Abstract
We consider the conversion processes of a `whispering gallery' light wave in a taper fibre in which a travelling acoustic wave propagates into its taper end. Both spectral and temporal approaches are used. The results are compared with the results of the classical theory of interaction of many plane waves in a nonlinear medium. It is shown that phase matching between light and acoustic waves is supported automatically due to the corresponding increase in the light frequency in the process of joint movement of the waves in the taper end of the fibre. The material dispersion of the optical medium, the variance in temperature and the precision of geometrical sizes of the fibre do not considerably affect the phase matching.