Your hand opens and closes, opens and closes.
If it were always a fist or always stretched open, you would be paralysed.
Your deepest presence is in every small contracting and expanding,
the two as beautifully balanced and coordinated as birds’ wings.
~Rumi

Although we don’t usually notice them, ultrafast pulsed lasers are all around us. They are keep time in the atomic clocks on GPS satellites. Metrologists and chemists use them to measure the properties of atoms and molecules. Astronomers use them to measure the color of light from distant stars. Particle physicists use them in supercollidors. Materials scientists use them to measure the properties of semiconductors. Ultrafast lasers are even used in fusion research.

Because materials hit by a pulsed laser heat up less than materials hit by an unpulsed (or “CW”) laser, ultrafast pulsed lasers are used to cut very fragile objects and/or very small incisions. This includes precision machining and precision medical work like laser eye surgery.

And, of course, the world’s communications are carried by laser pulses through fiber optic cables.

Few people realize just how short these pulses are. A modern ultrafast pulsed laser can fire over 85 million times per second. And each burst of light is just one ten-quadrillionth of a second in duration—that’s 1/10000000000000 seconds.

In this article I discuss the mode-locking, the current best method to produce such incredibly short pulses of light. Mode-locking is made possible by a device called a “saturable absorber.” So let’s start with the quantum mechanics of saturable absorbers.

It All Starts in the Atom

The following discussion borrows heavily from my article on how lasers work. So if you remember that article, you can probably skip this.

The story of energy levels starts deep within the atom. I’ve previously discussed the fact that particles are waves and how this means that electrons can only have certain specific energies inside an atom. The energy and momentum of a particle control how many times its corresponding wave wiggles within a certain distance. As shown below, these wiggles (wavelengths) must fit in a circle around the nucleus of the atom–the electron can’t cut off its oscillation halfway through to fit itself into an orbit!

If the atom is part of a molecule (especially a crystal), the discrete allowed energies become so numerous that, together, they look like a continuous band. 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. Depending on the situation, they even neglect the momenta and only look at the allowed energies. This is what we’ll do. For example, the figure below shows a two-level atom with a single electron in the lowest energy state.

The Strange Dance of Light and Matter

When a photon—a light particle—hits the atom (or, alternatively, passes right through it), it has the potential to affect the electron. If we ignore quantum mechanics and look at this classically, the light would always accelerate the electron, since the electron is a charged particle and electromagnetic fields affect charged particles.

However, if the electron accelerated, it would gain kinetic energy. This gain is only allowed if the electron ends up with one of the allowed energies–and if the electron is accelerated, it will absorb the photon’s energy and momentum. So it can only 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.

Of course, electrons don’t stay in their excited state. They want to be in the lowest-energy state they can occupy. So eventually the electron will give off its energy somehow—often through heat—and drop down to the low energy state.

Now let’s imagine that an electron starts in a low-energy state and 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 right through the atom 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.

 Striking A Balance

Now let’s say that we have equal numbers of electrons in the ground state and the excited state, as shown below.

Then let’s say we send two photons of the appropriate energy through the material. One photon will be absorbed by an electron in the ground state. The other photon will induce stimulated emission and cause a new photon to be emitted, as shown below. Thus, two photons enter the material and two photons emerge from it, even though absorption took place. It’s as if no absorption occurred at all! When this happens, we say that the material has (or is) “saturated.” A material that can be saturated is called a “saturable absorber.”

(Of course, since quantum mechanics is inherently probabilistic, this isn’t what happens every time two photons pass through the material. But on average, this is what will happen.)

So how does a material become saturated? Simple: all we have to do is shine enough light at it! The more light hits the material, the more of its electrons will enter the excited state…and eventually, the material will saturate. If we decrease the amount of light we shine on the material, electrons will begin dropping into the ground state on their own and the careful balance between absorption and stimulated emission will break. Then the material will absorb again. Effectively, this means that a saturable absorber is opaque to dim light and transparent to bright light! As you may have guessed from the title of this post, this is an extremely useful property.

Saturable Absorbers and Lasers

Say that, somehow, we already have a laser pulse. A normal laser pulse starts low in intensity, becomes brighter and brighter as time passes until it peaks, and then decreases in intensity again. Now say we send one of these pulses through a saturable absorber. When the pulse is low-intensity, it will be absorbed, but the part of the pulse that’s very bright will pass right through (as shown below). Because the lower-intensity “wings” of the pulse are being cut off, this means that the total duration of the pulse will decrease, even though the maximum brightness of the pulse stays roughly the same.

I’ve mentioned before that a laser is essentially a gain medium (which produces the laser light) stuck between two mirrors, as shown below. Light constantly bounces between the the two mirrors in this “laser cavity.”

But if we also stick a saturable absorber in the cavity—say, on one of the mirrors—the behavior of the laser will change.

Although the brightness of the light in the cavity is roughly constant, it does fluctuate a bit.  Most of the light will be absorbed away by the saturable absorber, but the brightest fluctuations will saturate it and remain intact. Over time, these bright fluctuations in the cavity will eventually become pulses. These pulses will bounce around in the cavity hundreds of millions of times, each time passing through the absorber and shrinking a little in duration. Eventually, the laser cavity will contain only extremely bright, extremely short pulses of light…as short as one ten-quadrillionth of a second.

And that, ladies and gentlemen, is how an ultrafast pulsed laser is made!

Related Articles

If you enjoyed this post, you might like some of these too:

• I have a three-part series on quantum mechanics. The first post explains the experiments which tell us the world is quantum. The second uses the Bohr model of the atom to motivate the wave picture of quantum mechanics. And the third explains what matter waves really are.
• I wrote a post about how lasers work here.
• For a realistic picture of a physical saturable absorber, you might want to read my article on band structure.
• If you want more on optics and energy levels, you might enjoy my two-part series on scattering. The first part describes scattering using a “classical” physics and the second part describes the same phenomena using quantum physics.

Further Reading

Sadly, mode-locking is a fairly esoteric topic, so there aren’t many places I can point you to.

• As an undergraduate student, I studied how to mode-lock lasers using graphene, which is a honeycomb lattice of carbon atoms. If you’re math-y, my undergraduate honors thesis goes into a fair amount of detail into the mathematics of saturable absorption. You can find it here.
• When I worked on lasers, I worked in the Schibli lab under Thomas Schibli at the university of Colorado at Boulder. You might enjoy browsing their website.
• Professor Ursula Keller is one of the biggest names in ultrafast optics. She gave a 2.5 hour lecture on mode-locked lasers and their applications which you can find on Youtube.
• Optcomm, a laser company, has a short promotional video explaining mode-locking here.
• For the very brave, the classic scientific paper on passive mode-locking is this one by Ippen. (Sadly, it’s behind a paywall.)