Split-field finite-difference time-domain method for second-harmonic generation in two-dimensionally periodic structures

The split-field finite-difference time-domain method is extended to second-harmonic generation in two-dimensionally periodic structures. Making use of the full coefficient-tensor formalism, a coupled nonlinear system of equations, which must be solved at each update of the electromagnetic field, is developed. The accuracy of the method is verified by comparing the results to well-known one-dimensional problems. The results for L-shaped arrays are compared with results obtained with the Fourier modal method.This work is partially supported by the “Ministerio de Economía y Competitividad” of Spain under project FIS2011-29803-C02-01; by the “Generalitat Valenciana” of Spain under projects PROMETEO/2011/021, ISIC/2012/013, and GV/2014/076; and by the “Universidad de Alicante” of Spain under project GRE12-14