Interplay of cascaded Raman- and Brillouin-like scattering in nanostructured optical waveguides

We formulate a generic concept of engineering optical modes and mechanical resonances in a pair of optically-coupled light-guiding membranes for achieving cascaded light scattering to multiple Stokes and anti-Stokes orders. By utilizing the light pressure exerted on the webs and their induced flexural vibrations, featuring flat phonon dispersion curve with a non-zero cut-off frequency, we show how to realize exact phase-matching between multiple successive optical side-bands. We predict continuous-wave generation of frequency combs for fundamental and high-order optical modes mediated via backward- and forward-propagating phonons, accompanied by periodic reversal of the energy flow between mechanical and optical modes without using any kind of cavity. These results reveal new possibilities for tailoring light-sound interactions through simultaneous Raman-like intramodal and Brillouin-like intermodal scattering processes.