In
most laser applications it is necessary to focus, modify,
or shape the laser beam by using lenses and other optical
elements. In general, laserbeam propagation can be approximated
by assuming that the laser beam has an ideal Gaussian intensity
profile, corresponding to the theoretical TEM_{00}
mode. Coherent Gaussian beams have peculiar transformation
properties that require special consideration. In order to
select the best optics for a particular laser application,
it is important to understand the basic properties of Gaussian
beams. Unfortunately, the output from reallife lasers is
not truly Gaussian (although helium neon lasers and argonion
lasers are a very close approximation). To accommodate this
variance, a quality factor, M^{2} (called the “Msquare”
factor), has been defined to describe the deviation of the
laser beam from a theoretical Gaussian. For a theoretical
Gaussian, M^{2}=1; for a real laser beam, M^{2}>1.
Helium neon lasers typically have an M^{2} factor
that is less than 1.1. For ion lasers, the M^{2} factor
is typically between 1.1 and 1.3. Collimated TEM_{00}
diode laser beams usually have an M^{2} ranging from
1.1 to 1.7. For highenergy multimode lasers, the M^{2}
factor can be as high as 3 or 4. In all cases, the M^{2}
factor, which varies significantly, affects the characteristics
of a laser beam and cannot be neglected in optical designs.

In TEM_{00} mode, the beam emitted from a laser begins
as a perfect plane wave with a Gaussian transverse irradiance
profile as shown in the figure below. The Gaussian shape is
truncated at some diameter either by the internal dimensions
of the laser or by some limiting aperture in the optical train.
The commonly adopted definition is the diameter at which the
beam irradiance (intensity) has fallen to 1/e^{2}
(13.5%) of its peak, or axial, value.

