We study the elastic wave propagation in phononic-crystal strip waveguides cut from a silicon phononic-crystal plate with square-lattice vacuum holes through analyzing the band structure and transmission spectra. We show the influence of different cutting ways is crucial to the band-gap formation, and four types of native strip modes are deserved to be fully taken into account. The results show that though there is no band gap existing in the phononic-crystal plates with a low filling fraction, band gaps are created in their corresponding cut strip waveguide because the derivative traction-free boundaries strongly modulate the shear-horizontal bands.

In micromechanical resonators, energy loss via supports into the substrates may lead to a low quality factor. To eliminate the support loss, in this paper a phononic band-gap structure is employed. We demonstrate a design of phononic-crystal (PC) strips used to support extensional wine-glass mode ring resonators to increase the quality factor. The PC strips are introduced to stop elastic-wave propagation by the band-gap and deaf-band effects. Analyses of resonant characteristics of the ring resonators and the dispersion relations, eigenmodes, and transmission properties of the PC strips are presented. With the proposed resonator architecture, the finite-element simulations show that the leaky power is effectively reduced and the stored energy inside the resonators is enhanced simultaneously as the operating frequencies of the resonators are within the band gap or deaf bands. Realization of a high quality factor micromechanical ring resonator with minimized support loss is expected.

In this letter, we present results of a study on the directional enhanced radiation generated by a point resonant cavity operating at the band-gap frequency of a two-dimensional finite-size phononic crystal. We find that the directive radiation for operating frequency within the band gap comes from the direction-dependent transmittance property of the square-lattice phononic crystal. The directive-radiation characteristic can be capitalized on enhancing the emission from the phononic crystals by coupling the source with point-defect modes, and the enhanced directive radiation patterns with main lobe width less than 12.9° are demonstrated.

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