Fundamental and second-harmonic ultrasound field computation of inhomogeneous nonlinear medium with a generalized angular spectrum method

The simulation of nonlinear propagation of ultrasound waves is typically based on the Kuznetsov-Zabolotskaya- Khokhlov equation. A set of simulators has been proposed in the literature but none of them takes into account a possible spatial 3-D variation of the nonlinear parameter in the investigated medium. This paper proposes a generalization of the angular spectrum method (GASM) including the spatial variation of the nonlinear parameter. The proposed method computes the evolution of the fundamental and second-harmonic waves in four dimensions (spatial 3-D and time). For validation purposes, the one-way fields produced by the GASM are first compared with those produced by established reference simulators and with experimental one-way fields in media with a homogeneous nonlinear parameter. The same simulations are repeated for media having an axial variation of the nonlinear parameter. The mean errors estimated in the focal region are less than 4.0% for the fundamental and 5.4% for the second harmonic in all cases. Finally, the fundamental and second-harmonic fields simulated for media having nonlinear parameter variations in the axial, lateral, and elevation directions, which cannot be simulated with other currently available methods, are presented. The new approach is also shown to yield a reduction in computation time by a factor of 13 with respect to the standard nonlinear simulator.