How do you make a mode-locked laser?

Given

Mode-locked lasers are lasers that are capable of producing intense ultra-short pulses of light at a very high rate.

Concepts

Set 1

Take a bunch of atoms, excite them and place them in a box covered with mirrors in all directions. Send in one photon, a particle of light, to intercept one of these atoms. Unable to get more excited, the atom will get de-excited by emitting the interceptor photon and another photon identical to it. Because the box is covered with mirrors, these two photons bounce off a wall and intercept two more atoms. The same thing happens, over and over. A hole in the box allows the ‘extra’ photons to escape to the outside. This light is what you would see as laser light. Of course it’s a lot more complicated than that but if you had to pare it down to the barest essentials (and simplify it to a ridiculous degree), that’s what you’d get. The excited atoms that are getting de-excited together make up the laser’s gain medium. The mirror-lined box that contains the atoms, and has a specific design and dimensions, is called the optical cavity.

Set 2

Remember wave-particle duality? And remember Young’s double-slit experiment? The photons bouncing back and forth inside the optical cavity are also waves bouncing back and forth. When two waves meet, they interfere – either constructively or destructively. When they interfere destructively, they cancel each other out. When they interfere constructively, they produce a larger wave.

A view of a simulation of a double-slit experiment with electrons (particles). The destructively interfered waves are ‘visible’ as no-waves whereas the constructively interfered waves are visible as taller waves. Credit: Alexandre Gondran/Wikimedia Commons, CC BY-SA 4.0

As thousands of waves interfere with each other, only the constructively interfered waves survive inside the optical cavity. These waves are called modes. The frequencies of the modes are together called the laser’s gain bandwidth. Physicists can design lasers with predictable modes and gain bandwidth using simple formulae. They just need to tweak the optical cavity’s design and the composition of the gain medium. For example, a laser with a helium-neon gain medium has a gain bandwidth of 1.5 GHz. A laser with a titanium-doped sapphire gain medium has a gain bandwidth of 128,000 GHz.

Set 3

Say there are two modes in a laser’s gain medium. Say they’re out of phase. Remember the sine wave? It looks like this: ∿. A wave’s phase denotes the amount of the wave-shape it has completed. The modes are the waves that survive in the laser’s optical cavity. If there are only two modes and they’re out of phase, the laser’s light output is going to be sputtering – very on-and-off. If there are thousands of modes, the output is going to be a lot better: even if they are all out of phase, their sheer number is going to keep the output intensity largely uniform.

Two sinusoidal waves offset from each other by a phase shift θ. When θ = 0º, the waves will be in phase. Credit: Peppergrower/Wikimedia Commons, CC BY-SA 3.0

But there’s another scenario in which there are many modes and the modes are all in phase. In this optical cavity, the modes would all constructively interfere with each other and produce a highly amplified wave at periodic intervals. This big wave would appear as a short-duration but intense pulse of light – and the laser producing it would be called a mode-locked laser.

Like in the previous instance, there are simple formulae to calculate how often a pulse is produced, depending on the optical cavity design and the gain medium’s properties. These formulae also show that the wider the modes’ range of frequencies – i.e. the gain bandwidth – the shorter the duration of the light pulse will be. For example, the helium-neon laser has a lower gain bandwidth, so its lowest pulse duration is around 300 picoseconds. The titanium-doped sapphire laser has a higher gain bandwidth, so its lowest pulse duration is 3.4 femtoseconds. In the former duration, light would have travelled around 9 cm; in the latter, it would have travelled only 1 µm.

Brief interlude

  • An optical cavity of the sort described above is called a Fabry-Pérot cavity. The LIGO detector used to record and study gravitational waves uses a pair of Fabry-Pérot cavities to increase the distance each beam of laser light travels inside the structure, increasing the facility’s sensitivity to a level required to be affected by gravitational waves.
  • Aside from the concepts described above, ensuring a mode-locked laser works as intended requires physicists to adjust many other parts of the device. For example, they need to control the cavity’s dispersion (if waves of different frequencies propagate differently), the laser’s linewidth (the range of frequencies in the output), the shape of the pulse, and the physical attributes of the optical cavity and the gain medium (their temperature, e.g.).

Method

How do you ‘lock’ the modes together? The two most common ways are active and passive locking. Active locking is achieved by placing a material or a device that exhibits the electro-optic effect inside the optical cavity. In such a material, its optical properties change if an electric field is applied. A popular example is the crystal lithium niobate: in the presence of an electric field, its refractive index increases, meaning light takes longer to pass through it. Remember that the farther a light wave propagates, the more its phase evolves. So a wave’s phase can be ‘adjusted’ by passing it through the crystal and then tuning the applied electric field (very simplistically speaking), to get its phase right. What actually happens is more complicated, but by repeatedly modulating the light waves inside the cavity in this manner, the phases of all the waves can be synchronised.

A lithium niobate wafer. Credit: Smithy71, CC0

Passive locking dispenses with an external modulator (like the applied electric field); instead, it encourages the light waves to get their phases in sync by repeatedly interacting with a passive object inside the cavity. A common example is a semiconductor saturable absorber, which absorbs light of low intensity and transmits light of high intensity. A related technique is Kerr-lens mode-locking, in which low- and high-intensity waves are focused at different locations inside the cavity and the high intensity waves are allowed to exit. Kerr-lens mode-locking is capable of producing extremely intense pulses of laser light.

Conclusion

Thus, we have a mode-locked laser. They have several applications. Two that are relatively easier to explain are nuclear fusion and eye surgery. While ‘nuclear fusion’ describes a singular outcome, there are many ways to get there. One is to heat electrons and ions to a high temperature and confine them using magnetic fields, encouraging them to recombine. This is called magnetic confinement. Another way is to hold a small amount of hydrogen in a very small container (technically, a hohlraum) and then compress it further using ultra-short high-intensity laser pulses. This is the inertial containment method, and it can make use of mode-locked lasers. In refractive eye surgery, doctors use a series of laser pulses, each only a few femtoseconds long, to cut a portion of the cornea during LASIK surgery.

Addendum

If your priority is the laser’s intensity over the pulse duration or the repetition rate, you could use an alternative technique called giant pulse formation (a.k.a. Q-switching). The fundamental principle is simple – sort of like holding your farts in and letting out a big one later. When the laser is first being set up, the gain medium is pumped into the optical cavity. Once it is sufficiently full, the laser will start operating. In terms of energy – remember that the atoms making up the gain medium are excited. In the giant pulse formation technique, an attenuator is placed inisde the cavity: this device prevents photons from being reflected around. As a result, the laser can’t operate even when the gain medium is more than dense enough for the laser to operate.

After a point, the pumping is stopped. Some atoms in the medium might spontaneously emit some energy and become de-excited, but by and large, the optical cavity will contain a (relatively) large amount of energy that also remains stable over time – certainly more energy than if the laser had been allowed to start earlier. Once this steady state is reached, the attenuator is quickly switched to allow photons to move around inside the cavity. Because the laser then begins with a gain medium of higher density, its first light output has very high intensity. The ‘Q’ of ‘Q-switching’ refers to the cavity’s quality factor. On the flip side, in giant pulse formation, the gain medium’s density also drops rapidly, and subsequent pulses are not so intense. This compromises the laser’s repetition rate.


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