Abstract
We demonstrate phase-matched second harmonic generation in gallium nitride on silicon microdisks. The microdisks are integrated with side-coupling bus waveguides in a two-dimensional photonic circuit. The second harmonic generation is excited with a continuous wave laser in the telecom band. By fabricating a series of microdisks with diameters varying by steps of 8 nm, we obtain a tuning of the whispering gallery mode resonances for the fundamental and harmonic waves. Phase matching is obtained when both resonances are matched with modes satisfying the conservation of orbital momentum, which leads to a pronounced enhancement of frequency conversion.