In a first aspect, an apparatus includes a substrate having a planar surface, an optical demultiplexer located along the surface, and an optical cross-connect matrix located along the surface. The optical demultiplexer has N optical outputs. The optical cross-connect matrix has a first array of N optical input ports and a second array of N optical output ports. Each optical input port of the optical cross-connect matrix is optically connected to a corresponding one of the optical outputs of the optical demultiplexer. The output ports have a sequential ordering in the second array that is a nontrivial permutation of a sequential ordering of the corresponding input ports in the first array.