Illustrated Physics
physics, drawn
Concept

Bragg mirror — where it appears

A reflector made of alternating layers of two transparent materials, each about a quarter-wavelength thick, whose partial reflections add in step. Inside its stop band it reflects nearly all the light and absorbs almost none of it.

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

What a real coating leaves behind, and over what range. Reflectance against wavelength for a glass surface of index 1.52 in air, uncoated and with quarter-wave layers of 2 different indices, each a quarter of a wave thick at 550 nm. The ideal index is the geometric mean, 1.2329, and the layer made of it takes the reflectance to zero at the design wavelength exactly. No durable solid has that index: magnesium fluoride at 1.38 is the usual compromise and it leaves 1.26% at the design wavelength against 4.26% bare — a reduction of 3.4× rather than a removal. Both curves rise away from the design wavelength, because the thickness is a quarter of a wave only there, and the useful band is wide but not unlimited: the better coating stays under a quarter of the bare reflectance from 415 to 780 nm. The purple cast of a coated lens is that residual — the ends of the visible reflecting while the middle does not.

The layer that makes a reflection vanish

A wave meeting a step in impedance reflects, and nothing can be done about the step. Put a third medium between the two, a quarter of a wavelength thick and of exactly the intermediate impedance, and the reflection stops existing — not reduced, cancelled.

waves · Impedance A gap that every angle from air falls into. The stop bands of a stack of quarter-wave layers of index 4.6 and 1.6 — tellurium and polystyrene, the pair of the first such mirror — against frequency, in units of the design frequency, and the parallel index β = n₀ sin θ₀ the light brings along the layers; TE polarisation on the right, TM on the left. Shaded regions are gaps. Light from air can only have β between −1 and 1, the vertical lines; within those lines the gaps for both polarisations overlap between f = 0.848 and 1.321, the band marked across the figure, so every angle of incidence and both polarisations are reflected: a relative width of 43.6%. The TM gap narrows as β grows and closes at the internal Brewster index, 1.51, which light from air cannot reach.

The mirror that works from every direction

A stack of alternating transparent layers reflects nearly all the light of one colour arriving straight on, and less as the light tilts, because tilting moves the forbidden band. A structure that repeats in only one direction ought therefore to be a mirror for only a range of directions. It is not, if the layers differ enough: light arriving from air cannot bring enough sideways momentum to escape the forbidden band at any angle, for either polarisation, and a flat stack of plastic and tellurium reflects every angle over a band of frequencies almost half as wide as its centre.

waves · Periodic media

Named alongside it

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

Transfer matrixAcoustic impedanceAntireflectionBand gapBandwidthBrewster's angleDestructive interferenceGeometric meanImpedanceInterferenceLight coneOmnidirectional reflection

All concepts