 Alright, so let's dig a little more into the workings of how a laser actually generates the light when it generates this monochromatic, collimated, and coherent source of light. So first, I guess let's explain what this word laser means. Laser is actually an acronym which you may have heard before, but now we know enough to understand what the words in that acronym mean. The acronym laser stands for L stands for light, so A stands for amplification, and then the S and the E stand for stimulated emission. Process we talked about previously, so S and E, and then the R stands for radiation. So light amplification by stimulated emission of radiation, all that means is molecules in some excited state when they get tickled by a photon of the appropriate wavelength, a photon of energy that matches that difference between these two energy states that can induce or stimulate the emission of another photon as this molecule falls down to the ground state. So we've amplified the light, one photon has become two, using stimulated emission, and then radiation is just talking about the photon, the electromagnetic radiation. That's one photon here, two photons here, that's the radiation we're talking about. So that's all laser means is making more photons out of fewer using stimulated emission. There is a problem, however, with trying to construct a laser based on this principle. If I have a ground state, an excited state, I need to get some molecules up in the excited state. I need to generate at least one photon to kick things off and then hopefully that will stimulate more photons of the same wavelength and they'll be coherent with one another. So far so good, but there are some problems. First of all, if I have a lot of those molecules in my system, there's bound to be some in the ground state, so as these photons encounter molecules in the ground state, then what's going to happen is not all of them will make it through, and some of those photons will be absorbed in exciting molecules from the ground state to the upper state. In particular, so that absorption is doing the opposite of what we want. That's not amplifying the light, that's damping the light, that's consuming some of the photons. So we don't want absorption to happen, we only want stimulated emission to happen, and certainly there's going to be some ground state molecules around that will undergo absorption. That's bad from the point of view of generating a powerful laser. So there's actually quite a few problems with this approach. First of all, Boltzmann tells us that the probability of occupying the ground state or the excited state is proportional to e to the minus energy over kT. Energy of the excited state is larger, energy of the ground state is lower, so the population of the ground state, Boltzmann says, should be lower than, more populated, higher population in the ground state, less population in the excited state. If the system's at equilibrium, I'm always going to have more molecules down here in the ground state and fewer molecules in the upper state. What that means is absorption is going to be more prone to happening than stimulated emission. So Boltzmann equilibrium distribution of molecules is bad. Already that's enough to kill the idea of this laser if we keep the system at equilibrium. We could do a few things to address that. We can keep shining in more of these photons to get more molecules up in the upper state, but every time we undergo stimulated emission, every time one of these excited state molecules falls down to the ground state, that's going to reduce the population of the excited state. So every time we undergo stimulated emission, it's going to fight against this idea of having more molecules in the upper state. What we really want, rather than this Boltzmann distribution, we'd love to be able to have a lot of molecules up in the upper state, fewer molecules in the ground state. That is called a population inversion. Again, inversion is because it's against what the Boltzmann distribution says should be happening. Boltzmann says, depending on the temperature, there's going to be more molecules in the ground state than the upper state. We want to have more molecules in the upper state than the ground state. We want this population inversion. Boltzmann says that can't happen. Every time we undergo stimulated emission, it's fighting against that population inversion. It's dropping molecules from our upper state down to the ground state, and the only way, or at least the principal way to reverse that, the way of getting more molecules from the ground state up to the upper state is by absorbing a photon. These molecules can be excited up to the upper state with a photon, but when we try to do that, the exact photons that get absorbed to take a molecule from the ground state up to the upper state are the photons that we're interested in stimulating. It consumes the light, the radiation that we're interested in getting more of. All these things sort of combine to make it impossible to generate net amplification of the photons in a system that has only these two states because we can't keep it far enough away from equilibrium in order to maintain this population inversion. Luckily, though, most systems have more than just two states that we can use to undergo these sort of transitions. If we imagine a system that has three states rather than two, so here's a ground state, here's an excited state, and here's a different excited state, we can start out with a bunch of molecules in the ground state, and then bring in a photon with relatively high frequency short wavelength of the appropriate energy to excite molecules from the ground state up to this upper excited state. We're never going to succeed in getting a population inversion between these two states using just photons, but we can get a substantial number of molecules up in this upper state, just not quite as many as we have down here in the ground state. So we don't have a population inversion, but notice that we do now have a population inversion between these two states. So what's going to happen next is these molecules eventually are going to spontaneously fall back down, maybe to this state, maybe to this state. Sometimes they'll fall down to this state, and when they do that, they'll emit a photon. Notice this photon has less energy than this photon. The photon we've used to excite the molecules from the ground state up to this upper state, that's called the pumping transition, we're pumping molecules up to the upper state. This photon here in particular, this one we're going to call the lasing transition, this is where we're going to get amplification. So when molecules, they'll fall down to one of a variety of states, maybe this state, maybe the lower state. When they fall down to this state, they'll give off a photon. If they then encounter another molecule, if that photon encounters a molecule that happens to be in this state from having done the same thing, then we can get stimulated, oops, sorry, that's not right, we could get absorption, that would be bad, but if we don't get absorption, if we run into another one of the molecules in the upper state, then the molecule can fall down and we'll get stimulated emission when this molecule falls from the upper state down to the middle state. So as long as we have maintained a population inversion between the upper state and the middle state, then we can have more stimulated emission going on than we have absorption. Eventually this molecule and this molecule, they'll fall back down. In this application we're not interested in the photons that are given off there. That's actually not a bad thing for two reasons. Number one, it depletes this middle state, helping maintain the population inversion. As long as we can keep pumping molecules up to the upper state, enough to keep this state more populated than the middle state, we're happy when they leave and spontaneously fall down to the ground state. In addition, when these molecules fall back down to the ground state, they're there waiting in the ground state to be pumped back up. There's continuous supply of molecules in the ground state that can be pumped up to the upper state to help maintain this population inversion. So recapping, we do have a population inversion between these two states, even though we don't have one between this state and this state. So we can only have this amplification of light when we have the population inversion. So making use of three transitions with a pumping transition up to one and a lazing transition from transitions down to a different state is what enables us to have net amplification of the light via stimulated emission. So this is, again, just a general sketch of how the laser works with generic identification of these energy levels. We haven't talked about specific materials that could be used to generate a laser. In fact, most materials have not just three states but have a very large number of states. So that's both good and bad because it allows us some choice over which transitions to use as the lazing transition and bad because it makes the energy level diagrams relatively complicated. So the next thing we'll do is take a closer look at a more specific real physical system.