Hermite–Gaussian modes

Summary

The Hermite–Gaussian modes are a family of beam solutions of the paraxial wave equation in Cartesian coordinates. Each one is a Gaussian beam multiplied by Hermite polynomials in the two transverse coordinates, scaled by the beam width. They keep their shape as they propagate, apart from a change of scale, and they form a complete orthogonal family of transverse profiles. They are the transverse modes of laser resonators with rectangular symmetry, labelled $\mathrm{TEM}_{mn}$.