Illustrated Physics
physics, drawn
Concept

Coherent backscattering — where it appears

The doubling of light scattered exactly backwards from a random medium, where every path and its time-reversed partner interfere constructively. The narrow peak it makes is weak localisation, the precursor of Anderson localisation.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

Light that walks through a cloud. Seven photons entering a slab 8 scattering mean free paths thick from above, straight down, and followed until they leave, with every scattering equally likely to send them in any direction; their paths are projected onto the page. Of 20000 photons followed the same way, 82.5 per cent come back out of the top and 17.5 per cent out of the bottom. Diffusion theory predicts 18.2 per cent through the bottom. Only 10 photons cross without scattering at all, where e⁻⁸ predicts 6.7 — within the counting error of so few: nearly all of what is transmitted has walked, and the direction it arrived from is forgotten on the way.

The cloud light has to walk through

A beam crossing thirty scattering lengths of anything should keep e⁻³⁰ of itself — a ten-millionth of a millionth. A cloud thirty scattering lengths thick lets through nearly a third of the sunlight falling on it. The light has not crossed; it has walked, one scattering at a time, and a walk through a slab obeys a law with the shape of Ohm's rather than of an exponential.

optics · Scattering With interference kept, transmission falls exponentially; without it, only as one over the thickness. Light through stacks of randomly thick transparent layers, alternating indices 1 and 2.6, with thicknesses scattered by ±50 per cent about a quarter wave, on a logarithmic scale against the number of layers. The falling line is the transmission with the waves' interference kept, computed exactly by multiplying transfer matrices and averaged as the logarithm over 40 random stacks and five wavelengths. It falls in a straight line: the transmission drops by a factor of e every 17 layers, however thick the stack, which is exponential decay — localisation. The upper curve is the same stacks with every surface's reflection and transmission added as intensities, so that no interference survives. It falls only as one over the thickness, checked to grow in exact proportion, which is the diffusion of light through a cloud: at 400 layers it still transmits 1.0 per cent where the coherent stack typically transmits 4.5·10⁻¹¹.

The walk that interference can stop

Light scattered many times walks through a cloud, and a walk always gets through eventually — a slab twice as thick lets through half as much. Keep the waves' interference instead of adding intensities, and in one dimension the same disorder does something a walk cannot: it stops the light exponentially, traps it in modes with nothing special about where they sit, and turns transmission from a number into a spread over powers of ten. Whether the same can happen to light in three dimensions has been claimed, retracted and argued for thirty years.

optics · Scattering Grains that hide their own shadows. The share of the grain surface an observer can see that is also lit, against the angle between the observer's line of sight and the light's direction, for random layers of grains filling 10, 30, 50 per cent of the space, with the light 20° from the vertical. Computed by following sight lines to the first grain they meet and asking whether that point can see the source. At zero phase angle the share is exactly one: every surface the observer sees is lit, because the observer is looking along the light's own path. Away from it shadows come into view, and the share falls to 0.51, 0.63, 0.70 at 40°. The fall is fastest in the loosest layer — half of it is complete by 4.9° — and slowest in the densest, 14.2°, because long shadows between widely spaced grains need only a small change of viewpoint to be seen.

The full moon that is too bright

Half a moon shows half the lit disc, so it ought to be about half as bright as a full one — a little less, allowing for the angle. It is a tenth as bright. In the last few days before full the Moon brightens far faster than its growing area can explain, and the extra light is not reflected any more strongly. It comes from shadows disappearing. The lunar soil is a loose heap of grains, and when the Sun is directly behind the observer every grain hides its own shadow.

optics · Scattering

Named alongside it

The objects these essays reach for when they reach for this one.

DiffusionMultiple scatteringRandom walkAlbedoAnderson localisationAsymmetry parameterDisorderInterferenceLambertian surfaceMean free pathOpposition effectOptical depth

All concepts