An optical apparatus comprises a planar optical waveguide and at least one set of diffractive elements formed in or on the waveguide. The waveguide is arranged to confine propagating optical signals in at least one transverse dimension. The diffractive element set collectively exhibits a positional variation in diffractive amplitude, optical separation, or spatial phase over some portion of the set. The diffractive element set is collectively arranged to route, as an output optical signal, between corresponding input and output optical ports, a corresponding diffracted portion of an input optical signal. The diffractive element set is collectively arranged so that the input optical signal or the output optical signal is successively incident on the diffractive elements. The diffractive elements are arranged according to an interference pattern derived from computed interference between a simulated design input optical signal and a simulated design output optical signal, the interference pattern exhibiting said positional variation.