Predicting second-harmonic generation in shear wave beams in tissue-mimicking phantoms

Abstract

Planar nonlinear shear waves in isotropic media are subject to only cubic nonlinear effects and generate only odd harmonics during propagation. However, wavefront curvature in shear wave beams breaks the symmetry and yields quadratic nonlinear effects, and therefore, a second harmonic may be present in shear wave beams depending on the polarization of the wave. Focused radially polarized shear wave beams have been generated in tissue-mimicking phantoms [Cormack et al., IEEE TBME (2024)], and it is postulated that the second harmonic may be used to estimate the quadratic nonlinearity in such a medium as an additional biomarker for diseased tissue. Here, an analytical solution obtained in the paraxial approximation for nonlinear propagation of a shear wave beam in an absorbing medium [Spratt et al., AIP Conf. Proc. 1685, 080007 (2015)] is used to characterize the strength of second-harmonic generation. Feasibility of measuring the second harmonic experimentally in a weakly nonlinear, radially polarized focused shear wave beam propagating in a tissue-like medium is explored. Second-harmonic generation in focused shear wave beams with other polarizations is discussed. [P.G.K. was supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]