A laser source producing a spectrum of equally spaced frequencies for precision measurements.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.
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.
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.
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.
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.
| C_{xy}(f) | variable | Magnitude squared coherence at frequency f — coherence |
| P_{xy}(f) | variable | Cross-spectral density between signals x and y at frequency f — cross spectral density watt per hertz |
| P_{xx}(f) | variable | Power spectral density of signal x at frequency f — power spectral density watt per hertz |
| P_{yy}(f) | variable | Power spectral density of signal y at frequency f — power spectral density watt per hertz |
| | \cdot | | operator | Magnitude (absolute value) of a complex number — absolute value |
| f_{\text{high}} | variable | High frequency — frequency hertz |
| f_{\text{low}} | variable | Low frequency — frequency hertz |
| S | variable | spectral density as a function of frequency — spectral density watt per metre per hertz |
| f | variable | frequency — frequency hertz |
| a | variable | amplitude coefficient of the power law — amplitude coefficient watt per metre per hertz |
| α | variable | spectral index — spectral index |
| b | variable | constant noise floor — noise floor watt per metre per hertz |
| f_n | variable | frequency of the nth harmonic — frequency hertz |
| n | variable | harmonic number (positive integer) |
| f_0 | variable | fundamental frequency — frequency hertz |















