)
Common Standard: OC-192
"optical carrier"
(10 Gbits/s)
192 times base rate of 51.85 Mbits/s
next standards: OC-768 (40 Gbits/s), OC-3072 (160 Gbits/s)
lab: > 40 Tbits/s
every house in US can have
an active internet connection!
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Optical Networks
Information Bottleneck: The Network
Source: Alan Willner
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12
Network Router
router
information sent to router in "packets" with header
- typical packet length (data) 100-1000 bits
router needs to read address, send data down new channel,
possibly at a new wavelength
<= 10 Gbits/s: Optical-Electronic-Optical (OEO) conversion
Is OEO conversion feasible at higher speeds?
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Ultra-High Speed Network Router
all-optical
cross-connect
Possible Solution:
All-optical router
One (fairly major) unsolved problem:
There is no all-optical RAM or agile optical buffer
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Need for Buffers: Contention Resolution
A
1
2
D
C
3 C
B
Optical
Cross
Connect
Contention
2 C
3?
1
D
C
D
Packet 3 misrouted or dropped!
Resolution Schemes
Optical Buffers
Wavelength Shift
• Random access
• Finite set of
dynamic optical memory wavelengths
• Enables packet switching
Deflection Routing
• Decreased throughput
• High latency
Problem: An unbuffered optical switch architecture may
drop or misroute a packet when there is output port
contention, causing increased latency and/or packet loss.
Source: Alan Willner, USC
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Statement of the Problem
optical control field
A
t
B
How to we make an all-optical, controllable delay line
(buffer) or memory?
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Possible Solution: "Slow" and "Fast" Light
Speed of Pulse MUCH slower or
faster than the speed of light in vacuum
dispersive
media
R.W. Boyd and D.J. Gauthier
"Slow and "Fast" Light, in Progress in Optics, Vol. 43,
E. Wolf, Ed. (Elsevier, Amsterdam, 2002),
Ch. 6, pp. 497-530.
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Optical Pulse Propagation Review
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Propagating Electromagnetic Waves: Phase Velocity
monochromatic plane wave
E
z
E( z, t )  Ae
phase
i ( kz t )
 c. c
  kz  t
Points of constant phase move a
distance Dz in a time Dt
phase velocity
Dz  c
p   
Dt k n
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Propagating Electromagnetic Waves: Group Velocity
Lowest-order statement
of propagation without
distortion
d
0
d
different
p
group velocity
c
c
g 

dn ng
n 
d
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Variation in vg with dispersion
Vg
c
4
3
2
slow light
1
4
3
2
1
1
1
2
3
4
fast light
2
3
dn
d
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Schematic of Pulse Propagation at
Various Group Velocities
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Pulse Propagation: Slow Light
(Group velocity approximation)
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Pulse Propagation: Fast Light
(Group velocity approximation)
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Propagation "without distortion"
ng
1 dng
2
k ( )  ko  (   o ) 
(   o )  
c
2c d
dng
•
0
d
• pulse bandwidth not too large
"slow" light:
"fast" light:
 g  c (ng  1)
 g  c or  g  0 (ng  1)
Recent experiments on fast and slow light conducted
in the regime of low distortion
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Optical Pulse Propagation in
a Resonant System
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Set Optical Carrier Frequency Near
an Atomic Resonance
o
gas of
atoms
|e
 o   eg
susceptibility
Ne / 2m eg
2
|g

( o   eg )  i
atomic energy eigenstates
resonant enhancement
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Dispersion Near a Resonance
n  n'in"  1  2
n
refractive index
(max)
 01
.
absorption index
group index
(max)
g
n
 10
5
!!
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Problem: Large Absorption!
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Slow Light via EIT
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Solution: Electromagnetically Induced Transparency
|e
 o   eg
|g
 s , s
|c
c
Source: Hau et al., Nature 397, 594 (1999)
c
g 

dn ng
n 
d
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Group Index for EIT
ng ~106 !
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Experimental Setup of Hau et al.
relevant sodium energy levels
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Slow Light Observations of Hau et al.
vg as low as 17 m/s
ng of the order of 106!
Source: http://www.deas.harvard.edu/haulab/
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Fast Light via Atomic
Raman Scattering
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Fast-light via a gain doublet
c
c
g 

