Fundamentals and Applications of SlowLight in Room Temperature Solids

Robert W. Boyd

Institute of Optics and

Department of Physics and AstronomyUniversity of Rochester

with Mathew S. Bigelow, Nick Lepeshkin, AaronSchweinsberg, and Petros Zerom

Presented at the OSA Topical Meeting on Nonlinear Optics,Waikoloa, Hawaii, Auguest 2-6, 2004.

Interest in Slow Light

Intrigue: Can (group) refractive index really be 106?

Fundamentals of optical physics

Optical delay lines, optical storage, optical memories

Implications for quantum information

And what about fast light (v > c or negative)?

Boyd and Gauthier, “Slow and Fast Light,” in Progress in Optics, 43, 2002.

Approaches to Slow Light Propagation• Use of quantum coherence (to modify the spectral dependence of the atomic response)

e.g., electromagnetically induced transparency

• Use of artificial materials (to modify the optical properties at the macroscopic level)

e.g., photonic crystals (strong spectral variation ofrefractive index occurs near edge of photonicbandgap)

Slow Light in Atomic Vapors

Slow light propagation in atomic vapors, facilitated byquantum coherence effects, has been successfullyobserved by . . .

Challenge/Goal

Slow light in a room-temperature solid-state material.

Solution: Slow light enabled by cohernt population oscillations (a quantum coherence effect that is relatively insensitive to dephasing processes).

Slow Light in Ruby

Need a large dn/dw. (How?)

Kramers-Kronig relations: Want a very narrow absorption line.

Well-known (to the few people how know itwell) how to do so:

Make use of “spectral holes” due topopulation oscillations.

Hole-burning in a homogeneouslybroadened line; requires T2 << T1.

1/T2 1/T1

inhomogeneously broadened medium

homogeneously broadened medium(or inhomogeneously broadened)

PRL 90,113903(2003); see also news story in Nature.

Γba

=1T

12γ

ba=

2T

2

a

b b

a

cω

Γca

Γbc

atomicmedium

ω

ω + δω + δ

E1,

E3,

measure absorption

Spectral Holes Due to Population Oscillations

ρ ρbb aa w−( ) = δ δ δ δi t i tw t w w e w e≈ + +− −( ) ( ) ( ) ( )0

Population inversion:

δ T≤ / 11population oscillation terms important only for

ρ ω δ µω ω

δba

baba i T

E w E w+ =− +

+[ ]( )/

( ) ( )2

30

11

Probe-beam response:

α ω δδ β

β

w TT

+ = −+

=

( )

( /

( )02

21 2 2

1

1

Ω

TT T T12

1 21) ( )+ Ω

Probe-beam absorption:

linewidth

h

α0

Spectral Holes in HomogeneouslyBroadened Materials

Occurs only in collisionally broadened media (T2 << T1)

Boyd, Raymer, Narum and Harter, Phys. Rev. A24, 411, 1981.

pump-probe detuning (units of 1/T2)

Argon Ion LaserRuby

40 cm

FunctionGenerator

EO modulator

DigitalOscilloscope

Pinhole

Reference Detectoror

Signal Detector

Slow Light Experimental Setup

7.25-cm-long ruby laser rod (pink ruby)

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4D

elay

(m

s)

2000 400 600 800 1000Modulation Frequency (Hz)

P = 0.25 W

P = 0.1 W

Measurement of Delay Time for Harmonic Modulation

solid lines are theoretical predictions

For 1.2 ms delay, v = 60 m/s and ng = 5 x 106

512 µs

Time (ms)

0

0.2

0.4

0.6

0.8

1.0

1.2

No

rma

lize

d I

nte

nsity

Input Pulse

Output Pulse

0 10 20-10-20 30

Gaussian Pulse Propagation Through Ruby

No pulse distortion!

v = 140 m/s

ng = 2 x 106

Matt Bigelow and Nick Lepeshkin in the Lab

0 10 20 30 40time (ms)

input output

Slow Light in Ruby -- Greater Pulse Separation

60 degree delay = 1/6 of a period

Advantages of Coherent PopulationOscillations for Slow Light

Works in solidsWorks at room temperatureInsensitive of dephasing processesLaser need not be frequency stabilizedWorks with single beam (self-delayed)Delay can be controlled through input intensity

