Methods, apparatus and computer programs are provided for data replication, such as for replicating a database or updating a cache. A space between the lens 12 and the lens 13 are cemented together. Bottom-up indices are formed for the leaf nodes, where the bottom-up indices characterizes paths from selected leaf nodes to a root node of the top-down tree. In various embodiments, the frequency of the reference clock signal is the same as the resonant frequency of the crystal and the frequency of the output clock signal is a multiple of the resonant frequency of the crystal. The first and second dentate structures define an optical channel for the transmission of the first optical signal.