2ND-HARMONIC GENERATION IN NONLINEAR GRATING COUPLER

Second-harmonic (SH) wave in the grating coupler is investigated by us ing the singular perturbation technique with multiple space scales. In order to apply the perturbation technique, we first introduce the per turbation parameter concerned with the nonlinear coefficient and the d epth of the grating, and the multiple space scales in the propagation direction. Substituting the expansion of the field and the multiple sp ace scales into the nonlinear wave equation, we can get the governing equations to each order of the perturbation. From the solvability cond itions to have nontrivial solutions for each perturbation solution, th at coupled equations for the guided wave, incident wave, and radiated wave can be shown. Also, the radiated angle of fundamental and SH wave s and the radiated SH wave for input/output couplers are examined nume rically. (C) 1998 American Institute of Physics. [S0021-8979(98)09323- 2]