Lasers: Stimulated Emission and Population Inversion

1Light in step

Shine a torch and a laser pointer at a wall 50 m away. The torch makes a dim patch metres wide; the laser, with less than a thousandth of the torch's power, makes a bright dot a few centimetres across. The difference is not in how much energy the two give out, but in how the light is made. In a torch the atoms emit independently, at random moments and in random directions. In a laser one photon makes an atom emit another photon exactly like it, which makes another, and so on: billions of photons marching in step. The word laser describes this: Light Amplification by Stimulated Emission of Radiation. The first laser was a ruby crystal made to glow by Theodore Maiman in May 1960. This lesson explains how it works, building on the energy levels and photons of Senior 5.

2Three ways light meets an atom

Figure 3.1: Absorption, spontaneous emission and stimulated emission between two energy levels.

• Absorption. A photon whose energy matches the gap, $hf=E_2-E_{1}hf\; =\; E\_2\; -\; E\_1$, is absorbed and raises an electron to the upper level.
• Spontaneous emission. An excited electron falls back by itself after a short, random time (often about ${10}^{-8}10^\{-8\}$ s), emitting a photon in a random direction with a random phase. This is how lamps, the Sun and the hydrogen lines of Senior 5 produce light.
• Stimulated emission. In 1917 Albert Einstein showed that a passing photon of energy $E_2-E_{1}E\_2\; -\; E\_1$ can TRIGGER an excited atom to emit. The new photon is an exact copy of the first: the same frequency, the same phase, the same direction and the same polarisation. One photon in, two identical photons out: the light has been amplified.

3Population inversion

A photon passing through a material can either be absorbed by an atom in the lower level or stimulate emission from an atom in the upper level. Normally, at any temperature, far more atoms are in the lower level, so absorption wins and light is weakened, not amplified. To amplify, there must be MORE atoms in the upper level than in the lower one: a population inversion. It never happens on its own; energy must be pumped in, and the upper level must hold its atoms long enough.

Figure 3.2: A three-level laser, such as the ruby laser.

Atoms are pumped to a high, short-lived level $E_{3}E\_3$. They drop almost at once, without emitting light, to the metastable level $E_{2}E\_2$, where they stay about 100 000 times longer. Atoms pile up in $E_{2}E\_2$ faster than they leave it, until there are more in $E_{2}E\_2$ than in the ground level $E_{1}E\_1$. Now a single spontaneous photon from $E_{2}E\_2$ to $E_{1}E\_1$ stimulates others, and the avalanche of identical photons is the laser light. Four-level lasers, such as the helium–neon laser, have the laser transition end on a level ABOVE the ground state that empties quickly, which makes the inversion much easier to achieve.

4Building a laser

Figure 3.3: The three parts of a laser.

1. An active medium (gain medium): a crystal, gas, liquid dye or semiconductor with a suitable metastable level.
2. A pump that creates the population inversion: a flash lamp (ruby), an electric discharge (helium–neon, carbon dioxide) or an electric current (semiconductor diode lasers).
3. An optical cavity (resonator): two parallel mirrors. Photons travelling exactly along the axis are reflected back and forth hundreds of times, stimulating more emission at each pass; photons going any other way escape from the sides and are lost. One mirror lets about 1% of the light out as the beam.

5Properties of laser light

Coherence is what makes holograms and very precise interference measurements possible. Directionality is why a laser pulse fired at reflectors left on the Moon by Apollo astronauts in 1969 can be timed on its return, measuring the Earth–Moon distance to within centimetres.