Forward Brillouin Scattering Spectra in Multi-core Fibers

In this chapter, the analysis of forward stimulated Brillouin scattering in fibers comprised of multiple cores is presented. In such multi-core fibers, guided acoustic waves may be stimulated by optical fields in one core and induce photoelastic scattering of light waves in a different one. The photoelastic scattering leads to cross-phase modulation among optical fields in spatially distinct cores, which is mediated by the stimulation of guided acoustic modes. Cross-phase modulation may take place even among cores that are spaced far apart, where the direct coupling of optical power is arbitrarily weak. The process is quantified in terms of the spectrum of forward Brillouin scattering coefficient, defined earlier with respect to single-mode fibers. The spectrum of cross-phase modulation between the inner, on-axis core and an outer, off-axis core is mediated by guided acoustic modes of radial symmetry and torsional-radial modes of twofold azimuthal symmetry only. That spectrum therefore consists of a discrete set of narrowband resonances, in similarity with single-mode fibers. Cross-phase modulation between two off-axis cores takes place through guided acoustic modes of all azimuthal symmetries. The corresponding spectrum therefore becomes quasi-continuous across hundreds of MHz bandwidths. Modulation depends on the choices of cores and states of polarization.