Fast and accurate modeling of parametric array loudspeakers in the frequency domain

The parametric array loudspeaker (PAL) is known for its ability to generate highly directional audio beams. It has been widely used in a variety of audio applications, such as the sound field reproduction and active noise control. Fast and accurate computations of the audio sound field generated by a PAL are challenging due to the complexity of nonlinear interactions between airborne ultrasonic waves. This paper presents an overview of the commonly used computational methods in the frequency domain under the quasilinear assumption, which include the direct integration method, convolution directivity model, Gaussian beam expansions, cylindrical expansions, spherical expansions, and finite element methods. The computational efficiency and the accuracy of these methods in the near field, Westervelt far field, and the inverse-law far field are compared. Future challenges and perspectives are discussed.