Energy transport in diffusive waveguides

The guiding and transport of energy, for example of electromagnetic waves underpins many technologies that have shaped modern society, ranging from long distance optical fibre telecommunications to on-chip optical processors. Traditionally, a mechanism is required that exponentially localises the waves or particles in the confinement region, e.g. total internal reflection at a boundary. We introduce a waveguiding mechanism that relies on a different origin for the exponential confinement and that arises due to the physics of diffusion. We demonstrate this concept using light and show that photon density waves can propagate as a guided mode along a core-structure embedded in a scattering, opaque material, enhancing light transmission by orders of magnitude and along non-trivial, e.g. curved trajectories. This waveguiding mechanism can also occur naturally, for example in the cerebral spinal fluid surrounding the brain, along tendons in the human body and is to be expected in other systems that follow the same physics e.g. neutron diffusion.