Multicasting in a network is needed for a number of applications where a session requires connectivity between more than two participants. In this paper, we consider a wavelength-division multiplexing (WDM)-based all-optical network. We derive asymptotic upper bounds on the number of wavelengths needed to support multicasting capability in an all-optical network. The number of wavelengths in a WDM network continues to be a major constraint. The results derived here should be seen as the limit on scalability of all-optical networks that support multicasting. The derivation of the upper bound uses some properties of expander graphs.

All-optical networks are networks for which all data paths remain optical from input to output. With rapid development of optical technology, such networks are a viable choice for the high speed wide area networks of the future. Wavelength division multiple access (WDMA) currently provides the most mature technology for all-optical networks. The authors discuss a class of WDMA networks that are homogeneous in the sense that each node contains both an input/output port and a switch. They focus on the permutation routing problem and first, present a lower bound on the number of wavelengths required for permutation routing as a function of the size and degree of the network. They use particular topologies, including the multistage perfect shuffle, the Debruijn, and the hypercube, to find achievable upper bounds on the number of required wavelengths.>