Mode-locking - Laser Cavity Modes

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 that the laser is constructed from, and the range of frequencies that a laser may operate over is known as the gain bandwidth. For example, a typical helium-neon (HeNe) gas laser has a gain bandwidth of approximately 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 centred around 800 nm).

The second factor that determines 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 will constructively and destructively interfere 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 which 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, the separation distance of the mirrors L is usually much greater than the wavelength of light 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:

where c is the speed of light (≈3×108 m·s−1).

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 itself some bandwidth or narrow range of frequencies over which it operates, but typically this bandwidth, determined by the Q factor (see Inductor) of the cavity (see Fabry–Pérot interferometer), is much smaller than the inter-mode frequency separation.