2D or 3D FDTD for photonic crystal waveguides modeling?

The aim of this paper is to show how 2D approaches, often used to investigate numerically the real devices as they are faster and simpler respect to 3D techniques, may lead to wrong results in modeling Photonic Crystal structures. As a test case, the determination of the so called Mini Stop Band (MSB) for the fundamental mode in a W1 waveguide is considered. A MSB is found when the structure, reduced to a 2D one, is analyzed by either Finite Difference Time Domain (FDTD) or Plane Wave Method approaches, but disappears when the real device is investigated using the FDTD-3D technique. Moreover, discrepancies exist between the 2D and the 3D transmission curves. The 3D approach is then necessary to get accurate results and determine the structure correct behavior