Section 6.6 Lasers
The word “laser” is an acronym for Light Amplification by Stimulated Emission of Radiation. Einstein predicted the essential process of stimulated emission (described below) based on his analysis of how light interacts with atoms, but it took nearly a half-century until we were able to construct an operating laser. Now lasers appear in dozens of commercial products including supermarket scanners and blue-ray disc players. They are also used for cutting and shaping in manufacturing, as scalpels in delicate eye surgery, and as tools in countless scientific experiments.
So just what is stimulated emission? Consider a pair of energy levels for an electron in an atom, as shown in Figure 6.3, with energy difference \(\Delta E\text{.}\) These need not be neighboring energy levels. We have learned already about the processes of absorption and spontaneous emission, which are shown in parts (a) and (b) of Figure 6.3. Recall that the absorbed or emitted photon must have energy \(E_\text{ ph } =\Delta E\) due to energy conservation.
Einstein realized 1 there must also be a third process of stimulated emission, which involves an incoming photon of energy \(E_\text{ ph } = \Delta E\) and an electron in the upper energy level (see Figure 6.3c). This appears to be an unlikely candidate for a photon-electron interaction, since the electron is already in the upper energy level. But photons have spin \(s=1\text{,}\) which makes them bosons, and that means photons are “attracted” to be in the same state. The incoming photon induces the electron to jump down to the lower energy level and emit a second photon with the same energy, in essence “cloning” itself. In fact, this second photon is in exactly the same quantum state as the incoming photon. This means, among other things, that they have the same momentum vector, and so they are traveling in the same direction.
So how do we make a laser from this? The very first lasers consisted of a gas of atoms contained within a resonant cavity composed of a glass tube sealed at either end with mirrors, as shown in Figure 6.4. These atoms are chosen to have a suitable pair of energy levels, \(E_\text{ upper }\) and \(E_\text{ lower }\text{,}\) that will be used to create a population of photons with energy \(E_\text{ ph } =E_\text{ upper } -E_\text{ lower }\text{.}\) By putting energy into the system, many of the atoms are placed into the upper energy level. These excited atoms will spontaneously emit photons in random directions. Most of these photons end up simply absorbed by the walls, but the occasional emitted photon will be moving directly horizontal and therefore will stay in the tube, bouncing back and forth between the mirrors. And that means this photon will eventually come near another excited state atom and use stimulated emission to create a second photon. Now these two photons will stay in the tube and, with stimulated emission, each produce more identical photons. Eventually a large population of these horizontally moving photons will build up: that's the light amplification.
But there is a villain lurking: every atom that has emitted a photon, either spontaneously or by stimulated emission, is back down at the \(E_\text{ lower }\) energy level. These atoms are ready to absorb exactly the photons that we are carefully building up. The only way to win this battle is by numbers. Each stimulated emission event increases the number of photons by one, but each absorption event lowers it by one. So we need to ensure there are more atoms in the upper energy level than in the lower energy level, which is called a population inversion. 2
The technological challenge of making a laser was basically figuring out how to achieve the population inversion. The most common way of maintaining a population inversion in the laser is by a method called optical pumping in which outside energy is applied to excite atoms from the ground state \(E_1\) to an excited state \(E_3\text{,}\) as shown in Figure 6.5. Some excited state atoms decay to the metastable state \(E_2\text{,}\) which takes a long time to spontaneously decay. As a result, a larger number of atoms end up in the metastable state than in the ground state, which means we have achieved population inversion. Then stimulated emission from \(E_2\) to \(E_1\) is used to create the photons of energies \(E_\text{ ph } =E_2 - E_1\text{.}\)
What distinguishes laser light from ordinary light? There are three main properties: (1) all the photons have the same energy, or wavelength, so the beam is monochromatic; (2) all the photons are traveling in the same direction, so the beam is collimated; and (3) all the photons have the same quantum phase, so the beam is coherent. While coherence is an interesting property — it allows us to make holograms, for example — we will not be able to discuss it here. The collimation of the beam is what makes lasers good for surgery and for laser pointers: even after traveling some distance, the beam stays narrow with all the intensity contained in a small cross section. Finally, we used the fact that laser light was monochromatic when we did the two-slit interference lab.