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".
Laser cavity modes
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 or range of frequencies. A laser's bandwidth of operation is determined primarily by the 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 GHz (a wavelength range of about 0.002 nm at a central wavelength of 633 nm), whereas a titanium-doped sapphire (Ti:sapphire) solid-state laser has a bandwidth of about 128 THz (a 300 nm wavelength range centered at 800 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) mirrors facing each other, surrounding the gain medium of the laser (this arrangement is known as a Fabry–Pérot cavity). Since light is a wave, when bouncing between the mirrors of the cavity, the light constructively and destructively interferes with itself, leading to the formation of standing waves, or modes, between the mirrors. These standing waves form a discrete set of frequencies, known as the longitudinal modes 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 L is an exact multiple of half the wavelength of the light λ, such that L = qλ / 2, where q is an integer known as the mode order. In practice, L is usually much greater than λ, so the relevant values of q are large (around 105 to 106). Of more interest is the frequency separation between any two adjacent modes q and q + 1; this is given (for an empty linear resonator of length L) by Δν = c / 2L, where c is the speed of light (≈ 3×108 m/s). Using the above equation, a small laser with a mirror separation of 30 cm has a frequency separation between longitudinal modes of 0.5 GHz. Thus for the two lasers referenced above, with a 30 cm cavity, the 1.5 GHz bandwidth of the HeNe laser would support up to 3 longitudinal modes, whereas the 128 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 of the cavity (see Fabry–Pérot interferometer), is much smaller than the intermode frequency separation.
Mode-locking theory In a simple laser, each of these modes oscillates independently, with no fixed relationship between each other, in essence like a set of independent lasers, all emitting light at slightly different frequencies. The individual phase of the light waves in each mode is not fixed and may vary randomly due to such things as thermal changes in materials of the laser. In lasers with only a few oscillating modes, interference between the modes can cause beating effects in the laser output, leading to fluctuations in intensity; in lasers with many thousands of modes, these interference effects tend to average to a near-constant output intensity. If instead of oscillating independently, each mode operates with a fixed phase between it and the other modes, then the laser output behaves quite differently. Instead of a random or constant output intensity, the modes of the laser will periodically all constructively interfere with one another, producing an intense burst or pulse of light. Such a laser is said to be "mode-locked" or "phase-locked". These pulses occur separated in time by τ = 2L/c, where τ is the time taken for the light to make exactly one round trip of the laser cavity. This time corresponds to a frequency exactly equal to the mode spacing of the laser, Δν = 1/τ. The duration of each pulse of light is determined by the number of modes oscillating in phase (in a real laser, it is not necessarily true that all of the laser's modes are phase-locked). If there are N modes locked with a frequency separation Δν, then the overall mode-locked bandwidth is NΔν, and the wider this bandwidth, the shorter the pulse duration from the laser. In practice, the actual pulse duration is determined by the shape of each pulse, which is in turn determined by the exact amplitude and phase relationship of each longitudinal mode. For example, for a laser producing pulses with a Gaussian temporal shape, the minimum possible pulse duration Δt is given by
Δ t = 0.441 N Δ ν . {\displaystyle \Delta t={\frac {0.441}{N\,\Delta \nu }}.}
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