Laser stands for Light Amplification by Stimulated Emission of Radiation. Three things are needed: a gain medium (atoms with the right energy levels), a pump (a source of energy that excites the atoms), and an optical cavity (two mirrors that send the light back through the atoms again and again).

Absorption, spontaneous emission and stimulated emission. An atom can take energy from a photon of the right energy and move up a level (absorption). An excited atom can drop down by itself and give out a photon in a random direction (spontaneous emission). Or a passing photon of the right energy can stimulate the excited atom to drop down, and the atom gives out a second photon that is a clone of the first: the same energy, the same direction and in step (the same phase). One photon in, two photons out. That is amplification.

Population inversion. A photon passing through a gas of atoms can be absorbed by an atom in the lower level, or can stimulate an atom in the upper level. If most atoms are in the lower level (which is normal), absorption wins and the light is weakened. To amplify the light there must be more atoms in the upper level than in the lower level: a population inversion. This never happens in thermal equilibrium, so the atoms have to be pumped.

Why two levels are not enough. If you pump a two-level system with light, the pump light stimulates emission as well as absorption. The most you can get is half of the atoms in each level, so there is never an inversion. A three-level laser (such as the first laser, made with ruby) pumps atoms to a high level, from which they quickly drop to a long-lived upper level. The lower laser level is the ground state, so you have to pump more than half of all the atoms. A four-level laser (such as a helium-neon laser) has a lower laser level that empties quickly, so it is nearly empty and any atom in the upper level gives an inversion. It needs the least pump power.

The cavity and the threshold. One mirror reflects almost all of the light and the other lets a little of it out. A photon travelling to and fro past the excited atoms makes more and more clones. Each time the light goes round, it gains from stimulated emission and loses a part of the light through the output mirror. If the gain is less than the loss, the photons die out: the pump power is below the threshold. Above the threshold, the number of photons rises very quickly (the beam builds up from the few photons from spontaneous emission), until the stimulated emission uses up the upper level as fast as the pump fills it. Then the number of excited atoms stays at the threshold value, and the extra pump power goes into the beam.

Laser light and lamp light. In a lamp, each atom emits at a random time, in a random direction, with a random phase. The waves add up with random phases, so the intensity of N sources is only about N times that of one. In a laser, the light is coherent: all the waves are in step, so their amplitudes add up and the intensity is about N² times that of one. The laser light is also monochromatic (one wavelength) and directional (the mirrors allow only light along the axis to build up, so the beam hardly spreads). A cavity of length L can only hold standing waves with a whole number of half wavelengths, so the allowed frequencies are

f_n = n c / (2L)

and the modes are c/2L apart (500 MHz for a 30 cm cavity).

What the model leaves out. The atoms sit in a row between the mirrors and the photons move along the axis only. The numbers of atoms and photons are small so that you can see them, and each event is chosen at random (so the beam flickers). A real laser has billions of atoms and photons. Real spontaneous emission goes in all directions, and here only 4% of it goes along the axis.

Things to try. (1) With the four-level atoms and the pump off, then on, what happens to the number of atoms in the upper level and the photons in the cavity? (2) Find the smallest pump power that makes a beam (the threshold). (3) Compare the three kinds of atoms at the same strong pump. (4) Change the reflectivity of the output mirror. Why does a lower reflectivity need a stronger pump? (5) In the second tab, add up 40 sources. How much brighter is the laser than the lamp?