Propagation of nonparaxial Gaussian beams

Based on the nonparaxial moment theory of light beam propagation, the propagation characteristics of nonparaxial scalar Gaussian beam, nonparaxial TEM and TE vector Gaussian beams have been investigated. The results reveal that both the transversal beam widths follow a simple hyperbolic law upon propagation. The analytical expressions of the beam propagation factor, beam waist and far field divergence angle are presented, respectively. Furthermore, the formulae can be very concise for highly nonparaxial cases. TE or TM polarization will result in different propagating features in the two transversal directions. The maximum transverse divergence angles of nonparaxial scalar and vector Gaussain beams are different, which indicates that nonparaxial scalar Gaussian beam is no longer approximate at subwavelength scales. When extending to the paraxial case, the results obtained are slightly different from the formerly paraxial ones. Moreover, in this case the beam propagation factor will always be greater than unity. This research also denotes some properties of subwavelength optics.