Exact partial wave expansion of one-dimensional frozen wave-type beams for acoustic scattering

In this work, we propose an exact analytical description of acoustic frozen waves (AFWs) within the framework of partial wave expansion. An AFW is mathematically constructed from a discrete or continuous one-dimensional superposition of colinear Bessel beams, therefore, constituting an important type of longitudinally structured acoustic threads. The exact determination of the expansion coefficients-known as the beam shape coefficients-offers a fundamental tool for applications such as acoustic radiation force and scattering calculations for structured beams. We provide examples of reconstructions that might be useful in several applications, ranging from acoustic tweezers, volumetric displays, acoustic holography, medical imaging, biomedical ultrasonics, and cell treatment, among others.