Editing Mode locking (section)

==Mode-locking methods==

Methods for producing mode locking in a laser may be classified as either "active" or "passive". Active methods typically involve using an external signal to induce a [[modulation]] of the intracavity light. Passive methods do not use an external signal, but rely on placing some element into the laser cavity which causes self-modulation of the light.

===Active mode locking===

The most common active mode-locking technique places a standing wave [[electro-optic modulator]] into the laser cavity. When driven with an electrical signal, this produces a sinusoidal [[amplitude modulation]] of the light in the cavity. Considering this in the frequency domain, if a mode has optical frequency {{Mvar|&nu;}} and is amplitude-modulated at a frequency {{Mvar|f}}, then the resulting signal has [[sideband]]s at optical frequencies {{Math|''&nu;'' &minus; ''f''}} and {{Math|''&nu;'' + ''f''}}. If the modulator is driven at the same frequency as the cavity mode spacing {{Math|&Delta;''&nu;''}}, then these sidebands correspond to the two cavity modes adjacent to the original mode. Since the sidebands are driven in-phase, the central mode and the adjacent modes will be phase-locked together. Further operation of the modulator on the sidebands produces phase locking of the {{Math|''&nu;'' &minus; 2''f''}} and {{Math|''&nu;'' + 2''f''}} modes, and so on until all modes in the gain bandwidth are locked. As said above, typical lasers are multi-mode and not seeded by a root mode, so multiple modes need to work out which phase to use. In a passive cavity with this locking applied, there is no way to dump the [[entropy]] given by the original independent phases. This locking is better described as a coupling, leading to a complicated behavior and not clean pulses. The coupling is only dissipative because of the dissipative nature of the amplitude modulation; otherwise, the phase modulation would not work.

This process can also be considered in the time domain. The amplitude modulator acts as a weak "shutter" to the light bouncing between the mirrors of the cavity, attenuating the light when it is "closed" and letting it through when it is "open". If the modulation rate {{Mvar|f}} is synchronised to the cavity round-trip time {{Mvar|&tau;}}, then a single pulse of light will bounce back and forth in the cavity. The actual strength of the modulation does not have to be large; a modulator that attenuates 1% of the light when "closed" will mode-lock a laser, since the same part of the light is repeatedly attenuated as it traverses the cavity.

Related to this amplitude modulation (AM), active mode locking is [[frequency-modulation]] (FM) mode locking, which uses a modulator device based on the [[acousto-optic effect]]. This device, when placed in a laser cavity and driven with an electrical signal, induces a small, sinusoidally varying frequency shift in the light passing through it. If the frequency of modulation is matched to the round-trip time of the cavity, then some light in the cavity sees repeated upshifts in frequency, and some repeated downshifts. After many repetitions, the upshifted and downshifted light is swept out of the gain bandwidth of the laser. The only light unaffected is that which passes through the modulator when the induced frequency shift is zero, which forms a narrow pulse of light.

The third method of active mode locking is synchronous mode locking, or synchronous pumping. In this, the pump source (energy source) for the laser is itself modulated, effectively turning the laser on and off to produce pulses. Typically, the pump source is itself another mode-locked laser. This technique requires accurately matching the cavity lengths of the pump laser and the driven laser.

===Passive mode locking===

Passive mode-locking techniques are those that do not require a signal external to the laser (such as the driving signal of a modulator) to produce pulses. Rather, they use the light in the cavity to cause a change in some intracavity element, which will then itself produce a change in the intracavity light. A commonly used device to achieve this is a [[saturable absorber]].

A saturable absorber is an optical device that exhibits an intensity-dependent transmission, meaning that the device behaves differently depending on the intensity of the light passing through it. For passive mode locking, ideally a saturable absorber selectively absorbs low-intensity light, but transmits light of sufficiently high intensity. When placed in a laser cavity, a saturable absorber attenuates low-intensity constant-wave light (pulse wings). However, because of the somewhat random intensity fluctuations experienced by an un-mode-locked laser, any random, intense spike is transmitted preferentially by the saturable absorber. As the light in the cavity oscillates, this process repeats, leading to the selective amplification of the high-intensity spikes and the absorption of the low-intensity light. After many round trips, this leads to a train of pulses and mode locking of the laser.

Considering this in the frequency domain, if a mode has optical frequency {{Mvar|&nu;}} and is amplitude-modulated at a frequency {{Math|''nf''}}, then the resulting signal has [[sideband]]s at optical frequencies {{Math|''&nu;'' &minus; ''nf''}} and {{Math|''&nu;'' + ''nf''}} and enables much stronger mode locking for shorter pulses and more stability than active mode locking, but has startup problems.

Saturable absorbers are commonly liquid [[organic chemistry|organic]] dyes, but they can also be made from doped [[crystal]]s and [[semiconductors]]. Semiconductor absorbers tend to exhibit very fast response times (~100&nbsp;fs), which is one of the factors that determines the final duration of the pulses in a passively mode-locked laser. In a ''colliding-pulse mode-locked laser'' the absorber steepens the leading edge, while the [[lasing medium]] steepens the trailing edge of the pulse.

There are also passive mode-locking schemes that do not rely on materials that directly display an intensity-dependent absorption. In these methods, [[nonlinear optics|nonlinear optical]] effects in intracavity components are used to provide a method of selectively amplifying high-intensity light in the cavity and attenuation of low-intensity light. One of the most successful schemes is called [[Kerr-lens mode locking]] (KLM), also sometimes called "self-mode-locking". This uses a nonlinear optical process, the optical [[Kerr effect]], which results in high-intensity light being focused differently from low-intensity light. By careful arrangement of an aperture in the laser cavity, this effect can be exploited to produce the equivalent of an ultra-fast response-time saturable absorber.

===Hybrid mode locking===

In some semiconductor lasers, a combination of the two above techniques can be used. Using a laser with a saturable absorber and modulating the electrical injection at the same frequency the laser is locked at, the laser can be stabilized by the electrical injection. This has the advantage of stabilizing the phase noise of the laser and can reduce the timing jitter of the pulses from the laser.

===Mode locking by residual cavity fields===

Coherent phase-information transfer between subsequent laser pulses has also been observed from [[nanowire lasers]]. Here, the phase information has been stored in the residual photon field of coherent [[Rabi oscillations]] in the cavity. Such findings open the way to phase locking of light sources integrated onto chip-scale photonic circuits and applications, such as on-chip Ramsey comb spectroscopy.<ref name="nwpl">Mayer, B., et al. [https://www.nature.com/articles/ncomms15521 "Long-term mutual phase locking of picosecond pulse pairs generated by a semiconductor nanowire laser"]. Nature Communications 8 (2017): 15521.</ref>

===Fourier-domain mode locking===
{{main|Fourier domain mode locking}}

Fourier-domain mode locking (FDML) is a laser mode-locking technique that creates a continuous-wave, wavelength-swept light output.<ref name="FDML">R. Huber, M. Wojtkowski, J. G. Fujimoto, [http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-8-3225 "Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography"], Opt. Express 14, 3225–3237 (2006).</ref>  A main application for FDML lasers is [[optical coherence tomography]].