A laser pointer and a torch bulb both make red light, but they could hardly be more different. The torch throws a broad, spreading wash of every shade and every direction; the laser sends out a pencil-thin beam of a single pure colour that stays tight across a room — or, bounced off a mirror left on the Moon, still returns as a recognisable spot after a 770{,}000 kilometre round trip. That discipline — one colour, one direction, all the waves marching in step — is what the word laser promises: Light Amplification by Stimulated Emission of Radiation.

The single idea that makes it all possible hides in the middle of that acronym: stimulated emission, a way for one photon to clone itself that Einstein predicted in 1917, decades before anyone built a laser. On this page we meet the three ways light and atoms exchange energy, discover why the third one lets light amplify, learn the strange condition (population inversion) you must engineer to make it win, and assemble a working laser from a gain medium, a pump, and a pair of mirrors.

Three ways light meets an atom

Picture an atom (or molecule) with just two energy levels that concern us: a lower one E_1 and an upper one E_2, separated by a gap \Delta E = E_2 - E_1 = h\nu. Only a photon of exactly that energy can interact. Three things can happen:

• Absorption: a passing photon of energy h\nu is swallowed and its energy lifts the electron from E_1 to E_2. One photon in, none out.
• Spontaneous emission: an electron sitting in E_2 is not content there; after a random little delay it drops back to E_1 on its own, spitting out a photon in a random direction with a random phase. This is ordinary light — a glowing filament, a candle, a firefly.
• Stimulated emission: here is the magic. If a photon of the right energy passes an electron already up in E_2, it can coax the electron down early — and the emitted photon comes out a perfect twin of the one that triggered it: same direction, same phase, same frequency, same polarisation. One photon has become two identical photons.

That last process is a light amplifier. Feed one photon into a slab of excited atoms and, if stimulated emission dominates, you get two, then four, then eight — an avalanche of identical photons. That is where a laser's coherence comes from: every photon in the beam is a copy of copies of one ancestor.

Why you need a population inversion

There is a catch, and it is a deep one. Einstein showed that stimulated emission and absorption are exact mirror images — the same photon that can clone an excited electron can just as easily be absorbed by a ground-state one (the two "B coefficients" are equal). So whether a beam grows or shrinks as it crosses the medium depends only on a headcount: are there more atoms up in E_2 ready to emit, or down in E_1 ready to absorb?

In any normal, warm material the lower level always wins — populations fall off with energy (a Boltzmann distribution), so N_2 < N_1 and a beam is absorbed, not amplified. To get gain you must turn the population upside-down, forcing more atoms into the upper level than the lower:

A pure two-level atom can never be inverted by light alone (pump too hard and you only reach equality, N_2 = N_1, where the medium goes transparent). Real lasers use three or four levels, with a fast decay into a metastable upper laser level and a fast drain out of the lower one, so that the inversion can be built and held. The four-level scheme is so efficient it underlies most practical lasers.

Assembling a laser

Stimulated emission amplifies, but a single pass through the medium gains too little to matter. The trick is to make the light pass through again and again by trapping it between two mirrors — an optical cavity (or resonator). Now a photon travelling along the axis bounces back and forth, triggering a fresh clone at every excited atom it passes, and the axial beam grows exponentially. One mirror is made slightly leaky (say 99\% reflecting), and the small fraction that escapes each round trip is the laser beam. Follow the build:

The cavity does two more jobs beyond amplification. It picks the direction: only light travelling almost exactly along the axis survives many bounces, so the output is a tight beam. And it picks the colour: only wavelengths that fit a whole number of half-wavelengths between the mirrors resonate (the longitudinal modes, spaced \Delta\nu = c/2L apart), sharpening the output to an extraordinarily pure frequency. Amplification, direction, colour — the three signatures of laser light all trace back to stimulated emission tamed inside a resonator.

Worked examples

Example 1 — photon energy. A red helium–neon laser emits at \lambda = 633\ \text{nm}. Each photon carries energy

using the handy shortcut E(\text{eV}) = 1240/\lambda(\text{nm}). That 1.96\ \text{eV} is exactly the energy gap \Delta E between the two neon levels involved.

Example 2 — mode spacing. A cavity of length L = 0.30\ \text{m} resonates at frequencies spaced by

So the laser can oscillate on several such modes under its gain curve, each a razor-thin line 500\ \text{MHz} from the next.

Example 3 — inversion or not? A medium has N_2 = 6\times10^{17} atoms in the upper level and N_1 = 4\times10^{17} in the lower. Since N_2 > N_1, the population is inverted and a beam at the right frequency will be amplified. Swap the two numbers and the same beam would instead be absorbed.