fundamentals and applications of slow light in room ......inverse-saturable absorption produces...
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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!