SLIDE 1 Can a signal propagate superluminal (v>c) in dispersive medium?
1
SLIDE 2 Outline
- Experiment: superluminal (v>c) propagation.
- Reshaping due to gain/absorption
- A theoretical method to test if velocity is reliable?
- Answer: is superluminal?
- Acknowledgements.
2
SLIDE 3 Outline
- Experiment: superluminal (v>c) propagation.
- Reshaping due to gain/absorption
- A theoretical method to test if velocity is reliable?
- Answer: is superluminal?
- Acknowledgements.
2
SLIDE 4 Experiment
Dispersive Medium Source Detector
L
) ( ) ( ) (
I R
in n n
3
SLIDE 5 Experiment
Dispersive Medium Source Detector
L
) ( ) ( ) (
I R
in n n
3
SLIDE 6 Experiment
Dispersive Medium Source Detector
L
) ( ) ( ) (
I R
in n n
3
SLIDE 7 Experiment
Dispersive Medium Source Detector
L
c L t /
0
if travels with speed of light
) ( ) ( ) (
I R
in n n
3
SLIDE 8 Experiment
Dispersive Medium Source Detector
L
c L t /
0
if travels with speed of light superluminal propagation
[1] L. J.Wang, A. Kuzmich, and A. Dogariu, Nature (London) 406, 277 (2000).
t t
if [1]
) ( ) ( ) (
I R
in n n
3
SLIDE 9 Problem!
Dispersive Medium Source Detector
L
Pulse displaces: Where to choose the reference point for displacement? Pulse also reshapes due to gain/absorption.
4
SLIDE 10 Outline
- Experiment: superluminal (v>c) propagation.
- Reshaping due to gain/absorption.
- A theoretical method to test if velocity is reliable?
- Answer: is superluminal?
- Acknowledgements.
5
SLIDE 11 example for reshaping
Gain Medium
) ( ) ( ) (
I R
in n n
grows more w.r.t.
6
SLIDE 12 example for reshaping
Gain Medium
) ( ) ( ) (
I R
in n n
grows more w.r.t. peak of the pulse
6
SLIDE 13 example for reshaping
Gain Medium
) ( ) ( ) (
I R
in n n
shifts!
Pulse shifts right. not due to propagation
7
SLIDE 14 Problem: to distinguish
Dispersive Medium
) ( ) ( ) (
I R
in n n
shifts!
How to distinguish? Propagation reshaping shift transfer of the signal amplification of previous signal
8
SLIDE 15 experiments
Dispersive Medium
) ( ) ( ) (
I R
in n n
shifts!
experiments detect pulse peak averaged pulse detect amplified pulse!
9
SLIDE 16 Velocity definitions
pulse peak
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SLIDE 17 Velocity definitions
pulse peak
averaged pulse center
[2] J. Peatross, S. A. Glasgow, and M. Ware, Phys. Rev. Lett. 84, 2370 (2000).
[2]
Poynting-vector (could be Energy)
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SLIDE 18 Velocity definitions
pulse peak
averaged pulse center good agreement
[2] J. Peatross, S. A. Glasgow, and M. Ware, Phys. Rev. Lett. 84, 2370 (2000).
[2]
Poynting-vector (could be Energy)
values at detectors
10
SLIDE 19
Is velocity true?
Does the defined/measured velocity truly correspond to propagation of the original signal? Detector only observes the modified pulse. propagation reshape-shift
11
SLIDE 20 Outline
- Experiment: superluminal (v>c) propagation.
- Reshaping due to gain/absorption.
- A theoretical method to test if velocity is reliable?
- Answer: is superluminal?
- Acknowledgements.
12
SLIDE 21
Method to test velocities
A velocity definition
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SLIDE 22
Method to test velocities
A velocity definition compare
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SLIDE 23
Method to test velocities
A velocity definition compare if <x> or <t> movement is really due to flow
v1 and v2 must be very similar!
