superluminal group velocities (a.k.a. fast light) dan gauthier duke university department of...
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Superluminal Group Velocities
(a.k.a. Fast Light)
Dan Gauthier
Duke UniversityDepartment of Physics, The Fitzpatrick Center for Photonics and Communication Systems
SCUWPJanuary 17, 2010
Information on Optical Pulses
http://www.picosecond.com/objects/AN-12.pdf
Modern Optical Telecommunication Systems:Transmitting information encoded on optical fields
RZ data
clock
Where is the information on the waveform?
How fast does it travel?
1 0 1 1 0
Slow Light
Controllably adjust the speed of an optical pulse propagating through a dispersive optical material
Slow light:
control
Slow-light medium
g gc n ( )1
Motivation for Using “Slow” Light Optical buffers and all-optical tunable delays
for routers and data synchronization.
router
router
data packets
Outline
• Introduction to “Slow" and "Fast" Light• Fast and backward light• Reconcile with the Special Theory of Relativity
Pulse Propagation inDispersive Materials
Propagation through glass
Propagation Through Dispersive Materials
dispersivemedia
A: There is no single velocity that describes how light propagates through a dispersive material
A pulse disperses (becomes distorted) upon propagation
An infinite number of velocities!
Q: How fast does a pulse of light propagate through aa dispersive material?
Propagating Electromagnetic Waves: Phase Velocity
monochromatic plane wave
E z t Ae c ci kz t( , ) .( )
phase kz t
E
z
Points of constant phase move a distance z in a time t
phase velocity
p
zt k
cn
Dispersive Material: n = n()
Linear Pulse Propagation: Group Velocity
different p
Lowest-order statement of propagation withoutdistortion
dd
0
group velocity
g
g
c
ndnd
cn
Control group velocity: metamaterials, highly dispersive materials
Variation in vg with dispersion
4 3 2 1 1 2 3dnd
4
3
2
1
1
2
3
4
Vgc
slow light
fast light
Pulse Propagation: Slow Light(Group velocity approximation)
Achieving Slow Light
Boyd and Gauthier, in Progress of Optics 43, 497-530 (2002)Boyd and Gauthier, Science 306, 1074 (2009)
When is the dispersion large?
laserfield
2-level system
|1>
|2>
1
0.5
0
-0.5
0
0.5
-20
-10
0
-4 -2 0 2 4
frequency (a.u.)
abso
rptio
n
Index of refraction
Group
index
Absorptioncoefficient
n g -
1n
- 1
Electromagnetically-Induced Transparency (EIT)
1
0.5
0
-0.5
0
0.5
80
40
0
-40
-4 -2 0 2 4
n g -
1n
- 1
abso
rptio
n
3-level system
controlfield laser field
|1>
|2>
|3>
frequency (a.u.)
Index of refraction
Group
index
Absorptioncoefficient
S. Harris, etc.
EIT: Slowlight
Group velocities as low as 17 m/s observed!
Hau, Harris, Dutton, and Behroozi, Nature 397, 594 (1999)
Fast light theory, Gaussian pulses: C. G. B. Garrett, D. E. McCumber, Phys. Rev. A 1, 305 (1970).
Fast light experiments, resonant absorbers: S. Chu, S. Wong, Phys. Rev. Lett. 48, 738 (1982). B. Ségard and B. Macke, Phys. Lett. 109, 213 (1985). A. M. Akulshin, A. Cimmino, G. I. Opat, Quantum Electron. 32, 567 (2002).
