nonlinear propagation in space in time. neglect temporal dependence, and nonlinearities > than...
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![Page 1: NONLINEAR PROPAGATION IN SPACE IN TIME. Neglect temporal dependence, and nonlinearities > than Kerr Townes’ soliton Eigenvalue equation (normalized variables](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649f165503460f94c2c70f/html5/thumbnails/1.jpg)
NONLINEAR PROPAGATION
IN SPACE
IN TIME
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Neglect temporal dependence, and nonlinearities > than Kerr
Townes’soliton
Eigenvalue equation (normalized variables. Solution of type:
2D nonlinear Schroedinger equation
Normalization: and
Spatial Solitons
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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”
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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
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Propagation in the time domain
PHASE MODULATION
n(t)or
k(t)
E(t) = (t)eit-kz
(t,0) eik(t)d (t,0)
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DISPERSION
n()or
k()() ()e-ikz
Propagation in the frequency domain
Retarded frame and taking the inverse FT:
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PHASE MODULATION
DISPERSION
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Application to a Gaussian pulse
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1.7 m dia core
1.3 m diameter air holes
single mode at 530 nm
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core 1 m n = 0.1
core 2 m n = 0.3
GVDsilica
“POSITIVE DISPERSION”
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microstructure fiber
standard fiber
“POSITIVE DISPERSION”
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“Crystal fiber”“Grapefruitfiber”
“air-cladfiber”
“high deltamicrostructuredfiber”