Energy transfer between two molecules — one excited, one not — falls off as the sixth power of distance. This is the Forster mechanism: the excited molecule's electromagnetic field couples to the ground-state molecule through a dipole-dipole interaction that decays rapidly with separation. In practice, the range is a few nanometers. Beyond that, the interaction is too weak to compete with other relaxation pathways, and the energy dissipates locally instead of transferring.
Alvarez-Perez, De Liberato, and Hu (arXiv:2603.06184, March 2026) show that placing the molecules on a hyperbolic crystal slab extends the transfer range to multiple wavelengths — orders of magnitude beyond the near-field limit.
The mechanism is geometric. A hyperbolic crystal — like alpha-phase molybdenum trioxide — has a dielectric constant that is positive along one crystal axis and negative along another. This anisotropy changes the shape of the electromagnetic dispersion surface from an ellipsoid (normal materials) to a hyperboloid. The hyperboloid has asymptotes: specific directions along which the dispersion surface extends to arbitrarily high wavevectors. Phonon polaritons — hybrid vibrations of the crystal lattice and electromagnetic field — propagate along these asymptotic directions with anomalously high density of states.
The dipole-dipole interaction, mediated through these polaritons, does not decay isotropically. Along the asymptotic directions, the interaction potential diverges rather than decaying. The energy transfer is concentrated into narrow angular channels defined by the crystal's anisotropy. Along these channels, the sixth-power decay law is suspended. The transfer is not enhanced uniformly in all directions — it is focused, like a lens, into the directions where the crystal's hyperbolic geometry supports it. In other directions, the interaction is even weaker than in free space.
The material does not add energy to the transfer. It redirects the decay. The total interaction, integrated over all angles, is not anomalously large. But the directional concentration means that molecules aligned along the asymptotic directions interact over distances where their free-space counterparts would be invisible to each other.
Alvarez-Perez, De Liberato, and Hu, "Long-range mid-infrared energy transfer mediated by hyperbolic phonon polaritons," arXiv:2603.06184 (March 2026).