The rigorous coupled wave theory dealing with optics of discontinuous two-dimensional (2D) periodic structures is reformulated by using the complex Fourier factorization method, which is a generalized implementation of the fast Fourier factorization rules. The modified approach yields considerably improved convergence properties, as shown on three samples of 2D gratingsmade as periodically arranged cylindrical holes on the top of quartz, silicon, and gold substrates. The method can also be applied to the calculation of 2D photonic band-gap structures or nonperiodic cylindrical devices, and can be generalized to elements with arbitrary cross-sections.