Study into the Applicability of Laser Beam Quality Factor M^2

Study into the Applicability of Laser Beam Quality Factor M2

The applicable condition of single-frequency laser beam quality factor M2 is studied. Any real single-frequency laser beam can be classified as Gaussian mode and non-Gaussian mode according to the transverse field distribution. Non-Gaussian transverse field distribution can be analytically expressed as the sum of Hermite-Gaussian functions. The propagation function and M2 factor expression for non-Gaussian mode can be obtained by the second moment definition of laser beam spot. The analytical results show, the same as that of Gaussian mode, that the propagation function follows the hyperbolic law and the value of M2 factor is a constant for non-Gaussian mode. But, different non-Gaussian field distributions may have the same M2 value. That means M2 factor cannot reflect the quality of non-Gaussian laser beams correctly. We conclude that the M2 factor is applicable only to ideal Gaussian laser beam generated by stable resonators.