Illustrated Physics
physics, drawn
Concept

Wave plate — where it appears

An optical element that delays one polarisation relative to the other by a fixed fraction of a cycle. Made from birefringent material it is a thickness measured in wavelengths and works properly at one colour; made from two total internal reflections it depends on an index instead and works across a spectrum.

Named by 4 essays across one field — each of them below, with the objects they name alongside it.

The index that depends on which way the light is going. The two refractive indices of 3 uniaxial crystals, against the angle between the wave normal and the crystal's optic axis. The flat lines are the ordinary index, which is the same in every direction because the ordinary wave's field is always perpendicular to the axis. The curves are the extraordinary index, which runs from the ordinary value along the axis — where the two waves are identical and the crystal behaves like glass — to its extreme value at right angles to it. calcite (CaCO₃) has n_o = 1.6584 and n_e = 1.4864, so n_e − n_o = -0.1720; quartz (SiO₂) has n_o = 1.5443 and n_e = 1.5534, so n_e − n_o = 0.0091; lithium niobate has n_o = 2.3005 and n_e = 2.2075, so n_e − n_o = -0.0930. The sign of that difference is what makes a crystal positive or negative, and it decides which of the two images in a double-refracting crystal is the one that moves.

The crystal that answers twice

Lay a piece of calcite on a printed page and the print appears twice. One image sits still when the crystal is turned and the other goes round it. Nothing has been done to the light except pass it through a material whose response to a field is not a number.

optics · Polarisation 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 One measurement that separates unpolarised from polarised. What a rotating linear polariser passes, against its angle, for beams of the same total intensity and degrees of polarisation 0, 0.35, 0.7, 1. Every curve has the same average — a polariser passes half of any beam over a whole turn, whatever its state — and they differ only in how deeply they modulate. The depth of the modulation is the degree of polarisation, exactly: a fully polarised beam goes to zero at one angle and a beam with no preferred direction gives a flat line at a half. That is the whole measurement, and it is why "unpolarised" is a statement about a modulation depth rather than about what a wave is doing.

The light with no direction of shaking

Unpolarised light is not a state of a wave; it is the absence of one, and no description of a single wave can represent it. What can is a set of four numbers, all of them powers a detector reads — and they describe every beam there is, including the ones that are neither polarised nor not.

optics · Polarisation Light that turns with the molecules it passes. Through a layer of liquid crystal whose molecules turn steadily through 90° from the entrance face to the exit (dashed line), the direction of the light's polarisation against depth, for linearly polarised light entering along the molecules, in a thick cell and a thin one; u = 2dΔn/λ measures the layer's birefringence against the wavelength. In the thick cell the polarisation turns with the molecules, never more than a few degrees behind, and leaves rotated by 90°: 100.0 per cent of the light passes an analyser set along the exit molecules. In the thin cell the light barely notices the twist; its polarisation lags further and further behind and leaves turned only part of the way, with 31 per cent passing. Mauguin saw the first case in 1911: a birefringent medium that twists slowly enough drags the light's polarisation round with it.

The twist that carries light round a corner

Between two crossed polarisers, a sandwich of liquid crystal a few micrometres thick turns black to white. Its long molecules lie flat, but turned a quarter-turn from one face of the layer to the other, and polarised light entering along the molecules at one face comes out along them at the other — rotated by ninety degrees and able to pass the second polariser. Charles Mauguin found in 1911 that a slowly twisting birefringent layer drags light's polarisation round with it. Sixty years later the effect became the liquid-crystal display. The layers in those displays, though, are too thin to drag anything: the light inside them wanders off and comes back, at exactly the right thickness.

optics · Polarisation

Named alongside it

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

PolarisationBirefringenceCircular polarisationRefractive indexSuperpositionAchromaticAdiabatic followingAnisotropyCoherenceComplex amplitudeCrystalDensity matrix

All concepts