Editing Mode locking (section)

=== Principle of phase and mode locking ===
There are many ways to lock frequency, but the basic principle is the same, which is based on the feedback loop of the laser system. The starting point of the feedback loop is the quantity that must be stabilized (frequency or phase). To check whether frequency changes with time, a reference is needed. A common way to measure laser frequency is to link it with a geometrical property of an optical cavity. The [[Fabry–Pérot interferometer|Fabry-Pérot cavity]] is most commonly used for this purpose, consisting of two parallel mirrors separated by some distance. This method is based on the fact that light can resonate and be transmitted only if the optical path length of a single round trip is an integral multiple of the wavelength of the light. Deviation of a laser's frequency from this condition will decrease transmission of that frequency. The relation between transmission and frequency deviation is given by a [[Lorentzian Function|Lorentzian function]] with a full-width half-maximum line width

: <math>\Delta\nu_c = \frac{ \Delta\nu_{\text{FSR}}}{\mathcal{F}},</math>

where {{Math|1=&Delta;''&nu;''<sub>FSR</sub> = ''c''/2''L''}} is the frequency difference between adjacent resonances (i.e. the free spectral range) and {{Mvar|{{mathcal|F}}}} is the [[Fabry–Pérot interferometer|finesse]],

:<math>\mathcal{F}=\frac{ \pi R^{\frac{1}{2}} }{ 1-R },</math>

where {{Mvar|R}} is the reflectivity of mirrors. Therefore, to obtain a small cavity line width, mirrors must have higher reflectivity, so to reduce the line width of the laser to the lowest extent, a high finesse cavity is required.