Far-field divergence angle of nonparaxial rotationally symmetric Laguerre-Gaussian beams

Based on the second-order moment of the power density,the far-field divergence angle of nonparaxial rotationally symmetric Laguerre-Gaussian(LG) beams is derived and expressed in a sum of the series of the Gamma function.It is shown that the far-field divergence angle of nonparaxial rotationally LG beams approaches to an asymptotic value of 63.435° as the initial waist-width to wavelength ratio w0/λ approaches zero,which is independent of the order.For the special case of p=0 our result reduces to that of nonparaxial Gaussian beams.