1. Announcements
Please return slides

2. Reading Quiz
The quantity that determines the broadening of an optical pulse is a) b) c)

3. Reading Quiz
Dispersion changes the FT ______ compared to the case of no dispersion
a) power spectrum
b) phases
c) both

4. Group delay Light signals move with group velocity
So if light goes through glass of thickness d, how much is it delayed vs vacuum?
11 waves

5. Importance of phase in f(w)…review
11 waves
101 waves
Linear phase dependence:
Dt is the same.
Pulse is shifted

6. Importance of phase in f(w)… review
11 waves
101 waves
Dt is bigger,
lower frequencies are ahead
Quadratic dependence:

7. Plane waves and Fourier
We’ve studied FT at one point in space (e.g )
The pulse at all positions is (if it moves in z direction):

8. Assume E(w) is large only near some wo (typical for a pulse)

9. Put into FT-1: carrier wave moves the envelope rigidly
broadens the envelope
These products become convolutions in time

10. Pulse broadens and is “chirped”: lowest frequencies are ahead after going through glass.

11. Broadening of pulses after going through glass, from a photonics website
Output pulse duration versus initial pulse duration for dispersive pulse broadening with different levels of group delay dispersion (GDD). Note that shorter pulses are increasingly sensitive to dispersion. Substantial broadening occurs when the square of the pulse duration is smaller than the group delay dispersion.

12. Apparent faster-than-light pulses

13. Apparent faster-than-light pulses
Group velocity changes with w, so the pulse changes shape.
If the pulse’s w band is in the box on the figure, the portions of light in the pulse moving fastest (highest group velocity) are :___
higher frequencies
lower frequencies

14. Apparent faster-than-light pulses
The portion of the spectrum that is absorbed most is ______ frequencies
higher
lower

15. Apparent faster-than-light pulses
In absorbing media:
pulse if no absorption
pulse if no material
Peak has “moved” faster than speed of light simply because of absorption. But no information has traveled faster than c.

16. What kind of chirp would this pulse have?
higher frequencies first
lower frequencies first
no chirp
Would the peak of this pulse be ahead or behind a pulse with no absorption?
ahead
behind
no difference

18. Apparent faster-than-light pulses
Absorbing light from the middle of the spectrum can also reshape light pulse

19. Amplification of light due to stimulated emission
What changed in the Lorenz model?
n flips about n=1; k simply becomes negative!
If the pulse’s w band is in the box on the figure, the portions of light in the pulse moving fastest (highest group velocity) are :___
higher frequencies
lower frequencies

20. Can also get apparent faster-than light pulses with amplification from stimulated emission
Peak can “move” faster than speed of light simply because of amplification. But no information has traveled faster than c.