Energy transport in diffusive waveguides
The guiding and transport of energy, for example, of electromagnetic waves, underpins many modern technologies, ranging from long-distance optical fibre telecommunications to on-chip optical processors. Traditionally, a mechanism is required that exponentially localizes the waves or particles in the confinement region, such as total internal reflection at a boundary. Here we introduce a waveguiding mechanism that relies on a different origin for the exponential confinement and that arises owing to the physics of diffusion. We demonstrate this concept using light and show that the photon density 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, such as curved, trajectories. This waveguiding mechanism can also occur naturally, for example, in the cerebrospinal fluid surrounding the brain and along tendons in the human body, and is to be expected in other systems that follow the same physics such as neutron diffusion.
The scattering of light is ubiquitous and, one might argue, the fundamental mechanism by which we observe light in nature1,2,3,4. It is the reason the sky is blue and sunsets are red, and it is also the reason snow is white and apparently opaque5. In the presence of weak scattering, the full-wave equation approach can be used for simulating and understanding light propagation and, specifically, also for accounting for coherent effects and formation, for example, of speckle patterns6. However, for very strong scattering (the strong diffusive regime), coherent effects play a minor or negligible role, speckle patterns are no longer visible and a more useful description is provided by the radiative transport equation. This describes energy transport through a series of scattering processes and therefore also describes other seemingly unrelated regimes such as neutron diffusion7 that, very much like light, also have important imaging applications8,9,10.
