On mapping multidimensional weak tori on optical slab waveguides

Optics is acknowledged as the most viable means to meet the bandwidth needs of future interconnects. While the optical medium can easily deliver huge bandwidths, this bandwidth is difficult to harness; this is because of engineering and technological constraints associated with accommodating a large number of high-speed lasers and photodetectors within a small confine. We consider the problem of mapping weak multidimensional tori on optical slab waveguides. Our approach uses the fact that not all edges of a weak topology are used simultaneously; it uses this fact to employ a single laser/detector to work in multiple capacities at different times. We introduce the notion of aggregates to capture the cost of mapping a topology by our approach. We derive a non-trivial lower bound on this cost for a class of mappings and construct mappings, all of which surpass a naive method and some of which match the lower bound.