Second-harmonic generation in a double-tuned microwave cavity partly filled with nonlinear dielectric crystals

The conditions for optimal second-harmonic generation using dielectric crystals in a microwave cavity are investigated. The general relations, obtained by a vector Green's theorem, are specified to a rectangular cavity, where the eigenfunctions can be calculated explicitely. A good agreement is found between theory and experiments performed at a fundamental frequency of 9 GHz using LiNbO₃ as the crystal.