The previous RST postulates that the scattering field, within each modal partial wave, comprise of the resonance and the background components. The new RST is recently developed by the product expansion of the scattering functions in the field of acoustics. The new formulation suggests that the scattering coefficients consist of resonance, non-resonance, and their interactional portions. In the scattering problems of acoustic waves, the moduli and phase of the resonance coefficient are obtained correctly by the new RST. In our recent works the new RST was successfully applied to the scattering problem of electromagnetic waves for coated conducting cylinder and sphere. In this paper, the new RST is extended to the 2-dimensional scattering problem of electromagnetic waves for a homogeneous dielectric cylinder, and the numerical results are compared with the previous RST.