Synthesis of optical filters using ring resonator arrays

Multiple micro-optical four-port resonators, such as ring resonators, can be combined to obtain response functions not attainable with a single element. A matrix propagator method for analysis of multi-element filters is presented which takes into account bidirectional coupling among elements of a linear resonator array. Examples of filters attaining flat-top passbands, desirable for all-optical wavelength-division-multiplexed networks, are given.