| We have measured the optical transmittance of sub-wavelength hole arrays in metal films. We investigated the spectral behavior of transmittance (the peak positions, intensities, line-widths, and the dip positions) as a function of the geometrical parameters of the hole arrays, the angle of incidence, the polarization angle and the refractive indices of the substrates. We calculated the positions of transmittance peaks and dips with equations from the surface plasmon theory and the diffraction theory, and compared the calculated positions of peaks and dips with measured transmittance data. We found that there is a discrepancy of 3∼5% between the peak positions calculated with the surface plasmon equation and the peak positions in the measured transmittance data. We explain this discrepancy as possibly due to the approximations of the surface plasmon equation. However, the positions of the dips in the spectra, as calculated with the diffraction grating equation, were well matched to the measured data. We also observed splittings and shifts of the peaks and dips when changing the angle of incidence and the polarization of the light. We confirmed this spectral behavior qualitatively with calculation of momentum conservation equations for oblique incidence and showed that the diffraction modes are degenerate for s-polarization, while the modes are not degenerate for p-polarization. We studied the dependence of hole size and shape on the transmittance while also changing the in-plane polarization angle. We observed that the transmittance peak is strongly dependent on the length of the hole edge perpendicular to the polarization direction. In addition, we investigated the dependence on film thickness and the refractive index of dielectric substrate. |
