Routing and channel assignment is a key topic in optical interconnection networks, and it is a primary way to get insight into the capacity of interconnection networks. Based on the optical RP(k) network, the wavelength assignment of realizing the Hypercube communication with N=2n nodes on the optical RP(k) network is discussed. By defining the reverse order of the Hypercube, an algorithm to embed the n-D Hypercube into the RP(k) network is designed, which needs at most max{2,「5.2^n-5/3」} wavelengths. An algorithm to embed the n-D hypercube into the ring network is also proposed, with its congestion equal to 「N/3+N/12」. This is a better improvement than the known results, which is equal to 「N/3+N/4」. The two algorithms proposed in this paper are of great value in designing optical networks.