M. S. Bigelow, N. N. Lepeshkin, R. W. Boyd, Science 301, 200 (2003)
Fast-Light
0g gc or
Pulse Propagation: Fast Light (Group velocity approximation)
Fast-light via a gain doublet
Steingberg and Chiao, PRA 49, 2071 (1994)(Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000))
Achieve a gain doublet using stimulated Raman scattering with a bichromatic pump field
Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000)
probe frequency (MHz)
190 200 210 220 230 240 250
ga
in c
oe
ffic
ien
t, g
L
0
1
2
3
4
5
6
7
8
egl=7.4
egl=1,097
22.3 MHz
Fast light in a laser driven potassium vapor
large anomalousdispersion
AOM
o
waveformgenerator
Kvapor
Kvapor
d-
d+
d-
d+
time (ns)
-300 -200 -100 0 100 200 300
pow
er ( W
)
0
2
4
6
8
10
12
pow
er ( W
)
0.00.20.40.60.81.01.21.41.6
advanced vacuum
tadv=27.4 ns
Observation of large pulse advancement
tp = 263 ns A = 10.4% vg = -0.051c ng = -19.6
M.D. Stenner, D.J. Gauthier, and M.A. Neifeld, Nature 425, 695 (2003).
Reconcile with theSpecial Theory of Relativity
x
t
eventx
t
event
A
B
x
t
event
CD
a) b) c)
x
t
eventx
t
event
A
B
x
t
event
CD
a) b) c)
Problems with superluminal information transfer
Light cone
Minimum requirements of the optical field
L. Brillouin, Wave Propagation and Group Velocity, (Academic, New York, 1960).(compendium of work by A. Sommerfeld and L. Brillouin from 1907-1914)
A. Sommerfeld
A "signal" is an electromagnetic wavethat is zero initially.
front
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Sommerfeld.html
The front travels at c
Primary Finding of Sommerfeld
(assumes a Lorentz-model dielectric with a single resonance)
regardless of the details of the dielectric
Physical interpretation: it takes a finite time for the polarization of the medium to build up; the first part of the field passes straight through!
Generalization of Sommerfeld and Brillouin's work
t
Ppoint of non-analyticity
knowledge of the leading part of the pulse cannot be usedto infer knowledge after the point of non-analyticity
new information is available because of the "surprise"
Chiao and Steinberg find point of non-analyticitytravels at c. Therefore, they associate it with theinformation velocity.
Implications for fast-light
transmitter receiver
vacuum
transmitter receiver
transmitter receiver
with dispersive material
information still available at c!
Send the symbolsthrough our fast-lightmedium
time (ns)
-300 -200 -100 0 100 200 300
optic
al p
ulse
am
plitu
de (
a.u.
)
0.0
0.5
1.0
1.5
advanced
vacuum
"1"
"0"
time (ns)
-60 -40 -20 00.6
0.8
1.0
1.2
1.4
1.6
1.8
Y D
ata
0.2
0.4
0.6
0.8
1.0
1.2
vacuum
advanced
A
B
advanced
i adv c, ( . . ) 0 4 05
x
t
pulsepeak
fast-lightmedium
initial turn-onof shutter
x
t
pulsepeak
fast-lightmedium
initial turn-onof shutter
Fast light, backward light and the light cone
The pulse peak can do weird things, but can't go beyond the pulse front (outside the light cone)
Summary
• Slow and fast light allows control of the speed of optical pulses
• Amazing results using atomic systems
• Transition research to applications using existing telecommunications technologies
• Fast light gives rise to unusual behavior
• Interesting problem in E&M to reconcile with the special theory of relativity
Collaborators
Duke
Rochester R. Boyd, J. Howell
Cornell A. Gaeta
UCSC A. Willner
UCSB D. Blumenthal
U of Arizona M. Neifeld
http://www.phy.duke.edu/
A beam with two frequencies: The group velocity
Photos from: http://www-gap.dcs.st-and.ac.uk/~history/l
Sir Hamilton 1839 Lord Rayleigh 1877
E z t A k z t A k z tL L H H( , ) cos( ) cos( ) 2 2
20 40 60 80z
21.5
10.5
0.51
1.52Et
J.S. Russell 1844 G.G. Stokes 1876
F
HGIKJ
FHG
IKJ4
2 2 2 2A
n nz t
n nz tL L H H L H L L H H L Hcos sin
Speed of the envelope in dispersive materials( )n nH L