1. Study of linear propagation
Solution of 2nd order equation
Propagation through medium
No change in frequency spectrum z W
Z=0
To make F.T easier shift in frequency
Expand k value around central freq wl
Expand k to first order, leads to a group delay:

2. Study of linear propagation
Expansion orders in k(W)--- Material property

3. Combination of both: can be pulse broadening, compression,
Propagation in dispersive media: the pulse is chirped and broadening
Propagation in nonlinear media: the pulse is chirped
Combination of both: can be pulse broadening, compression,
Soliton generation

4. e(t,0) eik(t)d e(t,0) Propagation in the time domain PHASE MODULATION
E(t) = e(t)eiwt-kz
n(t) or
k(t)
e(t,0) eik(t)d
e(t,0)

5. e(DW,0) e(DW,0)e-ik(DW)z Propagation in the frequency domain
DISPERSION
n(W) or
k(W)
e(DW,0)
e(DW,0)e-ik(DW)z
Retarded frame and taking the inverse FT:

6. PHASE MODULATION
DISPERSION

7. Application to a Gaussian pulse