Multiple propagating modes in random polycrystals

Multiple-scattering theory predicts that the coherent elastic wave in a statistically isotropic polycrystal is not a single wave. Its dispersion equation admits multiple roots of a given polarization, but these extra modes have never been observed. Here, using grain-scale finite-element simulations of three-dimensional polycrystals, we resolve the coherent field in the frequency--wavenumber plane and directly observe the predicted multiplicity for both transverse and longitudinal excitations: a single mode at low frequencies gives way to two in the geometric regime as the wavelength approaches the grain correlation length. The measured modes follow the roots of the dispersion equation, which always carries a third root whose attenuation exceeds that of the others. It is this attenuation hierarchy, not the root count, that dictates how many modes propagate and can be observed. Coherent wave propagation in random media is thus inherently multimodal in the geometric regime, which we reach here for the first time in polycrystals.