Embodiments of a system that includes an array of single-chip modules (CMs) are described. This array includes a first CM, a second CM coupled to the first CM, and a third CM coupled to the second CM. A given CM, which can be the first CM, the second CM or the third CM, includes a semiconductor die that is configured to communicate data signals with other CMs through electromagnetically coupled proximity communication. These proximity connectors are proximate to a surface of the semiconductor die. Moreover, the first CM and the third CM are configured to optically communicate optical signals with each other via the second CM through an optical signal path.