As impressive as Hänsch’s results were, we knew that his motivation was to dispose of most of his complex apparatus. The techniques to accomplish this simplification, however, required that a mode-locked laser produce an enormous bandwidth, preferably an octave. (An octave is a factor of two in frequency, whether it be in music, electronics or optics.) Although titanium-sapphire lasers produced impressive bandwidth at the time, they could not yet yield an octave of light.
The final puzzle piece fell into place at the 1999 Conference on Lasers and Electro-Optics where Jinendra Ranka of Bell Laboratories presented a paper on a new kind of optical fiber known as microstructure fiber. In this medium, micrometer-size airholes in the fiber guide light along its core. The fiber’s properties allow pulses at the frequencies produced by a titanium-sapphire laser to travel along it without being stretched (as occurs in ordinary fiber and most other optical media). The lack of stretching keeps the pulse intensity high, which in turn leads to much greater spectral broadening than occurs in ordinary optical fiber [see “The Ultimate White Light,” by Robert R. Alfano; Scientific American, December 2006]. The results are visually stunning. The output of a titanium- doped sapphire laser is in the near-infrared, just beyond the limits of human vision. It appears as a faint red color to the eye. Spectral broadening in microstructure fiber converts that faint red to visible wavelengths, causing the fiber to glow with successive colors of the rainbow.
In the fall of 1999 we managed to acquire some of this magic fiber. The timing could not have been more perfect. We had just completed a series of experiments demonstrating the use of a titanium-sapphire laser to span a gap nearly three times wider than Hänsch’s initial demonstration. We already had an operating setup into which we could almost drop the new microstructure fiber. Within two weeks of receiving the express package from Bell Laboratories, we had done a proof-of-principle experiment showing that the spectral broadening in the microstructure fiber preserved the frequency comb structure in the original laser pulse.
The importance of an octave-spanning spectrum is that it allows the offset frequency to be measured directly as a radio frequency, thus surmounting the aforementioned barrier to using combs to measure other frequencies. There are several specific methods of determining the offset frequency given an octave-spanning spectrum, many of which can be traced to techniques employed in radio engineering for measuring frequencies before high-speed counters were readily available. (Counters do the job by simply counting how many oscillations occur in a radio wave per unit of time but cannot keep up with the much higher frequencies that light has.) We will now describe the simplest and most versatile of the methods for measuring the offset frequency— self-referencing.
The key idea is that an octave-spanning spectrum enables scientists to compare the frequencies of two comb lines at opposite ends of the spectrum with each other. If the offset frequency is zero, then each line at the low-frequency end of the spectrum has a corresponding line with exactly twice its frequency at the high-frequency end. Any deviation from this exact ratio turns out to be precisely the offset frequency. The scheme is called self-referencing because one is comparing the comb’s light against itself.
Self-referencing is carried out in practice by passing some of the laser light through a so-called second-harmonic generation crystal, which doubles the light’s frequency. Thus, one can split off the light that forms the lower-frequency end of the comb using a mirror that only reflects longer-wavelength light but passes shorter wavelengths, then send it through the doubling crystal, and finally direct both it and the light of the higher-frequency end of the comb onto the same photodetector. The combined light oscillates in intensity—it “beats”—in just the same fashion as the combined sound of a tuned and a mistuned note beats. In both cases, the frequency of the beats equals the amount of mistuning. For the light pulses, the beats have the same frequency as the comb’s offset frequency because every doubled low-end line will be mistuned by that amount from a high-end line. In electronics and optics, this procedure of combining signals to get the beat frequency is called heterodyne detection.