General Theory of the Resonant Spectrum of Multi-ring Resonators

A theory of the transmission characteristic formation for the generalized configuration of the multi-ring resonator is developed. The configuration contains an arbitrary number of the delay lines connected in parallel. Furthermore, each delay line is composed of an arbitrary number of the dispersive waveguides and coupled ring resonators. The numerical simulations of the transmission characteristics for the common cases of the multi-ring configurations are carried out using the developed theory. The obtained theoretical results are proved by the experimental investigation of the tunable spin-wave optoelectronic multi-loop resonator having parallel configuration.