GVD pulse broadening & chirp — standard vs dispersion-shifted fiber
Group velocity dispersion (GVD, β₂) causes different frequency components to travel at different speeds, broadening a Gaussian pulse by σ(z) = σ₀√(1+(z/L_D)²) where L_D = σ₀²/|β₂|. Anomalous dispersion (β₂<0) can balance nonlinearity to form solitons. Third-order dispersion β₃ asymmetrizes the pulse. Dispersion-shifted fiber (DSF) moves the zero-dispersion wavelength to 1550 nm.