Influence of sound diffraction on stimulated Brillouin scattering in a single-mode waveguide

A theoretical analysis is made of steady-state backward stimulated Brillouin scattering (STBS) in an optical waveguide under conditions such that the attenuation length of hypersound is less than, of the order of, or greater than the length of diffraction spreading of the hypersonic wave. The STBS gain, as well as the line width and profile, are found on the assumption that the acoustic properties of the medium are homogeneous. A relative reduction in the diffraction length $l_ d$ increases the line width $\Delta\omega$ in a cylindrical waveguide proportionally to $l^{-1}_ d$, whereas the static gain $g$ falls proportionally to $l_ d$; in a planar single-mode waveguide the corresponding dependences are $\Delta\omega\backsim l_d^{-1/2}$ and $g\backsim l_d^{1/2}$.