Two important parameters of a network for massively parallel computers are scalability and modularity. Scalability has two aspects: size and time (or generation). Size scalability refers to the property that the size of the network can be increased with nominal effect on the existing configuration. Also, the increase in size is expected to result in a linear increase in performance. Time scalability implies that the communication capabilities of a network should be large enough to support the evolution of processing elements through generations. A modular network enables the construction of a large network out of many smaller ones. The lack of these two important parameters has limited the use of certain types of interconnection networks in the area of massively parallel computers. We present a new modular optical interconnection network, called an optical multimesh hypercube (OMMH), which is both size and time scalable. The OMMH combines positive features of both the hypercube (small diameter, high connectivity, symmetry, simple routing, and fault tolerance) and the torus (constant node degree and size scalability) networks. Also presented is a three-dimensional optical implementation of the OMMH network. A basic building block of the OMMH network is a hypercube module that is constructed with free-space optics to provide compact and high-density localized hypercube connections. The OMMH network is then constructed by the connection of such basic building blocks with multiwavelength optical fibers to realize torus connections. The proposed implementation methodology is intended to exploit the advantages of both space-invariant free-space and multiwavelength fiber-based optical interconnect technologies. The analysis of the proposed implementation shows that such a network is optically feasible in terms of the physical size and the optical power budget.