Four-Wave Mixing

Physics: FWM (χ⁽³⁾ process): ω₁+ω₂ = ω₃+ω₄; degenerate FWM with two pumps ω₁,ω₂ generates sidebands ω₃ = 2ω₁−ω₂ and ω₄ = 2ω₂−ω₁. Phase matching Δk = k₃+k₄−k₁−k₂ = 0 requires anomalous dispersion in fiber. FWM causes crosstalk in WDM systems (harmful) but enables fiber optical parametric amplifiers and wavelength conversion (useful). Related χ⁽³⁾ effects: stimulated Raman scattering (SRS), stimulated Brillouin scattering (SBS), and self-phase modulation n = n₀ + n₂I (Kerr nonlinearity, n₂ ≈ 2.6×10⁻²⁰ m²/W in silica).