Determination of the threshold intensity of a laser beam for exciting stimulated Mandelstam-Brillouin scattering in the atmosphere

Stimulated Mandelstam-Brillouin scattering at small angles is considered in the case of a powerful laser beam propagating in the static mode in an unbounded medium. In contrast to the pulse mode, a hypersonic wave can be formed not only in the backward direction, but also in the forward direction at small angles. In this work, the latter case is considered as having the smallest value of the threshold intensity. It is shown that finite dimensions of the beam significantly change the excitation conditions for a scattered radiation owing to the mismatch of the wave triplet due to diffraction effects. Determination of the threshold intensity is shown to be possible using the well-known expressions for a plane wave only if the Fresnel number of the beam on the path the length of which is equal to the distance of the optical wave decay due to absorption in the medium is much larger than unity. Moreover, a large number of decay distances of the hypersonic wave must fall on the beam radius. When these conditions are not satisfied, the threshold intensity increases as compared to the plane wave.