Longitudinal and transverse modes

We will in this final part calculate the frequencies of the longitudinal modes of the resonator : the phase shift for a single pass in the resonator is equal to (see course) :

with , D the optical path (D=L+nl) , , and .

Consequently :

and for the transverse modes :

We find with L = 80 mm a 1,5 GHz gap between two consecutive longitudinal modes and 575 MHz between the fundamental mode and the first transverse mode (see figure 7).