Analysis of polarization dependence of a nano-slit using finite-difference-time-domain method

We analyzed the polarization dependent behavior of a nano-slit using a quasi-periodic finite-difference-time-domain (FDTD). In the simulation, the transmission decreases nearly to zero when the polarization is parallel to a slit, and the slit is narrower than a half wavelength. On the other hand, transmission of polarization perpendicular to the slit produces monotonic decrease with a decrease of the slit width. The polarization discrimination can be attributed to the different boundary conditions for two polarizations. According to a derived simple formula, the parallel polarization decays exponentially with the thickness of the slit when the width is smaller than a half wavelength. The exponential decay is verified by the simulation. In addition, the calculated transmission of aluminum nano-slit has a similar polarization behavior to that of a dielectric nano-slit.