Crosstalk-free mapping of two-dimensional weak tori on optical slab waveguides

While optical slab waveguides can deliver a huge bandwidth for the communication need through offering a huge number of communication channels, they require a large number of high speed lasers and photodetectors. This makes a limited use of the offered huge bandwidth. Some trials were proposed to implement communication networks on the slab waveguides [7]. However, the proposed mappings suffer from the possibility of crosstalk among different channels if they are to be used simultaneously. In this paper, we consider solving the problem of crosstalk when mapping weak two-dimensional tori on optical slab waveguides. We introduce the notion of diagonal pair and use it in the proposed mapping. The approach assigns edges to channels such that the mapping guarantees a crosstalk free communication between nodes (no two adjacent channels are used at the same communication step.) We also consider the cost of the mapping in terms of the number of lasers and the number of photodetectors. Our results show that the cost is within constants to the cost lower bound.