Learning in biological systems is thought to depend on the phenomena of clustering. For example, new experiences are most easily remembered by attaching them to a category of related prior knowledge, that is, by clustering. Clustering in the brain is thought by some to involve coupling of oscillator neurons. Therefore, we investigate clustering in frequency with an all-optical system. The system consists of a set of coupled microring lasers whose natural frequencies are set to the values to be clustered. We assume that closer values represent more similar information and that the values set the microring natural frequencies. A microring resonant frequency in such a system is influenced away from its natural frequency by interactions with its neighbors. As a result, the frequencies of the microrings will adjust themselves into a few groups or clusters. Equations are developed for a pair of microring resonators to show that the microring resonators will interact to perform clustering.
A microring resonator, a circular waveguide adjacent to a straight waveguide, performs selective band-stop filtering for optical telecommunications. Small size and versatility of functionality allow many microrings to be incorporated into a single integrated optic circuit. We desire small size, less than 20 micron radius; low insertion loss in band-stop outside resonance; perfect cancellation to zero in band-stop at resonance; and low refractive index difference between core and cladding. These requirements are conflicting: conventional silicon waveguides cannot achieve low enough loss at the desired bend radius. Current approaches use different materials with higher refractive index differences. Analysis and simulation provide evaluation of the trade-offs. Further, we propose, for the first time, conventional waveguides using Bragg reflectors surrounding the microring to reduce loss for improved performance. Simulation shows feasibility of this approach.