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Outline
Physics and Applications of "Slow" Light
Dan Gauthier
• Information and optical pulses
Duke University, Department of Physics, Fitzpatrick Center for Photonics
• Optical networks: The Problem
and Communication Systems
• Possible solution: "Slow" and "Fast" light
• Review of pulse propagation in dispersive media
Collaborators:
Michael Stenner, Heejeong Jeong, Andrew Dawes (Duke Physics)
Mark Neifeld (U. of Arizona, ECE, Optical Sciences Center)
• Optical pulse propagation in a resonant systems
Robert Boyd (U. of Rochester, Institute of Optics)
• Slow light via EIT
John Howell (U. of Rochester, Physics)
• Fast Light via Raman Scattering
Alexander Gaeta (Cornell, Applied Physics)
• Our Experiments
Alan Willner (USC, ECE)
Dan Blumenthal (UCSB, ECE)
• Fiber-Based Slow Light
Fitzpatrick Center Summer School, July 27, 2004
Funding from the U.S. National Science Foundation
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Digital Information
Information and Optical Pulses:
Basic Review
• 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
Using Light to Transmit Digital Information
image is divided into
pixels
Encode bits on a beam of light
... 01100001...
each pixel is assigned a number using a standard
e.g.: 8-bit color: one byte per color, three colors
Red, Green, Blue
to optical
fiber
modulator
laser
various modulation formats!
e.g., amplitude, phase, frequency
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Modern Optical Telecommunication Systems:
NRZ common for <= 10 Gbit/s
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Modern Optical Telecommunication Systems:
RZ common for > 10 Gbits/s
http://www.picosecond.com/objects/AN-12.pdf
NRZ data
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0
1
1
0
clock
http://www.picosecond.com/objects/AN-12.pdf
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1
0
RZ data
clock
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Why Optics?
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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"
Optical Networks
(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!
Information Bottleneck: The Network
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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
Source: Alan Willner
Is OEO conversion feasible at higher speeds?
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Ultra-High Speed Network Router
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Need for Buffers: Contention Resolution
A
all-optical
cross-connect
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D
C
3 C
B
Optical
Cross
Connect
Contention
2 C
3?
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D
C
D
Packet 3 misrouted or dropped!
Resolution Schemes
Possible Solution:
All-optical router
Optical Buffers
Wavelength Shift
• Random access
• Finite set of
dynamic optical memory wavelengths
• Enables packet switching
One (fairly major) unsolved problem:
There is no all-optical RAM or agile optical buffer
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
τ
B
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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
How to we make an all-optical, controllable delay line
(buffer) or memory?
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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Propagating Electromagnetic Waves: Phase Velocity
monochromatic plane wave
E
Optical Pulse Propagation Review
phase velocity
z
υp =
E ( z , t ) = Aei ( kz −ωt ) + c. c
phase
∆z ω c
= =
∆t k n
φ = kz − ωt
Points of constant phase move a
distance ∆z in a time ∆t
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Propagating Electromagnetic Waves: Group Velocity
Variation in vg with dispersion
Vg
ÅÅÅÅÅÅÅÅÅ
c
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Lowest-order statement
of propagation without
distortion
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dφ
=0
dω
different
υp
group velocity
c
υg =
=
dn ng
n +ω
dω
2
slow light
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-4
-3
-2
-1
-1
1
2
3
dn
w ÅÅÅÅÅÅÅÅÅ
dw
-2
c
-3
-4
fast light
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Pulse Propagation: Slow Light
(Group velocity approximation)
Schematic of Pulse Propagation at
Various Group Velocities
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Pulse Propagation: Fast Light
(Group velocity approximation)
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Propagation "without distortion"
k (ω ) = ko +
•
ng
1 dng
(ω − ω o ) +
(ω − ω o ) 2 + L
c
2c dω
dng
=0
dω
• pulse bandwidth not too large
"slow" light:
"fast" light:
υ g << c (ng >> 1)
υ g > c or υ g < 0 (ng < 1)
Recent experiments on fast and slow light conducted
in the regime of low distortion
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Set Optical Carrier Frequency Near
an Atomic Resonance
gas of
atoms
ωo
Optical Pulse Propagation in
a Resonant System
|e
ω o = ω eg
|g
atomic energy eigenstates
susceptibility
χ=−
Ne 2 / 2mω eg
(ω o − ω eg ) + iγ
resonant enhancement
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Dispersion Near a Resonance
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Problem: Large Absorption!
n = n'+in" ≈ 1 + 2πχ
refractive index
δn (max) ≈ 01
.
absorption index
group index
ng(max) ≈ 105
!!
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Solution: Electromagnetically Induced Transparency
Slow Light via EIT
|e
ω o = ω eg
|g
ω s , Ωs
|c
υg =
Source: Hau et al., Nature 397, 594 (1999)
c
dn
n +ω
dω
=
c
ng
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Group Index for EIT
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Experimental Setup of Hau et al.
ng ~106 !
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
Fast Light via Atomic
Raman Scattering
106!
Source: http://www.deas.harvard.edu/haulab/
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Achieve a gain doublet using stimulated Raman
scattering with a bichromatic pump field
Fast-light via a gain doublet
υg =
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c
dn
n +ω
dω
Steingberg and Chiao, PRA 49, 2071 (1994)
(Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000))
=
c
ng
rubidium
energy
levels
Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000))
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Experimental observation of fast light
Our Experiments on
"Fast" and "Slow" Light
ng ~ -310
… but the fractional pulse advancement is small
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Important Quantity for our Work: Pulse Advancement
tadv
anomalous
dispersion
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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
vacuum
tp
relative pulse advancement
A=tadv/tp
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Fast light in a laser driven potassium vapor
AOM
ωd-
ωo
ωd+
K
vapor
ωd-
waveform
generator
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ωd+
22.3 MHz
e gl=1,097
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gain coefficient, gL
Some of our toys
K
vapor
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large anomalous
dispersion
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gl
2
e =7.4
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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Observation of large pulse advancement
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advanced
vacuum
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2
0
-300
-200
-100
0
100
200
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!
ωo
ωd
L
K
vapour
Waveform
generator
ωd
a
b
1.5
120
1.0
80
ng
8
AOM
gain coefficient, gL
power (µW)
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
tadv=27.4 ns
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Slow Light via a single amplifying resonance
power (µW)
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0.5
40
0
0.0
-40
-4 -2 0
2
4
-4 -2 0
2
4
ωo-ωd-462 (MHz)
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Surely Dr. Watson, you must be joking ...
Slow Light Pulse Propagation
tdel= 67.5 ns
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Delayed
Vacuum
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2
0
-200
0
200
40
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25
20
15
10
5
0
• Experiments in Slow and Fast Light use atoms
Power (µW)
Power (µW)
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• 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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Time (ns)
vg ~ 0.008c
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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
Fiber-Based Fast and Slow Light
broad resonance
any resonance can give rise to slow light!!
e.g., Stimulated Brillouin and Raman Scattering
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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/
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