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