Irradiance

Irradiance is the power carried by light across a unit area, $E = dP/dA$. It is what heats a sample, saturates a detector, drives a nonlinear process or damages a coating, which power alone does not tell: one watt spread evenly over a square centimetre gives 1 W/cm², while the same watt focused to a Gaussian spot of 10 µm radius reaches a peak of 6.4 × 10⁵ W/cm².

In laser physics the same quantity is usually called intensity, and nonlinear optics formulas such as the Kerr index change $n_2 I$ use it in that sense. In radiometry, intensity means power per unit solid angle (W/sr), a different quantity, so the word should be read in its context. Power density is a third, informal name.

Gaussian beams

A Gaussian beam of power $P$ and $1/e^2$ radius $w$ has irradiance $I(r) = I_0 \exp(-2r^2/w^2)$, with peak

The peak is twice the average irradiance obtained by dividing the power by the $1/e^2$ area $\pi w^2$, a factor that is easy to drop and matters for damage and safety estimates. A 5 mW helium-neon beam with a 0.4 mm radius has a peak irradiance of 2.0 W/cm², compared with about 0.1 W/cm² (1000 W/m²) for direct sunlight at the ground under the standard AM1.5 condition.

Measurement

Irradiance is not usually measured directly. The total power comes from an optical power meter and the beam radius from a camera profiler or a knife-edge measurement, and the peak follows from the formula above for a Gaussian profile; for other profiles the camera image, normalized to the measured power, gives the irradiance map. A calibrated detector behind a pinhole much smaller than the beam gives the local irradiance directly, as power divided by the pinhole area. For pulsed beams the energy per area is the fluence, and the peak irradiance follows from it and the pulse duration.

References: E. Hecht, Optics, 5th ed. (Pearson, 2017), Ch. 3; A. E. Siegman, Lasers (University Science Books, 1986), Ch. 17; IEC 60904-3, Photovoltaic devices: Measurement principles with reference spectral irradiance data.