3D numerical modeling of parametric speaker using finite-difference time-domain

Parametric speakers produce sound by emitting ultrasound, and using the small nonlinearity in air to demodulate it back to audible sound. The use of ultrasound allows for producing very narrow audio beams, which finds application in a number of military and consumer scenarios. However, designing better parametric speakers has been hard: closed-form solution of the nonlinear wave equation for generic geometries is nearly impossible, and the only existing solution was derived for the simple case of a cylindrical beam. FDTD methods were considered not practical since the desired (audible) signal is orders of magnitude weaker than the ultrasound signal, and thus the noise floor (from the numerical approximation) will dwarf the audible signal. In this paper, we introduce a novel FDTD scheme that models nonlinear sound propagation for parametric speakers. By taking the difference between linear and nonlinear FDTD simulations, we successfully suppress the numerical noise floor and extract the audible signal. Both spectrum and radiation pattern of simulation match the measurements well. This offers a simulation tool for further research in creating advanced parametric speakers.