A frequency comb in its most basic sense is a highly precise tool for measuring different colors, or rather, it measures the frequencies of light at which these colors exist. Because of this, they are often termed ‘optical frequency combs’. The realisation of these frequency combs has come about because of the advances made to ultrafast lasers in recent years. To date, they can measure higher frequencies of light with a greater degree of accuracy than any other technology. In this article, we look at how they work and how they can be used as optical rulers and in optical clocks.
How Frequency Combs Work
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Experimental data from a NIST frequency comb. Image Credits: Wikimedia Commons
Optical frequency combs are a broad optical spectrum with discrete and equidistant frequency lines produced by using an ultrafast laser source. Even though the frequency distances are the same, the intensity of each frequency can vary. Optical frequency combs are also dependent upon the relationship between time and the frequency of the light. In simple physics terms, this equates to the number of oscillations per second. The time and frequency parameters are also inversely related to each other, so a longer time will equate to a smaller frequency number, and vice versa. Over time, the different light properties are converted into a frequency and this series of frequencies resembles a comb on the spectra. Each ‘tooth’ of the comb then corresponds to a different color based on how fast the light wave oscillates.
The production of the frequency comb spectra is only possible with a laser that emits ultrashort pulses with a regular pulse repetition rate, such as a mode-locked femtosecond laser. These lasers have also been used because they generate frequency combs with a wide broadband spectrum, and this broadband can be further extended by using strong nonlinearities with a low temporal coherence, such as supercontinuum generation, by using optical fibers outside of the laser resonator. Also, the faster the laser is at emitting a pulse, the wider the ‘frequency teeth’ are, and the easier it is to identify each colour in the spectrum.
The realisation of a frequency comb also relies on the periodicity of the laser being applied to the whole electric field of the pulse(s), and not just within the pulse envelopes. This includes the optical phases. This means that coherence between the pulses can be maintained and this reduces the noise within the spectra to produce defined ‘teeth’.
Optical Rulers
Frequency combs can be used as an optical ruler because of the comb’s ability to span the entire optical spectrum. These rulers can be used to precisely measure the light given off by other objects, such as stars, lasers and atoms. If all the frequencies in the spectrum are known, then the optical ruler can be used to identify unknown frequencies by measuring beat notes, i.e. a signal which has a measurable optical difference arising from two different non-orthogonal superimposed optical frequencies. These beat notes reveal the frequency difference between the unknown frequency being measured and the known frequencies of the comb, thus, they can be used to measure the frequency of incoming light.
Frequency Combs and Optical Clocks
Because frequency combs can be used to measure absolute optical frequencies, they can also be used to measure the microwave frequency in a caesium clock because the optical and microwave frequencies are related. Therefore, frequency combs can act as a type of optical clockwork, i.e. as the gears of a clock.
In caesium clocks, one second is defined as 9,192,631,770 oscillations between two energy levels of the caesium atom. Non-optical caesium clocks have a miniscule error rate of less than one second every 30 million years, yet, scientists are always trying to make them more accurate; and one way is through increasing the ticking rate of the clock. However, this method has been held back because of the inability to measure this increase, but this can now be realised by using the optical transitions to measure time rather than the microwave transitions in the caesium atom. Frequency combs have been utilized in these applications because they can measure the low microwave frequencies, which are the frequencies that are used to define a second. Thus, they become the gear of the optical clock.
Caesium clocks that don’t use frequency combs have an accuracy of 10-16, but the use of optical frequency combs has improved this to an accuracy of 10-17. However, this is only what is possible today and it is thought that there will be no limit to the levels of accuracy that could be achieved in the future.
Sources and Further Reading
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