COUPLED-MODE FORMALISM AND LINEAR-THEORY OF DIFFRACTION FOR A SIMPLIFIED ANALYSIS OF 2ND-HARMONIC GENERATION AT GRATING COUPLERS

We present a new approach to study second harmonic generation at grating couplers where we take full advantage of the fact that, in this type of second harmonic generation, there is a resonant excitation of normal modes of the grating coupler (guided wave or surface plasmon). Therefore the analysis reported here is developed in the framework of the coupled-mode formalism. This allows us to show that the associated diffraction phenomenon, which occurs in nonlinear optics, can be handled using the linear theory of diffraction. The resulting simplicity, which arises from the simultaneous use of the coupled-mode and linear diffraction theories, allows an easy physical insight in the process of second harmonic generation at grating couplers. Proceeding along these lines, we derive not only the guided wave amplitude but also that of the radiated diffracted orders at the second harmonic frequency.