Note that the subscripts n and m in the Eigenmode TEM_{ nm} are correlated to the number of nodes in the x and ydirections. In each case, adjacent lobes of the mode are 180° out of phase.
The propagation equation can also be written in cylindrical form in terms of radius (r) and angle (f). The eigenmodes (E_{rf}) for this equation are a series of axially symmetric modes, which, for stable resonators, are closely approximated by LaguerreGaussian functions, denoted by TEM_{rf}. For the lowest order mode, TEM_{00}, the HermiteGaussian and LaguerreGaussian functions are identical, but for higher order modes, they differ significantly, as shown in the figure below.

The mode, TEM_{01}*, also known as the "bagel" or "doughnut" mode, is considered to be a superposition of the HermiteGaussian TEM_{10} and TEM_{01} modes, locked in phase quadrature.
In realworld lasers, the HermiteGaussian modes predominate since strain, slight misalignment, or contamination on the optics tends to drive the system toward rectangular coordinates. Nonetheless, the LaguerreGaussian TEM_{10} "target" or "bullseye" mode is clearly observed in wellaligned gasion and helium neon lasers with the appropriate limiting apertures.
