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. 

Gaussian beam profile (theoretical TEM_{00} mode) 