Raman Scattering: when monochromatic light is scattered by a crystal, most photons scatter elastically (Rayleigh). A small fraction exchange energy with phonons:
Stokes scattering emits a phonon (shifted to lower frequency),
anti-Stokes absorbs one (higher frequency). The Raman spectrum is a fingerprint of lattice vibration modes.
ω_scattered = ω_laser ± ω_phonon | I_anti-Stokes/I_Stokes = exp(−ℏω_ph/k_BT)
Selection rules: only phonons at the Brillouin zone center (q≈0) are Raman-active. The D band in graphene (~1350 cm⁻¹) requires a defect for activation; the G band (~1580 cm⁻¹) is always active; the 2D band (~2700 cm⁻¹) is an overtone.