Transverse
modes have a field vector normal to the direction of propogation
and are determined by the geometry of the laser or waveguide
cavity and any limiting apertures. Waveguide modes are characterized
as TE (transverse electric) with the electric vector normal,
and TE (transverse magnetic) with the magnetic vector normal.
In general, laser modes that do not have wall boundary conditions
are designated TEM (transvers electric magnetic) with both
vectors normal to the direction of propogation. The lowest
order mode is the Gaussian TEM00. The appearance that higherorder
modes take depends upon whether the limiting apertures are
circular or rectancular. The three lowestorder modes for
a circularly symmetric cavity are shown below.

The
higher order the mode, the smaller the beam diameter (for
a given geometry), the lower the divergence, and the smaller
the M^{2} value (M^{2} = 1 for a pure TEM_{00}
beam). The higher order the mode, the more uniform the beam
crosssection. Very highordermode beams have a tophat shape
