| With the manufacture of nano-scale features in the last ten years, it is possible to do optical experiments on features as small as a tenth/hundredth wavelength. It turns out that the experimental data cannot be explained by classical diffraction theories. Thus, it is necessary to develop new methods or use existing approaches which are effective in other fields, to solve problems in photonics. We use finite difference time domain (FDTD), to study transmission properties of sub-wavelength slits in a metallic film. By doing simulations on periodic and single slits, we confirm that the TE mode has a cutoff while a TM mode always has a propagating mode in the small apertures. Then we find that the transmittance is minimum when the array period is equal to the wavelength of surface plasmon polariton (SPP) at normal incidence. In fact, the SPP-like waves exist in both periodic and isolated slits, and they help the transmittance of small apertures. In order to establish the role of SPP in the transmission mechanism, it is necessary to single out each mode from the total fields. We developed Bloch mode method (BMM) to calculate the amplitudes of the lowest N orders, and the amplitudes tell us which one is dominant (not including the guided mode) at high and low transmission. BMM converges very fast and it is more accurate than FDTD since it doesn't suffer from numerical dispersion. Both methods can resolve the Wood anomaly and SPP anomaly; however, FDTD converges very slowly at the SPP resonance and oscillates around the value obtained through BMM at the Wood anomaly. BMM is not sensitive to material types, incident angles, and anomalies; it will be a useful tool to investigate similar problems. |
