Optical switchers can fulfill the same functions as all-electrical switching systems and are expected to play a key role in the near future. In this thesis an analysis if an optical system that can potentially behave as an optical switcher is discussed. This configuration consists of three microring resonators which are coupled and tangential to one another in a topology that is similar to the Leibniz packing or Apollonian gasket. The ray-transfer matrix approach is used in order to represent the whole system by a single matrix. The structure receives an initial input signal and gives an output signal, which is changed by only a scalar factor. This description is equal to an eigenvalue problem, where the matrix of the system operates over an initial vector and results a product of a scalar (the eigenvalue) times the initial vector. Due to its unique geometry each ring is divided into two unequal segments. We introduce the loss coefficients to express the attenuation along those segments. The relation between the loss coefficients is being examined and the results are verified by simulations.