A silicon-like model crystal: one optical phonon obeying a three-phonon anharmonic law. Sweep the stage temperature and watch the Stokes peak shift and broaden while the anti-Stokes line grows with the phonon population — then raise the model laser power and see the focal spot run hotter than the stage setpoint.
Schematic teaching model. Peak position and width follow a three-phonon anharmonic law of the Balkanski type, ω(T) = ω₀ − C·[1 + 2/(eˣ − 1)] with x = ℎω₀/2kᴛT, using silicon-representative parameters (ω₀ = 526 cm⁻¹, C = 2.96 cm⁻¹, Γ₀ = 1.68 cm⁻¹); four-phonon terms are omitted, so the highest-temperature shift is slightly understated. The anti-Stokes/Stokes ratio is exp(−hcω/kᴛT) with the (νₗ±ω)⁴ scattering factor at 488 nm excitation. The laser-power steps (+0, +15, +60 K) are illustrative spot-heating offsets, not data for any instrument or sample; real self-heating depends on absorption, thermal conductivity, geometry, and objective. Lines are Lorentzian with a small noise floor for realism.