The concept of phase and frequency stabilization relies on the possibility to detect changes of the quantity that is wished to be stabilized. To do so this quantity has to be measured continuously, i.e. has to be compared to a reference. In the case of a laser´s phase or frequency, among others, this reference can be an atomic or molecular transition, an optical cavity with fixed mirror distance, another light source that is believed to be more stable, e.g. A second, Stable Laser or a frequency comb, or a wavelength meter. In this application note, different references are presented and their advantages and disadvantages in terms of stability and convenience are discussed.

For many applications, a good and simple way to stabilize a laser´s frequency is to compare it to an atomic or molecular transition. One advantage of this method is that optical transitions are rather narrow (typically several MHz). Furthermore, for experiments working with atoms, this method suggests itself because lasers can be locked directly to the atomic transition of interest. Therefore it is a proven method e.g. for laser cooling of atoms.

The most straightforward realization of a spectroscopy lock is to send part of the laser light through a cell which contains an atomic gas and measure the transmission with a photo diode. Light will be absorbed if the laser´s frequency is close to the resonance frequency of the atom, the closer it is the lower the transmission will be. The width of these spectral features are typically on the order of several MHz. However, the Doppler effect will lead to a broadening of these spectral features. At room temperature, e.g. for rubidium 87, this leads to a spectral width of approximately 0.3 GHz. How an error signal, which eliminates the effect of the Doppler broadening, can be generated, will be presented in the application note “Error Signal Generation”.

An alternative approach of measuring a laser´s frequency is to link it to the geometrical properties of an optical cavity. The most common type for this purpose is the Fabry-Pérot interferometer, i.e. two parallel mirrors facing each other. The approach is based on the idea that light can only resonate, and thus be transmitted, if twice the distance between the two mirrors, i.e. the optical path length of a round-trip, is an integer multiple of the wavelength. Deviations of the laser frequency from this condition will decrease the transmission. Close to resonance the relation between transmission and frequency deviation is given by a Lorentzian function with a full-width-at-half-maximum (FWHM) linewidth

\(\Delta\nu_c=\frac{\Delta\nu_{FSR}}{\mathcal{F}}\)

Another way to stabilize a laser´s phase or frequency is to compare it to a stable light source. A tool which has been developed for exactly this purpose is the frequency comb. Its spectrum exhibits peaks at fixed equidistant frequencies which is realized by mode-locking a spectrally broad laser. In the time domain this corresponds to a regular train of laser pulses with repetition rate \(f_{rep}\), which equals the separation between the peaks of the comb spectrum. The relative stability between individual peaks is obtained by locking \(f_{rep}\) to a radio frequency (RF) reference. To obtain absolute stability, in addition, either the offset frequency \(f_{CEO}\), called carrier-envelope offset, of the periodic pattern from zero has to be stabilized to a reference or a method called difference frequency generation, which passively sets \(f_{CEO}=0\), has to be implemented Therefore the long-term stability of the individual peaks is inherited from the underlying RF reference. It is therefore possible to transfer the long-term stability of e.g. an atomic clock to the regime of optical frequencies. Such a degree of stability cannot be offered by any other optical reference.

The frequency comb is the perfect tool if many lasers are to be stabilized to a common reference. Locking different lasers to a common reference is a particularly good idea if relative fluctuations between different lasers are of importance. Using a frequency comb, relative stability can be achieved between lasers separated in wavelength by several hundreds of nm. Additionally stabilizing a frequency comb to a short-term stable optical reference results in the best laser reference system available.