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SLIDE 24
Fourier space to work within
can be calculated using real-ω expansion can be calculated using real-k expansion
14
SLIDE 25
Fourier space to work within
can be calculated using real-ω expansion can be calculated using real-k expansion
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SLIDE 26
Method
A velocity definition compare if <x> or <t> is really due to flow
v1 and v2 must be very similar!
using real-ω using real-k
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SLIDE 27
in order to compare
can be calculated using real-ω expansion can be calculated using real-k expansion relate D1(ω) ↔ D2(k)
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SLIDE 28
D1(ω) ↔ D2(k)
LHS
A
incident
B
reflected RHS
D
transmitted
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SLIDE 29
D1(ω) ↔ D2(k)
LHS
A
incident
B
reflected RHS
D
transmitted ω is real
k is real
k
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SLIDE 30
D1(ω) ↔ D2(k)
LHS
A
incident
B
reflected RHS
D
transmitted RHSs equal at x=0 ω is real
k is real
k
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SLIDE 31
D1(ω) ↔ D2(k)
ω is real
k is real
k
branch-cuts
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SLIDE 32 D1(ω) ↔ D2(k)
ω is real
k is real
k
n(ω) no pole no branch-cut
between
C1 and C2 branch-cuts no pole no branch-cut
between C1 and C2
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SLIDE 33 D1(ω) ↔ D2(k)
ω is real
k is real
k
n(ω) no pole no branch-cut
between
C1 and C2 branch-cuts no pole no branch-cut
between C1 and C2
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SLIDE 34 D1(ω) ↔ D2(k) (if poles)
ω is real
k is real
k
branch-cuts has poles
poles
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SLIDE 35 D1(ω) ↔ D2(k) (if poles)
ω is real
k is real
k
branch-cuts has poles
poles
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SLIDE 36
Comparison of v1 and v2
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Gaussian wave-packet
SLIDE 37
Comparison of v1 and v2
20
Gaussian wave-packet Luminal regime
2 1
v v
SLIDE 38
Comparison of v1 and v2
at resonance (ωc ~ ω0) both v1 and v2 superluminal Gaussian wave-packet
20
Luminal regime
2 1
v v
SLIDE 39 Comparison of v1 and v2
at resonance (ωc ~ ω0) both v1 and v2 superluminal v1 , v2 differs
however
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Gaussian wave-packet Luminal regime
2 1
v v
SLIDE 40 Comparison of v1 and v2
at resonance (ωc ~ ω0) both v1 and v2 superluminal v1 , v2 differs velocity definition is inconsistent not reliable not correspond to a real flow
however
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Gaussian wave-packet Luminal regime
2 1
v v
SLIDE 41 Outline
- Experiment: superluminal (v>c) propagation.
- Reshaping due to gain/absorption.
- A theoretical method to test if velocity is reliable?
- Answer: is superluminal?
- Acknowledgements.
21
SLIDE 42 Experiment again
Nanda et al. corresponds to detection time
[3] Lipsa Nanda, Aakash Basu, and S. A. Ramakrishna, Phys. Rev. E 74, 036601 (2006).
[3]
showed
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SLIDE 43 Experiment again
Nanda et al. corresponds to detection time
[3] Lipsa Nanda, Aakash Basu, and S. A. Ramakrishna, Phys. Rev. E 74, 036601 (2006).
[3]
showed
I showed that this is not reliable
22
SLIDE 44 Experiment again
Nanda et al. corresponds to detection time
[3] Lipsa Nanda, Aakash Basu, and S. A. Ramakrishna, Phys. Rev. E 74, 036601 (2006).
[3]
values measured in experiment not correspond to flow not signal velocity
showed
I showed that this is not reliable
22
SLIDE 45 Experiment again
Nanda et al. corresponds to detection time
[3] Lipsa Nanda, Aakash Basu, and S. A. Ramakrishna, Phys. Rev. E 74, 036601 (2006).
[3]
values measured in experiment not correspond to flow not signal velocity no superluminal propagation
showed
I showed that this is not reliable
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SLIDE 46 Summary
- Cannot distinguish between propagation and reshaping.
- Signal velocity and Pulse-peak velocity differ.
- Introduced a method to check if a velocity corresponds a
physical flow?
- Detectors measure pulse-peak velocity.
- Observed is not superluminal propagation; it’s reshaping.
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SLIDE 47
Acknowledgement
TUBİTAK-KARİYER No: 112T927 TÜBİTAK-1001 No: 110T876 Special thanks to Victor Kozlov for illuminating discussions. I thank Gürsoy Akgüç for intensive help in the manuscript.
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