M² Factor

In 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 nternal 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.