Illustrated Physics
physics, drawn
Concept

Phase shift — where it appears

A change in the phase of a wave produced by a reflection, a transmission or a path, with no change in its amplitude. Past the critical angle for total internal reflection it is the only thing distinguishing one angle from another, and its difference between the two polarisations is a retardation with no material in it.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

Two ways of destroying a pulse, and their cancellation. The same starting pulse, carried forward three times by three equations that differ only in which terms are present, all shown at t = 0.097. Dotted: where it began. With the dispersive term alone the pulse spreads and sheds an oscillating tail, because its Fourier components travel at different speeds and drift out of step — the profile departs from what it was by 27 per cent of its own height. With the nonlinear term alone the tall part overtakes the shallow part and the front leans forward: the steepest gradient is 9.3 times what it started as and is on its way to vertical. With both, neither happens — the profile has moved to the right and is otherwise identical to what it was, to 2.7e-12 of its own height. The balanced run is a pseudo-spectral integration and the other two are exact, and the integration conserves the two quantities the equation conserves — mass to 2.2e-16 and the squared integral to 4.7e-15 — which is the check that the answer belongs to the equation rather than to the integrator. What the picture cannot show is why the cancellation is stable: a pulse of the wrong height for its width does not persist in the wrong shape, it sheds the excess as a dispersive tail and settles on the shape that works, which is why these objects turn up in canals and optical fibres rather than only in equations.

The pulse two failures keep alive

Dispersion spreads a pulse until it is nothing. Nonlinearity steepens it until it breaks. Each on its own destroys a disturbance, and there is exactly one height for each width at which the two cancel completely — leaving a shape that travels for ever and survives being run into by another one.

waves · Wave packets Past the critical angle, all that is left of a reflection is its phase. The phase each polarisation acquires on total internal reflection at an index ratio of 1.518, against angle of incidence, together with the difference between them. Below the critical angle of 41.19° there is a transmitted beam and the reflection coefficients are real; above it the transmitted wavenumber is imaginary, the coefficients have modulus exactly one — every photon comes back — and the only thing that distinguishes one angle from another is the phase. The two polarisations acquire different phases, and their difference peaks at 46.533° at an incidence of 51.05°, which the closed form puts at the same place. That difference is a retardation: a wave plate made out of an angle, with no birefringent material anywhere in it, and — because the expression contains only the index ratio — one that barely changes with colour.

The retarder with no crystal in it

A wave plate turns linear polarisation into circular by making one component travel a little further than the other, which requires a birefringent crystal cut to a thickness and works properly at one wavelength. Total internal reflection does the same job with a phase that comes from the geometry instead — and because a refractive index barely changes across the visible where a wavelength changes by a factor of two, the same block of ordinary glass is a quarter-wave plate for every colour at once.

optics · Polarisation The ripple that sits on top of an absorption edge. The Cu K absorption of copper foil, 293 K through its edge and for seven hundred electronvolts above it, with the smooth atomic background it would have if the absorbing atom were alone drawn beneath it. The difference between the two is the fine structure: a modulation reaching 11 per cent, dying away as the photon energy rises, and entirely absent from a free atom. It is there because the ejected electron is a wave that the neighbouring atoms scatter back onto the atom that emitted it, so the absorption depends on whether the returning wave arrives in step with the outgoing one — which depends on the distance to the neighbour and on nothing else about the sample.

The ripple that counts the neighbours

An absorption edge is drawn as a step and it is a step with a ripple on it — a modulation of eleven per cent in copper, five in a zinc site buried in a protein. The ripple is the ejected electron's own wave, scattered back onto the atom that emitted it, so its period is a distance. It is the only way of measuring where an atom's neighbours are that does not need a crystal.

waves · Attenuation

Named alongside it

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

AbsorptionAchromaticAttenuationBinding energyBirefringenceCircular polarisationComplex amplitudeConserved quantityCoordination numberDebye waller factorDispersionEvanescent wave

All concepts