A design methodology, a scheme for growth and an embedding algorithm, for building very large ATM networks over a wavelength-routed optical network layer are proposed. The overall design is multi-tiered and at each tier-subnetwork and internetwork-the WDM layer is acyclic, i.e., each and every optical path is terminated by a transmitter receiver pair. This prevents optical amplifier noise from recirculating in unterminated optical cycles. The subnetworks and internetwork of the ATM layer are set up based on "two-sided shuffle-exchange" type networks. In particular, they are generalized De Bruijn and generalized Kautz networks. These networks are almost optimal in terms of the diameter and they exist for any network size. We show that by appropriately sizing the ATM switches, very large average throughputs per user, equal to the peak rate (155 Mbps), are achievable. We also suggest a way to engineer the network so as to enable growth without changes at the optical layer. The network is designed so that users can be easily added, by adding more ports to the ATM switches at the ATM layer. This method does not require any rewiring of existing connections and the addition of users does not have any adverse impact on the average throughput per user. Finally, an optimal embedding algorithm is developed that achieves the De Bruijn and Kautz connectivity on a WDM network using the minimum number of wavelength routers and optimal fiber connections.