The spectrum of a laser oscillator

As previously stated, the cavity also filters the spectrum emitted by the laser. A linear cavity is basically the same as a Fabry-Pérot interferometer. Only waves of a certain frequency can be successfully propagated. This frequency is defined by where k is an integer, c the speed of light in a vacuum and L the optical length of the (linear) cavity. In the case of optical frequencies, k is very large and may reach tens of thousands for a cavity of a few centimetres. Waves that propagate with these frequencies in the cavity are known as longitudinal modes.

This filter is directly applied to the spectrum spontaneously emitted when the laser starts up. Progressively, the frequencies that cannot exist in the cavity disappear leaving only those that verify the equation above.

The spectrum emitted by a laser oscillator is thus composed of a comb of regularly spaced (C/2L) frequencies, usually centred on the spontaneous emission spectrum (Figure 12).

A laser is often described as monochromatic (for example, the helium-neon laser), a definition that must be well understood. In fact, broadly speaking, the spectral bandwidth of a laser is given by the width of the spontaneous emission: if the transition between the upper and lower levels is narrow, then the spontaneous emission will be fractions of a nanometre (this is the case for the red line in neon, which has a width equal to 1/1000th of a nanometre and a frequency of 1 GHz). The spectrum of a helium-neon laser is therefore “monochromatic” in the sense that only one colour is visible to the naked eye as the line is very narrow. Other types of laser have a much wider transition (for example, several hundreds of nanometres for the titanium-doped sapphire, which has a spontaneous emission spectrum ranging from 700 to more than 1000 nm) and consequently emit a spectrum that cannot be defined as monochromatic.

The spectral properties of lasers become even more interesting when just one frequency can be selected (using a series of filters placed in the optical cavity). This type of laser is defined as a single frequency or single mode laser. In this case, the width of the spectrum can be very much smaller than the spontaneous emission spectrum. For example, some helium-neon lasers have a spectral width of 1 Hz while the linewidth is measured in GHz.

To summarise, the optical cavity is capable of filtering the spontaneous emission in the form of discrete frequencies (the longitudinal modes). If only one mode is selected, the resulting laser radiation is of very high quality: a large number of photons are emitted in a very narrow beam only several Hz in width!