Acoustic gratings have attracted much attention due to their wide applications in acoustic collimation, focusing and imaging.

Rigorous analysis model with waveguide modes could solve the diffraction of acoustic gratings made of perfect rigid boundaries, but not the diffraction of parity-time-symmetric acoustic gratings without rigid walls.  

A research team from the Institute of Acoustics of the Chinese Academy of Sciences (IACAS) proposed a rigorous coupled-wave analytical method to analyze the diffraction of acoustic parity-time-symmetric gratings.  

The researchers expanded the sound pressure in every region as Fourier series to solve the diffraction sound field, and discussed the diffraction properties of parity-time-symmetric acoustic gratings using the rigorous coupled-wave analysis.

Experimental results showed that the total diffraction efficiency was greater than one for positive incidence, which indicated that the gain played a leading role in the propagation process. For negative incidence, the total diffraction efficiency was lower than one before the DVP and higher than one after the DVP.

The diffraction efficiency of +1st order was suppressed completely when the modulation ratio was 0.99. The sound energy was mainly localized in the gain parts for positive incidence, while the sound energy was evenly distributed in the gain and loss parts for negative incidence.

They also presented the relationships between the modulation amplitude and the modulation ratio of the DVP for different modulation approaches. 

The diffraction of acoustic gratings without rigid walls could be analyzed quickly and effectively by the method of rigorous coupled-wave analysis.

The research, published in Journal of the Acoustical Society of America, was supported by the National Natural Science Foundation of China.