most laser applications it is necessary to focus, modify,
or shape the laser beam by using lenses and other optical
elements. In general, laser-beam propagation can be approximated
by assuming that the laser beam has an ideal Gaussian intensity
profile, corresponding to the theoretical TEM00
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 real-life lasers is
not truly Gaussian (although helium neon lasers and argon-ion
lasers are a very close approximation). To accommodate this
variance, a quality factor, M2 (called the “M-square”
factor), has been defined to describe the deviation of the
laser beam from a theoretical Gaussian. For a theoretical
Gaussian, M2=1; for a real laser beam, M2>1.
Helium neon lasers typically have an M2 factor
that is less than 1.1. For ion lasers, the M2 factor
is typically between 1.1 and 1.3. Collimated TEM00
diode laser beams usually have an M2 ranging from
1.1 to 1.7. For high-energy multimode lasers, the M2
factor can be as high as 3 or 4. In all cases, the M2
factor, which varies significantly, affects the characteristics
of a laser beam and cannot be neglected in optical designs.
In TEM00 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/e2
(13.5%) of its peak, or axial, value.