Editing Mode locking (section)

==Laser cavity modes==
[[Image:modelock-1.png|thumb|right|350px|Laser mode structure]]
[[File:Modelocking.gif|thumb|right|350px|A mode-locked, fully reflecting cavity supporting the first 30 modes. The upper plot shows the first 8 modes inside the cavity (lines) and the total electric field at various positions inside the cavity (points). The lower plot shows the total electric field inside the cavity.]]

Although laser light is perhaps the purest form of light, it is not of a single, pure [[frequency]] or [[wavelength]]. All lasers produce light over some natural [[Bandwidth (signal processing)|bandwidth]] or range of frequencies. A laser's bandwidth of operation is determined primarily by the [[laser construction|gain medium]] from which the laser is constructed, and the range of frequencies over which a laser may operate is known as the gain bandwidth. For example, a typical [[helium–neon laser]] has a gain bandwidth of about 1.5&nbsp;[[Hertz|GHz]] (a wavelength range of about 0.002&nbsp;[[Nanometre|nm]] at a central wavelength of 633&nbsp;nm), whereas a titanium-doped sapphire ([[Ti-sapphire laser|Ti:sapphire]]) solid-state laser has a bandwidth of about 128&nbsp;THz (a 300&nbsp;nm wavelength range centered at 800&nbsp;nm).

The second factor to determine a laser's emission frequencies is the [[optical cavity]] (or resonant cavity) of the laser. In the simplest case, this consists of two plane (flat) [[mirror]]s facing each other, surrounding the gain medium of the laser (this arrangement is known as a [[Fabry–Pérot interferometer|Fabry–Pérot]] cavity). Since light is a [[wave]], when bouncing between the mirrors of the cavity, the light constructively and destructively [[Interference (wave propagation)|interferes]] with itself, leading to the formation of [[standing wave]]s, or [[Normal mode|modes]], between the mirrors. These standing waves form a discrete set of frequencies, known as the ''[[longitudinal mode]]s'' of the cavity. These modes are the only frequencies of light that are self-regenerating and allowed to oscillate by the resonant cavity; all other frequencies of light are suppressed by destructive interference. For a simple plane-mirror cavity, the allowed modes are those for which the separation distance of the mirrors {{Mvar|L}} is an exact multiple of half the wavelength of the light {{Mvar|&lambda;}}, such that {{Math|1=''L'' = ''q&lambda;'' / 2}}, where {{Mvar|q}} is an integer known as the mode order.

In practice, {{Mvar|L}} is usually much greater than {{Mvar|&lambda;}}, so the relevant values of ''{{Mvar|q}}'' are large (around 10<sup>5</sup> to 10<sup>6</sup>). Of more interest is the frequency separation between any two adjacent modes ''{{Mvar|q}}'' and {{Math|''q'' + 1}}; this is given (for an empty linear resonator of length ''{{Mvar|L}}'') by {{Math|1=&Delta;''&nu;'' = ''c'' / 2''L''}}, where {{Mvar|c}} is the [[speed of light]] (≈&nbsp;3×10<sup>8</sup>&nbsp;m/s).

Using the above equation, a small laser with a mirror separation of 30&nbsp;cm has a frequency separation between longitudinal modes of 0.5&nbsp;GHz. Thus for the two lasers referenced above, with a 30&nbsp;cm cavity, the 1.5&nbsp;GHz bandwidth of the HeNe laser would support up to 3 longitudinal modes, whereas the 128&nbsp;THz bandwidth of the Ti:sapphire laser could support approximately 250,000 modes. When more than one longitudinal mode is excited, the laser is said to be in "multi-mode" operation. When only one longitudinal mode is excited, the laser is said to be in "single-mode" operation.

Each individual longitudinal mode has some bandwidth or narrow range of frequencies over which it operates, but typically this bandwidth, determined by the [[Q factor|''Q'' factor]] of the cavity (see [[Fabry–Pérot interferometer]]), is much smaller than the intermode frequency separation.