# Amazing Laser Application 11: Frequency Combs!

What's the application? An optical frequency comb is a short-duration pulsed laser whose output can be viewed as a regularly spaced series of different frequencies. If the pulses are short enough, this can span the entire visible spectrum, giving a "comb" of colored lines on a traditional spectrometer. This can be used for a wide variety of applications, from precision time standards to molecular spectroscopy to astronomy.

What problem(s) is it the solution to? 1) "How do I compare this optical frequency standard to a microwave frequency standard?" 2) "How do I calibrate my spectrometer well enough to detect small planets around other stars?" 3) "How can I do precision molecular spectroscopy really quickly?" 4) "How can I do qubit rotations faster in my ion trap quantum computer?" among others.

How does it work? The key idea is that in order to make short pulses of light, mathematically, you need to add together large numbers of waves at different frequencies. I talk about this a little in the book, from which I'll lift this figure:

From bottom to top, this shows a single frequency, the sum of two different frequencies, then three different frequencies, then five. As you can see, adding mroe frequencies gets you a shorter pulse (where the waves are obvious) with a larger gap between pulses.

When you do this with the right sort of laser, you can generate a pulse whose length is given in femtoseconds (10-15s, or 0.000000000000001s). That kind of ridiculously short length requires an extremely broad range of frequencies to make it up, which can be pictured as a "comb" of lines of different frequencies, corresponding to the different colored lines seen in this figure lifted from the group of Theodor Hänsch, who shared the 2005 Nobel Prize for developing the technique:

The lines of the comb are separated by a frequency that is determined by the repetition rate of the laser, which can be controlled extremely precisely. If the "comb" is broad enough (the technical term is "octave-spanning") it's possible to find high-frequency lines that are at double the frequency of some of the low-frequency lines, which lets you nail down most of the systematic effects that would otherwise plague the measurement. And if you arrange things right, you can get one of the lines to line up with a line from an atomic standard (a rubidium atom, say, or a mercury ion), and lock the frequency of that line to the frequency of the atomic standard to the sort of precision that people expect from atomic clocks-- a few parts in 1016 or so. That gives you a collection of regularly spaced lines spanning more or less the entire visible spectrum, with all of their frequencies known to fifteen or so digits.

This is an incredible resource for all sorts of physics. For one thing, it gives you a way to make direct comparisons between atomic clocks running in very different regions of the spectrum. This is a huge issue, because atomic clocks based on visible or ultraviolet transitions offer a lot of advantages over traditional microwave clocks when it comes to accuracy, but it's very difficult to get an optical frequency down to something useful in the lab. The frequency comb lets you do that.

It can also be applied to spectroscopy in areas like astronomy. The figure above is from the Hänsch group's experiment using a frequency comb to calibrate a spectrometer for astronomical observations, and we had a very nice talk last week by Dr. Chih-Hao Li, who's doing similar work with Ron Walsworth's group at Harvard. The idea is that the comb gives you a way around one of the limitations in spectroscopy of stars, which is that the calibration of the instruments is difficult, and tends to change over time. That leads to an uncertainty in Doppler shifts measured for astronomical objects. The comb provides a nearly perfect calibration source, with atomic-clock precision over a huge range of wavelengths-- the Walsworth group's tests spanned almost 100nm in wavelength, and they think this could allow them to measure Doppler shifts of stars at levels corresponding to a few centimeters per second. That's about the size of the shift Earth would cause in the Sun's spectrum as we orbit, so that level of precision could allow the detection of Earth-like planets through Doppler shift measurements.

You can also apply the comb directly to spectroscopy, as Haänsch's co-laureate Jan Hall has done in spectroscopic experiments at JILA in Colorado. They use the comb to detect trace amounts of particular gases, based on the way they absorb some lines and not others. (If you click on the picture on the page linked, there's a spiffy animation to go with the press release.)

Even more recently, Chris Monroe used a frequency comb to drive transitions in a trapped ion, which could be a faster way of doing the operations needed for quantum computing, where you often need widely separated frequencies that are controlled with extreme precision.

Frequency comb sources are a relatively new technology, so people are still coming up with amazing things to do with them. It's one of the most exciting areas in AMO physics right now.

Why are lasers essential? The entire comb generation method depends on using a laser. There's absolutely no way to make this sort of source without the laser principle-- it's not just a really bright light, it's a really bright light with very special frequency and phase properties.

Why is it cool? Dude, ultra-precise spectroscopy at essentially any wavelength! Extrasolar Earth-like planets! Fast qubits! What more do you need?

Why isn't it cool enough? Only great big nerds really get excited about ultra-precise spectroscopy and all that other stuff. Sadly, many ordinary people are bereft of the soul needed to appreciate the utter coolness of frequency comb sources.

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So, what is generating the actual comb? I look at that diagram, and my reaction is, "Oh, he's feeding a 250 MHz comb and a laser into a mixer, and phase locking one of the output lines to a known higher frequency standard."

My only confusion is whether the block that is combining the two signals is supposed to be a non-linear crystal, thus, a mixer, or something completely other.

By John Novak (not verified) on 21 Apr 2010 #permalink

The comb spacing is determined by the pulse repetition rate, which in turn is determined by the length of the laser cavity. These lasers are "mode-locked," which means that, in some sense, you can think of the pulses as if there's one short pulse in the cavity with a little bit leaking out every time it hits the output coupler.

The repetition rate is stabilized by comparing it to an atomic clock (the output of which is typically a stabilized 100 MHz signal), and adjusting the cavity length with piezoelectric transducers on one of the mirrors. You can get the length stable to within a fraction of an optical wavelength without too much trouble.

Awesome post! I really enjoy this series. I'm a biologist, not a physicist, but I make use of spectroscopy from time to time, so this stuff is very informative for me.

I have a question. How are ultrashort x-ray pulses, such as from free electron x-ray lasers, produced? Is the process, and calibration, basically the same as with a laser comb?

Another really interesting way frequency combs are being used is for Fourier transform spectroscopy. Instead of using an interferometer, you can use two frequency combs with slightly different repetition frequencies and beat them against each other to downshift the optical frequencies to radio frequencies, making them much easier to measure. The upshot is that you can take spectra really fast with very high resolution over a relatively broad frequency range.

I did a literature review of this stuff last year and found it amazing.

Is this related to the "comb filter" found on modern television sets?