Can light localize in any three-dimensional disordered dielectric?
In plain words
Light trapping by disorder in three dimensions has been predicted for decades, but dense clouds of tiny scatterers do not localize because their near fields couple them too strongly. Whether any non-absorbing disordered dielectric can trap light remains unknown.
Precise statement
Vector electromagnetic waves in a 3D disordered, non-absorbing dielectric (index contrast $n$, filling fraction $f$, scatterer size $a$ relative to wavelength $\lambda$, structural correlations). Point-dipole ensembles show no localization at any density because of the longitudinal $1/r^3$ near-field coupling (Skipetrov and Sokolov, PRL 2014), and FDTD simulations of random dielectric sphere packings show none up to $n = 10$. Question: does any dielectric structure (correlated or hyperuniform networks near a photonic band edge, impurities in a solid matrix, high-index nonspherical particles) have a mobility edge, and can an experiment show it with signatures not mimicked by absorption or fluorescence (scale-dependent diffusion $D(L)$, normalized transmission fluctuations $\operatorname{var}(s_{ab}) > 7/3$, Thouless number $g < 1$).
What would settle it
Time- and size-resolved transmission measurements on an absorption-free 3D dielectric sample showing $D(L)$ decreasing to zero and $g < 1$, matched by full-wave simulations of the same structure.
Status in the literature
Unverified note
A 2023 FDTD study found localization for random metallic sphere aggregates and none for dielectric spheres up to $n = 10$; earlier TiO2 claims were attributed to fluorescence, and Skipetrov and Sokolov (Physical Review B 2025, https://doi.org/10.1103/t5nj-fz3p) predict localization for resonant impurities in a solid transparent matrix.