1. Propagation in the time domain PHASE MODULATION n(t) or k(t) E(t) =  (t) e i  t-kz  (t,0) e ik(t)d  (t,0)

2. Chirped pulse LEADS TO : Propagation through a medium with time dependent index of refraction Pulse compression: propagation through wavelength dependent index

3. DISPERSION n(  ) or k(  )  (  )  (  ) e -ik  z Propagation in the frequency domain Retarded frame and taking the inverse FT:

4. PHASE MODULATION DISPERSION

5. Application to a Gaussian pulse Inverse F.T.

6. Wigner function: What is the point? Uncertainty relation: Equality only holds for a Gaussian pulse (beam) shape free of any phase modulation, which implies that the Wigner distribution for a Gaussian shape occupies the smallest area in the time/frequency plane. Only holds for the pulse widths defined as the mean square deviation

7. APPLICATION OF SPACE-TIME ANALOGY TO TIME MULTIPLEXING

8. C H A... 5 3 2... F A X... X Y Z... C H A... 5 3 2... F A X... X Y Z... Electronics: 1ns, 12 bit Optical, 1 ps, 12 bit TIME MULTIPLEXING TIME DE-MULTIPLEXING PROPAGATION EMISSIONEMISSION RECEPTIONRECEPTION

9. C5FXC5FX C 5 F X PROPAGATIONPROPAGATION C 5 F X C5FXC5FX

10. White light interferometry

13. + 500  m glass

14. ADDING FILTERS

15. 0306090120 -0.5 0.0 0.5 1.0 Normalized Intensity (a.u.) Relative Delay (  m) 0100200300400 Relative Delay (fs) 2 mm of glass

16. Fourier transform