Illustrated Physics
physics, drawn
Concept

Waveplate — where it appears

A plate of birefringent material that delays one polarisation of light behind the other by a set fraction of a wavelength. A quarter-wave plate turns linear polarisation into circular; a half-wave plate rotates linear polarisation and reverses the handedness of circular.

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

A circuit on the sphere of polarisations. The Poincaré sphere, on which every polarisation state is a point: linear states around the equator, circular at the poles, and orthogonal states at opposite ends of a diameter. The triangle is a closed circuit — linear at 0°, then linear at 23°, then left circular, and back — taken along geodesics, which is what a sequence of ideal polarisers does. Bringing a state round it returns it to exactly the state it started in, and multiplied by a phase: 0.3927 radians here, against minus half the enclosed solid angle of -0.7854 steradians. The two agree exactly, and neither calculation knows about the other — the phase is the argument of a product of three overlaps between Jones vectors, and the solid angle is spherical geometry. Nothing about the elements used, their thickness, or the wavelength enters. A phase that depends only on the shape of a path is the signature of a geometric phase, and this is the oldest known example of one.

The phase that is only a shape

Take a beam of polarised light through a sequence of elements that returns it to the polarisation it started with, and it comes back with a phase it did not have before. That phase is not an optical path length — it does not depend on the thickness of anything, or on the wavelength, or on how slowly the sequence was carried out. It is minus half the area the path enclosed on the sphere of polarisation states, and nothing else.

optics · Polarisation A squeezed disc between crossed polarisers. The dark fringes seen in a 50 mm disc of polycarbonate, 6 mm thick, squeezed across a vertical diameter by 500 N and viewed between crossed circular polarisers in light of 550 nm: each dark line is a contour on which the principal stresses differ by a whole number of fringe values, from the stress-optic law with a coefficient of 78 Brewsters. At the centre the fringe order is 3.61; it climbs steeply towards the two loading points, where the fringes crowd together and the stress grows without limit, and falls to zero at the free edges level with the centre. The pattern is the exact stress field of an elastic disc under diametral load; every fringe can be counted from a dark point, and the count times the fringe value is the difference of the principal stresses at that place.

The stress that polarised light can see

Squeeze a disc of clear plastic and look at it between two crossed polarising filters, and it fills with dark lines and coloured bands that crowd towards the points where it is pressed. Each line is a contour of stress. Glass, plastic and most transparent solids become doubly refracting when they are loaded, in proportion to the difference between their largest and smallest stresses, and polarised light turns that difference into a pattern that can be counted. David Brewster found it in 1816, the same Brewster whose angle polarises reflected light, and for a century the way to learn the stresses in a bridge or a dam was to cut its shape from plastic, load it and photograph the fringes.

optics · Polarisation

Named alongside it

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

PolarisationAdiabatic theoremBirefringenceGeometric phaseInterferenceInterference coloursJones calculusPhotoelasticityPoincare spherePrincipal stressesRetardationSolid angle

All concepts