The present work theoretically investigates the electromagnetic resonance modes on two-dimensional (2-D) complex gratings consisting of a metallic grating, a dielectric film, and a metal substrate. We treat a complex grating as geometrical combination of two square grating elements with different sizes in a single unit cell. In order to identify various resonance modes, such as surface plasmon and magnetic resonance (or magnetic polariton) existing in gratings, the finite-difference time-domain method is employed in solving Maxwell's equation. Differently from 2-D simple grating structures, we observe the diverse magnetic polariton modes associated with each grating elements in a single unit cell. Furthermore, if two different grating elements are merged together, magnetic polariton will be branched out into multiple modes. These characteristics of 2-D complex grating will be desirable for achieving broad-band absorption, which is critical for energy harvesting applications. (C) 2015 Elsevier Ltd. All rights reserved.