Rate ∝ σ₂ × I² (intensity squared dependence)
Two-photon absorption (TPA) is a nonlinear optical process where a molecule simultaneously absorbs two photons, each with half the energy needed for the transition. The absorption rate depends on intensity squared (∝ I²), requiring high peak powers from ultrafast pulsed lasers (typically Ti:sapphire, ~800 nm, ~100 fs pulses). The TPA cross-section σ₂ is measured in Goeppert-Mayer units (1 GM = 10⁻⁵⁰ cm⁴·s/photon). Typical values: fluorescent proteins 1-300 GM, quantum dots 1000-50000 GM. TPA enables two-photon fluorescence microscopy — deeper tissue penetration (near-IR light scatters less), intrinsic optical sectioning, and reduced photobleaching. Applications include: brain imaging, optogenetics, 3D microfabrication, and photodynamic therapy.