Sagnac interferometer is made of a ring architecture as it can be observed in figure 15.
The interferometer input and output spot is . Both plane waves propagate according to ( , , , , ) and ( , , , , ) paths and so are contra-propagative. They follow identical paths. The wave 1 optical phase between the input and the output is
And the one for wave 2 is:
Thus, the phase difference between both waves is zero:
Because of the interferometer symmetry, any switch of one of the three mirrors has no influence on the fringes figure as the optical paths are all the same on the phase front. The difference of optical path between both waves is constant and zero.
As a consequence, the interferences signal is written
The fringes figure is uniform: It has a pale tone.
This interferometer is of interest in the case where the cavity is in rotation around an axis perpendicular to the figure plane. We can observe that in this case both light beams are out of phase at the interferometer output: the phase difference depends on the angular speed of rotation , of the speed of light and of the cavity surface according to the relationship
As there is not a strong effect, we are used to gyring a large number of turns of surface in order to amplify the output signal.
For a loop ray equals to , and , namely a fiber optic length of 1800m, we obtain a course difference of .
This effect is referred to as “Sagnac effect” and is used in fiber optic laser gyro . Fiber gyro sensitivity makes the detection of rotation errors of possible.