JILA scientists John Hall , Steve Cundiff , and Jun Ye are world leaders in research on frequency combs. Combs are spectra consisting of hundreds of thousands of evenly spaced sharp spectral lines (colors) produced by extremely stable ultrafast lasers. The line spacing in these spectra is so exact that combs can be used to precisely measure the frequency of hundreds of thousands of discreet colors of light. These new rulers of light are now providing measurement precision that was unheard of until 2003. Today, a remarkable journey of discovery is well underway in search of applications of this fabulous new technology. Between 1999 and 2004, groundbreaking research on the generation and characterization of optical frequency combs contributed to JILAn John Hall and Theodore Hänsch sharing the Nobel Prize in physics in 2005.

Optical frequency combs are central to the development of optical atomic clocks. Researchers are currently working on applications of combs in advanced laser radar, exquisitely sensitive chemical detectors, and secure optical communications systems. Laboratory scientists are using them to measure the energy levels of electrons and probe their dynamics inside atoms. And, thanks to frequency combs, revolutionary advances in our ability to exactly control chemical reactions with lasers are just around the corner.

In the past few years, researchers have even used frequency combs to span the huge frequency (and wavelength) gap between radio and light waves, connecting them in ways that were impossible until just a few years ago. This connection goes to the heart of our ability to measure frequency and time, enabling the developing of a new generation of atomic clocks based on optical transitions in atoms. These new clocks use frequency combs to count the oscillations of light produced by optical atomic transitions and convert them to useful electronic signals. The comb technology used in optical atomic clocks is so precise that every one of the colors in a laser pulse train can be exactly linked with one another to produce (and measure) a symphony of hundreds of thousands of pure optical tones.

### How are frequency combs made?

Mode-locked lasers generate optical frequency combs by creating regular trains of incredibly short pulses of light that last anywhere from 20 to 100 quadrillionths of a second (10^{-15} s), depending on the individual laser. Today, well-stabilized mode-locked lasers, together with associated electronics and a specialized interferometer for comparing comb lines, are sometimes referred to as "Frequency Comb Lasers" or simply "Optical Frequency Combs." If such a laser is well stabilized, then the pulse train creates a spectrum consisting of narrow spikes at integer multiples of the repetition rate of the laser, or ƒ_{rep}. This spectrum is called a frequency "comb" because it resembles a hair comb.

The pulses emitted by a frequency comb lasers are not identical. φ_{CE} is the small difference between the peak of the envelope and the peak of the light wave. φ_{CE} varies from pulse to pulse because the carrier wave and the envelope travel at different speeds inside the laser. This pulse-to-pulse change in φ_{CE} causes a small frequency shift in the entire comb by a specific amount ƒ_{0}, also known as the comb offset frequency. Like the repetition rate (ƒ_{rep}), the comb offset frequency is determined by the specific characteristics of an individual mode-locked laser. The measurement of these two parameters makes it possible to completely characterize a frequency comb in terms of both time and frequency and determine the evolution of φ_{CE}, or Δφ_{CE}.

### How do frequency combs work?

Optical frequency combs are particularly useful because the optical frequencies of comb lines can be determined by two radio frequencies, the repetition rate, and the offset frequency. High-speed photodiodes can readily measure the repetition rate. However, it wasn’t until 2000 that scientists at JILA figured out how to measure the offset frequency in a frequency comb that spanned an entire octave of frequencies. The octave-spanning spectrum allowed them to compare two comb lines at opposite ends of the spectrum with each other. If the offset frequency had been zero, then the two comb lines would have been found to have a frequency ratio of exactly 2. Instead, they found a small deviation, equal to the offset frequency, from this exact ideal ratio.

It turns out that the frequencies of two comb lines with a ratio of approximately 2 can be compared by doubling the frequency of the comb line on the low-frequency side of the spectrum. Frequency doubling is accomplished with second-harmonic generation crystals, which produce an output electric field that is the square of the input field. And, squaring a sine wave produces a sine wave at twice the frequency.

If the low frequency comb line has a frequency of νn = n•ƒ_{rep} + ƒ_{0}, then the comb line that is closest in frequency to twice νn has a frequency ν2n = 2n•ƒ_{rep} + ƒ_{0}. One can easily determine their frequency difference via a beat note that occurs when both illuminate the same photodetector (known as heterodyne detection, identical in concept to the "beating" sound used in tuning a musical instrument). This simple technique yields 2ν2n-νn = 2(n•ƒ_{rep} + ƒ_{0}) – (2n•ƒ_{rep} + ƒ_{0}) = ƒ_{0} and is known as "self-referencing." The output of heterodyne detection gives a signal that can be used to generate an error signal in a phase-locked feedback loop to stabilize the frequencies of all of the comb lines.

### A Measurement Revolution

Once optical frequency combs were invented, it was suddenly easy to precisely measure the frequency of light from any stable laser. For instance, since most mode-locked lasers operate at a repetition rate, ƒ_{rep}, of a gigahertz or less, it is easy to measure ƒ_{rep} and ƒ_{0}. Since the comb lines are spaced by ƒ_{rep}, the frequency difference, ƒ_{beat}, between an unknown laser and the closest comb line will be a frequency less than ƒ_{rep}. A heterodyne beat between it and the closest comb line can be easily measured relative to a cesium fountain atomic clock. With these three measurements, the optical frequency of a mode-locked laser can be given by ν_{CW} = n•ƒ_{rep} + ƒ_{0} ± ƒ_{beat}. The integer n and the correct sign can be determined with rough prior knowledge of ν_{CW}. A commercial wave meter provides sufficient accuracy, or, lacking that, they can be determined by systematically varying ƒ_{rep} and ƒ_{0} while monitoring ƒ_{beat}.

### What’s Ahead

There are many applications of optical frequency combs besides measuring optical frequencies. The most well-known of these, optical atomic clocks, is already pointing towards a redefinition of time in terms of an optical frequency quantum transition. However, selecting a particular ionic or atomic transition to replace cesium is expected to take careful evaluation to determine the best candidate.

Extending frequency comb technology across the electromagnetic spectrum is also a focus of intense research. At JILA, we have created a comb at infrared wavelengths using difference frequency generation. The creation of a frequency comb spanning the microwave through visible is straightforward. In 2011, the Ye group at JILAgenerated a frequency comb in the extreme ultraviolet (XUV) using a combination of a near infrared mode-locked laser and a high-finesse optical cavity. The cavity enhanced the intensity of the original laser light and allowed high harmonic generation into the XUV without an active amplifier. This extended comb will allow scientists to study the fine structure of atoms and molecules with coherent XUV light. Work continues on extending comb technology to even shorter wavelengths.