Details

The Hermite-Gaussian modes

are an important family of solutions of the paraxial wave equation

that describes the optical field, that is, the amplitude of the electric field in a laser beam propagating along . The transverse (-) intensity distribution of the beam is given by

.

In the above, is the phase of the beam, which is irrelevant when discussing the intensity and is called the beam radius. As the beam propagates changes in a characteristic manner. However, as seen from the expressions above, acts as a scaling parameter, so that the transverse beam pattern does not change along the propagation direction; it merely changes its scale, shown in this Demonstration for .

By setting

,

the integrated intensity is normalized to yield unit power

.