Is it possible to transmit information faster than the vacuum velocity of light? Einstien says no. But indeed the group velocity of a light pulse can be made larger than c! Let us see how is it possible.
7. • PHASE VELOCITY :
Rate at which the phase of the wave
propagates in space.
VELOCITY OF LIGHT
PHASE VELOCITY
8. Any waveform can be decomposed as a
weighted sum of different monochromatic
components
VELOCITY OF LIGHT
9. • GROUP VELOCITY :
Different monochromatic components travel
at different phase velocities and the velocity
of the maximum of the pulse is called group
velocity.
VELOCITY OF LIGHT
GROUP VELOCITY
17. PULSE DISTORTION
Normalized field amplitude in a dispersive
medium is governed by :
Where U(z,T)is the normalized amplitude
of the electric field in the dispersive medium.
1
19. PULSE DISTORTION
Solving 2 :
Frequency dependence in phase
Pulse gets distorted! Group velocity
does not make sense
20. INFORMATION IN A PULSE
(1868-1951)
Arnold Sommerfeld
In 1907, predicted that the front of a step
modulated pulse always propagates with
a velocity of c irrespective of the dispersion
of the medium.
Velocity of front = c
front
21. INFORMATION IN A PULSE
Later investigations in this field report that information is
stored only in points of a pulse that are non-analytic.
(Parker et al, Optics Communications , 229(2004), 23-27)
I is the total amount of differential information. p(x) is any
arbitrary continuously varying function of space. R
denotes the residues of the function.
22. INFORMATION IN A PULSE
c
Non-analytic points propagate with velocity=c.
28. SUMMARY
Information cannot travel faster than the vacuum speed
of light.
So forget about changing the past…
Be in the present…
And decorate the future…