NONLINEAR PROPAGATION IN SPACE IN TIME
Jan 04, 2016
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”