In a Kerr medium, intensity-dependent refractive index n = n₀ + n₂I induces a nonlinear phase shift φ_NL = (n₂ω/c) I(t) L. This SPM broadens the pulse spectrum symmetrically, generating new frequencies — the basis of supercontinuum generation.
φ_max = γ P₀ L where γ = n₂ω/(cA_eff). New frequency components: δω(t) = -dφ_NL/dt — leading edge red-shifted, trailing edge blue-shifted. At φ_max = π, spectrum splits. Mach-Zehnder modulators exploit this for soliton compression.