Optoelectronic oscillators have dominated the scene of microwave oscillators in the last few years thanks to their great performances regarding frequency stability and phase noise. However, miniaturization of such a device is an up to date challenge. Recently, devices based on phonon-photon interaction gather a lot of interest thanks to their extreme compactness and working frequency directly in the GHz. In this frame, a still missing element to obtain long-term frequency stability performances is an on-chip delay within the feedback loop. Here, we experimentally show filtering and slow propagation of 2 GHz acoustic waves on a Gallium Arsenide membrane heterogeneously integrated on silicon wafer. By engineering the dispersion of an acoustical waveguide, we evidence a group velocity below 1000 m/s for the mode able to propagate. Thus, an integrated delay implementation is at reach for potential improvement of opto-acoustic devices such as optomechanical oscillators or wireless applications.
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