Coupled-mode analysis of second harmonic generation in the form of Cerenkov radiation from a planar optical waveguide

Optical second harmonic generation (SHG) in the form of Cerenkov radiation from a planar waveguide is analyzed in detail by a coupled-mode theory, where a fundamental wave is taken as a guided mode, and a second harmonic wave is taken as a substrate radiation mode. An approximate solution is given which expresses the SHG efficiency in terms of waveguide parameters such as refractive indexes, a waveguiding layer thickness, and the optical nonlinearities of a waveguiding layer and a substrate. Numerical examples are plotted for LiNbO₃ crystals. Finally, the significant effect of a periodic modulation of the sign of an optical nonlinear d constant is discussed