How LIDT is specified
Damage thresholds are measured by exposing many sites on a sample at a range of fluences and finding the fluence below which no damage occurs (ISO 21254). In a 1-on-1 test each site sees a single pulse. In an S-on-1 test each site sees many pulses, which gives a lower threshold. ISO 21254 reports fluence through the effective beam area \(A_\text{eff} = \pi w^2/2\) for a Gaussian beam, so the value is the peak (on-axis) fluence. Some datasheets instead divide the energy by the 1/e² area, giving a number half as large. When the convention is unclear, treat the specification as a peak value. That is the conservative choice.
Scaling with pulse duration
From tens of picoseconds up to the microsecond range, damage in dielectric coatings and substrates is driven by absorption at defects followed by heating. The heated volume grows with the thermal diffusion length \(\propto\sqrt{\tau}\), so the fluence needed to reach a critical temperature scales as
This rule breaks down for ultrashort pulses. Below roughly 10 ps, damage changes from thermal, defect-dominated behavior to deterministic multiphoton and avalanche ionization, and the threshold falls more slowly than \(\sqrt{\tau}\) (Stuart et al., 1996). Do not scale a nanosecond specification into the femtosecond regime. Ask the vendor for ultrafast data instead. Extrapolating more than about three decades in pulse duration is also unreliable.
Scaling with wavelength
Shorter wavelengths damage optics more easily: photon energies are higher, defect absorption is stronger, and the standing-wave field in coatings changes. Vendors use different rules of thumb. Thorlabs scales pulsed thresholds with \(\sqrt{\lambda}\). Sill Optics states that halving the wavelength halves the LIDT, which is linear scaling. Moving to a shorter wavelength, the linear rule predicts the lower threshold. Moving to a longer one, the square-root rule does. The conservative option uses whichever is lower. Coatings are designed for specific wavelengths, so measured data at your wavelength always beats scaling.
CW lasers: linear power density
For CW and long-pulse lasers, damage is thermal and set by the steady-state temperature rise. For an absorbed Gaussian beam on a thick substrate, that rise scales as \(P_\text{abs}/(k\,w)\), with power divided by beam size, not area. CW thresholds are therefore quoted as a linear power density (Thorlabs convention):
So a beam twice as large tolerates twice the power, not four times as much. Peak irradiance (W/cm²) is shown for reference only. It is not the right figure of merit for CW damage.
Beam size, safety factors, and S-on-1
- Beam size. Most damage starts at sparse defects. A small test beam may sample no defect at all, while a large beam almost certainly hits several. A threshold measured with a small beam can therefore be optimistic for a much larger one. There is no universal scaling law, so add margin when your beam area is much larger than the test beam's.
- S-on-1 and incubation. Under millions of pulses, thresholds can fall well below 1-on-1 values. Use S-on-1 data for production systems.
- Contamination. Dust, fingerprints, and outgassed films absorb strongly and can reduce the effective threshold by a large factor. Keep optics clean, and purge enclosures for UV and high-power IR.
- Safety factor. Operate at no more than 1/2 to 1/3 of the scaled threshold. Sill Optics, for example, recommends staying below 50 % of the LIDT.
Worked example
A mirror is rated 10 J/cm² (peak) at 1064 nm, 10 ns. You want to use it at 532 nm with 20 ns, 5 mJ pulses in a 1.0 mm beam. The pulse-duration factor is \(\sqrt{2} = 1.414\). For wavelength, the conservative rule takes the linear factor of 0.5 (the √λ rule would give 0.707). The scaled LIDT is \(10 \times 1.414 \times 0.5 = 7.07\) J/cm². The operating peak fluence is \(2 \times 5\ \text{mJ}/(\pi \times 0.05^2\ \text{cm}^2) = 1.27\) J/cm², so the margin is 5.6×. That is comfortably inside a 2× safety factor.
Assumptions and limits
- The scaling laws are empirical. They estimate thresholds for comparing options and for specifying optics, and they do not guarantee survival.
- Normal incidence is assumed. At oblique incidence, the fluence on the surface falls by cos θ, but coating damage also depends on polarization and the field distribution.
- The beam diameter is the 1/e² diameter at the optic, not at focus. Hot spots, diffraction rings, and M² > 1 can raise local fluence above the Gaussian estimate.
References
- ISO 21254-1:2011, Lasers and laser-related equipment — Test methods for laser-induced damage threshold — Part 1: Definitions and general principles.
- B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1761 (1996).
- R. M. Wood, Laser-Induced Damage of Optical Materials, Institute of Physics Publishing (2003).