NONLINEAR PROPAGATION IN SPACE IN TIME

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

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”

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

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)

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:

PHASE MODULATION DISPERSION

Application to a Gaussian pulse

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

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

microstructure fiber “POSITIVE DISPERSION” standard fiber

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