The beam quality of nonparaxial Hermite-sine-Gaussian beam

Based on the theory of the second intensity moment of nonparaxial scalar beam and the method of angular spectrum, the expressions for the far-field divergence angle, waist width and M2 factor of nonparaxial Hermite-sine-Gaussian (HSiG) beams are derived. Calculation and analysis show the dependence of the far-field divergence angle of nonparaxial HSiG beams on the parameter w0/λ, as well as on order m, And it with even and odd orders approach 73.898° and 63.435° as w0/λ → 0. With increasing order m and the parameter w0/λ, the waist width increase monotonously, which is same as paraxial case. But nonparaxial M2 factor is different from paraxial case, it cannot only less than 1, but also approach 0 as w0/λ → 0.