23rd Day of Christmas: Optical Frequency Comb

This Advent during the 24 days leading up to Christmas I thought it would be fun to have a quick introduction of scientific apparatus, in particular tools used in atomic physics research. This is a way to say thanks to their hard work for our research, and a look at how many things are really needed to make a laboratory work!

Optical Frequency Comb

As mentioned before, diode lasers are common equipment in atomic physics labs because of their versatility and usefulness (not to mention relative ease of use). More recently another type of light source emerged as an important tool for research, the optical frequency comb.

Optical frequency combs got their name from the appearance of their frequency spectrum: a series of very narrow peaks at specific frequencies (wavelengths), with uniform separation from each other (like teeth of combs), spanning a relatively large range, see schematically the bottom image below. Looking at what kind of time sequence can create this sort of frequency spectrum, using Fourier transformation to relate the “time domain” and “frequency domain” of signals, we get a series of pulses that are separated in time by exactly the same distance. If for example the “comb tooth” are 100MHz away from each other in the frequency domain, then the pulses follow each other by 1/100MHz = 10ns (nanosecond). These pulses are generally very short, in the femtosecond range (1 millionth of a ns) – clearly the time-domain picture below is then not to scale.

The parameters of the comb are the “tooth spacing” which is connected to the pulse repetition rate, and the offset frequency which is connected to the phase shift of the light between the subsequent pulses. Then we can get the teeth’s frequencies by starting at the offset, and keep adding adding the repetition rate to it (as the image shows too).

Optical frequency comb scheme
Optical frequency comb scheme based on pulsed lasers (source)

So to create a frequency comb, we have to create a series of very short, very precisely timed laser pulses. One common way to do that is using mode-locked lasers. There  a short light pulse is travelling back and forth between two mirrors (acting as a resonator, similar to reference cavities), in its path there’s some piece of material that can amplify the light (such as a titanium sapphire crystal), and the resonator can be somehow modified (e.g. with active tools such as acousto-optic, electro-optic modulators, or with passive elements that absorb light when it is low intensity and let it through when it’s high intensity). One of the mirrors is not 100% reflective, but it also lets through a little bit of the light, so every time when the light pulse arrives, some of it will leave the resonator continues to the experiment as an ultrashort pulse.

The main ingredient, the titanium sapphire crystal in the mode-locked laser type of comb (the bright spot in the center)
The main ingredient, the titanium sapphire crystal in the mode-locked laser type of comb (the bright spot in the center, source)

The output pulses then often run through other optical elements to stretch the pulse further, usually aiming for at least one octave range (where the spectrum spans from one wavelength to twice the wavelength). In fact, the visible spectrum is  about one octave range, so optical frequency combs can create all the colours of the rainbow in one shot.

That’s all nice, but what can it be used for?

Usually the “teeth” of the combs are 80-100MHz apart from each other, which can be clearly distinguished. Then if we have another laser, mixing its light can be compared to one of the teeth of the comb we can get a signal at their difference frequency, which is then in the 0-50MHz range, a very convenient value to measure, and thus we can get the exact frequency of that laser (knowing the value of the tooth’s frequency). This we can do for the whole spectrum too, so in fact we can do spectroscopy of the entire range in one shot.

We can also to a very useful trick if the optical frequency comb spans at least an octave: we can compare two teeth an octave apart. By that we can actually get not just the relative frequency of a signal (as in vapor cells, reference cavities, and in the single frequency comb tooth comparison above), but the absolute frequency of the measured signal too. This wasn’t possible otherwise, the comparison was made always relatively to something else, ultimately referring back to the known size of something. Absolute frequency measurement removes a lot of unknowns and simplifies things.

Another use of frequency combs is that they can connect the standard atomic clocks operating in the microwave spectrum with very high stability, to the optical spectrum to provide the same accuracy to optical readings. All that is needed is to lock the repetition rate with a feedback loop to a good frequency reference.

With all this, the optical frequency combs bring a lot of versatility to spectroscopy and timekeeping, in a very useful package, at a level that is hard to overstate. In 2005 the Nobel Prize in Physics went to John L. Hall and Theodor W. Hänsch “for their contributions to the development of laser-based precision spectroscopy, including the optical frequency comb technique“. In the decade since, the techniques just got a lot better, more practical, and easier to use. I’d think before long optical frequency combs will be just as common in laboratories as diode lasers are now.

Further info:

If you liked this, come back tomorrow for another apparatus! And send this link to someone who you think would be interested! :)