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