Femtosecond combs lock frequencies

17 Jun 2002

Measuring time as precisely as possible is vital in basic research. Now an optical method can improve state-of-the-art techniques and is simple enough to market as a commercial instrument. Rob van den Berg reports.

From Opto & Laser Europe July/August 2001

Counting the ripples in a light wave has become easier than ever. In the past, such high-precision measurements required heroic efforts, but now the span of frequencies that stretch from the microwave to the optical domain can be measured using a combination of femtosecond-laser technology and special optical fibre.

The frequencies of atomic oscillations in a clock are important in precision time measurements: the clock's stability is proportional to the frequency at which it operates. An optical-frequency atomic clock is 5 x 10⁴ times as accurate as a 9 GHz caesium microwave standard clock. However, there are two obstacles to popularizing optical-frequency standards: no practical (electronic) device is fast enough to count the optical cycles that make up a unit of time; and it is difficult to produce stable, yet widely tunable, optical oscillators.

In the last few years, both of these problems have been solved by two independent research groups ? one led by Ted Hänsch in Garching near Munich, Germany, and the other by John Hall in Boulder, Colorado, US. They showed that pulsed femtosecond lasers can be made to span an "octave" in frequency, from the infrared to the ultraviolet, and at the same time form an accurate grid (or comb) of equidistant marker frequencies that are all phase-coherent.

This form of ultrahigh-precision optical metrology could soon be available as an accessible laboratory tool. Last year, Hall foresaw a commercial instrument being marketed within the next five years, but it will happen much sooner than that.

Ronald Holzwarth, who recently graduated from Hänsch's group, has started his own business, Menlo Systems, which introduced a prototype comb at Laser 2001 in Munich last month. He is currently talking to a number of university groups that are interested in using the comb in ultrahigh-resolution spectroscopy. The system will cost between Euro 200,000 and Euro 250,000. Holzwarth said: "To many groups it is worth the cost. They do not want to invent the wheel themselves, but they need the accuracy that only a comb can offer."

Measuring the optical frequency of a laser used to require several people and more than a room full of equipment. Building on the 9 GHz signal of a caesium clock, a series of frequency-doubled oscillators operating in the microwave to the optical domain defined a frequency chain. It was possible to determine the optical frequency of the laser by comparing its output with the specific frequencies of different oscillators in the series.

Making precise measurements using ultrafast lasers does not seem possible because a short pulse has a broad spectrum. In a laser, however, a pulse is generated between two mirrors that define specific laser-cavity modes. Any pulse inside the resonator can be described as a superposition of these mode frequencies.

In 1978 Ted Hänsch from the Max Planck Institute of Quantum Optics in Garching, Germany, demonstrated that the pulse train of a mode-locked laser behaves like a set of equally spaced modes, which resemble the teeth of a comb, and the spacing between the teeth is equal to the repetition rate of the laser. With such a comb he believed that the complicated frequency-multiplying scheme could be eliminated. It would, however, take some time before that idea could be tested. Even though frequency combs were first produced in the early 1990s, their enormous potential only became apparent after a ground-breaking experiment by the Garching group, which showed that the mode spacing of a mode-locked laser was indeed as uniform as theory predicted.

Hänsch and colleagues took two extreme modes - 20 THz apart - of a mode-locked titanium-sapphire laser and used them to phase-lock a diode laser. With the help of an optical-frequency interval divider, the midpoint between the two modes was determined and compared with the output of a third diode laser that was phase-locked to the centre mode of the frequency comb.

It was found that the mode spacing was constant to within a few parts in 10¹⁷and that it agreed with the pulse-repetition rate within an experimental uncertainty of a few parts in 10¹⁶. This allowed the researchers to compare the frequency of a well known caesium absorption line at 895 nm with the fourth harmonic of a methane-stabilized HeNe laser at 848 nm. The gap between the two was measured using 244,000 modes of the mode-locked laser. In these experiments, the optical comb was just wide enough to determine the difference between an established optical frequency and an unknown frequency.

