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 grati ng couplers where we take full advantage of the fact that, in this typ e of second harmonic generation, there is a resonant excitation of nor mal modes of the grating coupler (guided wave or surface plasmon). The refore the analysis reported here is developed in the framework of the coupled-mode formalism. This allows us to show that the associated di ffraction phenomenon, which occurs in nonlinear optics, can be handled using the linear theory of diffraction. The resulting simplicity, whi ch arises from the simultaneous use of the coupled-mode and linear dif fraction theories, allows an easy physical insight in the process of s econd harmonic generation at grating couplers. Proceeding along these lines, we derive not only the guided wave amplitude but also that of t he radiated diffracted orders at the second harmonic frequency.