Mode locking
Mode locking is a technique in optics by which a laser can be made to produce pulses of light of
extremely short duration, on the order of picoseconds (10 −12 s) or femtoseconds (10−15 s). A laser
operated in this way is sometimes referred to as a femtosecond laser, for example, in
modern refractive surgery. The basis of the technique is to induce a fixed phase relationship
between the longitudinal modes of the laser's resonant cavity. Constructive interference between
these modes can cause the laser light to be produced as a train of pulses. The laser is then said to
be "phase-locked" or "mode-locked".
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 ν and is amplitude-modulated at a frequency f, the
resulting signal has sidebands at optical frequencies ν − f and ν + f. If the modulator is driven at
the same frequency as the cavity mode spacing Δν, 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 ν − 2f and ν + 2f 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 f is synchronised to the
cavity round-trip time τ, 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 ν and is amplitude-
modulated at a frequency nf, the resulting signal has sidebands at optical
frequencies ν − nf and ν + 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 dyes, but they can also be made from
doped crystals and semiconductors. Semiconductor absorbers tend to exhibit very fast response
times (~100 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 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 focussed
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.
