Embodiments of a system that includes an array of chip modules (CMs) is described. In this system, a given CM in the array includes a semiconductor die that is configured to communicate data signals with one or more adjacent CMs through electromagnetic proximity communication using proximity connectors. Note that the proximity connectors are proximate to a surface of the semiconductor die. Moreover, the given CM is configured to communicate optical signals with other CMs through an optical signal path using optical communication, and the optical signals are encoded using wavelength-division multiplexing (WDM).