Theoretical investigation on the scale factor of a triple ring cavity to be used in frequency sensitive resonant gyroscopes

In this paper we study a multi-ring resonant structure including three evanescently coupled ring resonators (named triple ring resonator, TRR), with different ring radii and coupling coefficients, and coupled to two bus waveguides. The potential application of a TRR as a rotation sensor is analyzed and its advantages over a single ring resonator (SRR) under rotation conditions are also highlighted. When the coupled rings have different size and their inter-ring coupling coefficients are lower than the ring-bus coupling coefficients, the resonance frequency difference between two counter-propagating beams induced by rotation is enhanced with respect to that of a single ring resonator (SRR) with the same footprint. The scale factor of the rotating TRR, which depends on the structural parameters (i.e. inter-ring and ring-bus coupling coefficients, lengths of the rings, overall propagation loss within the rings), is up to 1.88 times the value of the scale factor of a SRR, which depends only on the ring radius, by assuming that the waveguide structure in both configurations is the same. This promising numerical achievement results in a reduction of the sensor footprint of about two times, with respect to a single ring with the same scale factor. The results obtained may be useful to define new configurations of frequency sensitive optical gyros in low-loss technology, having a small volume. In fact, by properly choosing the structural parameters, the spectral response of the TRR is forced to assume a shape more sensitive to the resonant frequency shift due to the rotation with respect to that one of a SRR.