Can a signal propagate superluminal (v>c) in dispersive medium? - PowerPoint PPT Presentation

1 Can a signal propagate superluminal (v>c) in dispersive medium? M. Emre Ta ş g ı n

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 Outline • Experiment: superluminal (v>c) propagation. • Reshaping due to gain/absorption • A theoretical method to test if velocity is reliable? • Answer: is superluminal? • Acknowledgements.

3 Experiment Source      n ( ) n ( ) in ( ) Detector R I Dispersive Medium L

3 Experiment Source      n ( ) n ( ) in ( ) Detector R I Dispersive Medium L

3 Experiment Source      n ( ) n ( ) in ( ) Detector R I Dispersive Medium L

3 Experiment Source      n ( ) n ( ) in ( ) Detector R I Dispersive Medium L  0  if travels t L / c with speed of light

3 Experiment Source      n ( ) n ( ) in ( ) Detector R I Dispersive Medium L  0  if travels t L / c with speed of light    superluminal t t if [1] 0 propagation [1] L. J.Wang, A. Kuzmich, and A. Dogariu, Nature (London) 406, 277 (2000).

4 Problem! Source Detector Dispersive Medium L Pulse displaces:  Where to choose the reference point for displacement?  Pulse also reshapes due to gain/absorption.

5 Outline • Experiment: superluminal (v>c) propagation. • Reshaping due to gain/absorption. • A theoretical method to test if velocity is reliable? • Answer: is superluminal? • Acknowledgements.

6 example for reshaping      n ( ) n ( ) in ( ) R I Gain Medium grows more w.r.t.

6 example for reshaping      n ( ) n ( ) in ( ) R I Gain Medium peak of the pulse grows more w.r.t.

7 example for reshaping shifts!      n ( ) n ( ) in ( ) R I Gain Medium Pulse not due to shifts propagation right.

8 Problem: to distinguish shifts!      n ( ) n ( ) in ( ) R I Dispersive Medium transfer of Propagation the signal How to distinguish? reshaping amplification of shift previous signal

9 experiments shifts!      n ( ) n ( ) in ( ) R I Dispersive Medium pulse peak detect experiments amplified pulse! detect averaged pulse

10 Velocity definitions  Displacement of the pulse peak

10 Velocity definitions  Displacement of the pulse peak Poynting-vector (could be Energy ) [2]  Energy/Poynting-vector averaged pulse center [2] J. Peatross, S. A. Glasgow, and M. Ware, Phys. Rev. Lett. 84, 2370 (2000).

10 Velocity definitions  Displacement of the pulse peak Poynting-vector (could be Energy ) [2]  Energy/Poynting-vector averaged pulse center good values at agreement detectors [2] J. Peatross, S. A. Glasgow, and M. Ware, Phys. Rev. Lett. 84, 2370 (2000).

11 Is velocity true? Does the defined/measured velocity truly correspond to propagation of the original signal ? Detector only observes the modified pulse. reshape-shift propagation

12 Outline • Experiment: superluminal (v>c) propagation. • Reshaping due to gain/absorption. • A theoretical method to test if velocity is reliable? • Answer: is superluminal? • Acknowledgements.

13 Method to test velocities A velocity definition

13 Method to test velocities A velocity definition compare

13 Method to test velocities A velocity definition compare if <x> or <t> movement is really due to flow v 1 and v 2 must be very similar!

14 Fourier space to work within can be calculated using real- ω expansion can be calculated using real-k expansion

14 Fourier space to work within can be calculated using real- ω expansion can be calculated using real-k expansion

15 Method A velocity definition compare using using real- ω real-k if <x> or <t> is really due to flow v 1 and v 2 must be very similar!

16 in order to compare can be calculated using real- ω expansion relate D 1 (ω) ↔ D 2 (k) can be calculated using real-k expansion

17 D 1 (ω) ↔ D 2 (k) A incident LHS B reflected D transmitted RHS

17 D 1 (ω) ↔ D 2 (k) A incident LHS B reflected D transmitted RHS  ω is real k k is real

17 D 1 (ω) ↔ D 2 (k) A incident LHS B reflected D transmitted RHS  ω is real k k is real RHSs equal at x=0

18 D 1 (ω) ↔ D 2 (k)  ω is real k k is real branch-cuts

18 D 1 (ω) ↔ D 2 (k)  ω is real k k is real branch-cuts no pole n( ω ) between C 1 and C 2 no branch-cut no pole between C 1 and C 2 no branch-cut

18 D 1 (ω) ↔ D 2 (k)  ω is real k k is real branch-cuts no pole n( ω ) between C 1 and C 2 no branch-cut no pole between C 1 and C 2 no branch-cut

19 D 1 (ω) ↔ D 2 (k) (if poles)  ω is real k k is real branch-cuts poles has poles

19 D 1 (ω) ↔ D 2 (k) (if poles)  ω is real k k is real branch-cuts poles has poles

20 Comparison of v 1 and v 2 Gaussian wave-packet

20 Comparison of v 1 and v 2 Gaussian wave-packet v  v Luminal regime 1 2

20 Comparison of v 1 and v 2 Gaussian wave-packet v  v Luminal regime 1 2 at resonance ( ω c ~ ω 0 ) both v 1 and v 2 superluminal

20 Comparison of v 1 and v 2 Gaussian wave-packet v  v Luminal regime 1 2 at resonance ( ω c ~ ω 0 ) however both v 1 , v 2 v 1 and v 2 differs superluminal

20 Comparison of v 1 and v 2 Gaussian wave-packet v  v Luminal regime 1 2 at resonance ( ω c ~ ω 0 ) however both v 1 , v 2 v 1 and v 2 differs superluminal velocity definition not reliable is inconsistent not correspond to a real flow

21 Outline • Experiment: superluminal (v>c) propagation. • Reshaping due to gain/absorption. • A theoretical method to test if velocity is reliable? • Answer: is superluminal? • Acknowledgements.

22 Experiment again [3] Nanda et al. showed corresponds to detection time [3] Lipsa Nanda, Aakash Basu, and S. A. Ramakrishna, Phys. Rev. E 74, 036601 (2006).

22 Experiment again [3] Nanda et al. showed corresponds to detection time I showed that this is not reliable [3] Lipsa Nanda, Aakash Basu, and S. A. Ramakrishna, Phys. Rev. E 74, 036601 (2006).

22 Experiment again [3] Nanda et al. showed values measured in experiment not correspond to flow corresponds to detection time not signal velocity I showed that this is not reliable [3] Lipsa Nanda, Aakash Basu, and S. A. Ramakrishna, Phys. Rev. E 74, 036601 (2006).

22 Experiment again [3] Nanda et al. showed values measured in experiment not correspond to flow corresponds to detection time not signal velocity I showed that this is not reliable no superluminal propagation [3] Lipsa Nanda, Aakash Basu, and S. A. Ramakrishna, Phys. Rev. E 74, 036601 (2006).

23 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.

24 Acknowledgement  Special thanks to Victor Kozlov for illuminating discussions.  I thank G ürsoy Akgüç for intensive help in the manuscript. TUBİTAK - KARİYER No: 112T927 TÜBİTAK -1001 No: 110T876