Brillouin scattering in planar waveguides. I. Numerical model

A model for the calculation of Brillouin spectra in planar waveguides is presented. The electromagnetic field in a mode of a planar waveguide is a current wave along the guide and a standing wave across the guide with an evanescent tail in the substrate. The modal electromagnetic field can be calculated if the refractive index profile across the waveguide is known. The model for the calculation of Brillouin spectra considers the spatial distribution of the exciting field in the mode, a simple spatial dependence of the elasto-optic coefficients, through the value of the refractive index, and neglects the refraction of phonons. A single parameter, i.e., the sound velocity, is necessary to calculate as many spectra as is the number of modes in the waveguide. Examples of step index waveguides of different thicknesses and of graded-index waveguides are calculated and the results are compared with those of a simpler model based on a ray-tracing approach. In multimode waveguides with a step index profile, it turns out that longitudinal phonons produce two main peaks with an energy separation which increases with the mode index m. In graded-index waveguides, m-1 peaks of comparable intensities may appear.