Alexandrite Displays both Saturable and Inverse-Saturable Absorption

T1,m = 260 mss1,m

s2,m

2E

rapid

rapid

4A2

4T2 or

4T1

T1,i ~ 50 mss1,i

rapid

4A2

4T2 or

4T1 2

E

Mirror Sites:

Inversion Sites:

a

b

Al, Cr

O

Be

Inverse-Saturable Absorption Produces Superluminal Propagation in Alexandrite

At 476 nm, alexandrite is an inverse saturable absorber

Negative time delay of 50 ms correponds to a velocity of -800 m/s

M. Bigelow, N. Lepeshkin, and RWB, Science, 2003

Science 301 , 200 (2003).

Probe Absorption and Delay at 488 nm

Hole at low frequencies, anti-hole at larger frequencies leads to slow light for long pulses and fast light for shorter pulses.

Causality and Superluminality

Ann. Phys. (Leipzig) 11, 2002.

Information Velocity in a Fast Light Medium

M.D. Stenner, D.J. Gauthier, and M.I. Neifeld, Nature 425, 695 (2003).

Pulses are not distinguishable "early."

vi ≤ c

0-0.5-1 0.5 1time (ms)

norm

aliz

ed in

tens

ity

input pulse

output pulse

Propagation of a Truncated Pulse through Alexandrite as a Fast-Light Medium

Smooth part of pulse propagates at group velocity

Discontinuity propagates at phase velocity

Slow and Fast Light --What Next?

Longer fractional delay(saturate deeper; propagate farther)

Find material with faster response(technique works with shorter pulses)

24

Slow and Fast Light in aEr-doped Fiber Amplifier

Signal at 1550 nm.Separate Pump and Probe Lasers.Longer Interaction Lengths.

Slow Light in an Erbium-Doped Fiber Amplifier

0 200 400 600 800 10000

2

4

6

modulation frequency, Hz

dela

y, m

s6 ms

outin

vg = 1.7 x 103 m/sng = 1.8 x 105

L = 10 m

after S. Jarabo, University of Zaragoza

Pump Power Dependence of Time Delay

Modelling Slow and Fast Light in Erbium

-0.05

0

0.05

0.10

0.15

0.20

10 100 1000 10,000

140 mJ100 mJ

80 mJ

70 mJ

modulation frequency, Hz

fract

iona

l adv

ance

men

t

numerical modelling

L = 13 mSiin= 0.640 mJPin= 140 mJ

data

modulation frequency, Hz

fract

iona

l adv

ance

men

t

0

0.05

0.10

0.15

10 100 1000 10,000

0-50-100 100

time (ns)

Nor

mal

ized

Inte

nsity

50

DiodeLaser Fiber Amplifier

50/50

SBS Generator

Modulator

PulseGenerator

SBS Amplifier

Isolator

Oscilloscope

DetectorCirculator

CirculatorPolarization

Control

RF AmplifierVariable

Attenuator

Slow-Light via Stimulated Brillouin Scattering • Rapid spectral variation of the refractive response associated with SBS gain leads to slow light propagation• Supports bandwidth of 100 MHz, group index of about 100• Even faster modulation for SRS

in out

• Joint project with Gaeta and Gauthier

early data

Implications of “Slow” Light

1. Controllable optical delay lines (a) Large total delay versus large fractional delay

(b) True time delay for synthetic aperture radar(c) Buffers for optical processors and routers

2. New interactions enabled by slow light (e.g., SBS)3. New possibilities with other materials

(a) Semiconductor (bulk and heterostructures) (b) Laser dyes (gain, Q-switch, mode-lock) (c) rare-earth doped solids, especially EDFA’s4. How weak a signal can be used with these method?5. Relation between slowness and enhanced nonlinearity

Thank you for your attention.

And thanks to NSF for financial support!