Analysis of Cascaded Brillouin Scattering in Optical Fibres

Cascaded Brillouin scattering is increasingly becoming of interest in many areas of pho- tonics (e.g. see [1] and [2]) and has been studied experimentally by many groups. In gain assisted experiments for example up to nearly 800 distinct lines have been observed[3] while in passive cavities, mode locking of a few Brillouin lines has recently been demonstrated[4]. We show that although each pair of lines interact through the creation of an acoustic phonon the resulting acoustic field nevertheless can be written as the sum of only two waves (a forward and backward propagating wave). This new analysis results in a set of strongly coupled amplitude equations for the fields that are derived here for the first time in the context of optical fibres. More-over we show that previous authors have mis- understood the nature of the acoustic field resulting in incorrect sets of coupled equations.