instrument

frequency comb

A laser source producing a spectrum of equally spaced frequencies for precision measurements.
39 related articles · 4 formulas

Description

A frequency comb is a laser source whose spectrum consists of a series of discrete, equally spaced frequency lines, like the teeth of a comb. It acts as a precise 'ruler' for measuring the frequency of light, linking optical frequencies (hundreds of terahertz) directly to microwave frequencies that can be counted with electronic clocks. This capability has revolutionized precision measurement, enabling optical atomic clocks that keep time with extraordinary accuracy and opening new avenues in spectroscopy, ranging, and quantum optics.

History

The frequency comb was developed in the late 1990s, with key contributions by Theodor Hänsch and John Hall, who shared the 2005 Nobel Prize in Physics for this work. The technique was enabled by the discovery of photonic crystal fibers for spectral broadening.

How it works

The comb is generated by a mode-locked laser emitting a train of ultrashort pulses. In the frequency domain, this pulse train corresponds to a series of equally spaced spectral lines. The spacing is exactly the pulse repetition rate, and the entire comb is offset from zero by a carrier-envelope offset frequency. Stabilizing both these frequencies against a reference (like an atomic clock) makes the comb a grid of known, countable frequencies. The titles in the corpus highlight applications: using a comb as a thermometer (measuring temperature via optical frequency shifts), generating squeezed light for quantum communication, and even creating 'combs' for magnetic waves.

In practice

Frequency combs are used in optical atomic clocks, high-precision spectroscopy, LIDAR for atmospheric sensing, and as calibration standards for astronomical spectrographs searching for exoplanets.

Fun fact

A frequency comb can measure the frequency of light so precisely that it would detect a change in the length of a ruler by less than the width of a single atom over a distance of a kilometer.

Concept graph →

Formulas

$$C_{xy}(f) = \frac{|P_{xy}(f)|^2}{P_{xx}(f) P_{yy}(f)}$$
Measures the linear correlation between two signals at frequency f.
What is in the formula
C_{xy}(f)variableMagnitude squared coherence at frequency f — coherence
P_{xy}(f)variableCross-spectral density between signals x and y at frequency f — cross spectral density watt per hertz
P_{xx}(f)variablePower spectral density of signal x at frequency f — power spectral density watt per hertz
P_{yy}(f)variablePower spectral density of signal y at frequency f — power spectral density watt per hertz
| \cdot |operatorMagnitude (absolute value) of a complex number — absolute value
c_{xy}(f)=\frac{|p_{xy}(f)|^2}{p_{xx}(f)p_{yy}(f)} · 2607.18136v3
$$f_{\text{high}} \propto f_{\text{low}}^2$$
High frequency scales with square of low frequency.
What is in the formula
f_{\text{high}}variableHigh frequency — frequency hertz
f_{\text{low}}variableLow frequency — frequency hertz
f_{\rmisco}\approx3.4*10^{20}{\rmhz}(\frac{f_{\rmsigw}}{\rmhz})^2 · 2607.01818
$$S(f) = a f^{-\alpha} + b$$
A spectrum modeled as a power law plus a constant noise floor.
What is in the formula
Svariablespectral density as a function of frequency — spectral density watt per metre per hertz
fvariablefrequency — frequency hertz
avariableamplitude coefficient of the power law — amplitude coefficient watt per metre per hertz
αvariablespectral index — spectral index
bvariableconstant noise floor — noise floor watt per metre per hertz
s(f)=af^{-α}+b · 2607.01095
$$f_n = n f_0$$
Harmonic frequencies are integer multiples of fundamental frequency.
What is in the formula
f_nvariablefrequency of the nth harmonic — frequency hertz
nvariableharmonic number (positive integer)
f_0variablefundamental frequency — frequency hertz
f_n=nf_0 · 2607.12315

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