You know,
I have one simple request.
And that is to have sharks
with frikkin laser beams
attached to their heads!
~Dr. Evil

Always look on the bright side
…unless you’re holding a laser pointing device.
~Unknown

The laser is, without a doubt, one of the most ubiquitous, archetypal technologies of modern times. And it is one of the most direct applications of quantum mechanics.  But how do lasers work?

It All Starts In The Atom

The story starts deep within the atom. I’ve previously discuss the fact that particles are waves and that this forces electrons to have only certain specific energies inside an atom. The energy and momentum of a particle control how many times the corresponding wave wiggles. And these must fit in a circle around the nucleus of the atom, as shown below.

If the atom is part of a molecule, especially a crystal, the discrete allowed energies become so numerous that they look like continuous bands. And this leads to band structure.

For clarity, physicists often imagine extremely simple atoms with only two or three allowed electron orbits, each of which is allowed only at a single specific energy and a single specific momentum. We then plot these energies as a function of their allowed momenta. The plot is called an “energy level diagram,” and it looks something like the figure below.

Between Light And Matter

 Now let’s imagine an electron sits in the lowest energy level, as shown below.

When a photon—a light particle—hits the atom (or alternatively passes right through it), it has the potential to affect the electron. Classically (i.e., without quantum mechanics), the light would accelerate the electron, since the electron is a charged particle and light is made up of electromagnetic fields and electromagnetic fields affect charged particles. However, if the electron accelerated, it will gain kinetic energy. This gain is only allowed if the electron ends up with one of the allowed energies.

If the electron is accelerated, it will absorb the photon, absorbing both the energy and momentum of the photon. So it is only allowed to absorb the photon if the electron’s new energy and momentum are allowed within the atom. Otherwise, surprisingly, the photon passes right through the atom unmolested, as shown below.

The same process works in reverse. Electrons are lazy and they want to be in the lowest possible energy state. So they’ll do whatever they can to drop from a high energy state to a lower one. And the easiest way for an electron to drop to a lower energy state is by
emitting a photon. The emitted photon must, of course, have energy and momentum such that the electron’s new energy state is allowed, as shown below. This process is known as fluorescence.

The rules determining how an electron may change energy and momentum are called “selection rules.”

Cheating Selection Rules

Of course, selection rules aren’t absolute. Quantum mechanics is inherently probabilistic, and the Heisenberg uncertainty principle forbids us from knowing all quantities perfectly well. This means that if we shine a beam of light on an atom such that most of the photons have the wrong energy and momentum for the electron to transition to a new energy level… every once and a while, by pure quantum chance, a photon will come along with the right energy and momentum and the electron will transition, as shown below.

Another way you can think about it is that, eventually, the electron itself moves a little bit out of the allowed energy levels and it can absorb one of the forbidden photons, as shown below.

Stimulated Emission

Now, let’s imagine that an electron starts in a low-energy state. And it is excited into a high energy state by a photon with the appropriate energy and momentum. Then, while the electron is still in this high-energy state, another photon with the same energy and momentum hits the atom. What happens?

Intuitively, the photon should pass harmlessly through the atom, unabsorbed, because the electron has nowhere to go. However, this isn’t what happens at all. The electron will drop down to a low-energy state and emit an identical photon, traveling in the same direction and with the same energy and momentum as the incident photon, as shown below. This is called stimulated emission, and it is the magic that makes lasers work.

Unfortunately, I can’t really give a good explanation for how stimulated emission works. The mathematics behind it, and that predicts it comes from time-dependent perturbation theory, a way to examine the quantum mechanics of complicated situations. I can say that absorption and stimulated emission are opposites. The math for each is the same. Indeed, process that’s most different is the most intuitive: fluorescence, where the atom decays without any stimulus at all.

Population Inversion and Gain

If we could take advantage of stimulated emission, we could use it to amplify a beam of light and make it very intense. More importantly, ever photon in the beam could be generated from a single seed photon. The beam could be made of clones, all traveling in the same direction, all with the same energy and momentum. This would let us control the properties of the beam very precisely. (This property is called coherence.)

Unfortunately, atoms like to fluoresce, which means that most electrons do not stay in a high-energy state for long enough for us to initiate stimulated emission. Is there a way around this?

There is a way around this problem! Some transitions between states take longer than others. (This has to do with the quantum mechanics of selection rules that I talked about earlier.) Furthermore, some transitions are more likely to occur naturally than others. In other words, if we select the right atom, we can control how electrons in it transition between states. We can find an atom where the electrons transition to a high energy state very quickly, but then decay into a middle state where they stay for a long time. If we do this fast enough, we can get all of our electrons into the middle state, as shown below. This is called a “population inversion.”

Once we have a population inversion, all it takes is one seed photon. We put a block of our inverted material (called a gain medium) in between two mirrors, as shown below. Then we make the material fluoresce once. It doesn’t really matter how. Eventually the material will fluoresce if it’s in population inversion.

Once one photon is between the two mirrors, it will bounce off of a mirror and pass through the gain medium, causing stimulated emission. Then two photons will bounce off of a mirror and pass through the gain medium, causing stimulated emission. Then four photons will bounce off of a mirror… Well you get the idea.

This is how laser light gets so intense.

Resonance

But why is laser light only one color? This is actually much easier to explain. It’s a consequence of the fact that the gain medium is placed between two mirrors. Remember that photons are both particles and waves. And that the wavelength of the wave determines the color of the light. Moreover, light waves are made up of electric and magnetic fields. The electric field of the light must be zero at the mirror, because mirrors are conductors. The electrons in the mirror move to cancel whatever electric field might otherwise exist.

This means that,  just as an electron orbiting a nucleus can only fit an integer number of wavelengths into the orbit, a light beam can only fit an integer number of wavelengths between the two mirrors, as shown below.Otherwise, the wavelength would not be zero.

This selection process is an example of a broader phenomenon called resonance. The mythbusters have a nice explanation of resonance in their episode on Tesla’s earthquake machine.

Applications?

Where don’t lasers have applications? We use them in medicine for laser eye surgery. We use them in our computers to read optical disks. We use them in our factories to cut metal. We use them to send light signals through fiber optic cables for communication. We use them to measure distance. We use them to measure time. We use them to generate fusion power, and we use them to help us calibrate our telescopes. I’ll talk about some of these ideas in future posts. If you’d like to hear about a specific application, let me know and I’ll see what I can do.

Further Reading

Where to even start? Here are some resources:

• PHET has a simulation of a laser suitable for classroom demonstrations. It just runs in a web applet.
• Minute Physics has a nice video. It uses Bosonic statistics to explain stimulated emission. I don’t really like this explanation, but it does give a good intuition.
• The National Ignition Facility, where they’re trying to use lasers to make fusion power has a nice article.
• How Stuff Works has an article on lasers too.
• LFI International has a nice article too.

Questions? Comments Insults?

As always, let me know if you have questions, comments, or hatemail. Or if you just want to speak your mind.