Note that the subscripts n and m in the Eigenmode
TEM nm are correlated
to the number of nodes in the x
and y directions. In each case, adjacent lobes of the
mode are 180กใ out of phase.
propagation equation can also be written in cylindrical form
in terms of radius (r) and angle (f). The eigenmodes
(Erf) for this equation are a series of axially
symmetric modes, which, for stable resonators, are closely
approximated by Laguerre-Gaussian functions, denoted by TEMrf. For the lowest order mode, TEM00,
the Hermite-Gaussian and Laguerre-Gaussian functions are identical,
but for higher order modes, they differ significantly, as
shown in the figure below.
mode, TEM01*, also known as the "bagel" or "doughnut"
mode, is considered to be a superposition of the Hermite-Gaussian
TEM10 and TEM01 modes, locked in phase
real-world lasers, the Hermite-Gaussian modes predominate
since strain, slight misalignment, or contamination on the
optics tends to drive the system toward rectangular coordinates.
Nonetheless, the Laguerre-Gaussian TEM10 "target"
or "bulls-eye" mode is clearly observed in well-aligned gas-ion
and helium neon lasers with the appropriate limiting apertures.