The M2 factor of nonparaxial Hermite-Gaussian beams and related problems

On the basis of the second-order moment of the power density and in the use of the series expansion, the expressions for the beam width, far-field divergence angle and M2 factor of nonparaxial Hermite-Gaussian (H-G) beams are derived and expressed in a sum of the series of the Gamma function. The theoretical results are illustrated with numerical examples. The M2 factor of nonparaxial H-G beams depends not only on the beam order m, but also on the waist-width to wavelength ratio w0/λ. The far-field divergence angles of nonparaxial H-G beams with even and odd orders approach their upper limits θmax=63.435∘ and 73.898∘, respectively, which results in M2<1 as w0/λ→0. For the special case of m=0 our results reduce to those of nonparaxial Gaussian beams. Some problems related to the characterization of the nonparaxial beam quality are also discussed.