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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, 2004Funding from the U.S. National Science Foundation

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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

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Information and Optical Pulses:Basic Review

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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" alphabeteach character assigned a number

e.g.: A = 41 (decimal) = 00101001 (binary) a = 97 = 01100001

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Digital Information: Images

image is divided intopixels

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

laser modulatorto optical

fiber

... 01100001...

various modulation formats!e.g., amplitude, phase, frequency

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http://www.picosecond.com/objects/AN-12.pdf

Modern Optical Telecommunication Systems:NRZ common for <= 10 Gbit/s

NRZ data

clock

1 0 1 1 0

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http://www.picosecond.com/objects/AN-12.pdf

Modern Optical Telecommunication Systems:RZ common for > 10 Gbits/s

RZ data

clock

1 0 1 1 0

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Why Optics? Fast Data Rates!

can transmit data at high rates over optical fibers in comparisonto 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 (10 Gbits/s)

"optical carrier" 192 times base rate of 51.85 Mbits/s

next standards: OC-768 (40 Gbits/s), OC-3072 (160 Gbits/s)

lab: > 40 Tbits/severy house in US can havean active internet connection!

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Optical Networks

11Information Bottleneck: The Network

Source: Alan Willner

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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

Is OEO conversion feasible at higher speeds?

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Ultra-High Speed Network Router

all-opticalcross-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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CD

D

Need for Buffers: Contention Resolution

OpticalCross

Connect

C

D

A

B

Contention

C

Packet 3 misrouted or dropped!

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.

Resolution Schemes

• Decreased throughputOptical Buffers Wavelength Shift Deflection Routing

• Random access dynamic optical memory

• Finite set of wavelengths • High latency

• Enables packet switching

C

1 2

3 1

23 ?

Source: Alan Willner, USC

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Statement of the Problem

A B

optical control field

How to we make an all-optical, controllable delay line (buffer) or memory?

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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.

Possible Solution: "Slow" and "Fast" Light

Speed of Pulse MUCH slower orfaster than the speed of light in vacuum

dispersivemedia

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Optical Pulse Propagation Review

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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 adistance z in a time t

phase velocity

p

zt k

cn

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Propagating Electromagnetic Waves: Group Velocity

Lowest-order statement of propagation withoutdistortion

dd

0

group velocity

g

g

c

ndnd

cn

different p

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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

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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"

k kn

c c

dn

do

g

o

g

o( ) ( ) ( )

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2

dn

dg

0•

• pulse bandwidth not too large

Recent experiments on fast and slow light conducted in the regime of low distortion

"slow" light:

"fast" light:

g gc n ( )1

g g gc or n 0 1( )

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Optical Pulse Propagation ina Resonant System

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Set Optical Carrier Frequency Near an Atomic Resonance

gas ofatoms

o

o eg

|g

|e

atomic energy eigenstates

Ne m

ieg

o eg

2 2/

( )

susceptibility

resonant enhancement

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Dispersion Near a Resonance

refractive index

absorption index

n n in ' " 1 2

group index ng(max) 105

n(max) .01

!!

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Problem: Large Absorption!

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Slow Light via EIT

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Solution: Electromagnetically Induced Transparency

o eg

|g

|e

|c

s s,

Source: Hau et al., Nature 397, 594 (1999)

g

g

c

ndnd

cn

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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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vg as low as 17 m/s

ng of the order of 106!

Slow Light Observations of Hau et al.

Source: http://www.deas.harvard.edu/haulab/

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Fast Light via AtomicRaman Scattering

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Fast-light via a gain doublet

Steingberg and Chiao, PRA 49, 2071 (1994)(Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000))

g

g

c

ndnd

cn

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Achieve a gain doublet using stimulated Raman scattering with a bichromatic pump field

Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000))

rubidiumenergylevels

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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 Advancementtadv

anomalousdispersion

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 opticalspectrum of the pulse

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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+

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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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

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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o-d-462 (MHz)

-4 -2 0 2 4

gain

coe

ffic

ient

, gL

0.0

0.5

1.0

1.5

a

-4 -2 0 2 4

n g

-40

0

40

80

120

b

Slow Light via a single amplifying resonance

AOM

o

d

d

L

Waveformgenerator

Kvapour

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Time (ns)

-200 0 200 400

Pow

er

(W

)

0

2

4

6

8

10

12

Pow

er

(W

)

0510152025303540

DelayedVacuum

tdel= 67.5 ns

Slow Light Pulse Propagation

vg ~ 0.008c

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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 opticalspectrum 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

P mWpump 71.

others:

4.7 mW1.9 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/