Laser Theory : Energy State Populations

For reasons that we cannot explain, it appears that all things in nature prefer to go to the lowest energy state available to them. This seems to be how nature behaves. Apples fall all the way to the ground, once they are let go by the tree branches they grew on. Of course unless they fall into a hole, in which case they go even lower than the ground level - to the bottom of the hole. To raise the energy of the fallen apple someone, or something, has to intervene. A child must pick it up off the ground, for example. Otherwise, the apple will remain at its lowest point. Similarly, atoms tend to prefer to always stay in their ground state, unless some intervening force causes them to reach an excited state. In the language used in the study of lasers, any process that feeds energy into a collection of atoms or molecules and causes them to vacate their ground state is referred to as an energy pump, or simply as a pump.

In most lamps electricity is used, by one mechanism or other, to pump atoms out of their ground-state into some excited state. We have already seen that incandescent bulbs produce light from Radiative transitions after excitation via collisions of the electrons in an electric current with the filament atoms. As we've also seen, other light sources, like the fluorescent lamps or neon tubes, use gas or vapor for their medium of excitation instead of a solid filament. In most lamps, the pumping mechanism is electricity. This is also the case for most lasers, but in some lasers optical pumping is the mechanism that is used to cause excitation. In optical pumping a light source generates photons with enough energy that they are able to get absorbed by the atoms in the lasing medium and cause them to go into an excited state.

Evidently, all excitations occur "instantaneously", but de-excitations can lag by a measurable time interval that depends on the properties of the excited state. That is to say, an atom in an excited state does not instantaneously de-excite. The time that it spends, on average, in that excited level is called the lifetime of that state. Lifetimes can vary in duration depending on the atom and on the energy level. Excited state lifetimes are typically a few nanoseconds (10-9 s, or a billionth of a second), but they could be as short as a picosecond (10-12 s, or a thousand times shorter still) or as long as a few milliseconds (10-3 s). The ground state, of course, has an infinitely long lifetime since an atom in its ground state can no longer decrease its energy. So, the most stable of states is the ground state. Long-lived states are referred to as meta-stable states.

In the case of Radiative emission, atoms happen to take two very distinctly different approaches: spontaneous emission, or stimulated emission. Spontaneous emission refers to the case when the excited atom de-excites, rather randomly whenever it "feels like it", and emits a photon. This photon has an energy equal to the difference between the two energy levels of the transition, but its direction of travel and its other properties, such as polarization are random. Stimulated emission was first theorized by Albert Einstein in 1917. For stimulated emission to occur a second, non-participating yet stimulating, photon must be present. The energy of this second photon must exactly match the allowed energy of the transition. Then the emitted photon will not only have the same energy as the stimulating one, but it will also travel in the same direction, and will be essentially identical to it.

So, independent of what type of medium is used in a laser, in the absence of a pump the atoms or molecules are almost all in their ground state. Let us imagine that we could count the number of atoms in our laser medium that are in each energy state and denote the ones which are in their ground state by Ngs , those in the first excite state by N1, those in the second excited state by N2 , and so on. Then in the absence of a pump we are mostly certain that N1= N2 = ... = 0, and Ngs = total number of all the atoms in the medium. Once the pump is turned on it will deplete the number of atoms that were originally in the ground state and increases the number of atoms in the excited states that it is pumping to. Because excited atoms de-excite quickly and return to their ground states by spontaneous emission, in almost all lasers even when the pump is feeding energy into the medium the number of atoms in their ground state remains many times more than atoms in any other energy state. That is to say, almost always we could safely state that:

N_{ground state} much bigger than N_{any other state} .

To make a laser we need to not only excite the atoms in the laser medium, but somehow encourage them to undergo a decay through stimulated emission. In stimulated emission a passer-by photon which has an energy exactly equal to the transition energy stimulates the atom to emit a photon, identical to the passer-by photon, instantly. The problem with this is that the same passer-by photon could instead get absorbed by a de-excited atom. So, aside from pumping the atoms to excited states, we need to use clever procedures to insure that there are more excited atoms that could use the passer-by photon for stimulated emission than there are de-excited atoms which could absorb it; i.e. we need to generate a population inversion. Although Einstein predicted stimulation emission in 1917, it was not found experimentally for over 10 years and took over another 30 years just to predict the possibility of a laser. This is basically because it was not considered possible to produce a population inversion because of the above inequality.