Definition: optical power per unit area

German: optische Intensität

The optical intensity I, e.g. of a laser beam, is the optical power per unit area, which is transmitted through an imagined surface perpendicular to the propagation direction. The units of the optical intensity (or light intensity) are W/m² or (more commonly) W/cm². The intensity is the product of photon energy and photon flux.

For a monochromatic propagating wave, such as a plane wave or a Gaussian beam, the local intensity is related to the amplitude E of the electric field via

where v_p is the phase velocity, c is the vacuum velocity of light, and n is the refractive index. For non-monochromatic waves, the intensity contributions of different spectral components can simply be added, if beat notes are not of interest.

Note that the above equation does not hold for arbitrary electromagnetic fields. For example, an evanescent wave may have a finite electrical amplitude while not transferring any power. The intensity should then be defined as the magnitude of the Poynting vector.

For a laser beam with a flat-top intensity profile (i.e., with a constant intensity over some area, and zero intensity outside), the intensity is simply the optical power P divided by the beam area. For a Gaussian beam with optical power P and Gaussian beam radius w, the peak intensity (on the beam axis) is

which is two times higher than is often assumed. The equation can be verified by integrating the intensity over the whole beam area, which must result in the total power.

In a multimode laser beam, generated in a laser where higher-order transverse resonator modes are excited, the shape of the transverse intensity profile can undergo significant changes as the relative optical phases of the modes change with time. The peak intensity can then vary, and may occur at locations at some distance from the beam axis.

The term intensity is often used in a non-quantitative or not very precise way, and not clearly distinguished from the optical power. For example, the intensity noise normally refers to noise (fluctuations) of the optical power, rather than the intensity.

Optical intensities are relevant in various situations:

• In conjunction with transition cross sections, intensities govern the rates of optical transitions, e.g. in laser gain medium. Strong saturation of an optical transition in the steady state occurs when the intensity exceeds the saturation intensity.
• The refractive index change via the Kerr effect in a transparent medium is the nonlinear index times the local intensity.
• Optical damage of a medium may occur for intensities above a certain damage threshold, which however can usually only be reached with optical pulses, and then depends on the pulse duration.
• Extremely high peak intensities can be achieved with amplified ultrashort pulses. For intensities of e.g. 10¹⁴ W/cm² or higher in a gas, high harmonic generation can occur.

Beam profilers can be used for measuring the shape of the intensity profile of a laser beam.

See also: Gaussian beams, laser beams, brightness, intensity noise

Category: general optics