Laser coherence

Why does laser light stay a narrow beam when a bulb's light has spread out within a metre?

The easy answer is that a laser is aimed and a bulb is not. But that cannot be the whole story, because a bulb at the focus of a good parabolic reflector — a searchlight — still spreads to tens of metres across within a kilometre, while an unremarkable laser spreads to well under a metre over the same distance. Both are made of light; both can have lenses in front of them. So what is it about the source that a lens cannot fix?

Begin with how a hot filament makes light. Each atom, excited by heat, drops to a lower state whenever it happens to, emitting a photon in a direction and phase of its own choosing. Nothing coordinates them, so the light leaving a bulb is an enormous number of short, unrelated wavetrains, jumbled in direction, phase and wavelength.

Now ask what a lens can do with that. A lens redirects rays, but it cannot make two rays that started from different points of the filament behave as though they started from one. There is a conserved quantity here — the product of the source's area and the angular spread of light leaving it, called étendue — and no arrangement of lenses and mirrors can reduce it. You can trade area for angle, but not eliminate either, so collimating a millimetre-wide filament to a narrow angle would require expanding the beam to an absurd diameter. A searchlight spreads not from sloppiness but from a conservation law.

So the interesting question becomes: how can a source have small étendue? Only by behaving as though the light came from one small patch with one smooth wavefront. That is what a laser arranges, by two mechanisms worth keeping distinct.

The first is stimulated emission. An atom already excited, met by a passing photon of the right energy, can be induced to drop early — and the photon it emits is not random. It shares the incoming photon's direction, phase, polarisation and frequency. The emitted light is a copy, so amplification here is phase-preserving, which ordinary emission is not.

The second is the cavity, the part usually left out. Put the excited medium between two mirrors. Light heading off-axis leaves after a bounce or two and is lost; light travelling along the axis passes through the medium again and again, being copied each time. The mirrors also impose a round-trip condition — only wavelengths that fit a whole number of times survive the repeated interference. The cavity is a filter with positive feedback, and what emerges is whichever single mode wins that competition, amplified enormously above the rest.

Notice that this makes the beam narrow before any lens is involved. The output is essentially one spatial mode — a single smooth wavefront across the whole aperture — so its étendue sits at the physical floor, and the remaining spread is only what diffraction demands of an aperture that size: for red light of 633 nanometres leaving a waist half a millimetre across, about 0.4 milliradians, or 0.4 metres over a kilometre. That is not the source being tidy; it is the source being at the limit.

Two properties get fused under the single word "coherence", and separating them dissolves most of the confusion.

Spatial coherence is whether the phase across the beam's width is correlated — whether the wavefront is one smooth surface or a patchwork. It governs directionality, and it is the property a lens cannot manufacture.

Temporal coherence is whether the phase stays predictable over time as the wave goes by, which is the same as saying the light is narrow in wavelength. Its measure is the coherence length, roughly the wavelength squared divided by the wavelength spread: white light at 550 nanometres centre and some 300 wide gives about one micrometre, while a helium-neon line narrow by a gigahertz or two gives tens of centimetres.

The two are genuinely independent. A bulb passed through a pinhole and a good colour filter becomes coherent in both senses — and almost entirely dark, because filtering discards nearly all the light. That is the point: filtering selects coherent light out of an incoherent source at ruinous cost, while a laser generates it, funnelling the pumped energy into the surviving mode instead of throwing the rest away.

Two honest qualifications. Directionality is a consequence of spatial coherence, not a definition of it — a laser expanded through a telescope is far less directional and no less coherent. And many real lasers are multimode: a cheap diode pointer has a visible spread and a far wider wavelength band than a helium-neon, so "laser" names a mechanism, not a guarantee of either coherence.

A boundary worth marking: elsewhere in this collection, flame emission colours explain why atoms emit at particular wavelengths, and guided light explains how a fibre confines a beam by reflection at its wall. Neither is at work here; the question is why light that has already left the source keeps a single wavefront.

• Why a population inversion is needed for stimulated emission to outrun absorption, and why two levels cannot supply it.
• How speckle — the grainy shimmer on a laser-lit wall — demonstrates coherence directly rather than being a defect.

Every term the collection defines is gathered in the glossary.