dn ng
n 
d
Steingberg and Chiao, PRA 49, 2071 (1994)
(Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000))
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Achieve a gain doublet using stimulated Raman
scattering with a bichromatic pump field
rubidium
energy
levels
Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000))
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Experimental observation of fast light
ng ~ -310
… but the fractional pulse advancement is small
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Our Experiments on
"Fast" and "Slow" Light
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Important Quantity for our Work: Pulse Advancement
tadv
anomalous
dispersion
vacuum
tp
relative pulse advancement
A=tadv/tp
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Key Observation
A ~ (gain coefficient) * (length of medium)
Does NOT depend on vg directly
Adjust spectral width of atomic resonance to optical
spectrum of the pulse
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Fast light in a laser driven potassium vapor
AOM
o
d-
d+
K
vapor
d-
waveform
generator
8
K
vapor
22.3 MHz
egl=1,097
7
gain coefficient, gL
d+
6
large anomalous
dispersion
5
4
3
egl=7.4
2
1
0
190
200
210
220
230
240
250
probe frequency (MHz)
Steingberg and Chiao, PRA 49, 2071 (1994)
Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000)
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Some of our toys
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12
10
power (W)
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
tadv=27.4 ns
8
6
advanced
vacuum
4
2
0
-300
-200
-100
0
100
200
power (W)
Observation of large pulse advancement
300
time (ns)
tp = 263 ns
A = 10.4%
vg = -0.051c
ng = -19.6
some pulse compression (1.9% higher-order dispersion)
H. Cao, A. Dogariu, L. J. Wang, IEEE J. Sel. Top. Quantum Electron. 9, 52 (2003).
B. Macke, B. Ségard, Eur. Phys. J. D 23, 125 (2003).
large fractional advancement - can distinguish different velocities!
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Slow Light via a single amplifying resonance
AOM
o
d
L
K
vapour
Waveform
generator
d
b
1.5
120
1.0
80
ng
gain coefficient, gL
a
0.5
40
0
0.0
-40
-4 -2 0
2
4
-4 -2 0
o-d-462 (MHz)
2
4
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Power (W)
12
tdel= 67.5 ns
10
8
6
Delayed
Vacuum
4
2
0
-200
0
Time (ns)
vg ~ 0.008c
200
400
40
35
30
25
20
15
10
5
0
Power (W)
Slow Light Pulse Propagation
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Surely Dr. Watson, you must be joking ...
• Experiments in Slow and Fast Light use atoms
• Effect only present close to a narrow atomic resonance
• Works for long pulses - slow data rates!
• Not easily integrated into a telcom system!
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Key Observation
A ~ (gain coefficient) * (length of medium)
Does NOT depend on vg directly
Adjust spectral width of atomic resonance to optical
spectrum of the pulse
short pulses
broad resonance
any resonance can give rise to slow light!!
e.g., Stimulated Brillouin and Raman Scattering
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Fiber-Based Fast and Slow Light
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Slow-Light via Stimulated Brillouin Scattering
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Gain and Dispersion 6.4-km-Long SMF-28 Fiber
Ppump  7.1 mW
others:
4.7 mW
1.9 mW
should see "large"
relative delay
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To Do
• Measure slow light via Brillouin scattering in a fiber for a
single optical pulse
• Optimize
• Multiple pulses
• Large relative pulse delay
• Measure slow light via Raman scattering (broader
resonances for shorter pulses)
• Delay a packet
• Integrate into a telcomm router (in my dreams ...)
• Integrate into a telcomm clock/data synchronizer
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Summary
• Future ultra-high-speed telecommunication systems
require all-optical components
• Data-rate bottleneck in network (routers)
• Slow and Fast Light pulse propagation with large
pulse delay or advancement may provide a solution
• It is possible to observe slow and fast light using
telcomm-compatible components
• Additional research needed to determine whether
technology is competitive with other approaches
http://www.phy.duke.edu/research/photon/qelectron/proj/infv/