Abstract
The possibility of surface wave generation by diffraction of pressure waves on deeply corrugated one-dimensional phononic crystal gratings is studied both theoretically and experimentally. Generation of leaky surface waves, indeed, is generally invoked in the explanation of the beam displacement effect that can be observed upon reflection on a shallow grating of an acoustic beam of finite width. True surface waves of the grating, however, have a dispersion that lies below the sound cone in water. They thus cannot satisfy the phase-matching condition for diffraction from plane waves of infinite extent incident from water. Diffraction measurements indicate that deeply corrugated one-dimensional phononic crystal gratings defined in a silicon wafer are very efficient diffraction gratings. They also confirm that all propagating waves detected in water follow the grating law. Numerical simulations however reveal that in the sub-diffraction regime, acoustic energy of a beam of finite extent can be transferred to elastic waves guided at the surface of the grating. Their leakage to the specular direction along the grating surface explains the apparent beam displacement effect.
Highlights
The propagation of elastic waves at the surface of phononic crystals in air has attracted a lot of attention, due to potential applications in, e.g., radio-frequency signal processing, sensing, and non-destructive evaluation.[1,2,3,4,5,6] Recently, surface waves propagating on periodically corrugated surfaces have been proposed to improve the acoustic beams emitted in fluids by transducers.[7,8] when a phononic crystal is immersed in water, the dispersion of surface waves becomes strongly dependent on the coupling between acoustic waves in the fluid and elastic waves in the solid parts
We have studied surface wave generation on deeply corrugated one-dimensional phononic crystal gratings by diffraction of acoustic pressure waves incident from water
It is known from phononic crystal theory that since the dispersion relation of true surface waves of the grating lies below the sound cone in water and must respect periodicity, they can not be excited from the diffraction of infinite plane waves incident from water
Summary
The propagation of elastic waves at the surface of phononic crystals in air has attracted a lot of attention, due to potential applications in, e.g., radio-frequency signal processing, sensing, and non-destructive evaluation.[1,2,3,4,5,6] Recently, surface waves propagating on periodically corrugated surfaces have been proposed to improve the acoustic beams emitted in fluids by transducers.[7,8] when a phononic crystal is immersed in water, the dispersion of surface waves becomes strongly dependent on the coupling between acoustic (pressure) waves in the fluid and elastic waves in the solid parts. It is rather easy to show that true, i.e., non leaky, surface waves attached to a periodic solid-fluid interface cannot be excited by diffraction of a plane wave incident from the fluid, if diffraction results from the periodicity of the interface.[9] This theoretical result for infinitely extended plane waves is apparently contradicted by the experimental existence of the ultrasonic beam displacement effect This interesting phenomenon appears for bounded beams incident on a corrugated interface in the sub-diffraction regime. Their leakage to the specular direction along the grating surface is very strong and explains the apparent beam displacement effect in the forward direction
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