Laser Damage Threshold
Scale an optic's rated pulsed laser damage threshold (LIDT) to your pulse duration with the √τ law and compare it with the 2E/(πw²) peak fluence of your Gaussian beam: margin and energy at threshold.
Enter the optic's rated damage threshold and the pulse duration it was measured at, from its data sheet (same wavelength as your laser). The defaults are an example, not a material value.
LIDT at Your Pulse
7.071 J/cm²
F_ref (τ/τ_ref)^0.5
Peak Fluence
1.019 J/cm²
2E/(πw²); mean over πw² 0.5093 J/cm²
Threshold / Peak
6.94×
below the rated threshold
Energy at Threshold
694.2 mJ
πw²F_th/2 for this beam
Damage threshold against pulse duration
- Scaled LIDT
- Peak fluence
- This pulse
Model
F_th(τ) = F_ref (τ/τ_ref)^a, a = ½ for τ ≳ 20 ps
F_peak = 2E/(πw²), w the 1/e² radius
The √τ law comes from heat diffusion during the pulse and was measured for fused silica and CaF₂ above about 20 ps (Stuart et al. 1996). Real optics scatter around it, as defects set the threshold. A Gaussian beam's peak fluence is twice the mean over πw² (the ISO 21254 effective area πw²/2), so compare it, not E/(πw²), with the rated value. Wavelength, spot size and repetition rate also change the threshold and are not modelled; continuous-wave ratings (W/cm) are a different quantity.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
F_th(τ) = F_ref (τ/τ_ref)^a with a = ½ (heat diffusion), measured above about 20 ps; real optics scatter around it. Peak fluence 2E/(πw²) of a TEM₀₀ beam (ISO 21254 effective area πw²/2). Above about 1 µs heating approaches the CW regime and the √τ law is not validated (the page warns). Wavelength, spot-size and repetition-rate effects are not modelled; the rated value comes from the optic's data sheet.
- Stuart B. C., Feit M. D., Herman S., Rubenchik A. M., Shore B. W., Perry M. D. (1996). Nanosecond-to-femtosecond laser-induced breakdown in dielectrics. Phys. Rev. B 53, 1749–1761. √τ scaling above about 20 ps (fused silica, CaF₂). doi:10.1103/PhysRevB.53.1749
- Wood R. M. (2003). Laser-Induced Damage of Optical Materials. IOP Publishing (CRC Press). doi:10.1201/9781420034059
- ISO 21254-1:2011. Lasers and laser-related equipment — Test methods for laser-induced damage threshold — Part 1: Definitions and general principles. Effective area of a Gaussian beam πw²/2.