New fast and memory-sparing method for rigorous electromagnetic analysis of 2D periodic dielectric structures

A method is presented that performs the exact electromagnetic analysis of 2D periodic dielectric structures of arbitrary profile or index distribution and possibly large period. The generalized source method is used to formulate the problem of light diffraction in the form of a volume integral equation reduced to a linear equation system, which is solvable by known fast algorithms. The calculation time and required memory are linearly proportional to the total number N_o of considered diffraction orders instead of N_o³ typical for conventional methods. Numerical examples are provided to demonstrate the potential of the method for the analysis of complex periodic structures.