Optical routing in meshes using the duplication model

A novel theoretical model for free-space optical communication is presented. The model (called the "duplication mesh" (DM)) uses a fixed set of light duplication schemes so that n processors can communicate in parallel. In order to transmit a message, a processor directs a light beam to one of the duplication schemes. The message is duplicated to a subset of destinations, and is received by any destination in the subset that did not detect a collision with other messages. The goal is to design a DM such that the number of duplication schemes is significantly smaller than the number of destinations. In this way the DM model corrects the unrealistic assumption of common optical models, that a processor can direct a light beam to any possible destination. The resulting optical architecture is a simple construction of holograms that duplicate light in fixed patterns and a set of laser diodes allowing each process or to select the desired hologram. Given an n × n mesh of processors we show that 1-1 routing of any n messages can be realized in O(log log n) steps using O(n log n log log n) duplication schemes or holograms