"That's the reason", said Thomas Udem, a post-doctoral student of Hänsch, "why we planned to use divider stages to cut up a large frequency span into smaller ones that could be measured using our comb. We thought that we needed a certain number of dividers, but as the available comb width increased we could manage with fewer, and even before we started the experiment, we discovered that we did not need any dividers at all." Thanks to a small piece of special fibre, the comb width had exploded.

The obvious way to broaden the frequency range of a comb is to use shorter pulses, because the spectral width is inversely proportional to the width of the pulse. Yet even though femtosecond lasers had been around for a while, extending the comb width proved to be no easy feat: the modes in the cavity were thought to suffer from pulse-energy fluctuations and other perturbations that induce a rapid pulse-to-pulse de-phasing.

It was John Hall's group at the National Institute of Standards and Technology (NIST) and the University of Colorado in Boulder that found a solution. They came up with an elegant method to control the absolute frequencies of the optical comb. The technique was based on comparing the frequency of comb lines at the low-frequency end of the optical spectrum with those at the high end. To make such an octave possible, the frequency span of a comb was enlarged in an optical fibre using self-phase modulation. This so-called Kerr-effect relies on the power-dependent refractive index of a non-linear medium.

In a regular silica fibre the pulse duration is stretched, due to chromatic dispersion, thereby lowering the peak power of the pulse and thus limiting the spectral range.

Udem said: "A group at Lucent Technologies [in the US] had succeeded in making a special air-silica microstructure fibre, which could be designed with a zero group velocity dispersion at any wavelength. This means that, while the pulse travels inside the fibre, its shape remains the same for a longer time, so that self-modulation is more effective." This would make it possible to form a phase-coherent octave between the infrared and the visible spectrum.

The Garching group started negotiating with Lucent to obtain a piece of the special fibre, but it went to Boulder first. Hall and his colleagues thus became the first to make a direct link between the optical and the microwave domain. By synchronizing the repetition frequency of a 12 fs pulse laser with an atomic caesium clock, they were able to determine the frequency of an iodine-stabilized Nd:YAG laser at 563 THz to within an accuracy of a few kilohertz.

Udem said: "Hall's group was kind enough to acknowledge that the basic ideas came from us and so both groups presented the results of this experiment together." In the meantime Udem and colleagues had found out that the University of Bath was also able to produce the photonic fibre and had set up a spin-off company, Blaze Photonics. "We got the fibre from the University of Bath, which had come up with these fibres at about the same time as, but independently of, the Lucent group," said Udem (figures 2 and 3).

The frequency-comb technique will enable greater accuracy in spectroscopy, and quantum electrodynamics can now be tested at a level that was previously unobtainable. Using this technique, experiments could shed light on the question of whether there is a difference between matter and antimatter, by accurately determining the properties of antihydrogen.

But most important of all, an optical alternative could be found for the caesium microwave frequency that is currently used in the SI definition of the second. The routes for realizing such optical frequency standards use either small clouds of neutral atoms as a reference or single ions confined in electromagnetic RF traps. Frequency standards that rely on the latter have the advantage that the particle is well localized in an ultrahigh vacuum and can be cooled to a state that is almost free of motion.

In this field, impressive progress has been made: subkilohertz resolution was reached using positively charged mercury, indium, strontium and ytterbium ions. These could lead to even better atomic clocks. Leo Hollberg leads a group at NIST that is involved in optical precision measurement. He said: "To obtain an improved standard, the frequency comb has to be operated in a backwards direction. One tooth of the comb must be locked to an optical frequency - for instance, a specific transition of the mercury ion - and then the self-referencing method and a doubled frequency used to stabilize the frequency offset. The repetition rate is then constrained. In this way you don't need a microwave or caesium frequency anymore."

Recent measurements on the mercury ion performed in Hollberg's group had a statistical uncertainty that was essentially limited by the definition of the SI second.

Hollberg said: "These combs have so far met all of our expectations. You can build two and they reproduce each other's results, better than we can know their absolute frequencies, because these are defined in terms of the caesium standard." According to Hollberg, an accuracy of one in 10¹⁸ is predicted. Ultimately, the question of whether clocks realized by different atomic resonances keep time at the same rate may be answered. See OLE June 2000 p17 and visit the following Websites for more details: Blaze Photonics, Max Planck Institute and NIST.