Deep-UV excimer photons (157–248 nm, 5.0–7.9 eV) carry enough energy to ionise trace lattice defects and trapped electrons in a fluoride crystal, leaving a hole trapped at an anion vacancy — an F-center. Each color center absorbs light at its own band, so their buildup steadily darkens an optic that started perfectly clear.
Per-pulse generation: ΔN = G(λ, F) · (1 − N / N_sat)
Photon-energy scaling: G ∝ (E_photon / E_gap)^p (p ≈ 3–4, multi-photon-like onset)
Thermal annealing: dN/dt = −k₀ · exp(−E_a / k_B·T) · N
Beer–Lambert: Transmission = exp(−σ · N · L)
Damage criterion: N ≥ N_crit → catastrophic absorption runaway
- Material — CaF₂ has a wider bandgap (~10 eV) and higher intrinsic damage threshold than MgF₂ (~11 eV bandgap but more native vacancies), so their generation rate G and critical density N_crit differ.
- Wavelength — shorter wavelength = higher photon energy E_photon, pushing G(λ,F) up steeply once E_photon approaches the bandgap; this is why 157 nm F₂-laser optics damage far more easily than 248 nm KrF optics at the same fluence.
- Fluence & repetition rate — higher fluence increases ΔN per pulse; a higher repetition rate leaves less time between pulses for the crystal to cool and thermally anneal existing centers back out, so heat and defects both accumulate faster.
- Anneal — a real fluoride window recovers slowly by thermal annealing (or a bake-out); the button here fast-forwards that recovery so you can compare a rested vs. fatigued optic.
Real-world relevance: this exact failure mode is why 193 nm ArF lithography and 157 nm F₂ lens elements are cut from ultra-pure, low-defect CaF₂ boules rather than fused silica — ordinary optical glass would cloud over after a few million pulses.