Fig. 11: Stimulation of acoustic modes above their cut-off frequencies.

a Solid blue—measured normalized gain coefficient of inter-modal forward stimulated Brillouin scattering between one optical wave in the fundamental \({{LP}}_{01}\) mode and another in the \({{LP}}_{02}\) mode. Dashed red—calculated normalized gain coefficient of the inter-modal scattering process through the \({R}_{0m}\) and \({{TR}}_{2m}\) acoustic modes. Agreement with experiment is very good. b, c Magnified view of the measured normalized inter-modal scattering spectrum (blue), alongside the measured normalized spectra of intra-modal scattering in the fundamental \({{LP}}_{01}\) mode. In both panels, \({R}_{0m}\) modes are shown in red and \({{TR}}_{2m}\) modes in green. In panel b, the resonance frequency of a dilatational \({R}_{0m}\) mode is higher by 3.4 MHz in the intra-modal trace. The corresponding difference for the \({{TR}}_{2m}\) shear mode shown in panel c is 1.9 MHz