Fundamental Complexity of Optical Systems

It is often claimed that future systems will necessarily be all-optical, because electronic devices are not fast enough to keep up with the increase in fiber capacity. However, two objections are commonly raised: first, optical systems need many basic optical components, which are typically very expensive; and second, optical systems need many switch reconfigurations, which are typically very slow. In this paper, we examine whether these two costs can be fundamentally bounded. First, we develop the equivalence between coding theory and optical system design by introducing the concept of super switches. Then, we show how the minimal expected number of switch reconfigurations is almost equal to the state space entropy of the optical system. Finally, we point out the trade-off between the two types of costs.