Illustrated Physics
physics, drawn
Concept

Optical cavity — where it appears

Two or more mirrors that send light back and forth so that it passes the same region many times, the heart of every laser and of precision interferometers. Whether a cavity holds a beam at all depends on its mirror curvatures and spacing through the product g1g2.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

The phase a beam gains through its focus. How far the phase of a focused beam, measured on its axis, runs ahead of a plane wave of the same frequency, in cycles, against distance from the focus in units of the Rayleigh range π w₀²/λ, for a beam focused to a point (solid) and one focused only in one direction, to a line (dashed). The point-focused beam lags a quarter of a cycle far before the focus and leads by a quarter far after, gaining half a cycle in all, most of it within a Rayleigh range of the focus: 0.25 of a cycle by z = zR, 0.40 by 3 zR. The line focus gains half as much, a quarter cycle. This is the Gouy phase, measured by Louis Georges Gouy in 1890.

The half cycle a focus adds

A beam of light brought to a focus and allowed to spread again comes out half a wavelength ahead of where a plain wave of the same colour would be, although no part of it travelled faster than light. Louis Georges Gouy found the shift in 1890 by interfering a focused beam with an unfocused one. It is the price of confinement: a beam narrow enough to focus is a spread of directions, the parts travelling at an angle make slower progress along the axis, and the spread is greatest at the focus. The same half cycle decides the frequencies at which every laser cavity can resonate.

optics · Diffraction The cavities that hold a beam. Every two-mirror cavity as a point (g1, g2), with g = 1 − L/R for each mirror. The shaded region, between the axes and the hyperbolas g1 g2 = 1, holds a ray for ever; everywhere else a ray is walked out. The commonest designs sit on the boundary: two flat mirrors (1, 1), the confocal cavity with the mirrors' foci together (0, 0), the concentric cavity with their centres together (−1, −1), and a flat mirror facing a curved one at its own radius (1, 0). A boundary cavity is stable in principle and marginal in practice, which is why the confocal one, sitting at the corner where the two shaded regions touch, is usually built a little inside it.

The two mirrors that hold a beam

A laser is two mirrors facing each other, and the light in it makes thousands of round trips before it leaves. Whether a ray stays between the mirrors for ever or is walked out after a few bounces depends on a single number, built from their spacing and their curvatures, and the answer has a sharp edge: two flat mirrors sit exactly on it, which is why the first lasers were so hard to align. The criterion is the one that decides whether a pumped swing grows, whether a wave crosses a crystal, and whether a particle beam stays in an accelerator.

optics · Imaging The power a cavity holds depends on where its mirror is. The power circulating in a cavity of finesse 10,000, a metre long and lit at 1064 nm, as a fraction of its value on resonance, against the detuning of the laser from the cavity's resonance in units of the cavity's half-linewidth (7.5 kHz). Lengthening the cavity lowers its resonance and moves every point of the curve to the right: 38 half-linewidths for each nanometre of mirror travel. On the blue side (laser above resonance, right) that motion loses power, so the radiation force on the mirror falls as the mirror moves out — a restoring spring, steepest at δ/γ = 0.58 (dashed tangent). On the red side the same motion gains power and pushes harder: a spring of the opposite sign.

The mirror held on a spring of light

Light bouncing between two mirrors pushes them apart, and how hard it pushes depends on how long the gap is, because the gap decides how much light the cavity holds. A mirror free to move therefore sits on a spring made of light: with a kilowatt stored in a metre-long cavity it is four-fifths as stiff as a steel wire a millimetre thick. The spring has a flaw no steel spring has. Stored light takes time to rise and fall, so the push always arrives a little late, and a late spring either winds the mirror up or calms it, depending only on which side of the cavity's resonance the laser sits.

astrophysics · Radiation pressure Lamp noise that a decay does not notice. 400 simulated measurements of an absorption of 1 × 10⁻⁷ per metre, with a source whose brightness jumps by 5 per cent between shots and a detector with 0.1 per cent noise. Read directly, as transmission through a metre of gas, each measurement scatters by 7 × 10⁻² per metre and the true value is five orders of magnitude below that. Read as a fitted decay from a cavity with 99.99 per cent mirrors, it scatters by 5 × 10⁻⁸, about a million times less. The slope of a logarithm has no information about how bright the pulse started, so a source's noise simply is not in the answer. Most of the method's sensitivity comes from this and only some from the long path.

The absorption measured with a stopwatch

The usual way to measure how much light a gas absorbs is to compare a beam before and after, and a very weak absorption vanishes in the flicker of the lamp. Trap a pulse between two excellent mirrors, and it bounces for ten kilometres inside a tube a metre long, leaking out a little at each bounce. How fast that leak dies measures the gas, and how bright the pulse began does not matter at all. A brightness measurement has become a measurement of time.

optics · Dispersion

Named alongside it

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

Gaussian beamAbsorption coefficientAngular spectrumBeer lambert lawCavity ring down spectroscopyDampingDielectric mirrorDiffractionFeedbackFinesseFloquet theoryGouy phase

All concepts