Illustrated Physics
physics, drawn
Concept

Metamaterial — where it appears

A structured material whose response to waves comes from the resonances of its engineered building blocks rather than from its constituents. Arrays of small resonators can give effective densities, stiffnesses or refractive indices that are negative or very large in a band near resonance.

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

Two intersections, and the rule that picks one. The phase-matching construction for light arriving at 40° from a medium of index 1 into one of index -1. The circles are each medium's own relation between wavevector and frequency; the vertical line is the tangential wavenumber, which the boundary conserves. The line crosses the second circle twice, and the construction alone does not say which point is the answer — the rule that does is that energy must travel away from the interface. For a positive index the energy runs along the wavevector and the upper point is taken. For a negative one the energy runs against it, so the lower point is taken, the wavevector points back toward the boundary, and the ray leaves at -40.0° — on the same side of the normal as it arrived. Nothing in the drawing has changed except which intersection is circled.

The ray on the wrong side of the normal

The phase-matching construction draws a circle and a line, and the line crosses the circle twice. Every earlier construction silently took the upper intersection. Which one is physical is decided by where the energy goes rather than by where the wavevector points, and in a medium whose group velocity opposes its phase velocity the answer is the other one — so the refracted ray leaves on the same side of the normal it arrived on, a flat slab focuses, and a lens can beat the diffraction limit until loss stops it.

optics · Refraction A light panel that blocks one band as a heavy one would. Sound transmission loss at normal incidence against frequency, on a logarithmic frequency axis. Dashed: a limp panel of 2 kg/m², following the mass law, 13.4 dB at 300 Hz. Dotted: the same panel made 3 kg/m² by adding 1 kg/m² of plain mass, 16.8 dB. Solid: the 2 kg/m² panel with the same added mass hung on springs tuned to 300 Hz (damping 0.02). It blocks 35 dB at 300 Hz — the loss the mass law would give a wall 26 kg/m² heavy — and just above, at 367 Hz, falls to 5.2 dB, far below even the bare panel's 15.1: there the panel lets sound through more easily than if the resonators were not there.

The wall made heavy only at one note

A wall stops sound by being hard to shake, and how hard a plain wall is to shake is its weight: that is the mass law, and it makes quiet walls heavy. Hang small masses on springs inside a light panel, tuned to one frequency, and near that frequency the panel becomes many times harder to shake than it weighs, because the hidden masses swing against it. A two-kilogram panel then blocks a tone as a wall thirteen times heavier would. The price comes just above the tuning, where the panel's dynamic mass passes through zero and it lets sound through more easily than if the masses were not there.

waves · Impedance

Named alongside it

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

Acoustic impedanceBand gapBoundary conditionDampingDispersionDynamic massEvanescent waveGroup velocityMass lawNegative refractionPermittivityPhase matching

All concepts