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Controlling vibrations in solids is crucial to tailor their elastic properties and interaction with light. Thermal vibrations represent a source of noise and dephasing for many physical processes at the quantum level. One strategy to avoid these vibrations is to structure a solid such that it possesses a phononic stop band, that is, a frequency range over which there are no available elastic waves. Here we demonstrate the complete absence of thermal vibrations in a nanostructured silicon membrane at room temperature over a broad spectral window, with a 5.3-GHz-wide bandgap centred at 8.4 GHz. By constructing a line-defect waveguide, we directly measure gigahertz guided modes without any external excitation using Brillouin light scattering spectroscopy. Our experimental results show that the shamrock crystal geometry can be used as an efficient platform for phonon manipulation with possible applications in optomechanics and signal processing transduction.

We propose a fast and non-destructive method to characterize the absolute diameter and uniformity of micrometer-scale fiber tapers using a pump and probe forward Brillouin scattering setup. The fundamental torsional-radial acoustic mode supported by the wire is excited using a pulsed pump laser and oscillates at a frequency that is inversely proportional to the taper waist diameter. This standing time-varying torsional-radial wave induces polarization modulation on a probe signal, whose spectrum structure reveals the sample diameter and its non-uniformity. By comparing our results with measurements using scanning-electron microscopy, a relative deviation of 1% or less was demonstrated, and diameter non-uniformity of less than 0.5% could be detected.