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

TL;DR

This paper identifies a universal wave pattern called 'gradient marker' that appears near gradient extrema in various wave systems, supported by analytical derivation and numerical validation across optics and quantum mechanics.

Contribution

It introduces the concept of the 'gradient marker' pattern as a universal phenomenon in inhomogeneous media and derives its analytical form in the adiabatic limit.

Findings

The 'gradient marker' pattern is observed near maxima/minima of the gradient.

Analytical expressions for the pattern are derived and confirmed by simulations.

Resonant states in continuum are identified in quantum wells.

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.