Kerr Nonlinear Optics
Self-phase modulation, spectral broadening, and optical soliton formation
NLSE Parameters
Nonlinear coeff. γ:
1.0
GVD β₂ (anomalous<0):
-1.0
Propagation distance z:
0.0
Pulse duration T₀:
1.0
SPM only (β₂=0)
Soliton (N=1)
GVD only (γ=0)
NLSE:
∂A/∂z = iγ|A|²A − (β₂/2)∂²A/∂t²
SPM:
nonlinearity chirps the pulse. Phase φ(t) = γ|A|²z → spectral broadening.
Soliton:
SPM and anomalous GVD balance exactly at N=1: A(z,t) = sech(t)e^{iz/2}.