 Wave propagation in a random medium

Wave propagation in a random medium studies how fluctuations of properties such as refractive index, mass density or sound speed change an incident wave. Different paths acquire different wave phases, and spatial inhomogeneities generate wave scattering. One realization can therefore show a complicated transmitted pattern even under simple illumination.

The coherent field $⟨u⟩$ is the ensemble average of the field, while the mean wave intensity in a scalar normalization is $⟨|u{|}^2⟩$. They obeyThus decay of the coherent field need not mean loss of total wave energy: randomized wave phases can transfer weight to fluctuating contributions. Comparing a phase-sensitive average with an average of detector intensities tests this distinction. Weak fluctuations can permit perturbation methods, whereas repeated wave scattering with retained interference can lead to Anderson localization.