Fluence

Fluence is the energy per unit area delivered to a surface by a pulse, or by an exposure of known duration. For pulsed lasers it is the natural measure of how hard a surface is being hit: whether a coating survives, a metal ablates or a tissue coagulates depends to first order on the fluence, and on the pulse duration, rather than on average power. It is the time integral of the irradiance over the pulse.

For a pulse of energy $E$ with a Gaussian spatial profile of $1/e^2$ radius $w$, the peak fluence at the beam centre is

again twice the energy divided by the $1/e^2$ area. A 1 mJ pulse focused to a 100 µm radius gives 6.4 J/cm².

Fluence and peak irradiance

Dividing the fluence by the pulse duration gives the peak irradiance. For a pulse with a Gaussian temporal shape and full width at half maximum $\tau$, $I_0 = 0.94\,F_0/\tau$; for the example above with a 10 ns pulse from a Q-switched laser, 6.0 × 10⁸ W/cm². Both numbers matter. Damage and ablation by nanosecond pulses are largely thermal and track the fluence, while a 100 fs pulse from a mode-locked laser at only 0.1 J/cm² already reaches 10¹² W/cm², enough for multiphoton absorption in transparent materials, so a damage threshold is only meaningful together with the pulse duration, wavelength and spot size it was measured at.

Measurement of a threshold

Energy comes from a pyroelectric or thermal energy meter, and the spot radius at the sample from a camera profiler or knife-edge measurement in an equivalent focal plane. For thresholds, the method of J. M. Liu is widely used: a Gaussian spot produces a damaged or ablated region of diameter $D$ where the local fluence exceeds the threshold $F_{th}$, so $D^2 = 2w^2\ln(F_0/F_{th})$. Plotting $D^2$ against the logarithm of pulse energy gives a straight line whose slope yields the effective spot radius and whose intercept yields the threshold, without an independent measurement of $w$.

References: J. M. Liu, Opt. Lett. 7, 196 (1982); A. E. Siegman, Lasers (University Science Books, 1986), Ch. 17; ISO 21254-1:2011, Lasers and laser-related equipment: Test methods for laser-induced damage threshold.