Multibeam interferometers

Until now, we have only talked about two-wave interferometers, but there are also multibeam interferometers.

The quintessence of this kind of interferometers is the Fabry–Pérot interferometer (FP), shown on figure 10. The transfer function of a Fabry-Pérot interferometer is famous [30]:

where  is the phase difference of the light after a round-trip in the cavity and F is the finesse characterizing the resolution of the phase difference of the component and it is written as:

where R is the reflection coefficient of the reflectors.

The free spectral range (i.e. the distance between two consecutive peaks) is another important characteristic of the Fabry-Pérot interferometer:

where c is the speed of light, L the distance between the reflectors and n is the refractive index of the medium.

The sensitivity of such a device is improved by the numerous round-trips of the co-propagative and counter-propagative waves. The typical reaction of a Fabry-Pérot interferometer for two kinds of finesse is shown in Figure 11. The higher the reflection coefficient of the reflectors is, the more round-trips in the cavity the waves do, and the finer it is.

In practice, it is quite difficult to put high-reflectivity reflectors at the end of fibers, however Stone [31] has proven it is possible to to realize a finesse of 300. The most common Fabry-Pérot interferometers simply use Fresnel reflection of 4% which happens at each extremity let naked in the air: their transmissions look like the low finesse shown in Figure 9. It is possible to use the Bragg grating as cavity mirrors, like Henderson proved it [32].