Enhanced acoustic transmission through a slanted grating

TL;DR

This paper demonstrates that orienting grating elements obliquely in an acoustic slab enhances total transmission at specific angles, generalizing the Brewster effect and providing explicit formulas for transmission behavior.

Contribution

It introduces a new configuration with oblique grating elements that achieves enhanced acoustic transmission, extending previous aligned array results with explicit angle dependence.

Findings

Total transmission occurs at specific oblique incidence angles.

Explicit formulas relate the intromission angle to grating orientation.

Full wave simulations confirm the analytical predictions.

Abstract

It is known that an acoustic wave incident on an infinite array of aligned rectangular blocks of a different acoustic material exhibits total transmission if certain conditions are met [1] which relate the unique "intromission" angle of incidence with geometric and material properties of the slab. This extraordinary acoustic transmission phenomenon holds for any slab thickness, making it analogous to a Brewster effect in optics, and is independent of frequency as long as the slab microstructure is sub-wavelength in the length-wise direction. Here we show that the enhanced transmission effect is obtained in a slab with grating elements oriented obliquely to the slab normal. The dependence of the intromission angle $\theta_i$ is given explicitly in terms of the orientation angle. Total transmission is achieved at incidence angles $\pm \theta_i$, with a relative phase shift between the transmitted amplitudes of the $+\theta_i$ and $- \theta_i$ cases. These effects are shown to follow from explicit formulas for the transmission coefficient. In the case of grating elements that are rigid the results have direct physical interpretation. The analytical findings are illustrated with full wave simulations.