NONLINEAR PROPAGATION

IN SPACE

IN TIME

Neglect temporal dependence, and nonlinearities > than Kerr

Townes’soliton

Eigenvalue equation (normalized variables. Solution of type:

2D nonlinear Schroedinger equation

Normalization: and

Spatial Solitons

1.0

0.5

0

43210

radius ( r / r0 )

Townes Gaussian

Scaling parameters:

SOLUTION: TOWNES SOLITON

Radius: o

Amplitude: oSuch that = critical powero o

2 2

TOWNES Soliton as

“Beam cleaner”

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

Propagation in the time domain

PHASE MODULATION

n(t)or

k(t)

E(t) = (t)eit-kz

(t,0) eik(t)d (t,0)

DISPERSION

n()or

k()() ()e-ikz

Propagation in the frequency domain

Retarded frame and taking the inverse FT:

PHASE MODULATION

DISPERSION

Application to a Gaussian pulse

1.7 m dia core

1.3 m diameter air holes

single mode at 530 nm

core 1 m n = 0.1

core 2 m n = 0.3

GVDsilica

“POSITIVE DISPERSION”

microstructure fiber

standard fiber

“POSITIVE DISPERSION”

“Crystal fiber”“Grapefruitfiber”

“air-cladfiber”

“high deltamicrostructuredfiber”