This Demonstration considers the intensity distribution of Hermite-Gaussian transverse electromagnetic (TEM) modes produced by a laser. These modes are solutions of the paraxial wave equation in Cartesian coordinates. They represent the transverse (-) intensity distribution of a laser beam propagating in the direction.
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 .
the integrated intensity is normalized to yield unit power