Illustrated Physics
physics, drawn
Concept

Gaussian beam — where it appears

A beam of light whose intensity falls off as a Gaussian away from its axis, the shape a laser emits. It narrows to a waist and spreads again over a Rayleigh range, gaining the Gouy phase as it passes, and it is the lowest mode a stable optical cavity holds.

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

Also named here as optical cavity — the same set of essays touches all of them, so they are one junction rather than several.

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

Named alongside it

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

Optical cavityAngular spectrumDiffractionFloquet theoryGouy phaseLaserRay transfer matrixRayleigh rangeStabilityTransverse modeUncertainty principleUnstable resonator

All concepts