Analytical study on characteristics of dual microring resonators combined with the add-drop and all-pass types

Abstract

This paper presents an analytical study on characteristics of dual microring resonators combined with the add-drop and all-pass types, which can provide novel filtering and delaying characteristics. Analytical expressions of transmission spectra and normalized delays of the dual microring resonators are developed using the transfer matrix method. The effects of coupling coefficients and loss on both transmission spectra and delays are then investigated. The analytical study shows that two resonance peaks of transmission spectra are existent. Under lossless coupling, the resonance frequency of the transmission spectra increases as the ring-ring coupling coefficient increases. However, it is independent on the ring-bus coupling coefficient. The valley amplitude of the transmission spectra increases as the ring-bus coupling coefficient increases, which is also independent on the ring-ring coupling coefficient. Generally, three delay peaks are existent. The corresponding frequencies of delay peaks on either side of the centre frequency are partially coincident with the normalized resonance frequencies of transmission spectra. The normalized delays can develop from three delay peaks to two delay peaks or single delay peak under specified coupling coefficients and loss.