Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings

Theoretical analysis of second-harmonic generation (SHG) phase matched with gratings in a channel waveguide is presented from the viewpoint of device design. The analysis includes cases where efficiency is high and residual phase mismatch is involved. Nonlinear couples mode equations, with general expressions for effective SHG coefficients and coupling coefficients, are derived, solved, and discussed for uniform and chirped gratings. It was found that very high efficiency with broadened phase matching bandwidth can be simultaneously obtained with chirped gratings. The results are summarized in graphic data with normalized parameters, and guidelines and criterion for optimum design are given