Breaking the symmetry of momentum conservation using evanescent acoustic fields

Although the conservation of momentum is a fundamental law in physics, its constraints are not fulfilled for wave propagation at material boundaries, where incident waves give rise to evanescent field distributions. Whilst non-linear susceptibility tensor terms can provide solutions in the optical regime, this framework cannot be applied directly to acoustic waves. Now by considering a complete representation of wave interactions and scattering at boundaries, we are able to show a generic formalism of sum-frequency mixing for the whole scattering field including all evanescent waves. This general case was studied analytically and verified both numerically and experimentally, showing that considering evanescent waves leads to an anomalous non-linear interaction which enhances sum-frequency generation. This new interpretation not only provides a deeper understanding of the momentum conservation laws in acoustics but also promises translation of this new understanding into optics and photonics, to enhance non-linear interactions.