Nonlinear interaction characteristics between acoustical transmitters in multiple parametric arrays

The application of multiple parametric arrays (MPAs) has gained significant attention in recent years. Unfamiliar research indicated that the nonlinear interaction between acoustical transmitters plays a crucial role in the acoustic field formation of MPAs, however, the characteristics of such nonlinear interaction remain an underexplored area underlying the beam formation. This study investigates MPAs' acoustic beam using steerable Gaussian beam expansion under paraxial approximation. From the perspective of acoustic field structure, the mechanisms and parameter influence law on nonlinear coupling strength among distinct acoustical transmitters are elucidated. The transmitting array gains (TAGs) of MPAs are derived as a superposition of linear and coupling terms, and the enhancement effect of increasing array elements on TAG is analyzed. Furthermore, generation mechanisms of highly directional beams and vortex beams are explored. Controlling the phase difference at high frequencies as ±π/2 can exploit nonlinear coupling to achieve a narrower beam width than a conventional in-phase array. Adjusting the phase difference with azimuth angle enables the generation of vortex beam with an analysis of the orbital number and transmitters' number impacts. Experimental results validate the theoretical analysis of the nonlinear interaction characteristics, providing a robust physical foundation for the further manipulation of MPAs.