Double-Ring Resonator Optical Gyroscopes

A double-ring fiber resonator consists of two coplanar rings of approximately equal lengths closed upon themselves and coupled together with a 3 x 3 coupler. This coupled resonator exhibits transmission spectra more complex than a single-ring resonator, including one or two resonances per free spectral range, depending on the length mismatch between rings. Analytical expressions are derived for the rotation sensitivity of such a structure used as a gyroscope based on the Sagnac effect. Numerical simulations show that with suitable wavelength biasing of the probe laser, the rotation sensitivity is the maximum when the coupling constant is equal to the round-trip loss of each ring, and when the length mismatch is equal to lambda/2 [mod. lambda] for planar couplers and zero [mod. lambda] for triangular couplers. An interesting property of this structure is that for any value of the mismatch there is a coupling constant that maximizes the sensitivity, and this maximum sensitivity depends weakly on the length mismatch. The reason is that changing themismatch redistributes the light intensity between the two rings, but it essentially does not change the number of times light recirculates around the two rings combined, to which the sensitivity is proportional. However, if the probe-laser frequency is locked to one of the rings and the coupling constant kept fixed at its optimum value, independent thermal fluctuations of the length of the second ring will cause significant variations in the sensitivity. It is shown that when all three parameters are optimized (length mismatch, coupling, and probe wavelength), the transmission of the double-ring resonator takes the exact form of that of a singlering resonator of equal loss and length, and that it also has exactly the same rotation sensitivity.