1. NONLINEAR PROPAGATION
IN SPACE
IN TIME

2. Spatial Solitons
Neglect temporal dependence, and nonlinearities > than Kerr
Normalization:
and
Eigenvalue equation (normalized variables. Solution of type:
Townes’
soliton
2D nonlinear Schroedinger equation

3. Such that = critical power o Amplitude: o
Scaling parameters:
Radius: o
Such that = critical power o 2
Amplitude: o
SOLUTION: TOWNES SOLITON
TOWNES Soliton as
“Beam cleaner”

4. 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

5. 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)

6. 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:

7. PHASE MODULATION
DISPERSION

8. Application to a Gaussian pulse

9. 1.7 mm dia core
1.3 mm diameter air holes
single mode at 530 nm

10. core 2 mm
Dn = 0.3
“POSITIVE DISPERSION”
core 1 mm
Dn = 0.1
GVD
silica

11. microstructure fiber
“POSITIVE DISPERSION”
standard fiber

12. “Grapefruit
fiber”
“Crystal fiber”
“high delta
microstructured
fiber”
“air-clad
fiber”