Kerr Effect & Nonlinear Optics
n(r,t) = n₀ + n₂·I(r,t) — intensity-dependent refractive index
Pulse Envelope & Phase (SPM)
Spectral Broadening (SPM)
Self-Focusing: Beam Profile vs z
B-integral & Phase Accumulation
Kerr Effect: The refractive index depends on light intensity: n = n₀ + n₂·I. For silica, n₂ ≈ 2.6×10⁻²⁰ m²/W. This tiny nonlinearity has massive consequences at high intensities.
Self-Phase Modulation (SPM): A pulse traveling distance z acquires phase φ(t) = -n₂·I(t)·k₀·z. The time-varying phase creates new frequency components: instantaneous frequency δω = -∂φ/∂t. Leading edge is red-shifted, trailing edge blue-shifted — spectral broadening.
B-integral: B = (2π/λ)∫n₂·I·dz measures accumulated nonlinear phase. B > π causes severe spectral distortion.
Solitons: When anomalous dispersion (β₂ < 0) balances SPM (n₂ > 0), a soliton forms — the pulse propagates without distortion. The fundamental soliton condition: N² = γP₀T₀²/|β₂| = 1.