"Gradient marker" - a universal wave pattern in inhomogeneous continuum

Abstract

Wave transport in a media with slow spatial gradient of its characteristics is found to exhibit a universal wave pattern ("gradient marker") in a vicinity of the maxima/minima of the gradient. The pattern is common for optics, quantum mechanics and any other propagation governed by the same wave equation. Derived analytically in adiabatic limit, it has an elegantly simple yet nontrivial single-cycle profile, which is found in perfect agreement with numerical simulations for specific examples. We also found resonant states in continuum in the case of quantum wells, and formulated criterium for their existence.