# Rulers of Light: Using Lasers to Measure Distance and Time

A revolutionary kind of laser light called an optical frequency comb makes possible a more precise type of atomic clock and many other applications

In contrast, one operator can use an optical comb to cover the entire optical spectrum, not merely like a pianist at a piano but like a keyboardist playing an electronic synthesizer that can be programmed to mimic any musical instrument or even an entire orchestra. Comb technology, in effect, enables symphonies of hundreds of thousands of pure optical tones.

Anatomy of a Comb
Optical frequency combs are generated by devices called mode-locked lasers, which create ultrashort pulses of light. To understand the important features of such pulses, begin by imagining the light wave of the other chief kind of laser, a continuous-wave (CW) laser. Ideally, such a wave would be an endless stream of perfectly regular oscillations (representing the light wave’s electric field), every wave crest and trough having the same amplitude and arriving at an unchanging rate. A pulse from a mode locked laser, in contrast, is a short series of wave crests and troughs whose amplitude rises from zero to a maximum and then falls back to zero. The shortest pulses, with durations of less than 10 femtoseconds, contain just a few full oscillations of the light wave. The general outline of the pulse—its overall rise and fall—is called its envelope. One can think of the pulse as being like the earlier continuous wave (the “carrier wave”), with that wave’s amplitude multiplied by the changing height of the envelope.

The carrier wave consists of light of one pure frequency. A plot of its spectrum would have a single spike at that frequency, representing the presence of that frequency alone. You might expect that the pulse you are imagining would also consist of light only at that frequency—after all, it is just the single-frequency carrier wave with its amplitudes changed—but that is not how waves and spectra work. Instead the pulse is made up of light of many frequencies all traveling together. The frequencies form a small, continuous band centered on the carrier frequency. The shorter the pulse, the broader the spread of frequencies.

Two additional features of the pulses emitted by mode-locked lasers are keys to the development of optical frequency combs. First, shifting the envelope a little relative to the carrier wave results in slightly different pulses. The peak of the pulse envelope may occur at the same time as a crest of the carrier, but it may also be shifted to any other stage of the oscillation. The amount of displacement is called the phase of the pulse.

Second, mode-locked lasers emit trains of pulses at a very regular rate, called the repetition rate. The frequency spectrum of such a train of pulses does not form a continuum spread on each side of the carrier frequency but rather breaks into many discrete frequencies. Plotted, the spectrum looks like the teeth of a hair comb, spaced at precisely the laser’s repetition rate.

A typical repetition rate is around one gigahertz (a billion cycles per second), somewhat slower than modern computer processors. An optical comb that spanned the visible spectrum would have 400,000 teeth if they were spaced at one gigahertz. Scientists can measure repetition rates in the gigahertz (microwave) range very accurately using high-speed photodiodes, which detect each pulse in turn—and an optical comb would appear to leverage that accuracy up to visible wavelengths. Why not, then, use the teeth of the frequency comb as reference points to measure against?

There is, however, a catch. It relates to the phase. Everything is fine if the phase of every pulse in the train is exactly the same, because in that case the comb teeth will be precisely at integer multiples of the repetition rate. Thus, you would know the teeth positions once you had measured the laser’s repetition rate.

But it usually happens that the phase changes from one pulse to the next by some unpredictable but fixed amount. In that case, the comb teeth are shifted in frequency away from the exact integer multiples of the repetition rate by an amount called the offset frequency. To know the frequencies of the comb teeth, one must measure that frequency as well as the repetition rate. Measuring the offset frequency was a barrier to progress with optical combs. This barrier fell resoundingly in 2000. It took the combined efforts of scientists from two separate branches of laser research and the discovery of a new material.

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1. 1. phayez 12:45 AM 12/27/08

Before the blogs were canceled here on Sci Am I had a blog under the username "PHAYEZ" which dealt with, among other things, time and measurement. I put forward that time only exists as a feature of three dimensional existence. Time is the "velocity/distance of 3D matter relative to the velocity/distance of other 3D matter". Outside of three dimensions "TIME" as such does not exist and infinity is equal to zero "time". Also outside of three dimensions measurements cannot be made of anything which makes mathematics, with all due respect, irrelevant since the language of mathematics has, as a syntax, products of measurement. The existence and non-existence of time is a spatial relationship oxymoron which is difficult to grasp when you are an entity who is wholly dependent on being made up of atoms which are moving through space.
One final comment, if I may, on the speed limit of light and the fact that even information cannot exceed the speed of light. At the speed of light time is zero, in other words for the light there is no time that passes so that regardless of where it arrives, it arrives instantaneously. Nothing can move faster than instantaneously, even information...
Pierre

2. 2. timteb 06:18 AM 5/31/11

Phayez,
I would have been interested to read your blog, as you theory is an inverse of that I conceived, namely that particulate was formed in a one dimensional state, that being time and only thereafter is space formed when particulate combines. I nearly agree with the speed of light. Einstein's relativity is based on the speed of light but it does not hold in my reality as we do not see light at all, but feel time "ripples" in spacetime. The speed of light is the speed of the photon, what we see is the ripple of time in the fabric of space. If you can, read my long winded website www.realityofphysics.com for a different view! regards

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