In this paper, the two-dimensional Finite-Difference Time-Domain method by using an efficient effective permittivity schemes is presented. For validation, a 60º photonic-crystal waveguide bend is used. The obtained transmission agrees very well with other two-dimensional simulation method such as the two-dimensional finite-element method and the two-dimensional multiple multipole method. Particles shaped as e.g. spheres and ellipses with different refractive indices have been studied under plane wave illumination that has a tightly-focused photonic nanojet. Their waists are smaller than the diffraction limit, they propagate over several optical wavelengths without significant diffraction and the beam reaches a high intensity.